version
stringclasses 1
value | hypothesis
stringlengths 8
103
| hypothesis_formula
stringlengths 3
36
| facts
stringlengths 0
691
| facts_formula
stringlengths 0
374
| proofs
sequencelengths 0
1
| proofs_formula
sequencelengths 0
1
| negative_hypothesis
stringlengths 8
88
â | negative_hypothesis_formula
stringlengths 3
37
â | negative_proofs
sequencelengths 0
1
| negative_original_tree_depth
int64 0
17
â | original_tree_steps
int64 1
5
| original_tree_depth
int64 1
5
| steps
int64 1
5
â | depth
int64 1
5
â | num_formula_distractors
int64 0
5
| num_translation_distractors
int64 0
0
| num_all_distractors
int64 0
5
| proof_label
stringclasses 3
values | negative_proof_label
stringclasses 2
values | world_assump_label
stringclasses 3
values | negative_world_assump_label
stringclasses 2
values | prompt_serial
stringlengths 71
750
| proof_serial
stringlengths 11
312
| prompt_serial_formula
stringlengths 52
422
| proof_serial_formula
stringlengths 11
216
|
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.3 | ãã®ã¿ã®ã¿ãLv.21ã¯é²ãæã | {D}{b} | fact1: ãã®ãŸããŸãLv.92ã¯è©±ãæã fact2: ãã®ããããLv.56ãçžå¿ãããªããã®ã¿ã®ã¿ãLv.21ã¯é²ãæã fact3: ä»®ã«ãã®ããããLv.56ãèŠåºã ãé£ããšãããããã¯çžå¿ãã fact4: ãã®ããããLv.56ã¯å±ããªã fact5: ããä»®ã«ãã®ããããLv.56ãå±ããªããšãããããã¯è©±ãæãããããèŠåºã ãé£ã | fact1: {A}{eh} fact2: {C}{a} -> {D}{b} fact3: {B}{a} -> {C}{a} fact4: ¬{E}{a} fact5: ¬{E}{a} -> ({A}{a} & {B}{a}) | [
"fact5 & fact4 -> int1: ãã®ããããLv.56ã¯è©±ãæããèŠåºã ãé£ã; int1 -> int2: ãã®ããããLv.56ã¯èŠåºã ãé£ã; int2 & fact3 -> int3: ãã®ããããLv.56ã¯çžå¿ãã; int3 & fact2 -> hypothesis;"
] | [
"fact5 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact3 -> int3: {C}{a}; int3 & fact2 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸããŸãLv.92ã¯è©±ãæã fact2: ãã®ããããLv.56ãçžå¿ãããªããã®ã¿ã®ã¿ãLv.21ã¯é²ãæã fact3: ä»®ã«ãã®ããããLv.56ãèŠåºã ãé£ããšãããããã¯çžå¿ãã fact4: ãã®ããããLv.56ã¯å±ããªã fact5: ããä»®ã«ãã®ããããLv.56ãå±ããªããšãããããã¯è©±ãæãããããèŠåºã ãé£ã ; $hypothesis$ = ãã®ã¿ã®ã¿ãLv.21ã¯é²ãæã ; $proof$ = | fact5 & fact4 -> int1: ãã®ããããLv.56ã¯è©±ãæããèŠåºã ãé£ã; int1 -> int2: ãã®ããããLv.56ã¯èŠåºã ãé£ã; int2 & fact3 -> int3: ãã®ããããLv.56ã¯çžå¿ãã; int3 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{eh} fact2: {C}{a} -> {D}{b} fact3: {B}{a} -> {C}{a} fact4: ¬{E}{a} fact5: ¬{E}{a} -> ({A}{a} & {B}{a}) ; $hypothesis$ = {D}{b} ; $proof$ = | fact5 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact3 -> int3: {C}{a}; int3 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ç©ãããªã | ¬{C}{c} | fact1: ãããã®ããããLv.90ã¯ææåãããšãããããã®ã¿ã®ã¿ãLv.9ã¯èæãããªããç©ãããšããããšã¯ãªãããšããããšã¯åœã§ãªã fact2: ããããã®ããããLv.90ãé«ããšããã°ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ç©ãã fact3: ããããããã¢ã³ã¹ã¿ãŒã¯é¢åèãããšããããšã¯çå®ã§ãããªãããã¯ææåãã fact4: ãã®ã·ã«ã·ãLv.21ã¯ã¿ã£ãšããªã fact5: ããä»®ã«ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ã¿ã£ãšããªããšããããšã¯ãªããšããã°ããã®ã·ã«ã·ãLv.21ã¯ç©ãããªãããšããããšã¯æãç«ã€ fact6: ç©ãããªãã¢ã³ã¹ã¿ãŒã¯é«ããã¿ã£ãšããªã | fact1: {E}{a} -> (¬{D}{ig} & ¬{C}{ig}) fact2: {A}{a} -> {C}{c} fact3: (x): {F}x -> {E}x fact4: {B}{b} fact5: ¬{B}{c} -> ¬{C}{b} fact6: (x): ¬{C}x -> ({A}x & {B}x) | [] | [] | ãã®ã¿ã®ã¿ãLv.9ã¯ã¿ã£ãšããªã | {B}{ig} | [
"fact7 -> int1: ãããä»®ã«ãã®ã¿ã®ã¿ãLv.9ãç©ãããªããšããããã®ã¿ã®ã¿ãLv.9ã¯é«ããå ããŠã¿ã£ãšããªãããšããããšã¯æ£ãã; fact9 -> int2: ããä»®ã«ãã®ããããLv.90ãé¢åèããšããããã®ããããLv.90ã¯ææåãã;"
] | 6 | 5 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ããããLv.90ã¯ææåãããšãããããã®ã¿ã®ã¿ãLv.9ã¯èæãããªããç©ãããšããããšã¯ãªãããšããããšã¯åœã§ãªã fact2: ããããã®ããããLv.90ãé«ããšããã°ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ç©ãã fact3: ããããããã¢ã³ã¹ã¿ãŒã¯é¢åèãããšããããšã¯çå®ã§ãããªãããã¯ææåãã fact4: ãã®ã·ã«ã·ãLv.21ã¯ã¿ã£ãšããªã fact5: ããä»®ã«ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ã¿ã£ãšããªããšããããšã¯ãªããšããã°ããã®ã·ã«ã·ãLv.21ã¯ç©ãããªãããšããããšã¯æãç«ã€ fact6: ç©ãããªãã¢ã³ã¹ã¿ãŒã¯é«ããã¿ã£ãšããªã ; $hypothesis$ = ãã®ãŸã«ã
ãŸã«ãLv.99ã¯ç©ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {E}{a} -> (¬{D}{ig} & ¬{C}{ig}) fact2: {A}{a} -> {C}{c} fact3: (x): {F}x -> {E}x fact4: {B}{b} fact5: ¬{B}{c} -> ¬{C}{b} fact6: (x): ¬{C}x -> ({A}x & {B}x) ; $hypothesis$ = ¬{C}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ãã·ãLv.0ã¯é£ã¹çµãããªãããã€çµã³ä»ãæããªãããšããããšã¯æãç«ããªã | ¬(¬{B}{a} & ¬{C}{a}) | fact1: ãèç«ããããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããããšããã¢ã³ã¹ã¿ãŒã¯èç«ããããªãã°ããã®ã·ãã·ãLv.0ã¯é£ã¹çµãããšããããšã¯ãªããããã«çµã³ä»ãæããªãããšããããšã¯ééã£ãŠãã fact3: ããé£ã¹çµããããšããããšã¯æ¬åœãªãã¢ã³ã¹ã¿ãŒã¯ãã | fact1: (Ex): {A}x fact2: (x): {A}x -> ¬(¬{B}{a} & ¬{C}{a}) fact3: (Ex): {B}x | [
"fact1 -> int1: ãèç«ããããã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: (Ex): {A}x; int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãèç«ããããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããããšããã¢ã³ã¹ã¿ãŒã¯èç«ããããªãã°ããã®ã·ãã·ãLv.0ã¯é£ã¹çµãããšããããšã¯ãªããããã«çµã³ä»ãæããªãããšããããšã¯ééã£ãŠãã fact3: ããé£ã¹çµããããšããããšã¯æ¬åœãªãã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ããã®ã·ãã·ãLv.0ã¯é£ã¹çµãããªãããã€çµã³ä»ãæããªãããšããããšã¯æãç«ããªã ; $proof$ = | fact1 -> int1: ãèç«ããããã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): {A}x fact2: (x): {A}x -> ¬(¬{B}{a} & ¬{C}{a}) fact3: (Ex): {B}x ; $hypothesis$ = ¬(¬{B}{a} & ¬{C}{a}) ; $proof$ = | fact1 -> int1: (Ex): {A}x; int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŸããŸã¡ãLv.61ã¯ã¢ã¯ã»ã¹ãæããŠæå®ãé£ãããšããããšã¯æãç«ããªã | ¬({B}{a} & {A}{a}) | fact1: ãã®ãŸããŸã¡ãLv.61ã¯ã¢ã¯ã»ã¹ãæã fact2: ãã®ãŸããŸã¡ãLv.61ã¯æå®ãé£ã | fact1: {B}{a} fact2: {A}{a} | [
"fact2 -> int1: ãã®ãŸããŸã¡ãLv.61ã¯æå®ãé£ã; int1 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãŸããŸã¡ãLv.61ã¯ã¢ã¯ã»ã¹ãæã fact2: ãã®ãŸããŸã¡ãLv.61ã¯æå®ãé£ã ; $hypothesis$ = ããã®ãŸããŸã¡ãLv.61ã¯ã¢ã¯ã»ã¹ãæããŠæå®ãé£ãããšããããšã¯æãç«ããªã ; $proof$ = | fact2 -> int1: ãã®ãŸããŸã¡ãLv.61ã¯æå®ãé£ã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{a} fact2: {A}{a} ; $hypothesis$ = ¬({B}{a} & {A}{a}) ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.39ã¯æ³šææ·±ã | {A}{a} | fact1: ããã®ã·ãã·ãLv.39ã¯å¥ããæãããšããããšã¯ç¢ºãã fact2: äœããã®ã¢ã³ã¹ã¿ãŒãé¢äžåºæ¥ãªããšãããããã¯è©±ãé£ããšããããšã¯ãªãäžæ¹ã§ç©ã
ãã fact3: ããä»®ã«ãã®ã·ãã·ãLv.39ã泚ææ·±ãããããå¥ããæããªããã®ã¿ã«ã¿ãLv.68ã¯åæ€èšãããªã fact4: ãã®ã¿ã«ã¿ãLv.68ã¯åæ€èšã fact5: 話ãé£ããªããããŸãã«ç©ã
ããã¢ã³ã¹ã¿ãŒã¯åæ€èšãããªã fact6: ãã®ã·ãã·ã«ã
Lv.0ãæ¯é
ãããšããããã®ã¿ã«ã¿ãLv.68ã¯æ¯é
ãã fact7: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãåæ€èšãããªããªãå¥ããæããŠããã«æ³šææ·±ã fact8: ä»®ã«ãã®ã¿ã«ã¿ãLv.68ãæ¯é
ãããšããããã®ã·ãã·ãLv.39ã¯é¢äžåºæ¥ãªãããããæŒãæããªã | fact1: {B}{a} fact2: (x): ¬{F}x -> (¬{D}x & {E}x) fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: {C}{b} fact5: (x): (¬{D}x & {E}x) -> ¬{C}x fact6: {H}{c} -> {H}{b} fact7: (x): ¬{C}x -> ({B}x & {A}x) fact8: {H}{b} -> (¬{F}{a} & ¬{G}{a}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.39ã¯æ³šææ·±ã; assump1 & fact1 -> int1: ãã®ã·ãã·ãLv.39ã¯æ³šææ·±ãããã®äžå¥ããæã; int1 & fact3 -> int2: ãã®ã¿ã«ã¿ãLv.68ã¯åæ€èšãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; assump1 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact3 -> int2: ¬{C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.39ã¯æ³šææ·±ã | {A}{a} | [
"fact11 -> int4: ããä»®ã«ãã®ã·ãã·ãLv.39ãåæ€èšãããªããªããã®ã·ãã·ãLv.39ã¯å¥ããæããŠæ³šææ·±ã; fact13 -> int5: ä»®ã«ãã®ã·ãã·ãLv.39ã話ãé£ããªãããããããã¯ç©ã
ãããšãããããã®ã·ãã·ãLv.39ã¯åæ€èšãããªãããšããããšã¯çå®ã ; fact10 -> int6: ä»®ã«ãã®ã·ãã·ãLv.39ã¯é¢äžåºæ¥ãªããªãã°ã話ãé£ããšããããšã¯ãªããŠããã¯ç©ã
ããããšããããšã¯ç¢ºãã§ãã;"
] | 7 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããã®ã·ãã·ãLv.39ã¯å¥ããæãããšããããšã¯ç¢ºãã fact2: äœããã®ã¢ã³ã¹ã¿ãŒãé¢äžåºæ¥ãªããšãããããã¯è©±ãé£ããšããããšã¯ãªãäžæ¹ã§ç©ã
ãã fact3: ããä»®ã«ãã®ã·ãã·ãLv.39ã泚ææ·±ãããããå¥ããæããªããã®ã¿ã«ã¿ãLv.68ã¯åæ€èšãããªã fact4: ãã®ã¿ã«ã¿ãLv.68ã¯åæ€èšã fact5: 話ãé£ããªããããŸãã«ç©ã
ããã¢ã³ã¹ã¿ãŒã¯åæ€èšãããªã fact6: ãã®ã·ãã·ã«ã
Lv.0ãæ¯é
ãããšããããã®ã¿ã«ã¿ãLv.68ã¯æ¯é
ãã fact7: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒãåæ€èšãããªããªãå¥ããæããŠããã«æ³šææ·±ã fact8: ä»®ã«ãã®ã¿ã«ã¿ãLv.68ãæ¯é
ãããšããããã®ã·ãã·ãLv.39ã¯é¢äžåºæ¥ãªãããããæŒãæããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.39ã¯æ³šææ·±ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.39ã¯æ³šææ·±ã; assump1 & fact1 -> int1: ãã®ã·ãã·ãLv.39ã¯æ³šææ·±ãããã®äžå¥ããæã; int1 & fact3 -> int2: ãã®ã¿ã«ã¿ãLv.68ã¯åæ€èšãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{a} fact2: (x): ¬{F}x -> (¬{D}x & {E}x) fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: {C}{b} fact5: (x): (¬{D}x & {E}x) -> ¬{C}x fact6: {H}{c} -> {H}{b} fact7: (x): ¬{C}x -> ({B}x & {A}x) fact8: {H}{b} -> (¬{F}{a} & ¬{G}{a}) ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: {A}{a}; assump1 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact3 -> int2: ¬{C}{b}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽã«ããŽã«ã
Lv.13ã¯å¹³ã£ãããªã | ¬{C}{b} | fact1: ä»®ã«ãã®ãŽã«ããŽã«ã
Lv.13ã¯éããæããªãã°ãå¹³ã£ããããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã fact2: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯æããããªããå¹³ã£ããããšããããšã¯ééãã§ãããšãããå¹³ã£ãããªã fact3: ããããã®ã¿ãã¿ãLv.48ãæããããªããã®ãŽã«ããŽã«ã
Lv.13ã¯éããæã fact4: ãã®ã¿ãã¿ãLv.48ã¯æããã fact5: ãã®ã¿ãã¿ã«ã
Lv.30ã¯å¹³ã£ãã | fact1: {B}{b} -> {C}{b} fact2: (x): ¬(¬{A}x & {C}x) -> ¬{C}x fact3: {A}{a} -> {B}{b} fact4: {A}{a} fact5: {C}{hq} | [
"fact3 & fact4 -> int1: ãã®ãŽã«ããŽã«ã
Lv.13ã¯éããæã; int1 & fact1 -> hypothesis;"
] | [
"fact3 & fact4 -> int1: {B}{b}; int1 & fact1 -> hypothesis;"
] | ãã®ãŽã«ããŽã«ã
Lv.13ã¯å¹³ã£ãããªã | ¬{C}{b} | [
"fact6 -> int2: ããä»®ã«ããã®ãŽã«ããŽã«ã
Lv.13ã¯æããããšããããšã¯ãªãäžæ¹ã§å¹³ã£ããããšããããšã¯äºå®ãšç°ãªããšãããšãã®ãŽã«ããŽã«ã
Lv.13ã¯å¹³ã£ãããªã;"
] | 4 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŽã«ããŽã«ã
Lv.13ã¯éããæããªãã°ãå¹³ã£ããããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã fact2: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯æããããªããå¹³ã£ããããšããããšã¯ééãã§ãããšãããå¹³ã£ãããªã fact3: ããããã®ã¿ãã¿ãLv.48ãæããããªããã®ãŽã«ããŽã«ã
Lv.13ã¯éããæã fact4: ãã®ã¿ãã¿ãLv.48ã¯æããã fact5: ãã®ã¿ãã¿ã«ã
Lv.30ã¯å¹³ã£ãã ; $hypothesis$ = ãã®ãŽã«ããŽã«ã
Lv.13ã¯å¹³ã£ãããªã ; $proof$ = | fact3 & fact4 -> int1: ãã®ãŽã«ããŽã«ã
Lv.13ã¯éããæã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{b} -> {C}{b} fact2: (x): ¬(¬{A}x & {C}x) -> ¬{C}x fact3: {A}{a} -> {B}{b} fact4: {A}{a} fact5: {C}{hq} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact3 & fact4 -> int1: {B}{b}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãªLv.40ã¯ãæããªã | ¬{AA}{a} | fact1: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯äŒŽãæããšããã°ãããã¯å¥œãããããšããããšã¯åã§ãªã fact2: ãããããã®ãŸããŸãªLv.40ã¯ãæãäžæ¹ã§æå³æ·±ããªãããšããããšã¯æãç«ããªããªããã®ãã¡ãããLv.52ã¯åããšãã fact3: ãã®ãã¡ãããLv.52ã¯åããšããªã fact4: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯äŒŽãæã | fact1: (x): {D}x -> {C}x fact2: ¬({AA}{a} & ¬{AB}{a}) -> {B}{b} fact3: ¬{B}{b} fact4: (x): {D}x | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããããã®ãŸããŸãªLv.40ã¯ãæããã©æå³æ·±ããªãããšããããšã¯ééãã ããšããããšã¯ç¢ºãã§ãã; fact2 & assump1 -> int1: ãã®ãã¡ãããLv.52ã¯åããšãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŸããŸãªLv.40ã¯ãæããæå³æ·±ããšããããšã¯ãªã; int3 -> hypothesis;"
] | [
"void -> assump1: ¬({AA}{a} & ¬{AB}{a}); fact2 & assump1 -> int1: {B}{b}; int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: ({AA}{a} & ¬{AB}{a}); int3 -> hypothesis;"
] | ãã®ãŸããŸãªLv.40ã¯ãæããªã | ¬{AA}{a} | [
"fact6 -> int4: ããããã®ãœããœãLv.14ã䌎ãæããšãããããã¯å¥œããã; fact5 -> int5: ãã®ãœããœãLv.14ã¯äŒŽãæã; int4 & int5 -> int6: ãã®ãœããœãLv.14ã¯å¥œããã;"
] | 6 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯äŒŽãæããšããã°ãããã¯å¥œãããããšããããšã¯åã§ãªã fact2: ãããããã®ãŸããŸãªLv.40ã¯ãæãäžæ¹ã§æå³æ·±ããªãããšããããšã¯æãç«ããªããªããã®ãã¡ãããLv.52ã¯åããšãã fact3: ãã®ãã¡ãããLv.52ã¯åããšããªã fact4: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯äŒŽãæã ; $hypothesis$ = ãã®ãŸããŸãªLv.40ã¯ãæããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããããã®ãŸããŸãªLv.40ã¯ãæããã©æå³æ·±ããªãããšããããšã¯ééãã ããšããããšã¯ç¢ºãã§ãã; fact2 & assump1 -> int1: ãã®ãã¡ãããLv.52ã¯åããšãã; int1 & fact3 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŸããŸãªLv.40ã¯ãæããæå³æ·±ããšããããšã¯ãªã; int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {D}x -> {C}x fact2: ¬({AA}{a} & ¬{AB}{a}) -> {B}{b} fact3: ¬{B}{b} fact4: (x): {D}x ; $hypothesis$ = ¬{AA}{a} ; $proof$ = | void -> assump1: ¬({AA}{a} & ¬{AB}{a}); fact2 & assump1 -> int1: {B}{b}; int1 & fact3 -> int2: #F#; [assump1] & int2 -> int3: ({AA}{a} & ¬{AB}{a}); int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.55ã¯æããä»ã | {B}{b} | fact1: ããããã®ã·ãã·ãªLv.63ãæŽã¿æããšããããã®ãœããœãLv.55ã¯åããæããªã fact2: ããä»®ã«ãã®ãœããœãLv.55ãå ªãé£ãäžæ¹ã§ãããåããæããªããšãããããã¯æããä»ã fact3: ãã®ã·ãã·ãªLv.63ã¯æŽã¿æã fact4: ãã®ãœããœãLv.55ã¯åããæããªã fact5: ãã®ãœããœãLv.55ãæŽã¿æããå ªãé£ããšãããšãã®ãœããœãLv.55ã¯æããä»ã fact6: ãã®ã·ãã·ãªLv.63ãæŽã¿æããšããããã®ãœããœãLv.55ã¯å ªãé£ããã©ããã¯åããæããªã | fact1: {A}{a} -> ¬{AB}{b} fact2: ({AA}{b} & ¬{AB}{b}) -> {B}{b} fact3: {A}{a} fact4: ¬{AB}{b} fact5: ({A}{b} & {AA}{b}) -> {B}{b} fact6: {A}{a} -> ({AA}{b} & ¬{AB}{b}) | [
"fact6 & fact3 -> int1: ãã®ãœããœãLv.55ã¯å ªãé£ãäžæ¹ã§ããã¯åããæããªã; int1 & fact2 -> hypothesis;"
] | [
"fact6 & fact3 -> int1: ({AA}{b} & ¬{AB}{b}); int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ã·ãã·ãªLv.63ãæŽã¿æããšããããã®ãœããœãLv.55ã¯åããæããªã fact2: ããä»®ã«ãã®ãœããœãLv.55ãå ªãé£ãäžæ¹ã§ãããåããæããªããšãããããã¯æããä»ã fact3: ãã®ã·ãã·ãªLv.63ã¯æŽã¿æã fact4: ãã®ãœããœãLv.55ã¯åããæããªã fact5: ãã®ãœããœãLv.55ãæŽã¿æããå ªãé£ããšãããšãã®ãœããœãLv.55ã¯æããä»ã fact6: ãã®ã·ãã·ãªLv.63ãæŽã¿æããšããããã®ãœããœãLv.55ã¯å ªãé£ããã©ããã¯åããæããªã ; $hypothesis$ = ãã®ãœããœãLv.55ã¯æããä»ã ; $proof$ = | fact6 & fact3 -> int1: ãã®ãœããœãLv.55ã¯å ªãé£ãäžæ¹ã§ããã¯åããæããªã; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> ¬{AB}{b} fact2: ({AA}{b} & ¬{AB}{b}) -> {B}{b} fact3: {A}{a} fact4: ¬{AB}{b} fact5: ({A}{b} & {AA}{b}) -> {B}{b} fact6: {A}{a} -> ({AA}{b} & ¬{AB}{b}) ; $hypothesis$ = {B}{b} ; $proof$ = | fact6 & fact3 -> int1: ({AA}{b} & ¬{AB}{b}); int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãããã¡ãLv.28ã¯é·ãã | {A}{a} | fact1: ãããã¢ã³ã¹ã¿ãŒã¯åããé£ããªãããããåãé£ãããšããããšã¯æãç«ããªããªãããã¯é·ããªã fact2: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é·ãã | fact1: (x): ¬(¬{C}x & {B}x) -> ¬{A}x fact2: (x): {A}x | [
"fact2 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é·ãã; int1 -> hypothesis;"
] | [
"fact2 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯ã匱ã | (x): {EC}x | [
"fact3 -> int2: ããã®ãããã¡ãLv.28ã¯åããé£ããšããããšã¯ãªããããã¯åãé£ãããšããããšã¯äºå®ã§ãªããšããããã®ãããã¡ãLv.28ã¯é·ããªã;"
] | 5 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã¢ã³ã¹ã¿ãŒã¯åããé£ããªãããããåãé£ãããšããããšã¯æãç«ããªããªãããã¯é·ããªã fact2: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é·ãã ; $hypothesis$ = ãã®ãããã¡ãLv.28ã¯é·ãã ; $proof$ = | fact2 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é·ãã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬(¬{C}x & {B}x) -> ¬{A}x fact2: (x): {A}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact2 -> int1: (x): {A}x; int1 -> hypothesis; __PROVED__ |
0.3 | ã·ã«ã·ãLv.8äºä»¶ã¯èµ·ãããªã | ¬{D} | fact1: ãã«ããLv.58äºä»¶ããã³ãŽããŽãLv.71äºä»¶ã©ã¡ãããèµ·ãã fact2: ãã«ããLv.58äºä»¶ãèµ·ãã fact3: ãã«ããLv.58äºä»¶ã¯çºçããªããšããããšã¯ãæµãæããšããããšãçããããœããœã¡ãLv.94äºä»¶ãèµ·ããããšããããšãçºçããã fact4: ãæµãæããšããããšãèµ·ããããšããããšã¯ç¢ºãã§ãã fact5: ãŽããŽãLv.71äºä»¶ã¯å
¥å¶ããããšãèªçºãã fact6: ãæµãæããšããããšãšå
¥å¶ããããšãçºçããããšããããšã¯ãã·ã«ã·ãLv.8äºä»¶ã¯èµ·ãããªãããšããããšãçºçããã | fact1: ({E} & {A}) fact2: {E} fact3: ¬{E} -> ({C} & {IF}) fact4: {C} fact5: {A} -> {B} fact6: ({C} & {B}) -> ¬{D} | [
"fact1 -> int1: ãŽããŽãLv.71äºä»¶ãèµ·ãã; fact5 & int1 -> int2: å
¥å¶ããããšãèµ·ãã; int2 & fact4 -> int3: æµãæããšããããšãçãããå
¥å¶ããããšãèµ·ãã; int3 & fact6 -> hypothesis;"
] | [
"fact1 -> int1: {A}; fact5 & int1 -> int2: {B}; int2 & fact4 -> int3: ({C} & {B}); int3 & fact6 -> hypothesis;"
] | ã¿ã«ã¿ã«ãLv.22äºä»¶ããã³ãœããœã¡ãLv.94äºä»¶ã©ã¡ãããçãã | ({EJ} & {IF}) | [] | 4 | 4 | 4 | 4 | 4 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã«ããLv.58äºä»¶ããã³ãŽããŽãLv.71äºä»¶ã©ã¡ãããèµ·ãã fact2: ãã«ããLv.58äºä»¶ãèµ·ãã fact3: ãã«ããLv.58äºä»¶ã¯çºçããªããšããããšã¯ãæµãæããšããããšãçããããœããœã¡ãLv.94äºä»¶ãèµ·ããããšããããšãçºçããã fact4: ãæµãæããšããããšãèµ·ããããšããããšã¯ç¢ºãã§ãã fact5: ãŽããŽãLv.71äºä»¶ã¯å
¥å¶ããããšãèªçºãã fact6: ãæµãæããšããããšãšå
¥å¶ããããšãçºçããããšããããšã¯ãã·ã«ã·ãLv.8äºä»¶ã¯èµ·ãããªãããšããããšãçºçããã ; $hypothesis$ = ã·ã«ã·ãLv.8äºä»¶ã¯èµ·ãããªã ; $proof$ = | fact1 -> int1: ãŽããŽãLv.71äºä»¶ãèµ·ãã; fact5 & int1 -> int2: å
¥å¶ããããšãèµ·ãã; int2 & fact4 -> int3: æµãæããšããããšãçãããå
¥å¶ããããšãèµ·ãã; int3 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: ({E} & {A}) fact2: {E} fact3: ¬{E} -> ({C} & {IF}) fact4: {C} fact5: {A} -> {B} fact6: ({C} & {B}) -> ¬{D} ; $hypothesis$ = ¬{D} ; $proof$ = | fact1 -> int1: {A}; fact5 & int1 -> int2: {B}; int2 & fact4 -> int3: ({C} & {B}); int3 & fact6 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããšããããã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªãããšããããšã¯ééã£ãŠãã | ¬({A}{a} -> ¬{D}{b}) | fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒãæ°Žã£ãœããšããããšã¯ãªããªãããã¯çµ¶ãé£ããŠæŽã«æµ
é»ããªã fact2: ããããã®ãŸã®ãŸãLv.6ãæµ
é»ããŠãã€ããã絶ãé£ããšããããã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªã fact3: ãã®ã·ã¡ãã·ã«Lv.52ã¯æµ
é»ã fact4: ãã®ãŽã«ããŽã¡ã
Lv.46ã¯é¢åèããªã fact5: ããã®ãŸã®ãŸãLv.6ã¯çµ¶ãé£ãããšããããšã¯äºå®ã fact6: ãããã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããªãã°ãã®ã·ã«ãã·ã«Lv.84ã¯é¢åèã fact7: ä»®ã«ãã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããªãã°ããã¯æµ
é»ã fact8: ãããã®ãŸã®ãŸãLv.6ãé¢åèããªãã°ãã®ã·ã«ãã·ã«Lv.84ã¯æµ
é»ããªã | fact1: (x): ¬{A}x -> ({C}x & ¬{B}x) fact2: ({B}{a} & {C}{a}) -> ¬{D}{b} fact3: {B}{de} fact4: ¬{D}{hu} fact5: {C}{a} fact6: {A}{a} -> {D}{b} fact7: {A}{a} -> {B}{a} fact8: {D}{a} -> ¬{B}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸã®ãŸãLv.6ã¯æ°Žã£ãœã; fact7 & assump1 -> int1: ãã®ãŸã®ãŸãLv.6ã¯æµ
é»ã; int1 & fact5 -> int2: ãã®ãŸã®ãŸãLv.6ã¯æµ
é»ããŠãŸã絶ãé£ã; int2 & fact2 -> int3: ãã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact7 & assump1 -> int1: {B}{a}; int1 & fact5 -> int2: ({B}{a} & {C}{a}); int2 & fact2 -> int3: ¬{D}{b}; [assump1] & int3 -> hypothesis;"
] | ãã®ã·ã«ãã·ã«Lv.84ã¯çµ¶ãé£ããªã | ¬{C}{b} | [
"fact9 -> int4: ããã®ãŸã®ãŸãLv.6ã¯æ°Žã£ãœããªãããšããããšã¯æ£ãããªãã°çµ¶ãé£ããŠæµ
é»ããªã;"
] | 5 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒãæ°Žã£ãœããšããããšã¯ãªããªãããã¯çµ¶ãé£ããŠæŽã«æµ
é»ããªã fact2: ããããã®ãŸã®ãŸãLv.6ãæµ
é»ããŠãã€ããã絶ãé£ããšããããã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªã fact3: ãã®ã·ã¡ãã·ã«Lv.52ã¯æµ
é»ã fact4: ãã®ãŽã«ããŽã¡ã
Lv.46ã¯é¢åèããªã fact5: ããã®ãŸã®ãŸãLv.6ã¯çµ¶ãé£ãããšããããšã¯äºå®ã fact6: ãããã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããªãã°ãã®ã·ã«ãã·ã«Lv.84ã¯é¢åèã fact7: ä»®ã«ãã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããªãã°ããã¯æµ
é»ã fact8: ãããã®ãŸã®ãŸãLv.6ãé¢åèããªãã°ãã®ã·ã«ãã·ã«Lv.84ã¯æµ
é»ããªã ; $hypothesis$ = ããã®ãŸã®ãŸãLv.6ãæ°Žã£ãœããšããããã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªãããšããããšã¯ééã£ãŠãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸã®ãŸãLv.6ã¯æ°Žã£ãœã; fact7 & assump1 -> int1: ãã®ãŸã®ãŸãLv.6ã¯æµ
é»ã; int1 & fact5 -> int2: ãã®ãŸã®ãŸãLv.6ã¯æµ
é»ããŠãŸã絶ãé£ã; int2 & fact2 -> int3: ãã®ã·ã«ãã·ã«Lv.84ã¯é¢åèããªã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{A}x -> ({C}x & ¬{B}x) fact2: ({B}{a} & {C}{a}) -> ¬{D}{b} fact3: {B}{de} fact4: ¬{D}{hu} fact5: {C}{a} fact6: {A}{a} -> {D}{b} fact7: {A}{a} -> {B}{a} fact8: {D}{a} -> ¬{B}{b} ; $hypothesis$ = ¬({A}{a} -> ¬{D}{b}) ; $proof$ = | void -> assump1: {A}{a}; fact7 & assump1 -> int1: {B}{a}; int1 & fact5 -> int2: ({B}{a} & {C}{a}); int2 & fact2 -> int3: ¬{D}{b}; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | æãŸãæããšããããšã¯çºçããªã | ¬{A} | fact1: ãŽããŽã¡ãLv.43äºä»¶ã¯èµ·ããªã fact2: 説æãæããšããããšãèµ·ãããšããããšã¯æãŸãæããšããããšããããã¯åå¿ããããšãã©ã¡ããã«é²ããã fact3: åå¿ããããšãèµ·ãããšããããšã¯æãŸãæããšããããšãèªçºãã fact4: 説æãæããšããããšãçãã fact5: åå¿ããããšã¯èª¬æãæããšããããšã¯èµ·ããªããšããããšã«åž°çµãã fact6: ããåæ®æãããšããããšã¯çããªããšãããšåå¿ããããšã§ã¯ãªããŠèª¬æãæããšããããšãèµ·ãã fact7: èç«ããããšããããšãèµ·ãã | fact1: ¬{CU} fact2: ({A} v {B}) -> ¬{C} fact3: {B} -> {A} fact4: {C} fact5: {B} -> ¬{C} fact6: ¬{D} -> (¬{B} & {C}) fact7: {AH} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæãŸãæããšããããšãèµ·ãã; assump1 -> int1: æãŸãæããšããããšãçããããŸãã¯åå¿ããããšãèµ·ãããã©ã¡ããã§ãã; int1 & fact2 -> int2: 説æãæããšããããšã¯èµ·ãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ãããæãŸãæããšããããšãèµ·ãã | {A} | [] | 6 | 5 | 3 | 5 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãŽããŽã¡ãLv.43äºä»¶ã¯èµ·ããªã fact2: 説æãæããšããããšãèµ·ãããšããããšã¯æãŸãæããšããããšããããã¯åå¿ããããšãã©ã¡ããã«é²ããã fact3: åå¿ããããšãèµ·ãããšããããšã¯æãŸãæããšããããšãèªçºãã fact4: 説æãæããšããããšãçãã fact5: åå¿ããããšã¯èª¬æãæããšããããšã¯èµ·ããªããšããããšã«åž°çµãã fact6: ããåæ®æãããšããããšã¯çããªããšãããšåå¿ããããšã§ã¯ãªããŠèª¬æãæããšããããšãèµ·ãã fact7: èç«ããããšããããšãèµ·ãã ; $hypothesis$ = æãŸãæããšããããšã¯çºçããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæãŸãæããšããããšãèµ·ãã; assump1 -> int1: æãŸãæããšããããšãçããããŸãã¯åå¿ããããšãèµ·ãããã©ã¡ããã§ãã; int1 & fact2 -> int2: 説æãæããšããããšã¯èµ·ãããªã; int2 & fact4 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{CU} fact2: ({A} v {B}) -> ¬{C} fact3: {B} -> {A} fact4: {C} fact5: {B} -> ¬{C} fact6: ¬{D} -> (¬{B} & {C}) fact7: {AH} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact4 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ç²é«ããšããããšãèµ·ãã | {C} | fact1: ãã調ã¹æããšããããšãçããããŸãã¯ã·ã¡ãã·ã«ã
Lv.36äºä»¶ãçãããäž¡æ¹ãšãã§ãããªãã°ãç²é«ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact2: ä»®ã«ãŸã¡ããŸã«ã
Lv.70äºä»¶ã¯èµ·ãããªããªãã¿ã¡ã
ã¿ã«ã
Lv.17äºä»¶ãèµ·ãããã¿ã¡ãã¿ãLv.39äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã§ãã fact3: ããœããœãLv.78äºä»¶ã¯èµ·ãããªãããšããããšã¯ãã·ã¡ãã·ã«ã
Lv.36äºä»¶ã¯çããªãããšããããšãçºçããã fact4: ãåãæããšããããšã¯èµ·ããªããããããœããœãLv.78äºä»¶ã¯èµ·ããªãããšããããšã¯ãŽã¡ããŽã«Lv.59äºä»¶ãèµ·ããªããšããããšã¯å¥æ©ã§ãã | fact1: ({A} v {B}) -> ¬{C} fact2: ¬{I} -> ({H} v {G}) fact3: ¬{D} -> ¬{B} fact4: ¬{F} -> (¬{E} & ¬{D}) | [] | [] | ç²é«ããšããããšãèµ·ãã | {C} | [] | 8 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã調ã¹æããšããããšãçããããŸãã¯ã·ã¡ãã·ã«ã
Lv.36äºä»¶ãçãããäž¡æ¹ãšãã§ãããªãã°ãç²é«ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact2: ä»®ã«ãŸã¡ããŸã«ã
Lv.70äºä»¶ã¯èµ·ãããªããªãã¿ã¡ã
ã¿ã«ã
Lv.17äºä»¶ãèµ·ãããã¿ã¡ãã¿ãLv.39äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã§ãã fact3: ããœããœãLv.78äºä»¶ã¯èµ·ãããªãããšããããšã¯ãã·ã¡ãã·ã«ã
Lv.36äºä»¶ã¯çããªãããšããããšãçºçããã fact4: ãåãæããšããããšã¯èµ·ããªããããããœããœãLv.78äºä»¶ã¯èµ·ããªãããšããããšã¯ãŽã¡ããŽã«Lv.59äºä»¶ãèµ·ããªããšããããšã¯å¥æ©ã§ãã ; $hypothesis$ = ç²é«ããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: ¬{I} -> ({H} v {G}) fact3: ¬{D} -> ¬{B} fact4: ¬{F} -> (¬{E} & ¬{D}) ; $hypothesis$ = {C} ; $proof$ = | __UNKNOWN__ |
0.3 | æ³¥èããšããããšãçºçãããããŸãã«èªçºãæããšããããšã¯çºçãã | ({E} & {F}) | fact1: ããä»®ã«ãèšãæããšããããšãçãããã·ãã·ã¡ãLv.14äºä»¶ã¯èµ·ãããªãããšããããšã¯æ£ãããªããªãã°çšé ããšããããšã¯çããªã fact2: èªçºãæããšããããšãèµ·ãã fact3: ãããçãæããšããããšã¯èµ·ãããªããªãã°ãæ³¥èããšããããšãçãããããã«èªçºãæããšããããšãèµ·ããããšããããšã¯åã fact4: çãæããšããããšãçãã fact5: çžäŒããããšã¯çšé ããšããããšã«ç¹ãã fact6: çšé ããšããããšã¯æ³¥èããšããããšãèªçºãã fact7: ããããLv.99äºä»¶ãçãããšããããšã¯çžäŒããããšã¯çºçããªããšããããšãé»æ¢ãã fact8: çãæããšããããšããã³ããããLv.99äºä»¶ãèµ·ãã | fact1: ¬({H} & ¬{G}) -> ¬{D} fact2: {F} fact3: ¬{A} -> ¬({E} & {F}) fact4: {A} fact5: {C} -> {D} fact6: {D} -> {E} fact7: {B} -> {C} fact8: ({A} & {B}) | [
"fact8 -> int1: ããããLv.99äºä»¶ãèµ·ãã; int1 & fact7 -> int2: çžäŒããããšãèµ·ãã; int2 & fact5 -> int3: çšé ããšããããšãçºçãã; int3 & fact6 -> int4: æ³¥èããšããããšãèµ·ãã; int4 & fact2 -> hypothesis;"
] | [
"fact8 -> int1: {B}; int1 & fact7 -> int2: {C}; int2 & fact5 -> int3: {D}; int3 & fact6 -> int4: {E}; int4 & fact2 -> hypothesis;"
] | ãæ³¥èããšããããšããã³èªçºãæããšããããšãçããããšããããšã¯åã§ãã | ¬({E} & {F}) | [] | 7 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãèšãæããšããããšãçãããã·ãã·ã¡ãLv.14äºä»¶ã¯èµ·ãããªãããšããããšã¯æ£ãããªããªãã°çšé ããšããããšã¯çããªã fact2: èªçºãæããšããããšãèµ·ãã fact3: ãããçãæããšããããšã¯èµ·ãããªããªãã°ãæ³¥èããšããããšãçãããããã«èªçºãæããšããããšãèµ·ããããšããããšã¯åã fact4: çãæããšããããšãçãã fact5: çžäŒããããšã¯çšé ããšããããšã«ç¹ãã fact6: çšé ããšããããšã¯æ³¥èããšããããšãèªçºãã fact7: ããããLv.99äºä»¶ãçãããšããããšã¯çžäŒããããšã¯çºçããªããšããããšãé»æ¢ãã fact8: çãæããšããããšããã³ããããLv.99äºä»¶ãèµ·ãã ; $hypothesis$ = æ³¥èããšããããšãçºçãããããŸãã«èªçºãæããšããããšã¯çºçãã ; $proof$ = | fact8 -> int1: ããããLv.99äºä»¶ãèµ·ãã; int1 & fact7 -> int2: çžäŒããããšãèµ·ãã; int2 & fact5 -> int3: çšé ããšããããšãçºçãã; int3 & fact6 -> int4: æ³¥èããšããããšãèµ·ãã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({H} & ¬{G}) -> ¬{D} fact2: {F} fact3: ¬{A} -> ¬({E} & {F}) fact4: {A} fact5: {C} -> {D} fact6: {D} -> {E} fact7: {B} -> {C} fact8: ({A} & {B}) ; $hypothesis$ = ({E} & {F}) ; $proof$ = | fact8 -> int1: {B}; int1 & fact7 -> int2: {C}; int2 & fact5 -> int3: {D}; int3 & fact6 -> int4: {E}; int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ã«ã
ã¿ãLv.10ã¯äžãç¶ãã | {A}{a} | fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åºåãã fact2: èŠåæ£ããã¢ã³ã¹ã¿ãŒã¯äžãç¶ããäžæ¹ã§é 圢ãããšããããšã¯ãªã fact3: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯è©±ãæã fact4: ããããã¢ã³ã¹ã¿ãŒã¯ç§»ç®¡ãã | fact1: (x): {IL}x fact2: (x): {C}x -> ({A}x & ¬{B}x) fact3: (x): {ET}x fact4: (x): {HL}x | [] | [] | ãã®ã·ãã·ãLv.35ã¯äžãç¶ãã | {A}{bn} | [
"fact5 -> int1: ãã®ã·ãã·ãLv.35ãèŠåæ£ãããªãããã¯äžãç¶ããäžæ¹ã§é 圢ããªã;"
] | 5 | 2 | 2 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åºåãã fact2: èŠåæ£ããã¢ã³ã¹ã¿ãŒã¯äžãç¶ããäžæ¹ã§é 圢ãããšããããšã¯ãªã fact3: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯è©±ãæã fact4: ããããã¢ã³ã¹ã¿ãŒã¯ç§»ç®¡ãã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ãLv.10ã¯äžãç¶ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): {IL}x fact2: (x): {C}x -> ({A}x & ¬{B}x) fact3: (x): {ET}x fact4: (x): {HL}x ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ã¿ã«ã
ã¿ãLv.94äºä»¶ãèµ·ãã | {G} | fact1: ä»®ã«ãããã«ãLv.75äºä»¶ã¯èµ·ããªããšããã°ãããããLv.55äºä»¶ã¯çããªãããããã«Lv.68äºä»¶ãèµ·ããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ãã§ãã fact2: ããããã·ã¡ã
ã·ã®Lv.65äºä»¶ã¯èµ·ããªãããããã¯ãŸã«ããŸã«ãLv.39äºä»¶ãçããããããã¯ã©ã¡ããã§ããããšããããšã¯æãç«ã€ããšããããšã¯æ¬åœã§ãªããªãã°ã¿ã«ã
ã¿ãLv.94äºä»¶ãçºçãã fact3: ããããœã«ãœãLv.93äºä»¶ã¯çºçããªããªãã°ãé£ã¹æããšããããšã§ã¯ãªãã¿ã«ã
ã¿ãLv.94äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãã fact4: ä»®ã«ã¢ãŠããœãŒã¹ããããšã¯çããªããªãã°ãã·ã¡ã
ã·ã®Lv.65äºä»¶ã¯èµ·ãããªãããŸã«ããŸã«ãLv.39äºä»¶ã¯çºçããããšããããšã¯ééãã fact5: æå®ãé£ããšããããšãèµ·ãã fact6: ããŸã«ããŸã«ãLv.39äºä»¶ã¯çºçããªãããšããããšã¯ã¢ãŠããœãŒã¹ããããšã¯çããªããšããããšã«ç±æ¥ãã fact7: ãŸã«ããŸã«ãLv.39äºä»¶ã¯èµ·ããªããªãã°ãã¢ãŠããœãŒã¹ããããšãšæå®ãé£ããšããããšã©ã¡ãããçºçããããšããããšã¯æãç«ããªã fact8: ã¢ãŠããœãŒã¹ããããšã¯æå®ãé£ããšããããšããã³ãœã«ãœãLv.93äºä»¶ãçããã«é²ããã | fact1: ¬{AO} -> ¬(¬{CL} v {IH}) fact2: ¬(¬{F} v {E}) -> {G} fact3: ¬{B} -> ¬(¬{A} & {G}) fact4: ¬{D} -> ¬(¬{F} v {E}) fact5: {C} fact6: ¬{D} -> ¬{E} fact7: ¬{E} -> ¬({D} & {C}) fact8: ({C} & {B}) -> ¬{D} | [] | [] | ãã¿ã«ã
ã¿ãLv.94äºä»¶ã¯çããªãããšããããšã¯æãç«ã€ | ¬{G} | [] | 7 | 5 | 5 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãããã«ãLv.75äºä»¶ã¯èµ·ããªããšããã°ãããããLv.55äºä»¶ã¯çããªãããããã«Lv.68äºä»¶ãèµ·ããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ãã§ãã fact2: ããããã·ã¡ã
ã·ã®Lv.65äºä»¶ã¯èµ·ããªãããããã¯ãŸã«ããŸã«ãLv.39äºä»¶ãçããããããã¯ã©ã¡ããã§ããããšããããšã¯æãç«ã€ããšããããšã¯æ¬åœã§ãªããªãã°ã¿ã«ã
ã¿ãLv.94äºä»¶ãçºçãã fact3: ããããœã«ãœãLv.93äºä»¶ã¯çºçããªããªãã°ãé£ã¹æããšããããšã§ã¯ãªãã¿ã«ã
ã¿ãLv.94äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãã fact4: ä»®ã«ã¢ãŠããœãŒã¹ããããšã¯çããªããªãã°ãã·ã¡ã
ã·ã®Lv.65äºä»¶ã¯èµ·ãããªãããŸã«ããŸã«ãLv.39äºä»¶ã¯çºçããããšããããšã¯ééãã fact5: æå®ãé£ããšããããšãèµ·ãã fact6: ããŸã«ããŸã«ãLv.39äºä»¶ã¯çºçããªãããšããããšã¯ã¢ãŠããœãŒã¹ããããšã¯çããªããšããããšã«ç±æ¥ãã fact7: ãŸã«ããŸã«ãLv.39äºä»¶ã¯èµ·ããªããªãã°ãã¢ãŠããœãŒã¹ããããšãšæå®ãé£ããšããããšã©ã¡ãããçºçããããšããããšã¯æãç«ããªã fact8: ã¢ãŠããœãŒã¹ããããšã¯æå®ãé£ããšããããšããã³ãœã«ãœãLv.93äºä»¶ãçããã«é²ããã ; $hypothesis$ = ã¿ã«ã
ã¿ãLv.94äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{AO} -> ¬(¬{CL} v {IH}) fact2: ¬(¬{F} v {E}) -> {G} fact3: ¬{B} -> ¬(¬{A} & {G}) fact4: ¬{D} -> ¬(¬{F} v {E}) fact5: {C} fact6: ¬{D} -> ¬{E} fact7: ¬{E} -> ¬({D} & {C}) fact8: ({C} & {B}) -> ¬{D} ; $hypothesis$ = {G} ; $proof$ = | __UNKNOWN__ |
0.3 | ã¡ããæããšããããšãçãã | {C} | fact1: ã湿ã£ãœããšããããšãšä»ãããšãçããããšããããšã¯æãç«ããªã fact2: ãä»®ã«ã湿ã£ãœããšããããšã¯çºçãããä»ãããšã¯çºçããªãããšããããšã¯ééã£ãŠãããšãããã¡ããæããšããããšãèµ·ããããšããããšã¯ç¢ºãã§ãã fact3: ãããœã¡ããœã¡ãLv.90äºä»¶ãèµ·ãããªãã·ãã·ã«Lv.18äºä»¶ãçºçããªãããããä»ãããšã¯çºçããªã fact4: ã¡ããæããšããããšã¯çããªããšããããšã¯ãä»ãããšãçããããšããããšã«é»ãŸãã fact5: 湿ã£ãœããšããããšã¯çããªã fact6: ä»ãããšã¯çºçããªã fact7: ä»®ã«ãã芪ãããšããããšãèµ·ããäžæ¹ã§å°é ãå§ããããšã¯èµ·ãããªãããšããããšã¯åã§ãªãããšããããšã¯èª€ãã ãšããã°ããã°ãããšããããšãçºçãã | fact1: ¬({A} & {B}) fact2: ¬({A} & ¬{B}) -> {C} fact3: {E} -> (¬{D} & ¬{B}) fact4: {B} -> {C} fact5: ¬{A} fact6: ¬{B} fact7: ¬({AP} & ¬{DU}) -> {FJ} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããã湿ã£ãœããšããããšãèµ·ãããä»ãããšã¯èµ·ããªãããšããããšã¯çå®ã§ãã; assump1 -> int1: 湿ã£ãœããšããããšãçãã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ã湿ã£ãœããšããããšãèµ·ãããä»ãããšã¯èµ·ããªãããšããããšã¯ééãã ; int3 & fact2 -> hypothesis;"
] | [
"void -> assump1: ({A} & ¬{B}); assump1 -> int1: {A}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬({A} & ¬{B}); int3 & fact2 -> hypothesis;"
] | ã¡ããæããšããããšã¯èµ·ãããªã | ¬{C} | [] | 6 | 5 | 3 | 5 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ã湿ã£ãœããšããããšãšä»ãããšãçããããšããããšã¯æãç«ããªã fact2: ãä»®ã«ã湿ã£ãœããšããããšã¯çºçãããä»ãããšã¯çºçããªãããšããããšã¯ééã£ãŠãããšãããã¡ããæããšããããšãèµ·ããããšããããšã¯ç¢ºãã§ãã fact3: ãããœã¡ããœã¡ãLv.90äºä»¶ãèµ·ãããªãã·ãã·ã«Lv.18äºä»¶ãçºçããªãããããä»ãããšã¯çºçããªã fact4: ã¡ããæããšããããšã¯çããªããšããããšã¯ãä»ãããšãçããããšããããšã«é»ãŸãã fact5: 湿ã£ãœããšããããšã¯çããªã fact6: ä»ãããšã¯çºçããªã fact7: ä»®ã«ãã芪ãããšããããšãèµ·ããäžæ¹ã§å°é ãå§ããããšã¯èµ·ãããªãããšããããšã¯åã§ãªãããšããããšã¯èª€ãã ãšããã°ããã°ãããšããããšãçºçãã ; $hypothesis$ = ã¡ããæããšããããšãçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããã湿ã£ãœããšããããšãèµ·ãããä»ãããšã¯èµ·ããªãããšããããšã¯çå®ã§ãã; assump1 -> int1: 湿ã£ãœããšããããšãçãã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ã湿ã£ãœããšããããšãèµ·ãããä»ãããšã¯èµ·ããªãããšããããšã¯ééãã ; int3 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({A} & {B}) fact2: ¬({A} & ¬{B}) -> {C} fact3: {E} -> (¬{D} & ¬{B}) fact4: {B} -> {C} fact5: ¬{A} fact6: ¬{B} fact7: ¬({AP} & ¬{DU}) -> {FJ} ; $hypothesis$ = {C} ; $proof$ = | void -> assump1: ({A} & ¬{B}); assump1 -> int1: {A}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬({A} & ¬{B}); int3 & fact2 -> hypothesis; __PROVED__ |
0.3 | ä¹ãéãããããšããã³çµã¿äžããããšãèµ·ãã | ({A} & {B}) | fact1: ã¯ãããªããšããããšãçãã fact2: ä¹ãéãããããšãçºçãã fact3: ä¹ãéãããããšããã³ã¿ãã¿ãLv.35äºä»¶ãèµ·ããã¯çµã¿äžããããšãçããªããšããããšã¯å¥æ©ã§ãã | fact1: {DL} fact2: {A} fact3: ¬{B} -> ({A} & {BH}) | [
"fact2 -> int1: ä¹ãéãããããšãçºçãã;"
] | [
"fact2 -> int1: {A};"
] | ã¿ãã¿ãLv.35äºä»¶ãçºçãã | {BH} | [] | 6 | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã¯ãããªããšããããšãçãã fact2: ä¹ãéãããããšãçºçãã fact3: ä¹ãéãããããšããã³ã¿ãã¿ãLv.35äºä»¶ãèµ·ããã¯çµã¿äžããããšãçããªããšããããšã¯å¥æ©ã§ãã ; $hypothesis$ = ä¹ãéãããããšããã³çµã¿äžããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {DL} fact2: {A} fact3: ¬{B} -> ({A} & {BH}) ; $hypothesis$ = ({A} & {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.66ã¯å·®ãåºããŸãããäŒããæããšããããšã¯ãªã | ({AA}{a} & ¬{AB}{a}) | fact1: ä»®ã«ãã®ã·ãã·ãLv.66ã¯ç ããšãããšããã®ãœã¡ããœãLv.91ã¯å¯Ÿæããç掻ãæããªãããšããããšã¯æãç«ããªã fact2: ç ãã¢ã³ã¹ã¿ãŒã¯å·®ãåºããŸããããã©äŒããæããªã fact3: ãã®ã·ãã·ãLv.66ã¯èŠé£ã fact4: ããã®ã·ãã·ãLv.66ã¯å·®ãåºããŸããäžæ¹ã§ããã¯å¯ã蟺ç¡ããªãããšããããšã¯ééãã | fact1: {A}{a} -> ¬({CE}{ef} & ¬{BD}{ef}) fact2: (x): {A}x -> ({AA}x & ¬{AB}x) fact3: {B}{a} fact4: ¬({AA}{a} & ¬{JJ}{a}) | [] | [] | 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.66ã¯å·®ãåºããŸãããäŒããæããšããããšã¯ãªã | ({AA}{a} & ¬{AB}{a}) | [
"fact5 -> int1: ãã®ã·ãã·ãLv.66ãç ããªãå·®ãåºããŸããããã©äŒããæããªã;"
] | 4 | 4 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ã·ãã·ãLv.66ã¯ç ããšãããšããã®ãœã¡ããœãLv.91ã¯å¯Ÿæããç掻ãæããªãããšããããšã¯æãç«ããªã fact2: ç ãã¢ã³ã¹ã¿ãŒã¯å·®ãåºããŸããããã©äŒããæããªã fact3: ãã®ã·ãã·ãLv.66ã¯èŠé£ã fact4: ããã®ã·ãã·ãLv.66ã¯å·®ãåºããŸããäžæ¹ã§ããã¯å¯ã蟺ç¡ããªãããšããããšã¯ééãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ã·ãã·ãLv.66ã¯å·®ãåºããŸãããäŒããæããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} -> ¬({CE}{ef} & ¬{BD}{ef}) fact2: (x): {A}x -> ({AA}x & ¬{AB}x) fact3: {B}{a} fact4: ¬({AA}{a} & ¬{JJ}{a}) ; $hypothesis$ = ({AA}{a} & ¬{AB}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | è£ä¿®åºæ¥ãããšã¯çããªã | ¬{A} | fact1: æµã¿æ·±ããšããããšãçãã fact2: ã¿ã€ãã«ããããšããããšãèµ·ãã fact3: ä»®ã«è£ä¿®åºæ¥ãããšãšæµã¿æ·±ããšããããšã©ã¡ãããçãããšãããšã¿ã€ãã«ããããšããããšã¯çºçããªã | fact1: {B} fact2: {C} fact3: ({A} & {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããè£ä¿®åºæ¥ãããšãèµ·ãã; assump1 & fact1 -> int1: è£ä¿®åºæ¥ãããšããã³æµã¿æ·±ããšããããšãèµ·ãã; int1 & fact3 -> int2: ã¿ã€ãã«ããããšããããšã¯çºçããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: æµã¿æ·±ããšããããšãçãã fact2: ã¿ã€ãã«ããããšããããšãèµ·ãã fact3: ä»®ã«è£ä¿®åºæ¥ãããšãšæµã¿æ·±ããšããããšã©ã¡ãããçãããšãããšã¿ã€ãã«ããããšããããšã¯çºçããªã ; $hypothesis$ = è£ä¿®åºæ¥ãããšã¯çããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããè£ä¿®åºæ¥ãããšãèµ·ãã; assump1 & fact1 -> int1: è£ä¿®åºæ¥ãããšããã³æµã¿æ·±ããšããããšãèµ·ãã; int1 & fact3 -> int2: ã¿ã€ãã«ããããšããããšã¯çºçããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {B} fact2: {C} fact3: ({A} & {B}) -> ¬{C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 & fact1 -> int1: ({A} & {B}); int1 & fact3 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŸã«ããŸã®Lv.17ã¯éºãããšããããšã¯æãç«ã€ | {A}{a} | fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯éºã | fact1: (x): {A}x | [
"fact1 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯éºã; int1 -> hypothesis;"
] | [
"fact1 -> int1: (x): {A}x; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯éºã ; $hypothesis$ = ããã®ãŸã«ããŸã®Lv.17ã¯éºãããšããããšã¯æãç«ã€ ; $proof$ = | fact1 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯éºã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {A}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact1 -> int1: (x): {A}x; int1 -> hypothesis; __PROVED__ |
0.3 | ãŽããŽãLv.47äºä»¶ã¯çããªã | ¬{F} | fact1: æž
ããšããããšã¯çºçãããããã«ãŽããŽãLv.92äºä»¶ã¯çºçãã fact2: ã·ãªã·ã«ã
Lv.12äºä»¶ã¯çããªã fact3: ã¿ã®ã¿ã®Lv.38äºä»¶ãèµ·ãããšããããšã¯ã埡æŽèœããããšãèµ·ããããšããããšããã£ããã§ãã fact4: ããããŽããŽãLv.92äºä»¶ã¯èµ·ãããªããšãããæž
ããšããããšããã³ãŽããŽãLv.47äºä»¶äž¡æ¹ãšããçãã fact5: ãŽããŽãLv.92äºä»¶ã¯åŸ¡æŽèœããããšãåŒãèµ·ãã fact6: ãŽããŽãLv.92äºä»¶ã¯çºçããªããšããããšã¯ããŽããŽãLv.47äºä»¶ãèµ·ãããæž
ããšããããšãèµ·ããããšããããšãçãããã fact7: ç³ãèš³ç¡ããšããããšã¯ãœããœãLv.7äºä»¶ãèµ·ãããšããããšãæã fact8: ãã¿ã®ã¿ã®Lv.38äºä»¶ãçãããæŽã«ãããã¡ãLv.83äºä»¶ãèµ·ããããšããããšã¯ãŽããŽãLv.47äºä»¶ãåé¿ãã fact9: æž
ããšããããšãèµ·ãã | fact1: ({A} & {B}) fact2: ¬{GG} fact3: {C} -> {D} fact4: ¬{B} -> ({A} & {F}) fact5: {B} -> {C} fact6: ¬{B} -> ({F} & {A}) fact7: {HE} -> {K} fact8: ({D} & {E}) -> ¬{F} fact9: {A} | [
"fact1 -> int1: ãŽããŽãLv.92äºä»¶ãçºçãã; int1 & fact5 -> int2: 埡æŽèœããããšãèµ·ãã; int2 & fact3 -> int3: ã¿ã®ã¿ã®Lv.38äºä»¶ãèµ·ãã;"
] | [
"fact1 -> int1: {B}; int1 & fact5 -> int2: {C}; int2 & fact3 -> int3: {D};"
] | ãŽããŽãLv.47äºä»¶ãèµ·ãã | {F} | [] | 6 | 5 | 5 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: æž
ããšããããšã¯çºçãããããã«ãŽããŽãLv.92äºä»¶ã¯çºçãã fact2: ã·ãªã·ã«ã
Lv.12äºä»¶ã¯çããªã fact3: ã¿ã®ã¿ã®Lv.38äºä»¶ãèµ·ãããšããããšã¯ã埡æŽèœããããšãèµ·ããããšããããšããã£ããã§ãã fact4: ããããŽããŽãLv.92äºä»¶ã¯èµ·ãããªããšãããæž
ããšããããšããã³ãŽããŽãLv.47äºä»¶äž¡æ¹ãšããçãã fact5: ãŽããŽãLv.92äºä»¶ã¯åŸ¡æŽèœããããšãåŒãèµ·ãã fact6: ãŽããŽãLv.92äºä»¶ã¯çºçããªããšããããšã¯ããŽããŽãLv.47äºä»¶ãèµ·ãããæž
ããšããããšãèµ·ããããšããããšãçãããã fact7: ç³ãèš³ç¡ããšããããšã¯ãœããœãLv.7äºä»¶ãèµ·ãããšããããšãæã fact8: ãã¿ã®ã¿ã®Lv.38äºä»¶ãçãããæŽã«ãããã¡ãLv.83äºä»¶ãèµ·ããããšããããšã¯ãŽããŽãLv.47äºä»¶ãåé¿ãã fact9: æž
ããšããããšãèµ·ãã ; $hypothesis$ = ãŽããŽãLv.47äºä»¶ã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A} & {B}) fact2: ¬{GG} fact3: {C} -> {D} fact4: ¬{B} -> ({A} & {F}) fact5: {B} -> {C} fact6: ¬{B} -> ({F} & {A}) fact7: {HE} -> {K} fact8: ({D} & {E}) -> ¬{F} fact9: {A} ; $hypothesis$ = ¬{F} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ãããæ»ãæããšããããšãèµ·ãã | {B} | fact1: ãã©ã³ã¹è¯ããšããããšãèµ·ãã fact2: ããã©ã³ã¹è¯ããšããããšã¯èµ·ãããªãããšããããšã¯é Œããããšããããšããã£ããã§ãã fact3: ã·ãã·ã¡ãLv.88äºä»¶ã¯èµ·ããªããšããããšã¯ããŸããŸãªLv.10äºä»¶ãçããã飲ã¿å°œããããšãçããããããã¯äž¡æ¹ãšãã§ããããšããããšã«ããçãã fact4: é Œããããšããããšãæ»ãæããšããããšã¯ãã©ã³ã¹è¯ããšããããšã¯çºçããªããšããããšãåŒãèµ·ãã | fact1: {C} fact2: {A} -> ¬{C} fact3: ({IQ} v {BT}) -> ¬{HM} fact4: ({A} v {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæ»ãæããšããããšãèµ·ãã; assump1 -> int1: é ŒããããšããããšããŸãã¯æ»ãæããšããããšãèµ·ãã; int1 & fact4 -> int2: ãã©ã³ã¹è¯ããšããããšã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã©ã³ã¹è¯ããšããããšãèµ·ãã fact2: ããã©ã³ã¹è¯ããšããããšã¯èµ·ãããªãããšããããšã¯é Œããããšããããšããã£ããã§ãã fact3: ã·ãã·ã¡ãLv.88äºä»¶ã¯èµ·ããªããšããããšã¯ããŸããŸãªLv.10äºä»¶ãçããã飲ã¿å°œããããšãçããããããã¯äž¡æ¹ãšãã§ããããšããããšã«ããçãã fact4: é Œããããšããããšãæ»ãæããšããããšã¯ãã©ã³ã¹è¯ããšããããšã¯çºçããªããšããããšãåŒãèµ·ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããæ»ãæããšããããšãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæ»ãæããšããããšãèµ·ãã; assump1 -> int1: é ŒããããšããããšããŸãã¯æ»ãæããšããããšãèµ·ãã; int1 & fact4 -> int2: ãã©ã³ã¹è¯ããšããããšã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C} fact2: {A} -> ¬{C} fact3: ({IQ} v {BT}) -> ¬{HM} fact4: ({A} v {B}) -> ¬{C} ; $hypothesis$ = {B} ; $proof$ = | void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽã¡ãLv.81ã¯æãåºããªã | ¬{E}{a} | fact1: ãä»®ã«ããã¢ã³ã¹ã¿ãŒãéããªããšãããšç©ã
ããããšããããšã¯æãç«ã€ fact2: ããããã¢ã³ã¹ã¿ãŒã幌ããšããã°ããã¯æãåºããªããŠäœãæããªã fact3: ãããããã®ãŸããŸãLv.35ã¯éããªãããšããããšã¯æ£ãããšãããšãã®ãŽããŽã¡ãLv.81ã¯ç©ã
ãããŠæãé£ã fact4: ä»®ã«ãã®ãŽããŽã«Lv.99ãç©ã
ãããªãã°ããã¯æãé£ã fact5: ãã®ãŽããŽã«Lv.99ã¯éãããšããããšã¯ãªã fact6: ãã®ãŸããŸãLv.35ã¯å¹Œã fact7: ãããã®ãŽããŽã«Lv.99ãæãé£ããªããã®ãŽããŽã¡ãLv.81ã¯åãé£ã fact8: ä»®ã«ãã®ãŽããŽã¡ãLv.81ãåãé£ããšãããšããã¯æãåºã | fact1: (x): ¬{B}x -> {C}x fact2: (x): {G}x -> (¬{E}x & ¬{F}x) fact3: ¬{B}{b} -> ({C}{a} & {A}{a}) fact4: {C}{aa} -> {A}{aa} fact5: ¬{B}{aa} fact6: {G}{b} fact7: {A}{aa} -> {D}{a} fact8: {D}{a} -> {E}{a} | [
"fact1 -> int1: ããããã®ãŽããŽã«Lv.99ãéããªããšããã°ãã®ãŽããŽã«Lv.99ã¯ç©ã
ãã; int1 & fact5 -> int2: ãã®ãŽããŽã«Lv.99ã¯ç©ã
ãã; int2 & fact4 -> int3: ãã®ãŽããŽã«Lv.99ã¯æãé£ã; int3 & fact7 -> int4: ãã®ãŽããŽã¡ãLv.81ã¯åãé£ã; int4 & fact8 -> hypothesis;"
] | [
"fact1 -> int1: ¬{B}{aa} -> {C}{aa}; int1 & fact5 -> int2: {C}{aa}; int2 & fact4 -> int3: {A}{aa}; int3 & fact7 -> int4: {D}{a}; int4 & fact8 -> hypothesis;"
] | ãã®ãŽããŽã¡ãLv.81ã¯ç©ã
ãã | {C}{a} | [
"fact11 -> int5: ä»®ã«ãã®ãŸããŸãLv.35ã幌ããšããã°ããã¯æãåºããªããŠããã«äœãæããªã; int5 & fact9 -> int6: ãã®ãŸããŸãLv.35ã¯æãåºããªããŠãããäœãæããšããããšã¯ãªã; int6 -> int7: ããã®ãŸããŸãLv.35ã¯æãåºããªãããšããããšã¯çå®ã§ãã;"
] | 7 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãä»®ã«ããã¢ã³ã¹ã¿ãŒãéããªããšãããšç©ã
ããããšããããšã¯æãç«ã€ fact2: ããããã¢ã³ã¹ã¿ãŒã幌ããšããã°ããã¯æãåºããªããŠäœãæããªã fact3: ãããããã®ãŸããŸãLv.35ã¯éããªãããšããããšã¯æ£ãããšãããšãã®ãŽããŽã¡ãLv.81ã¯ç©ã
ãããŠæãé£ã fact4: ä»®ã«ãã®ãŽããŽã«Lv.99ãç©ã
ãããªãã°ããã¯æãé£ã fact5: ãã®ãŽããŽã«Lv.99ã¯éãããšããããšã¯ãªã fact6: ãã®ãŸããŸãLv.35ã¯å¹Œã fact7: ãããã®ãŽããŽã«Lv.99ãæãé£ããªããã®ãŽããŽã¡ãLv.81ã¯åãé£ã fact8: ä»®ã«ãã®ãŽããŽã¡ãLv.81ãåãé£ããšãããšããã¯æãåºã ; $hypothesis$ = ãã®ãŽããŽã¡ãLv.81ã¯æãåºããªã ; $proof$ = | fact1 -> int1: ããããã®ãŽããŽã«Lv.99ãéããªããšããã°ãã®ãŽããŽã«Lv.99ã¯ç©ã
ãã; int1 & fact5 -> int2: ãã®ãŽããŽã«Lv.99ã¯ç©ã
ãã; int2 & fact4 -> int3: ãã®ãŽããŽã«Lv.99ã¯æãé£ã; int3 & fact7 -> int4: ãã®ãŽããŽã¡ãLv.81ã¯åãé£ã; int4 & fact8 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{B}x -> {C}x fact2: (x): {G}x -> (¬{E}x & ¬{F}x) fact3: ¬{B}{b} -> ({C}{a} & {A}{a}) fact4: {C}{aa} -> {A}{aa} fact5: ¬{B}{aa} fact6: {G}{b} fact7: {A}{aa} -> {D}{a} fact8: {D}{a} -> {E}{a} ; $hypothesis$ = ¬{E}{a} ; $proof$ = | fact1 -> int1: ¬{B}{aa} -> {C}{aa}; int1 & fact5 -> int2: {C}{aa}; int2 & fact4 -> int3: {A}{aa}; int3 & fact7 -> int4: {D}{a}; int4 & fact8 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ãã·ãLv.55ã¯äžžã£ãããªã | ¬{F}{c} | fact1: ãã®ã·ãã·ã«ãLv.19ã¯åŸ¡åºããããã¯ãããç¡ã fact2: ãã®ã·ã«ã·ãªLv.41ã¯åºèªãããããã¯å€ãããã fact3: ä»®ã«ãã®ã·ã«ã·ãªLv.41ãæ¯ã翳ãããã€åŸ¡åºããšãããšãã®ã·ãã·ã«ãLv.19ã¯çãŸãããªã fact4: ãã®ã·ã«ã·ãªLv.41ã¯å€ãããã fact5: ãã®ã·ã«ã·ãªLv.41ã¯æ¯ã翳ã fact6: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çãŸãããšããããããã¯åŸ¡åºãäžæ¹ã§æ¯ã翳ããªãããšããããšã¯äºå®ã§ãªã fact7: ä»®ã«ãã®ã·ãã·ã«ãLv.19ãçãŸãããªããªããã®ã·ãã·ãLv.55ã¯äžžã£ãããªã fact8: ããä»®ã«ãã®ã·ã«ã·ãªLv.41ãåºèªãããšããã埡åºã | fact1: ({C}{b} & {EK}{b}) fact2: ({A}{a} & {B}{a}) fact3: ({D}{a} & {C}{a}) -> ¬{E}{b} fact4: {B}{a} fact5: {D}{a} fact6: (x): {E}x -> ¬({C}x & ¬{D}x) fact7: ¬{E}{b} -> ¬{F}{c} fact8: {A}{a} -> {C}{a} | [
"fact2 -> int1: ãã®ã·ã«ã·ãªLv.41ã¯åºèªãã; int1 & fact8 -> int2: ããã®ã·ã«ã·ãªLv.41ã¯åŸ¡åºãããšããããšã¯æãç«ã€; int2 & fact5 -> int3: ãã®ã·ã«ã·ãªLv.41ã¯æ¯ã翳ããããã«åŸ¡åºã; int3 & fact3 -> int4: ãã®ã·ãã·ã«ãLv.19ã¯çãŸãããªã; int4 & fact7 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact5 -> int3: ({D}{a} & {C}{a}); int3 & fact3 -> int4: ¬{E}{b}; int4 & fact7 -> hypothesis;"
] | ãã®ã·ãã·ãLv.55ã¯äžžã£ãã | {F}{c} | [
"fact9 -> int5: ãã®ã·ãã·ã«ãLv.19ã¯çãŸãããªãã°ãã埡åºããããã¯æ¯ã翳ããªãããšããããšã¯çå®ã§ããããšããããšã¯åœã ;"
] | 7 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ãã·ã«ãLv.19ã¯åŸ¡åºããããã¯ãããç¡ã fact2: ãã®ã·ã«ã·ãªLv.41ã¯åºèªãããããã¯å€ãããã fact3: ä»®ã«ãã®ã·ã«ã·ãªLv.41ãæ¯ã翳ãããã€åŸ¡åºããšãããšãã®ã·ãã·ã«ãLv.19ã¯çãŸãããªã fact4: ãã®ã·ã«ã·ãªLv.41ã¯å€ãããã fact5: ãã®ã·ã«ã·ãªLv.41ã¯æ¯ã翳ã fact6: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çãŸãããšããããããã¯åŸ¡åºãäžæ¹ã§æ¯ã翳ããªãããšããããšã¯äºå®ã§ãªã fact7: ä»®ã«ãã®ã·ãã·ã«ãLv.19ãçãŸãããªããªããã®ã·ãã·ãLv.55ã¯äžžã£ãããªã fact8: ããä»®ã«ãã®ã·ã«ã·ãªLv.41ãåºèªãããšããã埡åºã ; $hypothesis$ = ãã®ã·ãã·ãLv.55ã¯äžžã£ãããªã ; $proof$ = | fact2 -> int1: ãã®ã·ã«ã·ãªLv.41ã¯åºèªãã; int1 & fact8 -> int2: ããã®ã·ã«ã·ãªLv.41ã¯åŸ¡åºãããšããããšã¯æãç«ã€; int2 & fact5 -> int3: ãã®ã·ã«ã·ãªLv.41ã¯æ¯ã翳ããããã«åŸ¡åºã; int3 & fact3 -> int4: ãã®ã·ãã·ã«ãLv.19ã¯çãŸãããªã; int4 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: ({C}{b} & {EK}{b}) fact2: ({A}{a} & {B}{a}) fact3: ({D}{a} & {C}{a}) -> ¬{E}{b} fact4: {B}{a} fact5: {D}{a} fact6: (x): {E}x -> ¬({C}x & ¬{D}x) fact7: ¬{E}{b} -> ¬{F}{c} fact8: {A}{a} -> {C}{a} ; $hypothesis$ = ¬{F}{c} ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact5 -> int3: ({D}{a} & {C}{a}); int3 & fact3 -> int4: ¬{E}{b}; int4 & fact7 -> hypothesis; __PROVED__ |
0.3 | ããŽã«ããŽãLv.85äºä»¶ãçããããã®ããLv.77äºä»¶ãçããããšããããšã¯æãç«ããªã | ¬({A} & {B}) | fact1: ãŽã«ããŽãLv.85äºä»¶ãçºçãã fact2: ãã®ããLv.77äºä»¶ãçºçãã fact3: ãããã¿ã«ã
ã¿ã¡ã
Lv.42äºä»¶ã¯èµ·ãããªããªããããŽã«ããŽãLv.85äºä»¶ãçããããã®ããLv.77äºä»¶ãçããããšããããšã¯æãç«ããªãããšããããšã¯ç¢ºãã§ãã | fact1: {A} fact2: {B} fact3: ¬{C} -> ¬({A} & {B}) | [
"fact1 -> int1: ãŽã«ããŽãLv.85äºä»¶ãçºçãã; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}; int1 & fact2 -> hypothesis;"
] | ããŽã«ããŽãLv.85äºä»¶ãçããããã®ããLv.77äºä»¶ãçããããšããããšã¯æãç«ããªã | ¬({A} & {B}) | [] | 6 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãŽã«ããŽãLv.85äºä»¶ãçºçãã fact2: ãã®ããLv.77äºä»¶ãçºçãã fact3: ãããã¿ã«ã
ã¿ã¡ã
Lv.42äºä»¶ã¯èµ·ãããªããªããããŽã«ããŽãLv.85äºä»¶ãçããããã®ããLv.77äºä»¶ãçããããšããããšã¯æãç«ããªãããšããããšã¯ç¢ºãã§ãã ; $hypothesis$ = ããŽã«ããŽãLv.85äºä»¶ãçããããã®ããLv.77äºä»¶ãçããããšããããšã¯æãç«ããªã ; $proof$ = | fact1 -> int1: ãŽã«ããŽãLv.85äºä»¶ãçºçãã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: {B} fact3: ¬{C} -> ¬({A} & {B}) ; $hypothesis$ = ¬({A} & {B}) ; $proof$ = | fact1 -> int1: {A}; int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.67ã¯çãŸãé£ã | {A}{a} | fact1: ãã®ãŽã¡ããŽãªLv.81ã¯çãŸãé£ããªã fact2: ã¿ã¿ã£ã¡ããªãã¢ã³ã¹ã¿ãŒã¯ããã£ã±ãããããã¯çãŸãé£ã fact3: ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ããªã fact4: ãã®ãŽããŽãLv.9ã¯åããæããªã fact5: ãã®ãŽããŽãLv.9ã¯ã¿ã¿ã£ã¡ã fact6: ããä»®ã«ãã®ãŽããŽãLv.9ãããã£ã±ããªãã°ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ã fact7: ãããã®ãœããœãLv.67ãçãŸãé£ããšãããšãã®ãŽããŽãLv.9ã¯ããã£ã±ã | fact1: ¬{A}{fk} fact2: (x): ¬{C}x -> ({B}x v {A}x) fact3: ¬{C}{c} fact4: ¬{JI}{b} fact5: {C}{b} fact6: {B}{b} -> {C}{c} fact7: {A}{a} -> {B}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.67ã¯çãŸãé£ã; fact7 & assump1 -> int1: ãã®ãŽããŽãLv.9ã¯ããã£ã±ã; int1 & fact6 -> int2: ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact7 & assump1 -> int1: {B}{b}; int1 & fact6 -> int2: {C}{c}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.67ã¯çãŸãé£ã | {A}{a} | [
"fact8 -> int4: ä»®ã«ãã®ãŽããŽãLv.9ã¯ã¿ã¿ã£ã¡ããªããšãããšããã®ãŽããŽãLv.9ã¯ããã£ã±ããããã¯çãŸãé£ãããšããããšã¯æãç«ã€;"
] | 5 | 5 | 4 | 5 | 4 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽã¡ããŽãªLv.81ã¯çãŸãé£ããªã fact2: ã¿ã¿ã£ã¡ããªãã¢ã³ã¹ã¿ãŒã¯ããã£ã±ãããããã¯çãŸãé£ã fact3: ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ããªã fact4: ãã®ãŽããŽãLv.9ã¯åããæããªã fact5: ãã®ãŽããŽãLv.9ã¯ã¿ã¿ã£ã¡ã fact6: ããä»®ã«ãã®ãŽããŽãLv.9ãããã£ã±ããªãã°ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ã fact7: ãããã®ãœããœãLv.67ãçãŸãé£ããšãããšãã®ãŽããŽãLv.9ã¯ããã£ã±ã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.67ã¯çãŸãé£ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœããœãLv.67ã¯çãŸãé£ã; fact7 & assump1 -> int1: ãã®ãŽããŽãLv.9ã¯ããã£ã±ã; int1 & fact6 -> int2: ãã®ãã«ã
ããLv.97ã¯ã¿ã¿ã£ã¡ã; int2 & fact3 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{fk} fact2: (x): ¬{C}x -> ({B}x v {A}x) fact3: ¬{C}{c} fact4: ¬{JI}{b} fact5: {C}{b} fact6: {B}{b} -> {C}{c} fact7: {A}{a} -> {B}{b} ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: {A}{a}; fact7 & assump1 -> int1: {B}{b}; int1 & fact6 -> int2: {C}{c}; int2 & fact3 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | äŒãæããšããããšã¯èµ·ããªã | ¬{B} | fact1: ããããã«ããã¡ãLv.24äºä»¶ãèµ·ãããšããã°ãŸããŸã¡ãLv.41äºä»¶ã¯çããªããããŸãã«å¥³æ§ããããšããããšã¯èµ·ããªã fact2: å
¥ãæããšããããšã¯çºçããªã fact3: 埡åªãããšããããšã¯äŒãæããšããããšã®åå ãšãªã fact4: åãªããšããããšãçãã fact5: ãåæºãæããšããããšãèµ·ããããšããããšã¯æãç«ã€ fact6: ããããŸããŸã¡ãLv.41äºä»¶ã¯çºçããªãããšããããšã¯ç¢ºãã ãšããã°åŸ¡åªãããšããããšãšåæºãæããšããããšäž¡æ¹ãšããèµ·ãã fact7: åæºãæããšããããšã¯ã埡åªãããšããããšãçºçããããããã¯äŒãæããšããããšãçããããŸãã¯äž¡æ¹ã§ããããšããããšã«é»ãŸãã | fact1: {F} -> (¬{D} & ¬{E}) fact2: ¬{BI} fact3: {A} -> {B} fact4: {DS} fact5: {C} fact6: ¬{D} -> ({A} & {C}) fact7: ({A} v {B}) -> ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããäŒãæããšããããšãèµ·ãã; assump1 -> int1: 埡åªãããšããããšãèµ·ããããŸãã¯äŒãæããšããããšãèµ·ããããŸãã¯äž¡æ¹ãšãã ; int1 & fact7 -> int2: åæºãæããšããããšã¯çºçããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact7 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ãããäŒãæããšããããšãèµ·ãã | {B} | [] | 8 | 5 | 3 | 5 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã«ããã¡ãLv.24äºä»¶ãèµ·ãããšããã°ãŸããŸã¡ãLv.41äºä»¶ã¯çããªããããŸãã«å¥³æ§ããããšããããšã¯èµ·ããªã fact2: å
¥ãæããšããããšã¯çºçããªã fact3: 埡åªãããšããããšã¯äŒãæããšããããšã®åå ãšãªã fact4: åãªããšããããšãçãã fact5: ãåæºãæããšããããšãèµ·ããããšããããšã¯æãç«ã€ fact6: ããããŸããŸã¡ãLv.41äºä»¶ã¯çºçããªãããšããããšã¯ç¢ºãã ãšããã°åŸ¡åªãããšããããšãšåæºãæããšããããšäž¡æ¹ãšããèµ·ãã fact7: åæºãæããšããããšã¯ã埡åªãããšããããšãçºçããããããã¯äŒãæããšããããšãçããããŸãã¯äž¡æ¹ã§ããããšããããšã«é»ãŸãã ; $hypothesis$ = äŒãæããšããããšã¯èµ·ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããäŒãæããšããããšãèµ·ãã; assump1 -> int1: 埡åªãããšããããšãèµ·ããããŸãã¯äŒãæããšããããšãèµ·ããããŸãã¯äž¡æ¹ãšãã ; int1 & fact7 -> int2: åæºãæããšããããšã¯çºçããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {F} -> (¬{D} & ¬{E}) fact2: ¬{BI} fact3: {A} -> {B} fact4: {DS} fact5: {C} fact6: ¬{D} -> ({A} & {C}) fact7: ({A} v {B}) -> ¬{C} ; $hypothesis$ = ¬{B} ; $proof$ = | void -> assump1: {B}; assump1 -> int1: ({A} v {B}); int1 & fact7 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãã«ã
ããLv.75ã¯æº¶ãæããªã | ¬{B}{a} | fact1: ä»®ã«ãã®ãœãªãœã®Lv.26ãæããæããªããªãã°ãã®ãã«ã
ããLv.75ã¯å€©äœ¿ããããªã fact2: ä»®ã«ããã®ãŸããŸãLv.72ã¯èŠãèŸããªããŠããã䌞ã³æããšããããšã¯ãªãããšããããšã¯èª€ãã§ãããšãããšãã®ãœãªãœã®Lv.26ã¯æããæããšããããšã¯ãªã fact3: 倩䜿ããããªãã¢ã³ã¹ã¿ãŒã¯ãã¶ãšããŠãŸãæž
ã
ãã fact4: ãããã®ãã«ã
ããLv.75ãéŠã°ãããªãã°æº¶ãæã | fact1: ¬{F}{b} -> ¬{E}{a} fact2: ¬(¬{G}{c} & ¬{H}{c}) -> ¬{F}{b} fact3: (x): ¬{E}x -> ({C}x & {D}x) fact4: {A}{a} -> {B}{a} | [] | [] | ãã®ãã«ã
ããLv.75ã¯æº¶ãæããªã | ¬{B}{a} | [
"fact6 -> int1: ããããã®ãã«ã
ããLv.75ã倩䜿ããããªããšãããšãã®ãã«ã
ããLv.75ã¯ãã¶ãšããŠæž
ã
ãã;"
] | 6 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãœãªãœã®Lv.26ãæããæããªããªãã°ãã®ãã«ã
ããLv.75ã¯å€©äœ¿ããããªã fact2: ä»®ã«ããã®ãŸããŸãLv.72ã¯èŠãèŸããªããŠããã䌞ã³æããšããããšã¯ãªãããšããããšã¯èª€ãã§ãããšãããšãã®ãœãªãœã®Lv.26ã¯æããæããšããããšã¯ãªã fact3: 倩䜿ããããªãã¢ã³ã¹ã¿ãŒã¯ãã¶ãšããŠãŸãæž
ã
ãã fact4: ãããã®ãã«ã
ããLv.75ãéŠã°ãããªãã°æº¶ãæã ; $hypothesis$ = ãã®ãã«ã
ããLv.75ã¯æº¶ãæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{F}{b} -> ¬{E}{a} fact2: ¬(¬{G}{c} & ¬{H}{c}) -> ¬{F}{b} fact3: (x): ¬{E}x -> ({C}x & {D}x) fact4: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ãLv.12ã¯åœããé£ããªã | ¬{D}{b} | fact1: ããã®ã·ãã·ãLv.12ã¯æãèŠãªãäžæ¹ã§ããã¯ææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªããšããã°ãã®ã·ãã·ãLv.12ã¯åœããé£ã fact2: ããããã®ãŽããŽãLv.2ã¯æãèŠããšããããšã¯ãªãããããéã£ãœãããšããããšã¯èª€ãã§ãããªããã®ãŽããŽãLv.2ã¯ææ®ç£ç£ããªã fact3: ãã®ããããªLv.80ã¯ãæããªã fact4: ãããã®ããããªLv.80ã¯ææ®ç£ç£ãããšãããšããã®ã·ãã·ãLv.12ã¯æãèŠãªããææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªã fact5: ãæããªãã¢ã³ã¹ã¿ãŒã¯èãæããŠæŽã«æŒžæžãã fact6: ããã®ã·ãã·ãLv.12ã¯æãèŠããææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªã fact7: ãã®ã¿ãã¿ã¡ãLv.97ã¯æãèŠããæªç·ŽããŸãã | fact1: ¬(¬{C}{b} & {A}{b}) -> {D}{b} fact2: ¬(¬{C}{c} & {B}{c}) -> ¬{A}{c} fact3: ¬{E}{a} fact4: {A}{a} -> ¬(¬{C}{b} & {A}{b}) fact5: (x): ¬{E}x -> ({T}x & {BJ}x) fact6: ¬({C}{b} & {A}{b}) fact7: ({C}{ji} & {IF}{ji}) | [] | [] | ãã®ã·ãã·ãLv.12ã¯åœããé£ããªã | ¬{D}{b} | [] | 6 | 4 | 4 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®ã·ãã·ãLv.12ã¯æãèŠãªãäžæ¹ã§ããã¯ææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªããšããã°ãã®ã·ãã·ãLv.12ã¯åœããé£ã fact2: ããããã®ãŽããŽãLv.2ã¯æãèŠããšããããšã¯ãªãããããéã£ãœãããšããããšã¯èª€ãã§ãããªããã®ãŽããŽãLv.2ã¯ææ®ç£ç£ããªã fact3: ãã®ããããªLv.80ã¯ãæããªã fact4: ãããã®ããããªLv.80ã¯ææ®ç£ç£ãããšãããšããã®ã·ãã·ãLv.12ã¯æãèŠãªããææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªã fact5: ãæããªãã¢ã³ã¹ã¿ãŒã¯èãæããŠæŽã«æŒžæžãã fact6: ããã®ã·ãã·ãLv.12ã¯æãèŠããææ®ç£ç£ããããšããããšã¯äºå®ãšç°ãªã fact7: ãã®ã¿ãã¿ã¡ãLv.97ã¯æãèŠããæªç·ŽããŸãã ; $hypothesis$ = ãã®ã·ãã·ãLv.12ã¯åœããé£ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{C}{b} & {A}{b}) -> {D}{b} fact2: ¬(¬{C}{c} & {B}{c}) -> ¬{A}{c} fact3: ¬{E}{a} fact4: {A}{a} -> ¬(¬{C}{b} & {A}{b}) fact5: (x): ¬{E}x -> ({T}x & {BJ}x) fact6: ¬({C}{b} & {A}{b}) fact7: ({C}{ji} & {IF}{ji}) ; $hypothesis$ = ¬{D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ã¡ã
ã·ã«ãLv.76ã¯éèãããšããããšã¯çå®ã | {D}{b} | fact1: ããããã®ãŽããŽãLv.65ãåŠæ€ããªãã°æž©ãåã fact2: ä»®ã«ãã®ãŽããŽãLv.65ã絶ãé£ããªããšãããšæ»ãäžããããã€åŠæ€ã fact3: ãã®ãŽããŽãLv.65ã¯çµ¶ãé£ããªã fact4: ãã®ãŽããŽãLv.65ãæž©ãåããšãããšãã®ã·ã¡ã
ã·ã«ãLv.76ã¯éèã | fact1: {B}{a} -> {C}{a} fact2: ¬{E}{a} -> ({A}{a} & {B}{a}) fact3: ¬{E}{a} fact4: {C}{a} -> {D}{b} | [
"fact2 & fact3 -> int1: ãã®ãŽããŽãLv.65ã¯æ»ãäžãããæŽã«ããã¯åŠæ€ã; int1 -> int2: ããã®ãŽããŽãLv.65ã¯åŠæ€ããšããããšã¯ãªãããšããããšã¯æãç«ããªã; int2 & fact1 -> int3: ãã®ãŽããŽãLv.65ã¯æž©ãåã; int3 & fact4 -> hypothesis;"
] | [
"fact2 & fact3 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact1 -> int3: {C}{a}; int3 & fact4 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ãŽããŽãLv.65ãåŠæ€ããªãã°æž©ãåã fact2: ä»®ã«ãã®ãŽããŽãLv.65ã絶ãé£ããªããšãããšæ»ãäžããããã€åŠæ€ã fact3: ãã®ãŽããŽãLv.65ã¯çµ¶ãé£ããªã fact4: ãã®ãŽããŽãLv.65ãæž©ãåããšãããšãã®ã·ã¡ã
ã·ã«ãLv.76ã¯éèã ; $hypothesis$ = ããã®ã·ã¡ã
ã·ã«ãLv.76ã¯éèãããšããããšã¯çå®ã ; $proof$ = | fact2 & fact3 -> int1: ãã®ãŽããŽãLv.65ã¯æ»ãäžãããæŽã«ããã¯åŠæ€ã; int1 -> int2: ããã®ãŽããŽãLv.65ã¯åŠæ€ããšããããšã¯ãªãããšããããšã¯æãç«ããªã; int2 & fact1 -> int3: ãã®ãŽããŽãLv.65ã¯æž©ãåã; int3 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{a} -> {C}{a} fact2: ¬{E}{a} -> ({A}{a} & {B}{a}) fact3: ¬{E}{a} fact4: {C}{a} -> {D}{b} ; $hypothesis$ = {D}{b} ; $proof$ = | fact2 & fact3 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact1 -> int3: {C}{a}; int3 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã¡ããœã«ãLv.47ã¯ããæ°ç¡ããªã | ¬{D}{c} | fact1: 移ãæããªãã¢ã³ã¹ã¿ãŒã¯ç§»åãæããç©ã fact2: æãŒãã¢ã³ã¹ã¿ãŒã¯ããæ°ç¡ã fact3: ããããã®ã¿ã¡ãã¿ãLv.83ã¯ç©ããšãããããã®ãŽã¡ããŽãªLv.31ã¯ççœããã©ç©ããšããããšã¯ãªãããšããããšã¯åã fact4: ããä»®ã«ããã®ãŽã¡ããŽãªLv.31ã¯ççœãããããç©ããªãããšããããšã¯äºå®ãšç°ãªãã°ãã®ãœã¡ããœã«ãLv.47ã¯ããæ°ç¡ããªã fact5: ççœããªãã¢ã³ã¹ã¿ãŒã¯ç©ããããã«æãŒã fact6: ãããã®ã¿ã¡ãã¿ãLv.83ãè¡šæããªããªãã°ãã®ã¿ã¡ãã¿ãLv.83ã¯æãŒããããŸãã«ç©ã fact7: ãã®ãŽã¡ããŽãªLv.31ã¯è¡šæããªã fact8: ãããã®ãŽã¡ããŽãªLv.31ã¯ççœãããããç©ãããšããããšã¯æãç«ã€ããšããããšã¯åœã§ãã | fact1: (x): ¬{AE}x -> ({AO}x & {B}x) fact2: (x): {A}x -> {D}x fact3: {B}{a} -> ¬({C}{b} & ¬{B}{b}) fact4: ¬({C}{b} & ¬{B}{b}) -> ¬{D}{c} fact5: (x): ¬{C}x -> ({B}x & {A}x) fact6: ¬{E}{a} -> ({A}{a} & {B}{a}) fact7: ¬{E}{b} fact8: ¬({C}{b} & {B}{b}) | [] | [] | ãã®ãœã¡ããœã«ãLv.47ã¯ããæ°ç¡ã | {D}{c} | [
"fact10 -> int1: ä»®ã«ãã®ãœã¡ããœã«ãLv.47ãæãŒããªãããæ°ç¡ã; fact9 -> int2: ãããã®ã¿ã¡ãã¿ãLv.83ãççœããªããªãã°ããã¯ç©ãããããæãŒã;"
] | 5 | 4 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: 移ãæããªãã¢ã³ã¹ã¿ãŒã¯ç§»åãæããç©ã fact2: æãŒãã¢ã³ã¹ã¿ãŒã¯ããæ°ç¡ã fact3: ããããã®ã¿ã¡ãã¿ãLv.83ã¯ç©ããšãããããã®ãŽã¡ããŽãªLv.31ã¯ççœããã©ç©ããšããããšã¯ãªãããšããããšã¯åã fact4: ããä»®ã«ããã®ãŽã¡ããŽãªLv.31ã¯ççœãããããç©ããªãããšããããšã¯äºå®ãšç°ãªãã°ãã®ãœã¡ããœã«ãLv.47ã¯ããæ°ç¡ããªã fact5: ççœããªãã¢ã³ã¹ã¿ãŒã¯ç©ããããã«æãŒã fact6: ãããã®ã¿ã¡ãã¿ãLv.83ãè¡šæããªããªãã°ãã®ã¿ã¡ãã¿ãLv.83ã¯æãŒããããŸãã«ç©ã fact7: ãã®ãŽã¡ããŽãªLv.31ã¯è¡šæããªã fact8: ãããã®ãŽã¡ããŽãªLv.31ã¯ççœãããããç©ãããšããããšã¯æãç«ã€ããšããããšã¯åœã§ãã ; $hypothesis$ = ãã®ãœã¡ããœã«ãLv.47ã¯ããæ°ç¡ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{AE}x -> ({AO}x & {B}x) fact2: (x): {A}x -> {D}x fact3: {B}{a} -> ¬({C}{b} & ¬{B}{b}) fact4: ¬({C}{b} & ¬{B}{b}) -> ¬{D}{c} fact5: (x): ¬{C}x -> ({B}x & {A}x) fact6: ¬{E}{a} -> ({A}{a} & {B}{a}) fact7: ¬{E}{b} fact8: ¬({C}{b} & {B}{b}) ; $hypothesis$ = ¬{D}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããä»®ã«çŽãããããªããšããããåäŸã£ãœããŠæŽã«ç¶ç¶ãé£ãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{A}x -> ¬({AA}x & {AB}x) | fact1: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãããªããªããªããããã¯èŒãããããã€åæããããšããããšã¯ééãã§ãã | fact1: (x): ¬{CG}x -> ¬({DU}x & {FG}x) | [] | [] | ãä»®ã«ãããªããšããããšã¯ãªããšãããšãèŒããããŠãã€åæããããšããããšã¯æ¬åœã§ãªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{CG}x -> ¬({DU}x & {FG}x) | [
"fact2 -> int1: ä»®ã«ããã®ã¿ãã¿ã«ãLv.89ã¯ãããªããªãããšããããšã¯æ£ãããšãããšããã®ã¿ãã¿ã«ãLv.89ã¯èŒããããŠåæããããšããããšã¯ééãã§ãã; int1 -> hypothesis;"
] | 2 | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | PROVED | UNKNOWN | PROVED | $facts$ = fact1: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãããªããªããªããããã¯èŒãããããã€åæããããšããããšã¯ééãã§ãã ; $hypothesis$ = ãããä»®ã«çŽãããããªããšããããåäŸã£ãœããŠæŽã«ç¶ç¶ãé£ãããšããããšã¯ééã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{CG}x -> ¬({DU}x & {FG}x) ; $hypothesis$ = (Ex): ¬{A}x -> ¬({AA}x & {AB}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã«ãã¿ã¡ãLv.86ã¯åŸãã£ãœããªã | ¬{B}{aa} | fact1: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯æ³£ãåããªããæŽã«åããã©ããªãããšããããšã¯æãç«ããªããšããã°åŸãã£ãœãããšããããšã¯äºå®ã fact2: ãããä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯æ°æã¡è¯ããªããŠãããæ£ããªãããšããããšã¯çå®ã§ãªããšãããšããã¯åãã¡é£ãããšããããšã¯æ£ãã fact3: ãããã®ãœã«ããœã«ãLv.84ãæ³£ãåããšããã°ããã¯å èœãã fact4: ãããã®ã¿ã«ãã¿ã¡ãLv.86ã¯æ³£ãåããšããããšã¯ãªããæŽã«åããã©ããªãããšããããšã¯åœã ããšããããšã¯æ¬åœã fact5: ãããã®ãŽã«ãŽãLv.50ã¯èšãåºãé£ããªããŠæŽã«åããã©ããªãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªã fact6: 圹ãããã¢ã³ã¹ã¿ãŒã¯å¥œããã fact7: ããšããã¢ã³ã¹ã¿ãŒã¯ç«ãŠå§ããªããŠããã«èšéããªãããšããããšã¯æãç«ããªããªãã°å®ã£ãœã | fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact2: (x): ¬(¬{BL}x & ¬{EH}x) -> {DT}x fact3: {AA}{ia} -> {AJ}{ia} fact4: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact5: ¬(¬{CG}{ic} & ¬{AB}{ic}) fact6: (x): {II}x -> {AM}x fact7: (x): ¬(¬{BI}x & ¬{DK}x) -> {IM}x | [
"fact1 -> int1: ä»®ã«ããã®ã¿ã«ãã¿ã¡ãLv.86ã¯æ³£ãåããªããŠãã®äžåããã©ããªãããšããããšã¯æãç«ããªããšããããåŸãã£ãœãããšããããšã¯æãç«ã€; int1 & fact4 -> hypothesis;"
] | [
"fact1 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa}; int1 & fact4 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 5 | 0 | 5 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯æ³£ãåããªããæŽã«åããã©ããªãããšããããšã¯æãç«ããªããšããã°åŸãã£ãœãããšããããšã¯äºå®ã fact2: ãããä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯æ°æã¡è¯ããªããŠãããæ£ããªãããšããããšã¯çå®ã§ãªããšãããšããã¯åãã¡é£ãããšããããšã¯æ£ãã fact3: ãããã®ãœã«ããœã«ãLv.84ãæ³£ãåããšããã°ããã¯å èœãã fact4: ãããã®ã¿ã«ãã¿ã¡ãLv.86ã¯æ³£ãåããšããããšã¯ãªããæŽã«åããã©ããªãããšããããšã¯åœã ããšããããšã¯æ¬åœã fact5: ãããã®ãŽã«ãŽãLv.50ã¯èšãåºãé£ããªããŠæŽã«åããã©ããªãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªã fact6: 圹ãããã¢ã³ã¹ã¿ãŒã¯å¥œããã fact7: ããšããã¢ã³ã¹ã¿ãŒã¯ç«ãŠå§ããªããŠããã«èšéããªãããšããããšã¯æãç«ããªããªãã°å®ã£ãœã ; $hypothesis$ = ãã®ã¿ã«ãã¿ã¡ãLv.86ã¯åŸãã£ãœããªã ; $proof$ = | fact1 -> int1: ä»®ã«ããã®ã¿ã«ãã¿ã¡ãLv.86ã¯æ³£ãåããªããŠãã®äžåããã©ããªãããšããããšã¯æãç«ããªããšããããåŸãã£ãœãããšããããšã¯æãç«ã€; int1 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact2: (x): ¬(¬{BL}x & ¬{EH}x) -> {DT}x fact3: {AA}{ia} -> {AJ}{ia} fact4: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact5: ¬(¬{CG}{ic} & ¬{AB}{ic}) fact6: (x): {II}x -> {AM}x fact7: (x): ¬(¬{BI}x & ¬{DK}x) -> {IM}x ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | fact1 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa}; int1 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ãã¡ããã«ã
Lv.89ã¯å¬ããã | {A}{a} | fact1: ãããã®ãã¡ããã«ã
Lv.89ãå¬ãããããŸãã¯ããã¯æãããããããã¯ã©ã¡ããã§ãããšãããéããæããªã fact2: ãã®ãã¡ããã«ã
Lv.89ã¯éããæã fact3: éããæããªãã¢ã³ã¹ã¿ãŒã¯æããããå¬ããã | fact1: ({A}{a} v {B}{a}) -> ¬{C}{a} fact2: {C}{a} fact3: (x): ¬{C}x -> ({B}x & {A}x) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãã¡ããã«ã
Lv.89ã¯å¬ããã; assump1 -> int1: ãã®ãã¡ããã«ã
Lv.89ã¯å¬ãããããŸãã¯æããã; int1 & fact1 -> int2: ãã®ãã¡ããã«ã
Lv.89ã¯éããæããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 & fact1 -> int2: ¬{C}{a}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ãã¡ããã«ã
Lv.89ã¯å¬ããã | {A}{a} | [
"fact4 -> int4: ãã®ãŽã¡ã
ãŽã¡ãLv.69ã¯éããæããªããšããããããã¯æããããããŸãã«å¬ãããããšããããšã¯äºå®ã ;"
] | 5 | 5 | 3 | 5 | 3 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããã®ãã¡ããã«ã
Lv.89ãå¬ãããããŸãã¯ããã¯æãããããããã¯ã©ã¡ããã§ãããšãããéããæããªã fact2: ãã®ãã¡ããã«ã
Lv.89ã¯éããæã fact3: éããæããªãã¢ã³ã¹ã¿ãŒã¯æããããå¬ããã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ãã¡ããã«ã
Lv.89ã¯å¬ããã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãã¡ããã«ã
Lv.89ã¯å¬ããã; assump1 -> int1: ãã®ãã¡ããã«ã
Lv.89ã¯å¬ãããããŸãã¯æããã; int1 & fact1 -> int2: ãã®ãã¡ããã«ã
Lv.89ã¯éããæããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A}{a} v {B}{a}) -> ¬{C}{a} fact2: {C}{a} fact3: (x): ¬{C}x -> ({B}x & {A}x) ; $hypothesis$ = {A}{a} ; $proof$ = | void -> assump1: {A}{a}; assump1 -> int1: ({A}{a} v {B}{a}); int1 & fact1 -> int2: ¬{C}{a}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | æªããšããããšã¯çããªã | ¬{A} | fact1: å°æ®ºããããšã¯çããªããšããããšã¯ãŽããŽãªLv.13äºä»¶ããããã¯ãã·ã¡ãã·ãªLv.77äºä»¶ãèµ·ããããšããããšããããã¯ã©ã¡ãããçãããã fact2: æªããšããããšã¯ãŽããŽãªLv.13äºä»¶ã¯èµ·ããªããšããããšãé²ã fact3: ãå°æ®ºããããšã¯èµ·ãããªããŠå ããŠç¯ãé£ããšããããšã¯çºçããªãããšããããšã¯æ¬²ãããšããããšãçãããšããããšã«èµ·å ãã fact4: ãããã®Lv.4äºä»¶ã¯ã欲ãããšããããšã¯çããªãããšããããšãé²ã fact5: ãé¢ç®ç¡ããšããããšã¯èµ·ãããªããçºãŸãæããšããããšãçããããšããããšã¯ã·ãã·ãLv.7äºä»¶ã«ããçãã fact6: ããé¢ç®ç¡ããšããããšã¯çããªããªããããã®Lv.4äºä»¶ãšå€ªãåºãããšäž¡æ¹ãçºçãã | fact1: ¬{D} -> ({B} v {C}) fact2: {A} -> {B} fact3: {F} -> (¬{D} & ¬{E}) fact4: {G} -> {F} fact5: {K} -> (¬{I} & {J}) fact6: ¬{I} -> ({G} & {H}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããæªããšããããšãèµ·ããããšããããšã¯çå®ã ; fact2 & assump1 -> int1: ãŽããŽãªLv.13äºä»¶ãèµ·ãã;"
] | [
"void -> assump1: {A}; fact2 & assump1 -> int1: {B};"
] | 以äžã®ããã«ä»®å®ããããæªããšããããšãèµ·ããããšããããšã¯çå®ã | {A} | [] | 10 | 4 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: å°æ®ºããããšã¯çããªããšããããšã¯ãŽããŽãªLv.13äºä»¶ããããã¯ãã·ã¡ãã·ãªLv.77äºä»¶ãèµ·ããããšããããšããããã¯ã©ã¡ãããçãããã fact2: æªããšããããšã¯ãŽããŽãªLv.13äºä»¶ã¯èµ·ããªããšããããšãé²ã fact3: ãå°æ®ºããããšã¯èµ·ãããªããŠå ããŠç¯ãé£ããšããããšã¯çºçããªãããšããããšã¯æ¬²ãããšããããšãçãããšããããšã«èµ·å ãã fact4: ãããã®Lv.4äºä»¶ã¯ã欲ãããšããããšã¯çããªãããšããããšãé²ã fact5: ãé¢ç®ç¡ããšããããšã¯èµ·ãããªããçºãŸãæããšããããšãçããããšããããšã¯ã·ãã·ãLv.7äºä»¶ã«ããçãã fact6: ããé¢ç®ç¡ããšããããšã¯çããªããªããããã®Lv.4äºä»¶ãšå€ªãåºãããšäž¡æ¹ãçºçãã ; $hypothesis$ = æªããšããããšã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{D} -> ({B} v {C}) fact2: {A} -> {B} fact3: {F} -> (¬{D} & ¬{E}) fact4: {G} -> {F} fact5: {K} -> (¬{I} & {J}) fact6: ¬{I} -> ({G} & {H}) ; $hypothesis$ = ¬{A} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãœããœãLv.65ã¯æŽã¿é£ããªãããšããããšã¯äºå®ã | ¬{C}{b} | fact1: ãããã®ã·ãã·ãLv.59ã¯åŽåŽããªãããããåªããããªããšããããéè³ãæãããšããããšã¯æ¬åœã fact2: ãããããã®ã·ãã·ãLv.59ã¯éè³ãæãããšããããšã¯ç¢ºãã§ãããšããã°ãã®ãœããœãLv.65ã¯æŽã¿é£ã fact3: ãã®ã·ãªã·ãLv.2ã¯åªããã fact4: ããé£ããªãã¢ã³ã¹ã¿ãŒã¯åŽåŽããªããããŸãã«åªããããªãããšããããšã¯ç¢ºãã fact5: ãã®ã·ãã·ãLv.59ã¯ãé£ããªã | fact1: (¬{AA}{a} & ¬{AB}{a}) -> {B}{a} fact2: {B}{a} -> {C}{b} fact3: {AB}{ig} fact4: (x): ¬{A}x -> (¬{AA}x & ¬{AB}x) fact5: ¬{A}{a} | [
"fact4 -> int1: ãã®ã·ãã·ãLv.59ã¯ãé£ããªããšãããããã®ã·ãã·ãLv.59ã¯åŽåŽããªããåªããããšããããšã¯ãªãããšããããšã¯åœã§ãªã; int1 & fact5 -> int2: ãã®ã·ãã·ãLv.59ã¯åŽåŽããªããããã«åªããããªã; int2 & fact1 -> int3: ããã®ã·ãã·ãLv.59ã¯éè³ãæãããšããããšã¯æ£ãã; int3 & fact2 -> hypothesis;"
] | [
"fact4 -> int1: ¬{A}{a} -> (¬{AA}{a} & ¬{AB}{a}); int1 & fact5 -> int2: (¬{AA}{a} & ¬{AB}{a}); int2 & fact1 -> int3: {B}{a}; int3 & fact2 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®ã·ãã·ãLv.59ã¯åŽåŽããªãããããåªããããªããšããããéè³ãæãããšããããšã¯æ¬åœã fact2: ãããããã®ã·ãã·ãLv.59ã¯éè³ãæãããšããããšã¯ç¢ºãã§ãããšããã°ãã®ãœããœãLv.65ã¯æŽã¿é£ã fact3: ãã®ã·ãªã·ãLv.2ã¯åªããã fact4: ããé£ããªãã¢ã³ã¹ã¿ãŒã¯åŽåŽããªããããŸãã«åªããããªãããšããããšã¯ç¢ºãã fact5: ãã®ã·ãã·ãLv.59ã¯ãé£ããªã ; $hypothesis$ = ããã®ãœããœãLv.65ã¯æŽã¿é£ããªãããšããããšã¯äºå®ã ; $proof$ = | fact4 -> int1: ãã®ã·ãã·ãLv.59ã¯ãé£ããªããšãããããã®ã·ãã·ãLv.59ã¯åŽåŽããªããåªããããšããããšã¯ãªãããšããããšã¯åœã§ãªã; int1 & fact5 -> int2: ãã®ã·ãã·ãLv.59ã¯åŽåŽããªããããã«åªããããªã; int2 & fact1 -> int3: ããã®ã·ãã·ãLv.59ã¯éè³ãæãããšããããšã¯æ£ãã; int3 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{AA}{a} & ¬{AB}{a}) -> {B}{a} fact2: {B}{a} -> {C}{b} fact3: {AB}{ig} fact4: (x): ¬{A}x -> (¬{AA}x & ¬{AB}x) fact5: ¬{A}{a} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact4 -> int1: ¬{A}{a} -> (¬{AA}{a} & ¬{AB}{a}); int1 & fact5 -> int2: (¬{AA}{a} & ¬{AB}{a}); int2 & fact1 -> int3: {B}{a}; int3 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãŽã«ããŽãLv.24äºä»¶ã¯çããªã | ¬{D} | fact1: ãã«ã
ãã«ãLv.12äºä»¶ã¯èµ·ãããªã fact2: ãåããšããããšãèµ·ããããšããããšã¯äºå®ã§ãã fact3: ããããLv.32äºä»¶ã¯ãã¡ã
ããLv.90äºä»¶ããã³ãã«ã
ãã«ãLv.12äºä»¶ãèµ·ããã«é»æ¢ããã fact4: æå°æªããšããããšã¯çããªã fact5: é€é¬Œã£ãœããšããããšãèµ·ãã fact6: æå°æªããšããããšã¯èµ·ãããªããšããããšã¯èŠéãããããšããã³ãŸã©ãã£ããããšããããšãèµ·ããã®ãã£ãããšãªã fact7: ããŸã©ãã£ããããšããããšã¯çºçããªãããšããããšã¯èŠéãããããšãšãŽã«ããŽãLv.24äºä»¶ãçºçããã«ç¹ãã fact8: ãããŸã©ãã£ããããšããããšãèµ·ããããã®äžé€é¬Œã£ãœããšããããšãèµ·ããã°ãŽã«ããŽãLv.24äºä»¶ã¯èµ·ãããªã fact9: ãæå°æªããšããããšã¯èµ·ããªãããšããããšã¯èŠéãããããšã¯èµ·ããªããšããããšãåé¿ãã | fact1: ¬{FA} fact2: {GR} fact3: ({JF} & {FA}) -> ¬{CS} fact4: ¬{E} fact5: {C} fact6: ¬{E} -> ({A} & {B}) fact7: ¬{B} -> ({A} & {D}) fact8: ({B} & {C}) -> ¬{D} fact9: ¬{E} -> {A} | [
"fact6 & fact4 -> int1: ãèŠéãããããšããã³ãŸã©ãã£ããããšããããšã©ã¡ãããèµ·ããããšããããšã¯æãç«ã€; int1 -> int2: ãŸã©ãã£ããããšããããšãçºçãã; int2 & fact5 -> int3: ãŸã©ãã£ããããšããããšãšé€é¬Œã£ãœããšããããšäž¡æ¹ãçºçãã; int3 & fact8 -> hypothesis;"
] | [
"fact6 & fact4 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact5 -> int3: ({B} & {C}); int3 & fact8 -> hypothesis;"
] | ãŽã«ããŽãLv.24äºä»¶ãçºçãã | {D} | [] | 6 | 4 | 4 | 4 | 4 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã«ã
ãã«ãLv.12äºä»¶ã¯èµ·ãããªã fact2: ãåããšããããšãèµ·ããããšããããšã¯äºå®ã§ãã fact3: ããããLv.32äºä»¶ã¯ãã¡ã
ããLv.90äºä»¶ããã³ãã«ã
ãã«ãLv.12äºä»¶ãèµ·ããã«é»æ¢ããã fact4: æå°æªããšããããšã¯çããªã fact5: é€é¬Œã£ãœããšããããšãèµ·ãã fact6: æå°æªããšããããšã¯èµ·ãããªããšããããšã¯èŠéãããããšããã³ãŸã©ãã£ããããšããããšãèµ·ããã®ãã£ãããšãªã fact7: ããŸã©ãã£ããããšããããšã¯çºçããªãããšããããšã¯èŠéãããããšãšãŽã«ããŽãLv.24äºä»¶ãçºçããã«ç¹ãã fact8: ãããŸã©ãã£ããããšããããšãèµ·ããããã®äžé€é¬Œã£ãœããšããããšãèµ·ããã°ãŽã«ããŽãLv.24äºä»¶ã¯èµ·ãããªã fact9: ãæå°æªããšããããšã¯èµ·ããªãããšããããšã¯èŠéãããããšã¯èµ·ããªããšããããšãåé¿ãã ; $hypothesis$ = ãŽã«ããŽãLv.24äºä»¶ã¯çããªã ; $proof$ = | fact6 & fact4 -> int1: ãèŠéãããããšããã³ãŸã©ãã£ããããšããããšã©ã¡ãããèµ·ããããšããããšã¯æãç«ã€; int1 -> int2: ãŸã©ãã£ããããšããããšãçºçãã; int2 & fact5 -> int3: ãŸã©ãã£ããããšããããšãšé€é¬Œã£ãœããšããããšäž¡æ¹ãçºçãã; int3 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{FA} fact2: {GR} fact3: ({JF} & {FA}) -> ¬{CS} fact4: ¬{E} fact5: {C} fact6: ¬{E} -> ({A} & {B}) fact7: ¬{B} -> ({A} & {D}) fact8: ({B} & {C}) -> ¬{D} fact9: ¬{E} -> {A} ; $hypothesis$ = ¬{D} ; $proof$ = | fact6 & fact4 -> int1: ({A} & {B}); int1 -> int2: {B}; int2 & fact5 -> int3: ({B} & {C}); int3 & fact8 -> hypothesis; __PROVED__ |
0.3 | ãã¿ãã¿ã¡ãLv.7äºä»¶ããã³ãããã«ãLv.32äºä»¶ãèµ·ããããšããããšã¯ééãã§ãã | ¬({A} & {B}) | fact1: ããä»®ã«åŒ±ããšããããšãèµ·ãããšããããå ªå¿ããããšã¯èµ·ããªããŠãœããœã«ãLv.63äºä»¶ãèµ·ããããšããããšã¯ééãã§ãã fact2: ããããå ªå¿ããããšã¯èµ·ããªããŠãœããœã«ãLv.63äºä»¶ã¯çºçããããšããããšã¯ééããªãã°ãããã«ãLv.32äºä»¶ã¯èµ·ãããªã fact3: å ªå¿ããããšã¯èµ·ãããªããšããããšã¯ãœããœã«ãLv.63äºä»¶ããŸãã¯åŒ±ããšããããšã«èªçºããã fact4: ã·ã¡ãã·ã«ã
Lv.25äºä»¶ãçºçãã fact5: ãã¿ã«ã¿ãLv.77äºä»¶ããã³ã¿ãã¿ã¡ãLv.7äºä»¶ãèµ·ããããšããããšã¯ãããã«ãLv.32äºä»¶ãçããªããšããããšã¯åå ã§ãã fact6: ãããã«ãLv.32äºä»¶ãçºçãã | fact1: {E} -> ¬(¬{C} & {D}) fact2: ¬(¬{C} & {D}) -> ¬{B} fact3: ({D} v {E}) -> ¬{C} fact4: {AO} fact5: ¬{B} -> ({BS} & {A}) fact6: {B} | [] | [] | ãã¿ãã¿ã¡ãLv.7äºä»¶ããã³ãããã«ãLv.32äºä»¶ãèµ·ããããšããããšã¯ééãã§ãã | ¬({A} & {B}) | [] | 6 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«åŒ±ããšããããšãèµ·ãããšããããå ªå¿ããããšã¯èµ·ããªããŠãœããœã«ãLv.63äºä»¶ãèµ·ããããšããããšã¯ééãã§ãã fact2: ããããå ªå¿ããããšã¯èµ·ããªããŠãœããœã«ãLv.63äºä»¶ã¯çºçããããšããããšã¯ééããªãã°ãããã«ãLv.32äºä»¶ã¯èµ·ãããªã fact3: å ªå¿ããããšã¯èµ·ãããªããšããããšã¯ãœããœã«ãLv.63äºä»¶ããŸãã¯åŒ±ããšããããšã«èªçºããã fact4: ã·ã¡ãã·ã«ã
Lv.25äºä»¶ãçºçãã fact5: ãã¿ã«ã¿ãLv.77äºä»¶ããã³ã¿ãã¿ã¡ãLv.7äºä»¶ãèµ·ããããšããããšã¯ãããã«ãLv.32äºä»¶ãçããªããšããããšã¯åå ã§ãã fact6: ãããã«ãLv.32äºä»¶ãçºçãã ; $hypothesis$ = ãã¿ãã¿ã¡ãLv.7äºä»¶ããã³ãããã«ãLv.32äºä»¶ãèµ·ããããšããããšã¯ééãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {E} -> ¬(¬{C} & {D}) fact2: ¬(¬{C} & {D}) -> ¬{B} fact3: ({D} v {E}) -> ¬{C} fact4: {AO} fact5: ¬{B} -> ({BS} & {A}) fact6: {B} ; $hypothesis$ = ¬({A} & {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸãLv.10ã¯è²Žæ¹ãããã埡æå
¥ããã | ({D}{d} v {E}{d}) | fact1: ãããã®ãŸã«ããŸãLv.71ãç¥ã
ãããšããã°ãã®ãŸããŸãLv.10ã¯è²Žæ¹ããã fact2: ããä»®ã«ãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããªããªãããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯å°æ±ããªãããšããããšã¯åœã§ãã fact3: ä»®ã«ããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯ããã¯å°æ±ããšããããšã¯ãªãããšããããšã¯äºå®ãšç°ãªããšããã°ããã¯ç¥ã
ãã fact4: 貎æ¹ããããªãã¢ã³ã¹ã¿ãŒã¯é·ã£ãããããå°æ±ã fact5: é·ã£ããããã¢ã³ã¹ã¿ãŒã¯ç¥ã
ãã fact6: ããããã®ã¿ã¡ãã¿ãLv.66ãé©ååºæ¥ããã©ã匱ããªããšãããšãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããªã fact7: ãããã®ãŸã«ããŸãLv.71ãã匱ãããããé©ååºæ¥ãã°ãã®ã¿ã¡ãã¿ãLv.66ã¯é·ã£ãããããªã fact8: ãã®ã¿ã¡ãã¿ãLv.66ã¯é©ååºæ¥ããã©ã匱ããªã fact9: ããããããã¢ã³ã¹ã¿ãŒã¯åŸ¡æå
¥ãããªããŠåŸ¡æ©ããªãããšããããšã¯ééã£ãŠãããšãããšè²Žæ¹ããããªã fact10: ãã®ã¿ã¡ãã¿ãLv.66ã¯é©ååºæ¥ããã©ããã¯è²Žæ¹ããããªã | fact1: {C}{c} -> {D}{d} fact2: ¬{B}{b} -> ¬({A}{c} v ¬{B}{c}) fact3: ¬({A}{c} v ¬{B}{c}) -> {C}{c} fact4: (x): ¬{D}x -> ({A}x & {B}x) fact5: (x): {A}x -> {C}x fact6: ({AA}{a} & ¬{AB}{a}) -> ¬{B}{b} fact7: ({AB}{c} & {AA}{c}) -> ¬{A}{a} fact8: ({AA}{a} & ¬{AB}{a}) fact9: (x): ¬(¬{E}x & ¬{F}x) -> ¬{D}x fact10: ({AA}{a} & ¬{D}{a}) | [
"fact6 & fact8 -> int1: ãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããšããããšã¯ãªã; int1 & fact2 -> int2: ããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯ããã¯å°æ±ããšããããšã¯ãªãããšããããšã¯èª€ãã ; int2 & fact3 -> int3: ãã®ãŸã«ããŸãLv.71ã¯ç¥ã
ãã; int3 & fact1 -> int4: ãã®ãŸããŸãLv.10ã¯è²Žæ¹ããã; int4 -> hypothesis;"
] | [
"fact6 & fact8 -> int1: ¬{B}{b}; int1 & fact2 -> int2: ¬({A}{c} v ¬{B}{c}); int2 & fact3 -> int3: {C}{c}; int3 & fact1 -> int4: {D}{d}; int4 -> hypothesis;"
] | ãã®ãŽã«ããŽã®Lv.27ã¯ç¥ã
ãã | {C}{ie} | [
"fact12 -> int5: ãããããã®ã¿ã¡ãã¿ãLv.66ã¯åŸ¡æå
¥ããããšããããšã¯ãªããŠå ããŠåŸ¡æ©ããªãããšããããšã¯æãç«ããªããšããã°ãã®ã¿ã¡ãã¿ãLv.66ã¯è²Žæ¹ããããªãããšããããšã¯åã ãšããããšã¯ãªã; fact13 -> int6: ããããã®ãŽã«ããŽã®Lv.27ã貎æ¹ããããªããšããããã®ãŽã«ããŽã®Lv.27ã¯é·ã£ããããããã®äžå°æ±ã; fact11 -> int7: ããããã®ãŽã«ããŽã®Lv.27ãé·ã£ãããããšããã°ãã®ãŽã«ããŽã®Lv.27ã¯ç¥ã
ãã;"
] | 7 | 5 | 5 | 5 | 5 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®ãŸã«ããŸãLv.71ãç¥ã
ãããšããã°ãã®ãŸããŸãLv.10ã¯è²Žæ¹ããã fact2: ããä»®ã«ãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããªããªãããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯å°æ±ããªãããšããããšã¯åœã§ãã fact3: ä»®ã«ããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯ããã¯å°æ±ããšããããšã¯ãªãããšããããšã¯äºå®ãšç°ãªããšããã°ããã¯ç¥ã
ãã fact4: 貎æ¹ããããªãã¢ã³ã¹ã¿ãŒã¯é·ã£ãããããå°æ±ã fact5: é·ã£ããããã¢ã³ã¹ã¿ãŒã¯ç¥ã
ãã fact6: ããããã®ã¿ã¡ãã¿ãLv.66ãé©ååºæ¥ããã©ã匱ããªããšãããšãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããªã fact7: ãããã®ãŸã«ããŸãLv.71ãã匱ãããããé©ååºæ¥ãã°ãã®ã¿ã¡ãã¿ãLv.66ã¯é·ã£ãããããªã fact8: ãã®ã¿ã¡ãã¿ãLv.66ã¯é©ååºæ¥ããã©ã匱ããªã fact9: ããããããã¢ã³ã¹ã¿ãŒã¯åŸ¡æå
¥ãããªããŠåŸ¡æ©ããªãããšããããšã¯ééã£ãŠãããšãããšè²Žæ¹ããããªã fact10: ãã®ã¿ã¡ãã¿ãLv.66ã¯é©ååºæ¥ããã©ããã¯è²Žæ¹ããããªã ; $hypothesis$ = ãã®ãŸããŸãLv.10ã¯è²Žæ¹ãããã埡æå
¥ããã ; $proof$ = | fact6 & fact8 -> int1: ãã®ãŽããŽã«ã
Lv.43ã¯å°æ±ããšããããšã¯ãªã; int1 & fact2 -> int2: ããã®ãŸã«ããŸãLv.71ã¯é·ã£ããããããããã¯ããã¯å°æ±ããšããããšã¯ãªãããšããããšã¯èª€ãã ; int2 & fact3 -> int3: ãã®ãŸã«ããŸãLv.71ã¯ç¥ã
ãã; int3 & fact1 -> int4: ãã®ãŸããŸãLv.10ã¯è²Žæ¹ããã; int4 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{c} -> {D}{d} fact2: ¬{B}{b} -> ¬({A}{c} v ¬{B}{c}) fact3: ¬({A}{c} v ¬{B}{c}) -> {C}{c} fact4: (x): ¬{D}x -> ({A}x & {B}x) fact5: (x): {A}x -> {C}x fact6: ({AA}{a} & ¬{AB}{a}) -> ¬{B}{b} fact7: ({AB}{c} & {AA}{c}) -> ¬{A}{a} fact8: ({AA}{a} & ¬{AB}{a}) fact9: (x): ¬(¬{E}x & ¬{F}x) -> ¬{D}x fact10: ({AA}{a} & ¬{D}{a}) ; $hypothesis$ = ({D}{d} v {E}{d}) ; $proof$ = | fact6 & fact8 -> int1: ¬{B}{b}; int1 & fact2 -> int2: ¬({A}{c} v ¬{B}{c}); int2 & fact3 -> int3: {C}{c}; int3 & fact1 -> int4: {D}{d}; int4 -> hypothesis; __PROVED__ |
0.3 | ã埡çŸãããšãããšæ±ãäžãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> {B}x | fact1: ããããã®ãŸã®ãŸã¡ãLv.30ãåãçµã¿æããªãã°ãã®ãŸã®ãŸã¡ãLv.30ã¯è§£ãæããšããããšã¯ãªããããã«æ¯ã
ãããªã fact2: ä»®ã«ãã®ãœã¡ã
ãœãLv.63ãèŠæããšããããšã¯ãªãããã®äžåè«ã£ãœããªããªãã°æ±ãäžãã fact3: ããä»®ã«ãã®ãœã¡ã
ãœãLv.63ã¯ç解ãé£ããšããããšã¯ãªããæŽã«è§£ãæããªããªãããã¯æ±ãäžãã fact4: ä»®ã«ãã®ãœã¡ã
ãœãLv.63ã埡çŸãããšããã°ç解ãé£ããªããããã«è§£ãæããªã | fact1: {GQ}{bb} -> (¬{AB}{bb} & ¬{EM}{bb}) fact2: (¬{HK}{a} & ¬{FI}{a}) -> {B}{a} fact3: (¬{AA}{a} & ¬{AB}{a}) -> {B}{a} fact4: {A}{a} -> (¬{AA}{a} & ¬{AB}{a}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã¡ã
ãœãLv.63ã¯åŸ¡çŸãã; fact4 & assump1 -> int1: ãã®ãœã¡ã
ãœãLv.63ã¯ç解ãé£ããªããŠãã®äžè§£ãæããªã; int1 & fact3 -> int2: ãã®ãœã¡ã
ãœãLv.63ã¯æ±ãäžãã; [assump1] & int2 -> int3: ããä»®ã«ãã®ãœã¡ã
ãœãLv.63ã埡çŸãããªããã®ãœã¡ã
ãœãLv.63ã¯æ±ãäžãã; int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact4 & assump1 -> int1: (¬{AA}{a} & ¬{AB}{a}); int1 & fact3 -> int2: {B}{a}; [assump1] & int2 -> int3: {A}{a} -> {B}{a}; int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ãŸã®ãŸã¡ãLv.30ãåãçµã¿æããªãã°ãã®ãŸã®ãŸã¡ãLv.30ã¯è§£ãæããšããããšã¯ãªããããã«æ¯ã
ãããªã fact2: ä»®ã«ãã®ãœã¡ã
ãœãLv.63ãèŠæããšããããšã¯ãªãããã®äžåè«ã£ãœããªããªãã°æ±ãäžãã fact3: ããä»®ã«ãã®ãœã¡ã
ãœãLv.63ã¯ç解ãé£ããšããããšã¯ãªããæŽã«è§£ãæããªããªãããã¯æ±ãäžãã fact4: ä»®ã«ãã®ãœã¡ã
ãœãLv.63ã埡çŸãããšããã°ç解ãé£ããªããããã«è§£ãæããªã ; $hypothesis$ = ã埡çŸãããšãããšæ±ãäžãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã¡ã
ãœãLv.63ã¯åŸ¡çŸãã; fact4 & assump1 -> int1: ãã®ãœã¡ã
ãœãLv.63ã¯ç解ãé£ããªããŠãã®äžè§£ãæããªã; int1 & fact3 -> int2: ãã®ãœã¡ã
ãœãLv.63ã¯æ±ãäžãã; [assump1] & int2 -> int3: ããä»®ã«ãã®ãœã¡ã
ãœãLv.63ã埡çŸãããªããã®ãœã¡ã
ãœãLv.63ã¯æ±ãäžãã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {GQ}{bb} -> (¬{AB}{bb} & ¬{EM}{bb}) fact2: (¬{HK}{a} & ¬{FI}{a}) -> {B}{a} fact3: (¬{AA}{a} & ¬{AB}{a}) -> {B}{a} fact4: {A}{a} -> (¬{AA}{a} & ¬{AB}{a}) ; $hypothesis$ = (Ex): {A}x -> {B}x ; $proof$ = | void -> assump1: {A}{a}; fact4 & assump1 -> int1: (¬{AA}{a} & ¬{AB}{a}); int1 & fact3 -> int2: {B}{a}; [assump1] & int2 -> int3: {A}{a} -> {B}{a}; int3 -> hypothesis; __PROVED__ |
0.3 | 泚ææ·±ããšããããšã¯èµ·ãããªããšããããšã¯ã¿ã£ãšããªããšããããšã«é²ããã | {A} -> {B} | fact1: ä»®ã«ããŽããŽãLv.3äºä»¶ã¯èµ·ãããªããäŒããé£ããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãããšããã°æ³šææ·±ããšããããšãèµ·ãã fact2: ãã¿ã£ãšããªããšããããšãçºçããããšããããšã¯æ¬åœã ãšããã°ãããŽããŽãLv.3äºä»¶ãçºçããªãããããäŒããé£ããšããããšã¯çºçããããšããããšã¯ç¢ºãã§ãªãããšããããšã¯äºå®ã | fact1: ¬(¬{AA} & {AB}) -> {B} fact2: {A} -> ¬(¬{AA} & {AB}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããã¿ã£ãšããªããšããããšãèµ·ãã; fact2 & assump1 -> int1: ããŽããŽãLv.3äºä»¶ãçºçããªããäŒããé£ããšããããšã¯çºçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã; int1 & fact1 -> int2: 泚ææ·±ããšããããšãèµ·ãã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: {A}; fact2 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact1 -> int2: {B}; [assump1] & int2 -> hypothesis;"
] | null | null | [] | null | 4 | 3 | 4 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ããŽããŽãLv.3äºä»¶ã¯èµ·ãããªããäŒããé£ããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãããšããã°æ³šææ·±ããšããããšãèµ·ãã fact2: ãã¿ã£ãšããªããšããããšãçºçããããšããããšã¯æ¬åœã ãšããã°ãããŽããŽãLv.3äºä»¶ãçºçããªãããããäŒããé£ããšããããšã¯çºçããããšããããšã¯ç¢ºãã§ãªãããšããããšã¯äºå®ã ; $hypothesis$ = 泚ææ·±ããšããããšã¯èµ·ãããªããšããããšã¯ã¿ã£ãšããªããšããããšã«é²ããã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããã¿ã£ãšããªããšããããšãèµ·ãã; fact2 & assump1 -> int1: ããŽããŽãLv.3äºä»¶ãçºçããªããäŒããé£ããšããããšã¯çºçããããšããããšã¯æãç«ã€ãšããããšã¯ãªã; int1 & fact1 -> int2: 泚ææ·±ããšããããšãèµ·ãã; [assump1] & int2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{AA} & {AB}) -> {B} fact2: {A} -> ¬(¬{AA} & {AB}) ; $hypothesis$ = {A} -> {B} ; $proof$ = | void -> assump1: {A}; fact2 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact1 -> int2: {B}; [assump1] & int2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ã
ãŸã®Lv.28ã¯ã¿ã£ãšãå¯æããªã | ¬{A}{a} | fact1: ãã®ãŸã«ã
ãŸã®Lv.28ã¯é転ãæããªããæ¯éããªããŠãã¥ãŒãããªãããšããããšã¯äºå®ãšç°ãªã fact2: ä»®ã«ãã®ãŸã«ã
ãŸã®Lv.28ãã¿ã£ãšãå¯æããšããã°ãã®ãŸã«ã
ãŸã®Lv.28ã¯é転ãæã | fact1: {B}{a} -> ¬(¬{D}{a} & ¬{C}{a}) fact2: {A}{a} -> {B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸã«ã
ãŸã®Lv.28ã¯ã¿ã£ãšãå¯æã; fact2 & assump1 -> int1: ãã®ãŸã«ã
ãŸã®Lv.28ã¯é転ãæã; int1 & fact1 -> int2: ããã®ãŸã«ã
ãŸã®Lv.28ã¯æ¯éãããšããããšã¯ãªãããã®äžãã¥ãŒãããªãããšããããšã¯ééãã ;"
] | [
"void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact1 -> int2: ¬(¬{D}{a} & ¬{C}{a});"
] | null | null | [] | null | 5 | 4 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãŸã«ã
ãŸã®Lv.28ã¯é転ãæããªããæ¯éããªããŠãã¥ãŒãããªãããšããããšã¯äºå®ãšç°ãªã fact2: ä»®ã«ãã®ãŸã«ã
ãŸã®Lv.28ãã¿ã£ãšãå¯æããšããã°ãã®ãŸã«ã
ãŸã®Lv.28ã¯é転ãæã ; $hypothesis$ = ãã®ãŸã«ã
ãŸã®Lv.28ã¯ã¿ã£ãšãå¯æããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} -> ¬(¬{D}{a} & ¬{C}{a}) fact2: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | 人éèããšããããšã¯èµ·ãããªããå ããŠææ
šæ·±ããšããããšã¯èµ·ããªã | (¬{E} & ¬{F}) | fact1: ããä»®ã«äººéèããšããããšãèµ·ããããã€ææ
šæ·±ããšããããšãçããã°èŠãããšããããšã¯èµ·ãããªã fact2: ãæ®çºãæããšããããšã¯èµ·ããªãããšããããšã¯ãèŠãããšããããšã¯èµ·ãããªãããŸãæ®çºãæããšããããšã¯çºçããªãããšããããšã®ãã£ãããšãªã fact3: åºæããšããããšãçãã fact4: ããèŠãããšããããšã¯çºçããªããŠæ®çºãæããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã ããšããããšã¯äººéèããšããããšãé²ã fact5: ææ
šæ·±ããšããããšã¯èµ·ããªã fact6: ä»®ã«ç«ãŠæããããšãçºçãããšããã°äžåãããšã¯çããªããåºæããšããããšãèµ·ãã fact7: æ®çºãæããšããããšã¯çºçããªããšããããšã¯ãåºæããšããããšãèµ·ããããŸãã¯ç«ãŠæããããšãèµ·ããããŸãã¯ã©ã¡ããã ããšããããšãåå ã | fact1: ({E} & {F}) -> ¬{D} fact2: ¬{C} -> (¬{D} & ¬{C}) fact3: {A} fact4: (¬{D} & ¬{C}) -> ¬{E} fact5: ¬{F} fact6: {B} -> (¬{FS} & {A}) fact7: ({A} v {B}) -> ¬{C} | [
"fact3 -> int1: åºæããšããããšãç«ãŠæããããšãèµ·ãã; int1 & fact7 -> int2: æ®çºãæããšããããšã¯èµ·ãããªã; int2 & fact2 -> int3: èŠãããšããããšã¯èµ·ãããªãããã€æ®çºãæããšããããšã¯çºçããªã; int3 & fact4 -> int4: 人éèããšããããšã¯èµ·ãããªã; int4 & fact5 -> hypothesis;"
] | [
"fact3 -> int1: ({A} v {B}); int1 & fact7 -> int2: ¬{C}; int2 & fact2 -> int3: (¬{D} & ¬{C}); int3 & fact4 -> int4: ¬{E}; int4 & fact5 -> hypothesis;"
] | äžåãããšã¯çããªã | ¬{FS} | [] | 7 | 5 | 5 | 5 | 5 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«äººéèããšããããšãèµ·ããããã€ææ
šæ·±ããšããããšãçããã°èŠãããšããããšã¯èµ·ãããªã fact2: ãæ®çºãæããšããããšã¯èµ·ããªãããšããããšã¯ãèŠãããšããããšã¯èµ·ãããªãããŸãæ®çºãæããšããããšã¯çºçããªãããšããããšã®ãã£ãããšãªã fact3: åºæããšããããšãçãã fact4: ããèŠãããšããããšã¯çºçããªããŠæ®çºãæããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã ããšããããšã¯äººéèããšããããšãé²ã fact5: ææ
šæ·±ããšããããšã¯èµ·ããªã fact6: ä»®ã«ç«ãŠæããããšãçºçãããšããã°äžåãããšã¯çããªããåºæããšããããšãèµ·ãã fact7: æ®çºãæããšããããšã¯çºçããªããšããããšã¯ãåºæããšããããšãèµ·ããããŸãã¯ç«ãŠæããããšãèµ·ããããŸãã¯ã©ã¡ããã ããšããããšãåå ã ; $hypothesis$ = 人éèããšããããšã¯èµ·ãããªããå ããŠææ
šæ·±ããšããããšã¯èµ·ããªã ; $proof$ = | fact3 -> int1: åºæããšããããšãç«ãŠæããããšãèµ·ãã; int1 & fact7 -> int2: æ®çºãæããšããããšã¯èµ·ãããªã; int2 & fact2 -> int3: èŠãããšããããšã¯èµ·ãããªãããã€æ®çºãæããšããããšã¯çºçããªã; int3 & fact4 -> int4: 人éèããšããããšã¯èµ·ãããªã; int4 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: ({E} & {F}) -> ¬{D} fact2: ¬{C} -> (¬{D} & ¬{C}) fact3: {A} fact4: (¬{D} & ¬{C}) -> ¬{E} fact5: ¬{F} fact6: {B} -> (¬{FS} & {A}) fact7: ({A} v {B}) -> ¬{C} ; $hypothesis$ = (¬{E} & ¬{F}) ; $proof$ = | fact3 -> int1: ({A} v {B}); int1 & fact7 -> int2: ¬{C}; int2 & fact2 -> int3: (¬{D} & ¬{C}); int3 & fact4 -> int4: ¬{E}; int4 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãéèŠãããšãããšé
ããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> {C}x | fact1: ãããã®ãããã®Lv.9ãå³ããããšãããšãã®ã¿ãã¿ã«ã
Lv.31ã¯é
ãäžæ¹ã§åºããªã fact2: ãã®ã¿ãã¿ã«ã
Lv.31ãæããããªãããã¯é
ã fact3: ããããã®ã¿ãã¿ã«ã
Lv.31ãéèŠãããšããã°ãã®ã¿ãã¿ã«ã
Lv.31ã¯æããã fact4: é
ãã¢ã³ã¹ã¿ãŒãåºããšããããšã¯ãªããšããããã®ãŸã¡ããŸã«ãLv.80ã¯é
ããªã | fact1: {D}{b} -> ({C}{a} & ¬{E}{a}) fact2: {B}{a} -> {C}{a} fact3: {A}{a} -> {B}{a} fact4: (x): ({C}x & ¬{E}x) -> ¬{C}{df} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ã«ã
Lv.31ã¯éèŠãã; fact3 & assump1 -> int1: ãã®ã¿ãã¿ã«ã
Lv.31ã¯æããã; int1 & fact2 -> int2: ãã®ã¿ãã¿ã«ã
Lv.31ã¯é
ã; [assump1] & int2 -> int3: ä»®ã«ãã®ã¿ãã¿ã«ã
Lv.31ãéèŠãããšãããšããã¯é
ã; int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis;"
] | ãã®ãŸã¡ããŸã«ãLv.80ã¯æããã | {B}{df} | [] | 6 | 5 | 4 | 5 | 4 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®ãããã®Lv.9ãå³ããããšãããšãã®ã¿ãã¿ã«ã
Lv.31ã¯é
ãäžæ¹ã§åºããªã fact2: ãã®ã¿ãã¿ã«ã
Lv.31ãæããããªãããã¯é
ã fact3: ããããã®ã¿ãã¿ã«ã
Lv.31ãéèŠãããšããã°ãã®ã¿ãã¿ã«ã
Lv.31ã¯æããã fact4: é
ãã¢ã³ã¹ã¿ãŒãåºããšããããšã¯ãªããšããããã®ãŸã¡ããŸã«ãLv.80ã¯é
ããªã ; $hypothesis$ = ãéèŠãããšãããšé
ããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ã¿ãã¿ã«ã
Lv.31ã¯éèŠãã; fact3 & assump1 -> int1: ãã®ã¿ãã¿ã«ã
Lv.31ã¯æããã; int1 & fact2 -> int2: ãã®ã¿ãã¿ã«ã
Lv.31ã¯é
ã; [assump1] & int2 -> int3: ä»®ã«ãã®ã¿ãã¿ã«ã
Lv.31ãéèŠãããšãããšããã¯é
ã; int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{b} -> ({C}{a} & ¬{E}{a}) fact2: {B}{a} -> {C}{a} fact3: {A}{a} -> {B}{a} fact4: (x): ({C}x & ¬{E}x) -> ¬{C}{df} ; $hypothesis$ = (Ex): {A}x -> {C}x ; $proof$ = | void -> assump1: {A}{a}; fact3 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{a}; [assump1] & int2 -> int3: {A}{a} -> {C}{a}; int3 -> hypothesis; __PROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããããã¡ãLv.41äºä»¶ãçãã | {A} | fact1: ãå»ã¿ã£ãœããšããããšã¯çºçããªãããšããããšã¯ããããã¡ãLv.41äºä»¶ãšç²ã£ãããšããããšãèµ·ããããšããããšã«ããçºçãã fact2: ããä»®ã«ãæããé£ããšããããšã¯èµ·ããªããå»ã¿ã£ãœããšããããšã¯çºçããªãããŸãã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããšãããšç²ã£ãããšããããšã¯çºçããªã fact3: ããä»®ã«ã¿ãã¿ãLv.91äºä»¶ãçºçãããšããã°ãæããé£ããšããããšã¯çºçããªãããããã¯å»ã¿ã£ãœããšããããšã¯çããªãããšããããšã¯åã§ãã fact4: ãç²ã£ãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact5: å»ã¿ã£ãœããšããããšãèµ·ãã fact6: ç²ã£ãããšããããšã¯èµ·ããªããšããããŸããŸã«ãLv.84äºä»¶ããã³ãããã¡ãLv.41äºä»¶äž¡æ¹ãšããèµ·ãã | fact1: ({A} & {B}) -> ¬{C} fact2: ¬(¬{D} v ¬{C}) -> ¬{B} fact3: {E} -> ¬(¬{D} v ¬{C}) fact4: {B} fact5: {C} fact6: ¬{B} -> ({GA} & {A}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããããã¡ãLv.41äºä»¶ãçãã; assump1 & fact4 -> int1: ãããã¡ãLv.41äºä»¶ãèµ·ããããããç²ã£ãããšããããšãçºçãã; int1 & fact1 -> int2: å»ã¿ã£ãœããšããããšã¯èµ·ãããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact4 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ããŸããŸã«ãLv.84äºä»¶ãçããããšããããšã¯æ£ãã | {GA} | [] | 8 | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãå»ã¿ã£ãœããšããããšã¯çºçããªãããšããããšã¯ããããã¡ãLv.41äºä»¶ãšç²ã£ãããšããããšãèµ·ããããšããããšã«ããçºçãã fact2: ããä»®ã«ãæããé£ããšããããšã¯èµ·ããªããå»ã¿ã£ãœããšããããšã¯çºçããªãããŸãã¯äž¡æ¹ã ããšããããšã¯æãç«ããªããšãããšç²ã£ãããšããããšã¯çºçããªã fact3: ããä»®ã«ã¿ãã¿ãLv.91äºä»¶ãçºçãããšããã°ãæããé£ããšããããšã¯çºçããªãããããã¯å»ã¿ã£ãœããšããããšã¯çããªãããšããããšã¯åã§ãã fact4: ãç²ã£ãããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact5: å»ã¿ã£ãœããšããããšãèµ·ãã fact6: ç²ã£ãããšããããšã¯èµ·ããªããšããããŸããŸã«ãLv.84äºä»¶ããã³ãããã¡ãLv.41äºä»¶äž¡æ¹ãšããèµ·ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããããã¡ãLv.41äºä»¶ãçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããããã¡ãLv.41äºä»¶ãçãã; assump1 & fact4 -> int1: ãããã¡ãLv.41äºä»¶ãèµ·ããããããç²ã£ãããšããããšãçºçãã; int1 & fact1 -> int2: å»ã¿ã£ãœããšããããšã¯èµ·ãããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: ¬(¬{D} v ¬{C}) -> ¬{B} fact3: {E} -> ¬(¬{D} v ¬{C}) fact4: {B} fact5: {C} fact6: ¬{B} -> ({GA} & {A}) ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: {A}; assump1 & fact4 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããªããŠãã€ç¶ç¶ãé£ããšããããšã¯ãªãããšããããšã¯ééãã | ¬(¬{E}{c} & ¬{F}{c}) | fact1: ãã®ã·ã«ãã·ã«ãLv.23ã¯ã©ãã€ã fact2: ãã®ãŽããŽã¡ãLv.10ã¯åž°çãã fact3: ãã®ãŸã®ãŸã«ã
Lv.0ã¯ç¶ç¶ãé£ããªã fact4: ãã®ãŸã®ãŸã«ã
Lv.0ã¯ã©ãã€ã fact5: ããããã®ãŽããŽã¡ãLv.10ãé£ãæ¢ããããã®äžåž°çããã°ãã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããšããããšã¯ãªã fact6: ãã®ãŸã®ãŸã«ã
Lv.0ã¯åž°çããªã fact7: ä»®ã«ãã®ã·ã«ãã·ã«ãLv.23ãç±ã
ãããšããã°ãã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ãã fact8: ããä»®ã«ãã®ã·ã«ãã·ã«ãLv.23ãã©ãã€ããšãããšãã®ã·ã«ãã·ã«ãLv.23ã¯ç±ã
ãã | fact1: {A}{a} fact2: {D}{b} fact3: ¬{F}{c} fact4: {A}{c} fact5: ({C}{b} & {D}{b}) -> ¬{E}{c} fact6: ¬{D}{c} fact7: {B}{a} -> {C}{b} fact8: {A}{a} -> {B}{a} | [
"fact8 & fact1 -> int1: ãã®ã·ã«ãã·ã«ãLv.23ã¯ç±ã
ãã; int1 & fact7 -> int2: ããã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ããããšããããšã¯ç¢ºãã ; int2 & fact2 -> int3: ãã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ããããããåž°çãã; int3 & fact5 -> int4: ãã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããªã; int4 & fact3 -> hypothesis;"
] | [
"fact8 & fact1 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{b}; int2 & fact2 -> int3: ({C}{b} & {D}{b}); int3 & fact5 -> int4: ¬{E}{c}; int4 & fact3 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ã·ã«ãã·ã«ãLv.23ã¯ã©ãã€ã fact2: ãã®ãŽããŽã¡ãLv.10ã¯åž°çãã fact3: ãã®ãŸã®ãŸã«ã
Lv.0ã¯ç¶ç¶ãé£ããªã fact4: ãã®ãŸã®ãŸã«ã
Lv.0ã¯ã©ãã€ã fact5: ããããã®ãŽããŽã¡ãLv.10ãé£ãæ¢ããããã®äžåž°çããã°ãã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããšããããšã¯ãªã fact6: ãã®ãŸã®ãŸã«ã
Lv.0ã¯åž°çããªã fact7: ä»®ã«ãã®ã·ã«ãã·ã«ãLv.23ãç±ã
ãããšããã°ãã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ãã fact8: ããä»®ã«ãã®ã·ã«ãã·ã«ãLv.23ãã©ãã€ããšãããšãã®ã·ã«ãã·ã«ãLv.23ã¯ç±ã
ãã ; $hypothesis$ = ããã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããªããŠãã€ç¶ç¶ãé£ããšããããšã¯ãªãããšããããšã¯ééãã ; $proof$ = | fact8 & fact1 -> int1: ãã®ã·ã«ãã·ã«ãLv.23ã¯ç±ã
ãã; int1 & fact7 -> int2: ããã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ããããšããããšã¯ç¢ºãã ; int2 & fact2 -> int3: ãã®ãŽããŽã¡ãLv.10ã¯é£ãæ¢ããããããåž°çãã; int3 & fact5 -> int4: ãã®ãŸã®ãŸã«ã
Lv.0ã¯éŠå°Ÿè¯ããªã; int4 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: {D}{b} fact3: ¬{F}{c} fact4: {A}{c} fact5: ({C}{b} & {D}{b}) -> ¬{E}{c} fact6: ¬{D}{c} fact7: {B}{a} -> {C}{b} fact8: {A}{a} -> {B}{a} ; $hypothesis$ = ¬(¬{E}{c} & ¬{F}{c}) ; $proof$ = | fact8 & fact1 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{b}; int2 & fact2 -> int3: ({C}{b} & {D}{b}); int3 & fact5 -> int4: ¬{E}{c}; int4 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ããããLv.9ã¯éãŸãæããªããçãŸãèœã¡ãªãããšããããšã¯æãç«ããªã | ¬(¬{D}{b} & ¬{C}{b}) | fact1: ããããã®ã¿ãã¿ãLv.56ãåžžé£ããããªããã®ã¿ãã¿ãLv.56ã¯åŠ¬ãŸãã fact2: ãã®ã¿ãã¿ãLv.56ã¯æããã fact3: ãããã®ã¿ãã¿ãLv.56ãæããããããã劬ãŸãããšããããã®ããããLv.9ã¯çãŸãèœã¡ããšããããšã¯ãªã fact4: ããããã¢ã³ã¹ã¿ãŒã¯æããããšãããšãããã¯éãŸãæããªããŠããã«ããã¯çãŸãèœã¡ãªãããšããããšã¯åœã§ãã fact5: ãã®ã¿ãã¿ãLv.56ã¯éãŸãæã fact6: ãã®ã¿ãã¿ãLv.56ã¯çãããªãããã€åŸ¡åãåããäžãããªã fact7: ãã®ããããLv.9ã¯åŠ¬ãŸãããŠãŸãæµ
ã fact8: ãã®ã¿ãã¿ãLv.56ã¯çãŸãèœã¡ã fact9: ããããã®ããããLv.9ãçãŸãèœã¡ãªããªãã°ãã®ããããLv.9ã¯éãŸãæããªããŠããã«çãŸãèœã¡ãªã fact10: ãã®ã¿ãã¿ãLv.56ã¯åžžé£ããã | fact1: {E}{a} -> {B}{a} fact2: {A}{a} fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: (x): {A}x -> ¬(¬{D}x & ¬{C}x) fact5: {D}{a} fact6: (¬{GA}{a} & ¬{EO}{a}) fact7: ({B}{b} & {BT}{b}) fact8: {C}{a} fact9: ¬{C}{b} -> (¬{D}{b} & ¬{C}{b}) fact10: {E}{a} | [
"fact10 & fact1 -> int1: ãã®ã¿ãã¿ãLv.56ã¯åŠ¬ãŸãã; fact2 & int1 -> int2: ããã®ã¿ãã¿ãLv.56ã¯æããããããã«åŠ¬ãŸããããšããããšã¯æãç«ã€; int2 & fact3 -> int3: ãã®ããããLv.9ã¯çãŸãèœã¡ãªã; int3 & fact9 -> hypothesis;"
] | [
"fact10 & fact1 -> int1: {B}{a}; fact2 & int1 -> int2: ({A}{a} & {B}{a}); int2 & fact3 -> int3: ¬{C}{b}; int3 & fact9 -> hypothesis;"
] | ããã®ããããLv.9ã¯éãŸãæããªããçãŸãèœã¡ãªãããšããããšã¯æãç«ããªã | ¬(¬{D}{b} & ¬{C}{b}) | [
"fact11 -> int4: ãããããã®ããããLv.9ã¯æãããããšããããšã¯äºå®ã§ãããšãããšãããã¯éãŸãæããšããããšã¯ãªããçãŸãèœã¡ãªãããšããããšã¯ééãã§ãã;"
] | 4 | 4 | 4 | 4 | 4 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããã®ã¿ãã¿ãLv.56ãåžžé£ããããªããã®ã¿ãã¿ãLv.56ã¯åŠ¬ãŸãã fact2: ãã®ã¿ãã¿ãLv.56ã¯æããã fact3: ãããã®ã¿ãã¿ãLv.56ãæããããããã劬ãŸãããšããããã®ããããLv.9ã¯çãŸãèœã¡ããšããããšã¯ãªã fact4: ããããã¢ã³ã¹ã¿ãŒã¯æããããšãããšãããã¯éãŸãæããªããŠããã«ããã¯çãŸãèœã¡ãªãããšããããšã¯åœã§ãã fact5: ãã®ã¿ãã¿ãLv.56ã¯éãŸãæã fact6: ãã®ã¿ãã¿ãLv.56ã¯çãããªãããã€åŸ¡åãåããäžãããªã fact7: ãã®ããããLv.9ã¯åŠ¬ãŸãããŠãŸãæµ
ã fact8: ãã®ã¿ãã¿ãLv.56ã¯çãŸãèœã¡ã fact9: ããããã®ããããLv.9ãçãŸãèœã¡ãªããªãã°ãã®ããããLv.9ã¯éãŸãæããªããŠããã«çãŸãèœã¡ãªã fact10: ãã®ã¿ãã¿ãLv.56ã¯åžžé£ããã ; $hypothesis$ = ããã®ããããLv.9ã¯éãŸãæããªããçãŸãèœã¡ãªãããšããããšã¯æãç«ããªã ; $proof$ = | fact10 & fact1 -> int1: ãã®ã¿ãã¿ãLv.56ã¯åŠ¬ãŸãã; fact2 & int1 -> int2: ããã®ã¿ãã¿ãLv.56ã¯æããããããã«åŠ¬ãŸããããšããããšã¯æãç«ã€; int2 & fact3 -> int3: ãã®ããããLv.9ã¯çãŸãèœã¡ãªã; int3 & fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {E}{a} -> {B}{a} fact2: {A}{a} fact3: ({A}{a} & {B}{a}) -> ¬{C}{b} fact4: (x): {A}x -> ¬(¬{D}x & ¬{C}x) fact5: {D}{a} fact6: (¬{GA}{a} & ¬{EO}{a}) fact7: ({B}{b} & {BT}{b}) fact8: {C}{a} fact9: ¬{C}{b} -> (¬{D}{b} & ¬{C}{b}) fact10: {E}{a} ; $hypothesis$ = ¬(¬{D}{b} & ¬{C}{b}) ; $proof$ = | fact10 & fact1 -> int1: {B}{a}; fact2 & int1 -> int2: ({A}{a} & {B}{a}); int2 & fact3 -> int3: ¬{C}{b}; int3 & fact9 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®ãã«ã
ããLv.1ã¯è²·ãæãããŸãå°æ±ãããšããããšã¯æãç«ã€ããšããããšã¯çå®ã§ãªã | ¬({F}{b} & {G}{b}) | fact1: ãã®ãœããœã¡ã
Lv.37ãåºå
¥ããæããšããããã®ãœããœã¡ã
Lv.37ã¯æšèŠãã fact2: åºããªãã¢ã³ã¹ã¿ãŒã¯äºæãããæµ
ãŸã fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æµ
ãŸãããšããããšã¯çå®ãªããã®ãœããœã¡ã
Lv.37ã¯åºããªãã¢ã³ã¹ã¿ãŒã§ãããŸãããæããšããããšã¯ãªã fact4: ä»®ã«ãã®ãœããœã¡ã
Lv.37ã¯åºããªããæŽã«ããæããªããšããã°ããã®ãœããœã¡ã
Lv.37ã¯åºå
¥ããæãããšããããšã¯ééãã§ãªã fact5: ããä»®ã«ãã®ãœããœã¡ã
Lv.37ãæšèŠãããšããããã®ãã«ã
ããLv.1ã¯è²·ãæã fact6: ãã®ãã«ã
ããLv.1ã¯å°æ±ã fact7: ããæµ
ãŸãããšããããšã¯æ£ãããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: {D}{a} -> {E}{a} fact2: (x): ¬{B}x -> ({DH}x & {A}x) fact3: (x): {A}x -> (¬{B}{a} & ¬{C}{a}) fact4: (¬{B}{a} & ¬{C}{a}) -> {D}{a} fact5: {E}{a} -> {F}{b} fact6: {G}{b} fact7: (Ex): {A}x | [
"fact7 & fact3 -> int1: ãã®ãœããœã¡ã
Lv.37ã¯åºããªããããŸãã«ããã¯ããæããªã; int1 & fact4 -> int2: ãã®ãœããœã¡ã
Lv.37ã¯åºå
¥ããæã; int2 & fact1 -> int3: ãã®ãœããœã¡ã
Lv.37ã¯æšèŠãã; int3 & fact5 -> int4: ãã®ãã«ã
ããLv.1ã¯è²·ãæã; int4 & fact6 -> hypothesis;"
] | [
"fact7 & fact3 -> int1: (¬{B}{a} & ¬{C}{a}); int1 & fact4 -> int2: {D}{a}; int2 & fact1 -> int3: {E}{a}; int3 & fact5 -> int4: {F}{b}; int4 & fact6 -> hypothesis;"
] | ãã®ãœããœã¡ã
Lv.37ã¯äºæãã | {DH}{a} | [
"fact8 -> int5: ããä»®ã«ãã®ãœããœã¡ã
Lv.37ãåºããªããšããã°ãã®ãœããœã¡ã
Lv.37ã¯äºæãããããã¯æµ
ãŸã;"
] | 5 | 5 | 5 | 5 | 5 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãœããœã¡ã
Lv.37ãåºå
¥ããæããšããããã®ãœããœã¡ã
Lv.37ã¯æšèŠãã fact2: åºããªãã¢ã³ã¹ã¿ãŒã¯äºæãããæµ
ãŸã fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æµ
ãŸãããšããããšã¯çå®ãªããã®ãœããœã¡ã
Lv.37ã¯åºããªãã¢ã³ã¹ã¿ãŒã§ãããŸãããæããšããããšã¯ãªã fact4: ä»®ã«ãã®ãœããœã¡ã
Lv.37ã¯åºããªããæŽã«ããæããªããšããã°ããã®ãœããœã¡ã
Lv.37ã¯åºå
¥ããæãããšããããšã¯ééãã§ãªã fact5: ããä»®ã«ãã®ãœããœã¡ã
Lv.37ãæšèŠãããšããããã®ãã«ã
ããLv.1ã¯è²·ãæã fact6: ãã®ãã«ã
ããLv.1ã¯å°æ±ã fact7: ããæµ
ãŸãããšããããšã¯æ£ãããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ãããã®ãã«ã
ããLv.1ã¯è²·ãæãããŸãå°æ±ãããšããããšã¯æãç«ã€ããšããããšã¯çå®ã§ãªã ; $proof$ = | fact7 & fact3 -> int1: ãã®ãœããœã¡ã
Lv.37ã¯åºããªããããŸãã«ããã¯ããæããªã; int1 & fact4 -> int2: ãã®ãœããœã¡ã
Lv.37ã¯åºå
¥ããæã; int2 & fact1 -> int3: ãã®ãœããœã¡ã
Lv.37ã¯æšèŠãã; int3 & fact5 -> int4: ãã®ãã«ã
ããLv.1ã¯è²·ãæã; int4 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{a} -> {E}{a} fact2: (x): ¬{B}x -> ({DH}x & {A}x) fact3: (x): {A}x -> (¬{B}{a} & ¬{C}{a}) fact4: (¬{B}{a} & ¬{C}{a}) -> {D}{a} fact5: {E}{a} -> {F}{b} fact6: {G}{b} fact7: (Ex): {A}x ; $hypothesis$ = ¬({F}{b} & {G}{b}) ; $proof$ = | fact7 & fact3 -> int1: (¬{B}{a} & ¬{C}{a}); int1 & fact4 -> int2: {D}{a}; int2 & fact1 -> int3: {E}{a}; int3 & fact5 -> int4: {F}{b}; int4 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããŸããŸã«ã
Lv.78äºä»¶ãçºçãã | {A} | fact1: ããŸããŸã«ã
Lv.78äºä»¶ããã³åœãŠä»ããããšãçããããšããããšã¯åŒ±ããšããããšãé»ã fact2: åœãŠä»ããããšãçºçãã fact3: ããä»®ã«ãããŸããŸã«ã
Lv.78äºä»¶ã§ã¯ãªãã·ã¡ãã·ãLv.96äºä»¶ãçããããšããããšã¯æ¬åœã ããšããããšã¯æãç«ããªããªãã·ã¡ãã·ãLv.96äºä»¶ã¯çºçããªã fact4: ç掻ãæããšããããšã¯èµ·ãããªã fact5: ä»®ã«åºå
¥ããæããšããããšãèµ·ãããšãããšé
èããšããããšã¯çããªããåœãŠä»ããããšã¯èµ·ãããªã fact6: ãŸã«ã
ãŸã«ãLv.0äºä»¶ã¯èµ·ãããªã fact7: ããä»®ã«åœãŠä»ããããšã¯èµ·ããªããªãã匱ããšããããšã¯çããªããŠããŸãã«ãŸããŸã«ã
Lv.78äºä»¶ã¯çºçããªãããšããããšã¯èª€ãã | fact1: ({A} & {B}) -> ¬{C} fact2: {B} fact3: ¬(¬{A} & {FB}) -> ¬{FB} fact4: ¬{K} fact5: {E} -> (¬{D} & ¬{B}) fact6: ¬{JG} fact7: ¬{B} -> ¬(¬{C} & ¬{A}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããŸããŸã«ã
Lv.78äºä»¶ãçºçãã; assump1 & fact2 -> int1: ãŸããŸã«ã
Lv.78äºä»¶ããã³åœãŠä»ããããšãèµ·ãã; int1 & fact1 -> int2: 匱ããšããããšã¯çºçããªã;"
] | [
"void -> assump1: {A}; assump1 & fact2 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C};"
] | 以äžã®ããã«ä»®å®ããããŸããŸã«ã
Lv.78äºä»¶ãçºçãã | {A} | [] | 7 | 5 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããŸããŸã«ã
Lv.78äºä»¶ããã³åœãŠä»ããããšãçããããšããããšã¯åŒ±ããšããããšãé»ã fact2: åœãŠä»ããããšãçºçãã fact3: ããä»®ã«ãããŸããŸã«ã
Lv.78äºä»¶ã§ã¯ãªãã·ã¡ãã·ãLv.96äºä»¶ãçããããšããããšã¯æ¬åœã ããšããããšã¯æãç«ããªããªãã·ã¡ãã·ãLv.96äºä»¶ã¯çºçããªã fact4: ç掻ãæããšããããšã¯èµ·ãããªã fact5: ä»®ã«åºå
¥ããæããšããããšãèµ·ãããšãããšé
èããšããããšã¯çããªããåœãŠä»ããããšã¯èµ·ãããªã fact6: ãŸã«ã
ãŸã«ãLv.0äºä»¶ã¯èµ·ãããªã fact7: ããä»®ã«åœãŠä»ããããšã¯èµ·ããªããªãã匱ããšããããšã¯çããªããŠããŸãã«ãŸããŸã«ã
Lv.78äºä»¶ã¯çºçããªãããšããããšã¯èª€ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããŸããŸã«ã
Lv.78äºä»¶ãçºçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: {B} fact3: ¬(¬{A} & {FB}) -> ¬{FB} fact4: ¬{K} fact5: {E} -> (¬{D} & ¬{B}) fact6: ¬{JG} fact7: ¬{B} -> ¬(¬{C} & ¬{A}) ; $hypothesis$ = {A} ; $proof$ = | __UNKNOWN__ |
0.3 | ã¿ã¡ãã¿ãLv.92äºä»¶ã¯èµ·ãããªã | ¬{D} | fact1: ä»®ã«é åãããããšãçããªããšããã°ã·ã«ã·ãLv.75äºä»¶ã¯çºçããããã€è¡è
¥ããšããããšãèµ·ãã fact2: è¡è
¥ããšããããšã¯ãé åãããããšã¯èµ·ãããªãããšããããšãåå ã fact3: ã¿ã¡ãã¿ãLv.92äºä»¶ã¯ã·ãã·ãLv.82äºä»¶ãšã·ã«ã·ãLv.75äºä»¶ãèµ·ããã«é»ãŸãã fact4: ã·ãã·ãLv.82äºä»¶ãçºçãã | fact1: ¬{E} -> ({A} & {B}) fact2: ¬{E} -> {B} fact3: ({C} & {A}) -> ¬{D} fact4: {C} | [] | [] | null | null | [] | null | 4 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ã«é åãããããšãçããªããšããã°ã·ã«ã·ãLv.75äºä»¶ã¯çºçããããã€è¡è
¥ããšããããšãèµ·ãã fact2: è¡è
¥ããšããããšã¯ãé åãããããšã¯èµ·ãããªãããšããããšãåå ã fact3: ã¿ã¡ãã¿ãLv.92äºä»¶ã¯ã·ãã·ãLv.82äºä»¶ãšã·ã«ã·ãLv.75äºä»¶ãèµ·ããã«é»ãŸãã fact4: ã·ãã·ãLv.82äºä»¶ãçºçãã ; $hypothesis$ = ã¿ã¡ãã¿ãLv.92äºä»¶ã¯èµ·ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{E} -> ({A} & {B}) fact2: ¬{E} -> {B} fact3: ({C} & {A}) -> ¬{D} fact4: {C} ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã®ãŸãLv.41ã¯èæãããªã | ¬{D}{c} | fact1: ãã®ãããã¡ãLv.81ã¯èæãã fact2: ããã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¹Žãç¶ããªãããšããããšã¯æãç«ã€ fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æ±ããããèæããããšããããšã¯ééã£ãŠãããªãèæãããªã fact4: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¥ã fact5: ãã®ãããã¡ãLv.81ãèŠãæããªãã°ãã®ãŸã®ãŸãLv.41ã¯èæãã fact6: ãããããã®ã¿ã¡ã
ã¿ã«ãLv.43ãæ±ããããšããã°ãã®ãããã¡ãLv.81ã¯èŠãæãããšããããšã¯çå®ã fact7: ãããã®ã¿ã¡ã
ã¿ã«ãLv.43ã蹎ãç¶ããªããšãããšè¥ããŠæ±ããã | fact1: {D}{b} fact2: ¬{E}{a} fact3: (x): ¬({B}x & {D}x) -> ¬{D}x fact4: {A}{a} fact5: {C}{b} -> {D}{c} fact6: {B}{a} -> {C}{b} fact7: ¬{E}{a} -> ({A}{a} & {B}{a}) | [
"fact2 & fact7 -> int1: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¥ããŠããã¯æ±ããã; int1 -> int2: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯æ±ããã; int2 & fact6 -> int3: ãã®ãããã¡ãLv.81ã¯èŠãæã; int3 & fact5 -> hypothesis;"
] | [
"fact2 & fact7 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact6 -> int3: {C}{b}; int3 & fact5 -> hypothesis;"
] | ãã®ãŸã®ãŸãLv.41ã¯èæãããªã | ¬{D}{c} | [
"fact8 -> int4: ãããããã®ãŸã®ãŸãLv.41ã¯æ±ãããããã€ããã¯èæããããšããããšã¯æãç«ããªããšãããšãã®ãŸã®ãŸãLv.41ã¯èæãããªã;"
] | 4 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãããã¡ãLv.81ã¯èæãã fact2: ããã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¹Žãç¶ããªãããšããããšã¯æãç«ã€ fact3: ä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æ±ããããèæããããšããããšã¯ééã£ãŠãããªãèæãããªã fact4: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¥ã fact5: ãã®ãããã¡ãLv.81ãèŠãæããªãã°ãã®ãŸã®ãŸãLv.41ã¯èæãã fact6: ãããããã®ã¿ã¡ã
ã¿ã«ãLv.43ãæ±ããããšããã°ãã®ãããã¡ãLv.81ã¯èŠãæãããšããããšã¯çå®ã fact7: ãããã®ã¿ã¡ã
ã¿ã«ãLv.43ã蹎ãç¶ããªããšãããšè¥ããŠæ±ããã ; $hypothesis$ = ãã®ãŸã®ãŸãLv.41ã¯èæãããªã ; $proof$ = | fact2 & fact7 -> int1: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯è¥ããŠããã¯æ±ããã; int1 -> int2: ãã®ã¿ã¡ã
ã¿ã«ãLv.43ã¯æ±ããã; int2 & fact6 -> int3: ãã®ãããã¡ãLv.81ã¯èŠãæã; int3 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{b} fact2: ¬{E}{a} fact3: (x): ¬({B}x & {D}x) -> ¬{D}x fact4: {A}{a} fact5: {C}{b} -> {D}{c} fact6: {B}{a} -> {C}{b} fact7: ¬{E}{a} -> ({A}{a} & {B}{a}) ; $hypothesis$ = ¬{D}{c} ; $proof$ = | fact2 & fact7 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {B}{a}; int2 & fact6 -> int3: {C}{b}; int3 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ããããLv.18äºä»¶ã¯èµ·ãããªã | ¬{A} | fact1: ã¿ãã¿ãLv.45äºä»¶ãçºçãã fact2: ããããããLv.18äºä»¶ããããã¯åå¿ãæããšããããšãèµ·ãããšãããšåããšããããšã¯çºçããªã fact3: ã¿ãã¿ãLv.60äºä»¶ã¯èµ·ããªã fact4: 貎æ¹ããããšããããšã¯çããªã fact5: ãåããšããããšãèµ·ããããšããããšã¯çå®ã fact6: æµäžæ·±ããšããããšã¯èµ·ãããªã fact7: ã·ã¡ã
ã·ãLv.3äºä»¶ãçºçããããŸãã¯ã¿ã«ã
ã¿ãªLv.19äºä»¶ãèµ·ããããããã¯ã©ã¡ããã | fact1: {FL} fact2: ({A} v {B}) -> ¬{C} fact3: ¬{S} fact4: ¬{DF} fact5: {C} fact6: ¬{HB} fact7: ({DH} v {BD}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããããLv.18äºä»¶ãèµ·ãã; assump1 -> int1: ããããLv.18äºä»¶ãçºçããããããã¯åå¿ãæããšããããšã¯çºçããããããã¯ã©ã¡ããã ; int1 & fact2 -> int2: åããšããããšã¯èµ·ããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 3 | 5 | 3 | 5 | 0 | 5 | PROVED | null | PROVED | null | $facts$ = fact1: ã¿ãã¿ãLv.45äºä»¶ãçºçãã fact2: ããããããLv.18äºä»¶ããããã¯åå¿ãæããšããããšãèµ·ãããšãããšåããšããããšã¯çºçããªã fact3: ã¿ãã¿ãLv.60äºä»¶ã¯èµ·ããªã fact4: 貎æ¹ããããšããããšã¯çããªã fact5: ãåããšããããšãèµ·ããããšããããšã¯çå®ã fact6: æµäžæ·±ããšããããšã¯èµ·ãããªã fact7: ã·ã¡ã
ã·ãLv.3äºä»¶ãçºçããããŸãã¯ã¿ã«ã
ã¿ãªLv.19äºä»¶ãèµ·ããããããã¯ã©ã¡ããã ; $hypothesis$ = ããããLv.18äºä»¶ã¯èµ·ãããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããããLv.18äºä»¶ãèµ·ãã; assump1 -> int1: ããããLv.18äºä»¶ãçºçããããããã¯åå¿ãæããšããããšã¯çºçããããããã¯ã©ã¡ããã ; int1 & fact2 -> int2: åããšããããšã¯èµ·ããªã; int2 & fact5 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {FL} fact2: ({A} v {B}) -> ¬{C} fact3: ¬{S} fact4: ¬{DF} fact5: {C} fact6: ¬{HB} fact7: ({DH} v {BD}) ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; assump1 -> int1: ({A} v {B}); int1 & fact2 -> int2: ¬{C}; int2 & fact5 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãœã«ã
ãœãLv.39äºä»¶ãçãã | {A} | fact1: ãœããœãLv.18äºä»¶ãçºçãã fact2: ããã¡ãããLv.94äºä»¶ã¯èµ·ãããªãäžæ¹ã§ç
ãããšããããšãèµ·ããããšããããšã¯æãç«ããªããªããœããœãLv.18äºä»¶ã¯èµ·ããªã fact3: ããããã¡ãããLv.94äºä»¶ãšç
ãããšããããšã©ã¡ãããèµ·ããããšããããšã¯æ¬åœã§ããããšããããšã¯åã ããšããããšã¯ééãã§ãªã fact4: ãããããœã«ã
ãœãLv.39äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã ãšãããããã¡ãããLv.94äºä»¶ãèµ·ããããã®äžç
ãããšããããšãèµ·ããããšããããšã¯ééãã fact5: ããœã«ã
ãœãLv.39äºä»¶ã¯èµ·ããªãããšããããšã¯æ¬åœã ãšãããšããã¡ãããLv.94äºä»¶ã¯çããªããŠç
ãããšããããšãèµ·ããããšããããšã¯åœã | fact1: {B} fact2: ¬(¬{AA} & {AB}) -> ¬{B} fact3: ¬({AA} & {AB}) fact4: ¬{A} -> ¬({AA} & {AB}) fact5: ¬{A} -> ¬(¬{AA} & {AB}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ã
ãœãLv.39äºä»¶ã¯èµ·ãããªã; fact5 & assump1 -> int1: ããã¡ãããLv.94äºä»¶ã¯çããªããŠç
ãããšããããšãèµ·ããããšããããšã¯åœã§ãã; int1 & fact2 -> int2: ãœããœãLv.18äºä»¶ã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact5 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact2 -> int2: ¬{B}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãœããœãLv.18äºä»¶ãçºçãã fact2: ããã¡ãããLv.94äºä»¶ã¯èµ·ãããªãäžæ¹ã§ç
ãããšããããšãèµ·ããããšããããšã¯æãç«ããªããªããœããœãLv.18äºä»¶ã¯èµ·ããªã fact3: ããããã¡ãããLv.94äºä»¶ãšç
ãããšããããšã©ã¡ãããèµ·ããããšããããšã¯æ¬åœã§ããããšããããšã¯åã ããšããããšã¯ééãã§ãªã fact4: ãããããœã«ã
ãœãLv.39äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã ãšãããããã¡ãããLv.94äºä»¶ãèµ·ããããã®äžç
ãããšããããšãèµ·ããããšããããšã¯ééãã fact5: ããœã«ã
ãœãLv.39äºä»¶ã¯èµ·ããªãããšããããšã¯æ¬åœã ãšãããšããã¡ãããLv.94äºä»¶ã¯çããªããŠç
ãããšããããšãèµ·ããããšããããšã¯åœã ; $hypothesis$ = ãœã«ã
ãœãLv.39äºä»¶ãçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœã«ã
ãœãLv.39äºä»¶ã¯èµ·ãããªã; fact5 & assump1 -> int1: ããã¡ãããLv.94äºä»¶ã¯çããªããŠç
ãããšããããšãèµ·ããããšããããšã¯åœã§ãã; int1 & fact2 -> int2: ãœããœãLv.18äºä»¶ã¯èµ·ãããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {B} fact2: ¬(¬{AA} & {AB}) -> ¬{B} fact3: ¬({AA} & {AB}) fact4: ¬{A} -> ¬({AA} & {AB}) fact5: ¬{A} -> ¬(¬{AA} & {AB}) ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: ¬{A}; fact5 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact2 -> int2: ¬{B}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœããœã«ã
Lv.45ã¯äžããæã | {A}{aa} | fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æã¿æŽããã fact2: ããããã¢ã³ã¹ã¿ãŒã¯æšããããããã¯é£ãã | fact1: (x): {FB}x fact2: (x): ({CH}x & {AJ}x) | [] | [] | null | null | [] | null | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æã¿æŽããã fact2: ããããã¢ã³ã¹ã¿ãŒã¯æšããããããã¯é£ãã ; $hypothesis$ = ãã®ãœããœã«ã
Lv.45ã¯äžããæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): {FB}x fact2: (x): ({CH}x & {AJ}x) ; $hypothesis$ = {A}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸã«ãLv.65ã¯é¢ä¿æ·±ããšããããšã¯ãªã | ¬{A}{a} | fact1: ããããã¢ã³ã¹ã¿ãŒã¯åºãå¿ãã fact2: é ããªãã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ãã泚ææ·±ã fact3: é ããªãã¢ã³ã¹ã¿ãŒã¯éé²ãããæŽã«é¢ä¿æ·±ã fact4: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ã fact5: ãããã®ãŸããŸãLv.34ãé¢ä¿æ·±ããšããããšã¯ãªããšããã°ãã®ãŸããŸã«ãLv.65ã¯é¢ä¿æ·±ããªã | fact1: (x): {GA}x fact2: (x): ¬{B}x -> ({A}x & {AT}x) fact3: (x): ¬{B}x -> ({FJ}x & {A}x) fact4: (x): {A}x fact5: ¬{A}{b} -> ¬{A}{a} | [
"fact4 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ã; int1 -> hypothesis;"
] | [
"fact4 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æ³šææ·±ã | (x): {AT}x | [
"fact6 -> int2: ããä»®ã«ããã®ãŸããŸã«ãLv.65ã¯é ããªãããšããããšã¯ç¢ºããªãã°ãã®ãŸããŸã«ãLv.65ã¯é¢ä¿æ·±ããããã«ããã¯æ³šææ·±ã;"
] | 5 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããã¢ã³ã¹ã¿ãŒã¯åºãå¿ãã fact2: é ããªãã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ãã泚ææ·±ã fact3: é ããªãã¢ã³ã¹ã¿ãŒã¯éé²ãããæŽã«é¢ä¿æ·±ã fact4: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ã fact5: ãããã®ãŸããŸãLv.34ãé¢ä¿æ·±ããšããããšã¯ãªããšããã°ãã®ãŸããŸã«ãLv.65ã¯é¢ä¿æ·±ããªã ; $hypothesis$ = ãã®ãŸããŸã«ãLv.65ã¯é¢ä¿æ·±ããšããããšã¯ãªã ; $proof$ = | fact4 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¢ä¿æ·±ã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {GA}x fact2: (x): ¬{B}x -> ({A}x & {AT}x) fact3: (x): ¬{B}x -> ({FJ}x & {A}x) fact4: (x): {A}x fact5: ¬{A}{b} -> ¬{A}{a} ; $hypothesis$ = ¬{A}{a} ; $proof$ = | fact4 -> int1: (x): {A}x; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ã | {A}{c} | fact1: ä»®ã«ããã®ãŽããŽã«Lv.27ã¯ãããŸãããªãããããã¯å ªãé£ããªãããããã¯ã©ã¡ããã§ããããšããããšã¯èª€ã£ãŠãããªãããã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ããªãããšããããšã¯æ¬åœã§ãã fact2: ãã®ãŽããŽã«Lv.27ã¯åãã£ãœã fact3: ãããããã®ãŽããŽã«Lv.27ã¯æ
ãšãããããããã¯ããã¯åãã£ãœããªãããšããããšã¯æãç«ããªããšããããã®ã·ã«ã·ã®Lv.92ã¯ãããŸãããªã fact4: ããä»®ã«ããã¢ã³ã¹ã¿ãŒã¯ã¢ã¡ãªã«ããããšãããšããããŸãããªãããŸãã¯ããã¯å ªãé£ããªãããšããããšã¯æãç«ããªã fact5: ãåãæãã¢ã³ã¹ã¿ãŒã¯ã¢ã¡ãªã«ãããããšããããšã¯æãç«ã€ fact6: ä»®ã«ããã¢ã³ã¹ã¿ãŒã¯å ªãé£ããšããããšã¯ãªããšããã°ãã²ãããããããã¯åœ¢å®¹ãé£ããšããããšã¯ãªãããšããããšã¯ééã£ãŠãã fact7: ãã®ã·ã«ã·ã®Lv.92ã¯ãããŸãã fact8: ãã®ãŽããŽã«Lv.27ãæ
ãšãããããããã¯åãã£ãœããªããäž¡æ¹ãšãã§ãããªãã°ãã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ã | fact1: ¬(¬{B}{a} v ¬{A}{a}) -> ¬{A}{c} fact2: {AB}{a} fact3: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{b} fact4: (x): {C}x -> ¬(¬{B}x v ¬{A}x) fact5: (x): {D}x -> {C}x fact6: (x): ¬{A}x -> ¬({CA}x v ¬{JI}x) fact7: {B}{b} fact8: ({AA}{a} v ¬{AB}{a}) -> {A}{c} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ãŽããŽã«Lv.27ã¯æ
ãšããããåãã£ãœããšããããšã¯ãªãããšããããšã¯ééãã ; fact3 & assump1 -> int1: ãã®ã·ã«ã·ã®Lv.92ã¯ãããŸãããªã; int1 & fact7 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŽããŽã«Lv.27ã¯æ
ãšããããåãã£ãœããªãããŸãã¯äž¡æ¹ãšãã ; int3 & fact8 -> hypothesis;"
] | [
"void -> assump1: ¬({AA}{a} v ¬{AB}{a}); fact3 & assump1 -> int1: ¬{B}{b}; int1 & fact7 -> int2: #F#; [assump1] & int2 -> int3: ({AA}{a} v ¬{AB}{a}); int3 & fact8 -> hypothesis;"
] | ãã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ããªã | ¬{A}{c} | [
"fact10 -> int4: ä»®ã«ãã®ãŽããŽã«Lv.27ã¯ã¢ã¡ãªã«ããããšãããããã®ãŽããŽã«Lv.27ã¯ãããŸãããªããå ªãé£ããªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ééã£ãŠãã; fact11 -> int5: ãããä»®ã«ãã®ãŽããŽã«Lv.27ãåãæããšããããã®ãŽããŽã«Lv.27ã¯ã¢ã¡ãªã«ãããããšããããšã¯æãç«ã€;"
] | 6 | 5 | 4 | 5 | 4 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ããã®ãŽããŽã«Lv.27ã¯ãããŸãããªãããããã¯å ªãé£ããªãããããã¯ã©ã¡ããã§ããããšããããšã¯èª€ã£ãŠãããªãããã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ããªãããšããããšã¯æ¬åœã§ãã fact2: ãã®ãŽããŽã«Lv.27ã¯åãã£ãœã fact3: ãããããã®ãŽããŽã«Lv.27ã¯æ
ãšãããããããã¯ããã¯åãã£ãœããªãããšããããšã¯æãç«ããªããšããããã®ã·ã«ã·ã®Lv.92ã¯ãããŸãããªã fact4: ããä»®ã«ããã¢ã³ã¹ã¿ãŒã¯ã¢ã¡ãªã«ããããšãããšããããŸãããªãããŸãã¯ããã¯å ªãé£ããªãããšããããšã¯æãç«ããªã fact5: ãåãæãã¢ã³ã¹ã¿ãŒã¯ã¢ã¡ãªã«ãããããšããããšã¯æãç«ã€ fact6: ä»®ã«ããã¢ã³ã¹ã¿ãŒã¯å ªãé£ããšããããšã¯ãªããšããã°ãã²ãããããããã¯åœ¢å®¹ãé£ããšããããšã¯ãªãããšããããšã¯ééã£ãŠãã fact7: ãã®ã·ã«ã·ã®Lv.92ã¯ãããŸãã fact8: ãã®ãŽããŽã«Lv.27ãæ
ãšãããããããã¯åãã£ãœããªããäž¡æ¹ãšãã§ãããªãã°ãã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ã ; $hypothesis$ = ãã®ãŸã«ã
ãŸãLv.22ã¯å ªãé£ã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããããã®ãŽããŽã«Lv.27ã¯æ
ãšããããåãã£ãœããšããããšã¯ãªãããšããããšã¯ééãã ; fact3 & assump1 -> int1: ãã®ã·ã«ã·ã®Lv.92ã¯ãããŸãããªã; int1 & fact7 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŽããŽã«Lv.27ã¯æ
ãšããããåãã£ãœããªãããŸãã¯äž¡æ¹ãšãã ; int3 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬(¬{B}{a} v ¬{A}{a}) -> ¬{A}{c} fact2: {AB}{a} fact3: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{b} fact4: (x): {C}x -> ¬(¬{B}x v ¬{A}x) fact5: (x): {D}x -> {C}x fact6: (x): ¬{A}x -> ¬({CA}x v ¬{JI}x) fact7: {B}{b} fact8: ({AA}{a} v ¬{AB}{a}) -> {A}{c} ; $hypothesis$ = {A}{c} ; $proof$ = | void -> assump1: ¬({AA}{a} v ¬{AB}{a}); fact3 & assump1 -> int1: ¬{B}{b}; int1 & fact7 -> int2: #F#; [assump1] & int2 -> int3: ({AA}{a} v ¬{AB}{a}); int3 & fact8 -> hypothesis; __PROVED__ |
0.3 | ã埡å¯ããšããããšãçãããæŽã«ãŸã¡ããŸãLv.54äºä»¶ãèµ·ããããšããããšã¯çå®ã§ãããšããããšã¯ãªã | ¬({B} & {C}) | fact1: ããã埡å¯ããšããããšã¯èµ·ãããªããšãããšéãåºãããšããã³ãŸããŸãªLv.95äºä»¶äž¡æ¹ãèµ·ãã fact2: ãŽããŽã«ã
Lv.47äºä»¶ãçºçãã fact3: ãŸã¡ããŸãLv.54äºä»¶ãçºçãã fact4: ãŸããŸãªLv.95äºä»¶ãçºçãããããŸãã«åŸ¡å¯ããšããããšã¯çºçãã fact5: ç¯ãé£ããšããããšãçãããªããåšããããšããããšã§ã¯ãªããŠãŸã¡ããŸãLv.54äºä»¶ãçºçããããšããããšã¯èª€ãã§ãã fact6: ãŸããŸãªLv.95äºä»¶ãçºçãã | fact1: ¬{B} -> ({JC} & {A}) fact2: {DF} fact3: {C} fact4: ({A} & {B}) fact5: {E} -> ¬(¬{D} & {C}) fact6: {A} | [
"fact4 -> int1: 埡å¯ããšããããšãèµ·ãã; int1 & fact3 -> hypothesis;"
] | [
"fact4 -> int1: {B}; int1 & fact3 -> hypothesis;"
] | éãåºãããšãèµ·ãã | {JC} | [] | 7 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããã埡å¯ããšããããšã¯èµ·ãããªããšãããšéãåºãããšããã³ãŸããŸãªLv.95äºä»¶äž¡æ¹ãèµ·ãã fact2: ãŽããŽã«ã
Lv.47äºä»¶ãçºçãã fact3: ãŸã¡ããŸãLv.54äºä»¶ãçºçãã fact4: ãŸããŸãªLv.95äºä»¶ãçºçãããããŸãã«åŸ¡å¯ããšããããšã¯çºçãã fact5: ç¯ãé£ããšããããšãçãããªããåšããããšããããšã§ã¯ãªããŠãŸã¡ããŸãLv.54äºä»¶ãçºçããããšããããšã¯èª€ãã§ãã fact6: ãŸããŸãªLv.95äºä»¶ãçºçãã ; $hypothesis$ = ã埡å¯ããšããããšãçãããæŽã«ãŸã¡ããŸãLv.54äºä»¶ãèµ·ããããšããããšã¯çå®ã§ãããšããããšã¯ãªã ; $proof$ = | fact4 -> int1: 埡å¯ããšããããšãèµ·ãã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{B} -> ({JC} & {A}) fact2: {DF} fact3: {C} fact4: ({A} & {B}) fact5: {E} -> ¬(¬{D} & {C}) fact6: {A} ; $hypothesis$ = ¬({B} & {C}) ; $proof$ = | fact4 -> int1: {B}; int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœã®Lv.12ã¯äž»åŒµãã | {F}{c} | fact1: ããä»®ã«ãã®ãŸã¡ããŸãLv.4ãå§æŸããªããšããããã®ãœããœã®Lv.12ã¯é·ãŒã fact2: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒãå§æŸãããšããããšã¯ãªããšãããããã¯ç§»ãé£ããªãããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãœããœã®Lv.12ãé·ãŒããªãã°ãã®ãœããœã®Lv.12ã¯äž»åŒµãã fact4: ãã®ã·ã«ã
ã·ãLv.24ã¯ç§»ãé£ããæ¯ã
ãã fact5: ä»®ã«ãã®ã·ã«ã
ã·ãLv.24ã移ãé£ããšããã°ãã®ãŸã¡ããŸãLv.4ã¯å§æŸãããšããããšã¯ãªããŠããã«é¢æ ãããªã | fact1: ¬{C}{b} -> {E}{c} fact2: (x): ¬{C}x -> ¬{A}x fact3: {E}{c} -> {F}{c} fact4: ({A}{a} & {B}{a}) fact5: {A}{a} -> (¬{C}{b} & ¬{D}{b}) | [
"fact4 -> int1: ããã®ã·ã«ã
ã·ãLv.24ã¯ç§»ãé£ãããšããããšã¯æ£ãã; int1 & fact5 -> int2: ããã®ãŸã¡ããŸãLv.4ã¯å§æŸããªããŠãããããã¯é¢æ ãããªãããšããããšã¯æãç«ã€; int2 -> int3: ãã®ãŸã¡ããŸãLv.4ã¯å§æŸãããšããããšã¯ãªã; int3 & fact1 -> int4: ãã®ãœããœã®Lv.12ã¯é·ãŒã; int4 & fact3 -> hypothesis;"
] | [
"fact4 -> int1: {A}{a}; int1 & fact5 -> int2: (¬{C}{b} & ¬{D}{b}); int2 -> int3: ¬{C}{b}; int3 & fact1 -> int4: {E}{c}; int4 & fact3 -> hypothesis;"
] | ãã®ãœããœã«Lv.77ã¯æ¯ã
ãããªããŠããã¯çœã£ãœããªã | (¬{B}{ar} & ¬{EU}{ar}) | [
"fact6 -> int5: ä»®ã«ãã®ã·ã«ã
ã·ãLv.24ãå§æŸããªããšããã°ããã¯ç§»ãé£ããªã;"
] | 5 | 5 | 5 | 5 | 5 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŸã¡ããŸãLv.4ãå§æŸããªããšããããã®ãœããœã®Lv.12ã¯é·ãŒã fact2: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒãå§æŸãããšããããšã¯ãªããšãããããã¯ç§»ãé£ããªãããšããããšã¯æãç«ã€ fact3: ããä»®ã«ãã®ãœããœã®Lv.12ãé·ãŒããªãã°ãã®ãœããœã®Lv.12ã¯äž»åŒµãã fact4: ãã®ã·ã«ã
ã·ãLv.24ã¯ç§»ãé£ããæ¯ã
ãã fact5: ä»®ã«ãã®ã·ã«ã
ã·ãLv.24ã移ãé£ããšããã°ãã®ãŸã¡ããŸãLv.4ã¯å§æŸãããšããããšã¯ãªããŠããã«é¢æ ãããªã ; $hypothesis$ = ãã®ãœããœã®Lv.12ã¯äž»åŒµãã ; $proof$ = | fact4 -> int1: ããã®ã·ã«ã
ã·ãLv.24ã¯ç§»ãé£ãããšããããšã¯æ£ãã; int1 & fact5 -> int2: ããã®ãŸã¡ããŸãLv.4ã¯å§æŸããªããŠãããããã¯é¢æ ãããªãããšããããšã¯æãç«ã€; int2 -> int3: ãã®ãŸã¡ããŸãLv.4ã¯å§æŸãããšããããšã¯ãªã; int3 & fact1 -> int4: ãã®ãœããœã®Lv.12ã¯é·ãŒã; int4 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{C}{b} -> {E}{c} fact2: (x): ¬{C}x -> ¬{A}x fact3: {E}{c} -> {F}{c} fact4: ({A}{a} & {B}{a}) fact5: {A}{a} -> (¬{C}{b} & ¬{D}{b}) ; $hypothesis$ = {F}{c} ; $proof$ = | fact4 -> int1: {A}{a}; int1 & fact5 -> int2: (¬{C}{b} & ¬{D}{b}); int2 -> int3: ¬{C}{b}; int3 & fact1 -> int4: {E}{c}; int4 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãããããã®ããããLv.33ã¯æ··ãããªãããã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ããªãããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã | ¬({B}{a} -> ¬{C}{b}) | fact1: ä»®ã«ãã®ããããLv.33ãæ··ããã°ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã fact2: ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã fact3: ãã®ããããLv.33ã¯æããã fact4: ãã®ãŽã¡ããŽã¡ã
Lv.45ãæããããšããããã®ããããLv.33ã¯å ªãé£ããªã fact5: ãããã®ããããLv.33ãæããããŠãããæ··ãããšããã°ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã | fact1: {B}{a} -> {C}{b} fact2: {C}{b} fact3: {A}{a} fact4: {A}{b} -> ¬{C}{a} fact5: ({A}{a} & {B}{a}) -> {C}{b} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ããããLv.33ã¯æ··ãã; fact3 & assump1 -> int1: ãã®ããããLv.33ã¯æããããæ··ãã;"
] | [
"void -> assump1: {B}{a}; fact3 & assump1 -> int1: ({A}{a} & {B}{a});"
] | null | null | [] | null | 4 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ã«ãã®ããããLv.33ãæ··ããã°ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã fact2: ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã fact3: ãã®ããããLv.33ã¯æããã fact4: ãã®ãŽã¡ããŽã¡ã
Lv.45ãæããããšããããã®ããããLv.33ã¯å ªãé£ããªã fact5: ãããã®ããããLv.33ãæããããŠãããæ··ãããšããã°ãã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ã ; $hypothesis$ = ãããããã®ããããLv.33ã¯æ··ãããªãããã®ãŽã¡ããŽã¡ã
Lv.45ã¯å ªãé£ããªãããšããããšã¯äºå®ã ããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} -> {C}{b} fact2: {C}{b} fact3: {A}{a} fact4: {A}{b} -> ¬{C}{a} fact5: ({A}{a} & {B}{a}) -> {C}{b} ; $hypothesis$ = ¬({B}{a} -> ¬{C}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã¡ããŸã®Lv.64ã¯ç©ã
ãã | {C}{b} | fact1: ãã®ããããLv.49ã¯çµæŒããããã®äžæã fact2: ãã®ããããLv.49ãçµæŒããã°ãã®ãŸã¡ããŸã®Lv.64ã¯ç©ã
ãã | fact1: ({A}{a} & {B}{a}) fact2: {A}{a} -> {C}{b} | [
"fact1 -> int1: ãã®ããããLv.49ã¯çµæŒãã; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ããããLv.49ã¯çµæŒããããã®äžæã fact2: ãã®ããããLv.49ãçµæŒããã°ãã®ãŸã¡ããŸã®Lv.64ã¯ç©ã
ãã ; $hypothesis$ = ãã®ãŸã¡ããŸã®Lv.64ã¯ç©ã
ãã ; $proof$ = | fact1 -> int1: ãã®ããããLv.49ã¯çµæŒãã; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: {A}{a} -> {C}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ããããLv.49ã¯èŒãæž¡ããªã | ¬{D}{d} | fact1: ãã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãããšããã°ããã®ããããLv.49ã¯åŠå®ãé£ãããšããããšã¯äºå®ã§ãã fact2: ããä»®ã«ãã®ã¿ãã¿ã¡ã
Lv.20ã¯æµ
é»ããªããªãããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªãããã£ããšããªãããšããããšã¯äºå®ãšç°ãªã fact3: ä»®ã«ãã®ã¿ãã¿ã¡ã
Lv.20ãèŒãæž¡ããšããã°ãã®ã·ãã·ãLv.33ã¯èŒãæž¡ã fact4: ãããã®ãœã«ããœã«ãLv.73ããã£ããšãããšãããšãã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãã fact5: ããããã®ãœã«ããœã«ãLv.73ã¯æµ
é»ããªããè·³èºããããšããããšã¯æãç«ããªããšãããšãã®ã¿ãã¿ã¡ã
Lv.20ã¯èŒãæž¡ã fact6: ããã®ã¿ãã¿ã¡ã
Lv.20ã¯æµ
é»ããªãããšããããšã¯çå®ã§ãã fact7: ãã®ããããLv.49ãåŠå®ãé£ããšãããšãã®ããããLv.49ã¯èŒãæž¡ã fact8: ããä»®ã«ããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªãããã£ããšããªãããšããããšã¯ééããªããã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãã | fact1: {B}{c} -> {C}{d} fact2: ¬{A}{a} -> ¬(¬{AA}{b} & ¬{AB}{b}) fact3: {D}{a} -> {D}{eb} fact4: {AB}{b} -> {B}{c} fact5: ¬(¬{A}{b} & {B}{b}) -> {D}{a} fact6: ¬{A}{a} fact7: {C}{d} -> {D}{d} fact8: ¬(¬{AA}{b} & ¬{AB}{b}) -> {B}{c} | [
"fact2 & fact6 -> int1: ããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªããŠãã€ãã£ããšããªãããšããããšã¯åœã ; int1 & fact8 -> int2: ããã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºããããšããããšã¯æ£ãã; int2 & fact1 -> int3: ãã®ããããLv.49ã¯åŠå®ãé£ã; int3 & fact7 -> hypothesis;"
] | [
"fact2 & fact6 -> int1: ¬(¬{AA}{b} & ¬{AB}{b}); int1 & fact8 -> int2: {B}{c}; int2 & fact1 -> int3: {C}{d}; int3 & fact7 -> hypothesis;"
] | ãã®ã·ãã·ãLv.33ã¯èŒãæž¡ã | {D}{eb} | [] | 7 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãããšããã°ããã®ããããLv.49ã¯åŠå®ãé£ãããšããããšã¯äºå®ã§ãã fact2: ããä»®ã«ãã®ã¿ãã¿ã¡ã
Lv.20ã¯æµ
é»ããªããªãããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªãããã£ããšããªãããšããããšã¯äºå®ãšç°ãªã fact3: ä»®ã«ãã®ã¿ãã¿ã¡ã
Lv.20ãèŒãæž¡ããšããã°ãã®ã·ãã·ãLv.33ã¯èŒãæž¡ã fact4: ãããã®ãœã«ããœã«ãLv.73ããã£ããšãããšãããšãã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãã fact5: ããããã®ãœã«ããœã«ãLv.73ã¯æµ
é»ããªããè·³èºããããšããããšã¯æãç«ããªããšãããšãã®ã¿ãã¿ã¡ã
Lv.20ã¯èŒãæž¡ã fact6: ããã®ã¿ãã¿ã¡ã
Lv.20ã¯æµ
é»ããªãããšããããšã¯çå®ã§ãã fact7: ãã®ããããLv.49ãåŠå®ãé£ããšãããšãã®ããããLv.49ã¯èŒãæž¡ã fact8: ããä»®ã«ããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªãããã£ããšããªãããšããããšã¯ééããªããã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºãã ; $hypothesis$ = ãã®ããããLv.49ã¯èŒãæž¡ããªã ; $proof$ = | fact2 & fact6 -> int1: ããã®ãœã«ããœã«ãLv.73ã¯äºæž¬ãé£ããªããŠãã€ãã£ããšããªãããšããããšã¯åœã ; int1 & fact8 -> int2: ããã®ã·ã¡ã
ã·ãLv.56ã¯è·³èºããããšããããšã¯æ£ãã; int2 & fact1 -> int3: ãã®ããããLv.49ã¯åŠå®ãé£ã; int3 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{c} -> {C}{d} fact2: ¬{A}{a} -> ¬(¬{AA}{b} & ¬{AB}{b}) fact3: {D}{a} -> {D}{eb} fact4: {AB}{b} -> {B}{c} fact5: ¬(¬{A}{b} & {B}{b}) -> {D}{a} fact6: ¬{A}{a} fact7: {C}{d} -> {D}{d} fact8: ¬(¬{AA}{b} & ¬{AB}{b}) -> {B}{c} ; $hypothesis$ = ¬{D}{d} ; $proof$ = | fact2 & fact6 -> int1: ¬(¬{AA}{b} & ¬{AB}{b}); int1 & fact8 -> int2: {B}{c}; int2 & fact1 -> int3: {C}{d}; int3 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æããããã©ã¿ã£ãšãå¯æããšããããšã¯ãªãããšããããšã¯èª€ãã§ãã | ¬({AA}{a} & ¬{AB}{a}) | fact1: ããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æããããã©ã¿ã£ãšãå¯æããªãããšããããšã¯èª€ãã§ãªããšãããšã©ãã€ã fact2: è
ç²æç¡ããªãã¢ã³ã¹ã¿ãŒã¯å
¥æãããã¿ã£ãšãå¯æããªã fact3: ããä»®ã«ãã®ãã¡ãããLv.79ãè
ç²æç¡ãããããã¯ãããã©ãã€ãããããã¯äž¡æ¹ã§ãããšããã°ãã®ãŸã¡ã
ãŸãLv.24ã¯è
ç²æç¡ããªã fact4: ãã®ãŸã¡ã
ãŸãLv.24ã¯ã©ãã€ããªã | fact1: ({AA}{a} & ¬{AB}{a}) -> {B}{a} fact2: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact3: ({A}{b} v {B}{b}) -> ¬{A}{a} fact4: ¬{B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æãããã©ã¿ã£ãšãå¯æããªã; fact1 & assump1 -> int1: ãã®ãŸã¡ã
ãŸãLv.24ã¯ã©ãã€ã; int1 & fact4 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: ({AA}{a} & ¬{AB}{a}); fact1 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: #F#; [assump1] & int2 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æãããã©ã¿ã£ãšãå¯æããªã | ({AA}{a} & ¬{AB}{a}) | [
"fact5 -> int3: ãããã®ãŸã¡ã
ãŸãLv.24ãè
ç²æç¡ããªããšãããããã¯å
¥æããäžæ¹ã§ã¿ã£ãšãå¯æããªã;"
] | 6 | 4 | 3 | 4 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æããããã©ã¿ã£ãšãå¯æããªãããšããããšã¯èª€ãã§ãªããšãããšã©ãã€ã fact2: è
ç²æç¡ããªãã¢ã³ã¹ã¿ãŒã¯å
¥æãããã¿ã£ãšãå¯æããªã fact3: ããä»®ã«ãã®ãã¡ãããLv.79ãè
ç²æç¡ãããããã¯ãããã©ãã€ãããããã¯äž¡æ¹ã§ãããšããã°ãã®ãŸã¡ã
ãŸãLv.24ã¯è
ç²æç¡ããªã fact4: ãã®ãŸã¡ã
ãŸãLv.24ã¯ã©ãã€ããªã ; $hypothesis$ = ããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æããããã©ã¿ã£ãšãå¯æããšããããšã¯ãªãããšããããšã¯èª€ãã§ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸã¡ã
ãŸãLv.24ã¯å
¥æãããã©ã¿ã£ãšãå¯æããªã; fact1 & assump1 -> int1: ãã®ãŸã¡ã
ãŸãLv.24ã¯ã©ãã€ã; int1 & fact4 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA}{a} & ¬{AB}{a}) -> {B}{a} fact2: (x): ¬{A}x -> ({AA}x & ¬{AB}x) fact3: ({A}{b} v {B}{b}) -> ¬{A}{a} fact4: ¬{B}{a} ; $hypothesis$ = ¬({AA}{a} & ¬{AB}{a}) ; $proof$ = | void -> assump1: ({AA}{a} & ¬{AB}{a}); fact1 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: #F#; [assump1] & int2 -> hypothesis; __PROVED__ |
0.3 | ããœããœã«Lv.58äºä»¶ã¯èµ·ãããªããå ããŠèã£ãœããšããããšã¯çºçããªãããšããããšã¯æãç«ããªã | ¬(¬{A} & ¬{B}) | fact1: ãœããœã«Lv.58äºä»¶ã¯çããªã fact2: èã£ãœããšããããšãèµ·ãã fact3: ãŸã«ã
ãŸãLv.9äºä»¶ã¯ããç·ããããšããããšãèµ·ããããã©æããããããšã¯èµ·ãããªãããšããããšã¯æ¬åœã ããšããããšã«é»ãŸãã fact4: ãããœããœã«Lv.58äºä»¶ãçãããèã£ãœããšããããšã¯èµ·ããªãããšããããšã¯çå®ã ããšããããšã¯ééãã§ãã fact5: ãŸã«ã
ãŸãLv.9äºä»¶ã¯çããªããšããããšã¯ãã²åŒ±ããšããããšããŸãã¯è¿åŽããããšããããã¯äž¡æ¹ãèµ·ããããšããããšãçãããã fact6: ãããœããœãLv.82äºä»¶ãèµ·ãããšããã°ãœããœã«Lv.58äºä»¶ã¯èµ·ããªããŠèã£ãœããšããããšã¯çããªã | fact1: ¬{A} fact2: {B} fact3: ({H} & ¬{G}) -> ¬{F} fact4: ¬({A} & ¬{B}) fact5: ¬{F} -> ({D} v {E}) fact6: {C} -> (¬{A} & ¬{B}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã«Lv.58äºä»¶ã¯èµ·ããªããèã£ãœããšããããšã¯èµ·ããªã; assump1 -> int1: èã£ãœããšããããšã¯çããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis;"
] | [
"void -> assump1: (¬{A} & ¬{B}); assump1 -> int1: ¬{B}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> hypothesis;"
] | 以äžã®ããã«ä»®å®ããããœããœã«Lv.58äºä»¶ã¯èµ·ããªããèã£ãœããšããããšã¯èµ·ããªã | (¬{A} & ¬{B}) | [] | 8 | 4 | 2 | 4 | 2 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãœããœã«Lv.58äºä»¶ã¯çããªã fact2: èã£ãœããšããããšãèµ·ãã fact3: ãŸã«ã
ãŸãLv.9äºä»¶ã¯ããç·ããããšããããšãèµ·ããããã©æããããããšã¯èµ·ãããªãããšããããšã¯æ¬åœã ããšããããšã«é»ãŸãã fact4: ãããœããœã«Lv.58äºä»¶ãçãããèã£ãœããšããããšã¯èµ·ããªãããšããããšã¯çå®ã ããšããããšã¯ééãã§ãã fact5: ãŸã«ã
ãŸãLv.9äºä»¶ã¯çããªããšããããšã¯ãã²åŒ±ããšããããšããŸãã¯è¿åŽããããšããããã¯äž¡æ¹ãèµ·ããããšããããšãçãããã fact6: ãããœããœãLv.82äºä»¶ãèµ·ãããšããã°ãœããœã«Lv.58äºä»¶ã¯èµ·ããªããŠèã£ãœããšããããšã¯çããªã ; $hypothesis$ = ããœããœã«Lv.58äºä»¶ã¯èµ·ãããªããå ããŠèã£ãœããšããããšã¯çºçããªãããšããããšã¯æãç«ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã«Lv.58äºä»¶ã¯èµ·ããªããèã£ãœããšããããšã¯èµ·ããªã; assump1 -> int1: èã£ãœããšããããšã¯çããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A} fact2: {B} fact3: ({H} & ¬{G}) -> ¬{F} fact4: ¬({A} & ¬{B}) fact5: ¬{F} -> ({D} v {E}) fact6: {C} -> (¬{A} & ¬{B}) ; $hypothesis$ = ¬(¬{A} & ¬{B}) ; $proof$ = | void -> assump1: (¬{A} & ¬{B}); assump1 -> int1: ¬{B}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ã«Lv.93ã¯å©çšãæãããã©åçµç¹åããªã | ({F}{c} & ¬{G}{c}) | fact1: ä»®ã«ãã®ããããªLv.1ãã§ã£ãããšããããã®ã¿ãã¿ã«ãLv.43ã¯å
¥ãæã fact2: ãã®ã·ãã·ã«Lv.93ã¯æå°æªããªããå©çšãæããåçµç¹åããªãããšããããšã¯ç¢ºãã§ãªã fact3: ãã®ããããªLv.1ã幌ããªããªãã°ãã®ããããªLv.1ã¯ã§ã£ãã fact4: ãã®ããããªLv.1ã¯å¹Œããªã fact5: ãããã®ã¿ãã¿ã«ãLv.43ãå
¥ãæããªããã®ã¿ãã¿ã«ãLv.43ã¯è¡šçŸãåŸã fact6: ãã®ã¿ãã¿ã«ãLv.43ãè¡šçŸãåŸããšããããã®ã·ãã·ã«Lv.93ã¯æå°æªã | fact1: {B}{a} -> {C}{b} fact2: {E}{c} -> ¬({F}{c} & ¬{G}{c}) fact3: {A}{a} -> {B}{a} fact4: {A}{a} fact5: {C}{b} -> {D}{b} fact6: {D}{b} -> {E}{c} | [
"fact3 & fact4 -> int1: ãã®ããããªLv.1ã¯ã§ã£ãã; int1 & fact1 -> int2: ãã®ã¿ãã¿ã«ãLv.43ã¯å
¥ãæã; int2 & fact5 -> int3: ãã®ã¿ãã¿ã«ãLv.43ã¯è¡šçŸãåŸã; int3 & fact6 -> int4: ãã®ã·ãã·ã«Lv.93ã¯æå°æªã; int4 & fact2 -> hypothesis;"
] | [
"fact3 & fact4 -> int1: {B}{a}; int1 & fact1 -> int2: {C}{b}; int2 & fact5 -> int3: {D}{b}; int3 & fact6 -> int4: {E}{c}; int4 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ããããªLv.1ãã§ã£ãããšããããã®ã¿ãã¿ã«ãLv.43ã¯å
¥ãæã fact2: ãã®ã·ãã·ã«Lv.93ã¯æå°æªããªããå©çšãæããåçµç¹åããªãããšããããšã¯ç¢ºãã§ãªã fact3: ãã®ããããªLv.1ã幌ããªããªãã°ãã®ããããªLv.1ã¯ã§ã£ãã fact4: ãã®ããããªLv.1ã¯å¹Œããªã fact5: ãããã®ã¿ãã¿ã«ãLv.43ãå
¥ãæããªããã®ã¿ãã¿ã«ãLv.43ã¯è¡šçŸãåŸã fact6: ãã®ã¿ãã¿ã«ãLv.43ãè¡šçŸãåŸããšããããã®ã·ãã·ã«Lv.93ã¯æå°æªã ; $hypothesis$ = ãã®ã·ãã·ã«Lv.93ã¯å©çšãæãããã©åçµç¹åããªã ; $proof$ = | fact3 & fact4 -> int1: ãã®ããããªLv.1ã¯ã§ã£ãã; int1 & fact1 -> int2: ãã®ã¿ãã¿ã«ãLv.43ã¯å
¥ãæã; int2 & fact5 -> int3: ãã®ã¿ãã¿ã«ãLv.43ã¯è¡šçŸãåŸã; int3 & fact6 -> int4: ãã®ã·ãã·ã«Lv.93ã¯æå°æªã; int4 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{a} -> {C}{b} fact2: {E}{c} -> ¬({F}{c} & ¬{G}{c}) fact3: {A}{a} -> {B}{a} fact4: {A}{a} fact5: {C}{b} -> {D}{b} fact6: {D}{b} -> {E}{c} ; $hypothesis$ = ({F}{c} & ¬{G}{c}) ; $proof$ = | fact3 & fact4 -> int1: {B}{a}; int1 & fact1 -> int2: {C}{b}; int2 & fact5 -> int3: {D}{b}; int3 & fact6 -> int4: {E}{c}; int4 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãèµ€ããããšãçãããšããããšããããã¯æŒãä»ãããŸãããšããããšã¯ãæãé£ããšããããšã¯çºçããªãããšããããšã«ããçããããšããããšã¯ééã£ãŠãã | ¬(¬{A} -> ({C} v {D})) | fact1: æãé£ããšããããšã¯èµ€ããããšãæŒãä»ãããŸãããšããããšãæã fact2: æãé£ããšããããšã¯ã·ã¡ã
ã·ãLv.16äºä»¶ã®åå ãšãªã fact3: çŸããé£ããšããããšããããã¯æ³¥èããšããããšãçãã fact4: ã·ã¡ã
ã·ãLv.16äºä»¶ã¯ãèµ€ããããšã¯èµ·ãããªãããšããããšãé»ã fact5: ãã·ã¡ã
ã·ãLv.16äºä»¶ã¯çºçããªãããšããããšã¯ãæãé£ããšããããšã¯çºçããªãããšããããšã«é»ãŸãã | fact1: {A} -> ({C} v {D}) fact2: {A} -> {B} fact3: ({JH} v {EA}) fact4: {B} -> {C} fact5: ¬{A} -> {B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããæãé£ããšããããšã¯çããªã; fact5 & assump1 -> int1: ã·ã¡ã
ã·ãLv.16äºä»¶ãçºçãã; int1 & fact4 -> int2: èµ€ããããšãèµ·ãã; int2 -> int3: èµ€ããããšãçãããæŒãä»ãããŸãããšããããšãçãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact5 & assump1 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 -> int3: ({C} v {D}); [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: æãé£ããšããããšã¯èµ€ããããšãæŒãä»ãããŸãããšããããšãæã fact2: æãé£ããšããããšã¯ã·ã¡ã
ã·ãLv.16äºä»¶ã®åå ãšãªã fact3: çŸããé£ããšããããšããããã¯æ³¥èããšããããšãçãã fact4: ã·ã¡ã
ã·ãLv.16äºä»¶ã¯ãèµ€ããããšã¯èµ·ãããªãããšããããšãé»ã fact5: ãã·ã¡ã
ã·ãLv.16äºä»¶ã¯çºçããªãããšããããšã¯ãæãé£ããšããããšã¯çºçããªãããšããããšã«é»ãŸãã ; $hypothesis$ = ãèµ€ããããšãçãããšããããšããããã¯æŒãä»ãããŸãããšããããšã¯ãæãé£ããšããããšã¯çºçããªãããšããããšã«ããçããããšããããšã¯ééã£ãŠãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããæãé£ããšããããšã¯çããªã; fact5 & assump1 -> int1: ã·ã¡ã
ã·ãLv.16äºä»¶ãçºçãã; int1 & fact4 -> int2: èµ€ããããšãèµ·ãã; int2 -> int3: èµ€ããããšãçãããæŒãä»ãããŸãããšããããšãçãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} -> ({C} v {D}) fact2: {A} -> {B} fact3: ({JH} v {EA}) fact4: {B} -> {C} fact5: ¬{A} -> {B} ; $hypothesis$ = ¬(¬{A} -> ({C} v {D})) ; $proof$ = | void -> assump1: ¬{A}; fact5 & assump1 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 -> int3: ({C} v {D}); [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã®ã¿ã¡ãLv.62ã¯ç·ã®åããããªã | ¬{A}{a} | fact1: ãã®ã·ã¡ãã·ãLv.84ãåæ®æãããšãããå¯åããªããŠãã€åãé£ããªã fact2: ãã®ãŸããŸã«ãLv.16ã¯æ
ãŸãããªããããã¯ãšãããããšããããšã¯ãªã fact3: ä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯åãé£ããŠç·ã®åãããããšããããšã¯æãç«ããªããšãããšãç·ã®åããããªãããšããããšã¯æ¬åœã§ãã fact4: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å¯åããªããªããããã¯åãé£ãããããç·ã®åãããããšããããšã¯ééãã§ãã fact5: ããä»®ã«ãåãé£ããªããã¢ã³ã¹ã¿ãŒããããšããããã®ã¿ã®ã¿ã¡ãLv.62ã¯ç·ã®åããããªã fact6: æ
ãŸãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã§ããããšããããªãã¢ã³ã¹ã¿ãŒã¯åãé£ããªã | fact1: {D}{b} -> (¬{C}{b} & ¬{B}{b}) fact2: (¬{AA}{aa} & ¬{AB}{aa}) fact3: (x): ¬({B}x & {A}x) -> ¬{A}x fact4: (x): ¬{C}x -> ¬({B}x & {A}x) fact5: (x): ¬{B}x -> ¬{A}{a} fact6: (x): (¬{AA}x & ¬{AB}x) -> ¬{B}x | [
"fact6 -> int1: ããããã®ãŸããŸã«ãLv.16ãæ
ãŸãããªããããã«ãšããããªããšãããåãé£ããªã; int1 & fact2 -> int2: ãã®ãŸããŸã«ãLv.16ã¯åãé£ããšããããšã¯ãªã; int2 -> int3: ãåãé£ããªããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact5 -> hypothesis;"
] | [
"fact6 -> int1: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}; int1 & fact2 -> int2: ¬{B}{aa}; int2 -> int3: (Ex): ¬{B}x; int3 & fact5 -> hypothesis;"
] | ããã®ã¿ã®ã¿ã¡ãLv.62ã¯ç·ã®åãããããšããããšã¯æ£ãã | {A}{a} | [] | 6 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ã¡ãã·ãLv.84ãåæ®æãããšãããå¯åããªããŠãã€åãé£ããªã fact2: ãã®ãŸããŸã«ãLv.16ã¯æ
ãŸãããªããããã¯ãšãããããšããããšã¯ãªã fact3: ä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯åãé£ããŠç·ã®åãããããšããããšã¯æãç«ããªããšãããšãç·ã®åããããªãããšããããšã¯æ¬åœã§ãã fact4: ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å¯åããªããªããããã¯åãé£ãããããç·ã®åãããããšããããšã¯ééãã§ãã fact5: ããä»®ã«ãåãé£ããªããã¢ã³ã¹ã¿ãŒããããšããããã®ã¿ã®ã¿ã¡ãLv.62ã¯ç·ã®åããããªã fact6: æ
ãŸãããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã§ããããšããããªãã¢ã³ã¹ã¿ãŒã¯åãé£ããªã ; $hypothesis$ = ãã®ã¿ã®ã¿ã¡ãLv.62ã¯ç·ã®åããããªã ; $proof$ = | fact6 -> int1: ããããã®ãŸããŸã«ãLv.16ãæ
ãŸãããªããããã«ãšããããªããšãããåãé£ããªã; int1 & fact2 -> int2: ãã®ãŸããŸã«ãLv.16ã¯åãé£ããšããããšã¯ãªã; int2 -> int3: ãåãé£ããªããã¢ã³ã¹ã¿ãŒã¯ãã; int3 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{b} -> (¬{C}{b} & ¬{B}{b}) fact2: (¬{AA}{aa} & ¬{AB}{aa}) fact3: (x): ¬({B}x & {A}x) -> ¬{A}x fact4: (x): ¬{C}x -> ¬({B}x & {A}x) fact5: (x): ¬{B}x -> ¬{A}{a} fact6: (x): (¬{AA}x & ¬{AB}x) -> ¬{B}x ; $hypothesis$ = ¬{A}{a} ; $proof$ = | fact6 -> int1: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}; int1 & fact2 -> int2: ¬{B}{aa}; int2 -> int3: (Ex): ¬{B}x; int3 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽããŽãLv.10ã¯æããšããããšã¯ãªã | ¬{E}{c} | fact1: ãã®ãŽããŽãLv.10ãåãããããªãããã¯æã fact2: ããä»®ã«ãã®ã·ãã·ã¡ãLv.8ããã€ã£ãããšããããšã¯ãªãããã©æããšãããšãã®ãŽããŽãLv.10ã¯æããªã fact3: ããããã®ã·ãã·ã¡ãLv.8ããã€ã£ãããªããã®ãŽããŽã«ãLv.63ã¯ãã€ã£ãã fact4: ä»®ã«ãã®ã·ãã·ã¡ãLv.8ãéäžè¶³ç¡ããšãããšãã®ãŽããŽãLv.10ã¯ãã£ãã fact5: ãã®ãããã¡ãLv.28ã¯å©ãèµ·ãããªã fact6: ä»®ã«ãã®ãŽããŽãLv.10ãæããšããããšã¯ãªããšãããšãã®ã·ãã·ã¡ãLv.8ã¯ãã£ããããããã¯éäžè¶³ç¡ãããããã¯äž¡æ¹ãšãã§ãã fact7: ããä»®ã«ãã®ã·ãã·ã¡ãLv.8ããã€ã£ãããšãããšãã®ãŽããŽãLv.10ã¯ãã£ãã fact8: ãããããã®ãããã¡ãLv.28ã¯å©ãèµ·ãããªãããšããããšã¯æ¬åœã ãšãããšãã®ã·ãã·ã¡ãLv.8ã¯éäžè¶³ç¡ããããã¯ãã€ã£ãã fact9: ããããã®ãŽããŽãLv.10ã¯åãããããªããŠå©ãèµ·ãããªãããšããããšã¯æãç«ããªããªããã®ãããã¡ãLv.28ã¯åãããã fact10: ãããããã®ãŽããŽãLv.10ããã£ãããªããã®ãŽããŽãLv.10ã¯åããããããšããããšã¯çå®ã | fact1: {D}{c} -> {E}{c} fact2: (¬{B}{a} & {E}{a}) -> ¬{E}{c} fact3: {B}{a} -> {B}{hq} fact4: {A}{a} -> {C}{c} fact5: ¬{F}{b} fact6: ¬{E}{c} -> ({C}{a} v {A}{a}) fact7: {B}{a} -> {C}{c} fact8: ¬{F}{b} -> ({A}{a} v {B}{a}) fact9: ¬(¬{D}{c} & ¬{F}{c}) -> {D}{b} fact10: {C}{c} -> {D}{c} | [
"fact5 & fact8 -> int1: ãã®ã·ãã·ã¡ãLv.8ã¯éäžè¶³ç¡ãããããã¯ããã¯ãã€ã£ããããããã¯äž¡æ¹ãšãã ; int1 & fact4 & fact7 -> int2: ãã®ãŽããŽãLv.10ã¯ãã£ãã; int2 & fact10 -> int3: ãã®ãŽããŽãLv.10ã¯åãããã; int3 & fact1 -> hypothesis;"
] | [
"fact5 & fact8 -> int1: ({A}{a} v {B}{a}); int1 & fact4 & fact7 -> int2: {C}{c}; int2 & fact10 -> int3: {D}{c}; int3 & fact1 -> hypothesis;"
] | ãã®ãŽããŽãLv.10ã¯æããšããããšã¯ãªã | ¬{E}{c} | [] | 5 | 4 | 4 | 4 | 4 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽããŽãLv.10ãåãããããªãããã¯æã fact2: ããä»®ã«ãã®ã·ãã·ã¡ãLv.8ããã€ã£ãããšããããšã¯ãªãããã©æããšãããšãã®ãŽããŽãLv.10ã¯æããªã fact3: ããããã®ã·ãã·ã¡ãLv.8ããã€ã£ãããªããã®ãŽããŽã«ãLv.63ã¯ãã€ã£ãã fact4: ä»®ã«ãã®ã·ãã·ã¡ãLv.8ãéäžè¶³ç¡ããšãããšãã®ãŽããŽãLv.10ã¯ãã£ãã fact5: ãã®ãããã¡ãLv.28ã¯å©ãèµ·ãããªã fact6: ä»®ã«ãã®ãŽããŽãLv.10ãæããšããããšã¯ãªããšãããšãã®ã·ãã·ã¡ãLv.8ã¯ãã£ããããããã¯éäžè¶³ç¡ãããããã¯äž¡æ¹ãšãã§ãã fact7: ããä»®ã«ãã®ã·ãã·ã¡ãLv.8ããã€ã£ãããšãããšãã®ãŽããŽãLv.10ã¯ãã£ãã fact8: ãããããã®ãããã¡ãLv.28ã¯å©ãèµ·ãããªãããšããããšã¯æ¬åœã ãšãããšãã®ã·ãã·ã¡ãLv.8ã¯éäžè¶³ç¡ããããã¯ãã€ã£ãã fact9: ããããã®ãŽããŽãLv.10ã¯åãããããªããŠå©ãèµ·ãããªãããšããããšã¯æãç«ããªããªããã®ãããã¡ãLv.28ã¯åãããã fact10: ãããããã®ãŽããŽãLv.10ããã£ãããªããã®ãŽããŽãLv.10ã¯åããããããšããããšã¯çå®ã ; $hypothesis$ = ãã®ãŽããŽãLv.10ã¯æããšããããšã¯ãªã ; $proof$ = | fact5 & fact8 -> int1: ãã®ã·ãã·ã¡ãLv.8ã¯éäžè¶³ç¡ãããããã¯ããã¯ãã€ã£ããããããã¯äž¡æ¹ãšãã ; int1 & fact4 & fact7 -> int2: ãã®ãŽããŽãLv.10ã¯ãã£ãã; int2 & fact10 -> int3: ãã®ãŽããŽãLv.10ã¯åãããã; int3 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{c} -> {E}{c} fact2: (¬{B}{a} & {E}{a}) -> ¬{E}{c} fact3: {B}{a} -> {B}{hq} fact4: {A}{a} -> {C}{c} fact5: ¬{F}{b} fact6: ¬{E}{c} -> ({C}{a} v {A}{a}) fact7: {B}{a} -> {C}{c} fact8: ¬{F}{b} -> ({A}{a} v {B}{a}) fact9: ¬(¬{D}{c} & ¬{F}{c}) -> {D}{b} fact10: {C}{c} -> {D}{c} ; $hypothesis$ = ¬{E}{c} ; $proof$ = | fact5 & fact8 -> int1: ({A}{a} v {B}{a}); int1 & fact4 & fact7 -> int2: {C}{c}; int2 & fact10 -> int3: {D}{c}; int3 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããŽã«ãŽãLv.49äºä»¶ãçãã | {A} | fact1: ããŽããŽãLv.45äºä»¶ã¯èµ·ããªãããšããããšã¯ãŽã«ãŽãLv.49äºä»¶ããã³ãœããœã¡ãLv.26äºä»¶ãèµ·ãããåå ã fact2: ãŽããŽãLv.45äºä»¶ãçºçãã fact3: ãœããœã¡ãLv.26äºä»¶ãçºçãã | fact1: ({A} & {B}) -> ¬{C} fact2: {C} fact3: {B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããŽã«ãŽãLv.49äºä»¶ãçãã; assump1 & fact3 -> int1: ãŽã«ãŽãLv.49äºä»¶ããã³ãœããœã¡ãLv.26äºä»¶ã©ã¡ãããçºçãã; int1 & fact1 -> int2: ãŽããŽãLv.45äºä»¶ã¯çºçããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããŽããŽãLv.45äºä»¶ã¯èµ·ããªãããšããããšã¯ãŽã«ãŽãLv.49äºä»¶ããã³ãœããœã¡ãLv.26äºä»¶ãèµ·ãããåå ã fact2: ãŽããŽãLv.45äºä»¶ãçºçãã fact3: ãœããœã¡ãLv.26äºä»¶ãçºçãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããŽã«ãŽãLv.49äºä»¶ãçãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããŽã«ãŽãLv.49äºä»¶ãçãã; assump1 & fact3 -> int1: ãŽã«ãŽãLv.49äºä»¶ããã³ãœããœã¡ãLv.26äºä»¶ã©ã¡ãããçºçãã; int1 & fact1 -> int2: ãŽããŽãLv.45äºä»¶ã¯çºçããªã; int2 & fact2 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: {C} fact3: {B} ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: {A}; assump1 & fact3 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ãããä»®ã«èª¿ã¹åºãããšãèµ·ãããšãããšã埡å®ããšããããšã¯èµ·ãããªãããã©ä»çãæããšããããšãèµ·ããããšããããšã¯ééãã ããšããããšã¯æãç«ããªã | ¬({A} -> ¬(¬{E} & {D})) | fact1: ã·ã«ã·ãªLv.5äºä»¶ãèµ·ããã°ã埡å®ããšããããšã¯èµ·ãããªãäžæ¹ã§ä»çãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact2: ãããã·ã«ã·ãªLv.5äºä»¶ãèµ·ãããšãããã埡å®ããšããããšãèµ·ãããããŸãã«ä»çãæããšããããšãçºçããããšããããšã¯èª€ãã ããšããããšã¯æãç«ã€ fact3: ããä»®ã«ã調ã¹åºãããšãèµ·ããããšããããšã¯äºå®ã§ãããšãããšã埡å®ããšããããšããã³ä»çãæããšããããšäž¡æ¹ãèµ·ããããšããããšã¯ééãã fact4: åŸå±ããããšãèµ·ãã fact5: ãåŠå®ãé£ããšããããšããã³ã€ããªããšããããšäž¡æ¹ãšããçããããšããããšã¯ééãã fact6: 調ã¹åºãããšã¯ãæšæããããšã¯çºçããªãããšããããšãåé¿ãã fact7: 埡å®ããšããããšã§ã¯ãªããŠä»çãæããšããããšãçãã fact8: æšæããããšãçºçãããšããããšã¯ãã·ã«ã·ãªLv.5äºä»¶ã¯èµ·ããªãããšããããšãé»ã | fact1: {C} -> ¬(¬{E} & {D}) fact2: {C} -> ¬({E} & {D}) fact3: {A} -> ¬({E} & {D}) fact4: {DT} fact5: ¬({AM} & {DM}) fact6: {A} -> {B} fact7: (¬{E} & {D}) fact8: {B} -> {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããã調ã¹åºãããšãçºçãã; fact6 & assump1 -> int1: æšæããããšãçãã; int1 & fact8 -> int2: ã·ã«ã·ãªLv.5äºä»¶ãèµ·ãã; int2 & fact1 -> int3: ã埡å®ããšããããšã¯èµ·ããªããä»çãæããšããããšãèµ·ããããšããããšã¯äºå®ã§ãªã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; fact6 & assump1 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact1 -> int3: ¬(¬{E} & {D}); [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 5 | 0 | 5 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ã·ã«ã·ãªLv.5äºä»¶ãèµ·ããã°ã埡å®ããšããããšã¯èµ·ãããªãäžæ¹ã§ä»çãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact2: ãããã·ã«ã·ãªLv.5äºä»¶ãèµ·ãããšãããã埡å®ããšããããšãèµ·ãããããŸãã«ä»çãæããšããããšãçºçããããšããããšã¯èª€ãã ããšããããšã¯æãç«ã€ fact3: ããä»®ã«ã調ã¹åºãããšãèµ·ããããšããããšã¯äºå®ã§ãããšãããšã埡å®ããšããããšããã³ä»çãæããšããããšäž¡æ¹ãèµ·ããããšããããšã¯ééãã fact4: åŸå±ããããšãèµ·ãã fact5: ãåŠå®ãé£ããšããããšããã³ã€ããªããšããããšäž¡æ¹ãšããçããããšããããšã¯ééãã fact6: 調ã¹åºãããšã¯ãæšæããããšã¯çºçããªãããšããããšãåé¿ãã fact7: 埡å®ããšããããšã§ã¯ãªããŠä»çãæããšããããšãçãã fact8: æšæããããšãçºçãããšããããšã¯ãã·ã«ã·ãªLv.5äºä»¶ã¯èµ·ããªãããšããããšãé»ã ; $hypothesis$ = ãããä»®ã«èª¿ã¹åºãããšãèµ·ãããšãããšã埡å®ããšããããšã¯èµ·ãããªãããã©ä»çãæããšããããšãèµ·ããããšããããšã¯ééãã ããšããããšã¯æãç«ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããã調ã¹åºãããšãçºçãã; fact6 & assump1 -> int1: æšæããããšãçãã; int1 & fact8 -> int2: ã·ã«ã·ãªLv.5äºä»¶ãèµ·ãã; int2 & fact1 -> int3: ã埡å®ããšããããšã¯èµ·ããªããä»çãæããšããããšãèµ·ããããšããããšã¯äºå®ã§ãªã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C} -> ¬(¬{E} & {D}) fact2: {C} -> ¬({E} & {D}) fact3: {A} -> ¬({E} & {D}) fact4: {DT} fact5: ¬({AM} & {DM}) fact6: {A} -> {B} fact7: (¬{E} & {D}) fact8: {B} -> {C} ; $hypothesis$ = ¬({A} -> ¬(¬{E} & {D})) ; $proof$ = | void -> assump1: {A}; fact6 & assump1 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact1 -> int3: ¬(¬{E} & {D}); [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ããããåãèœãšããªããªãã°ãèš³ç¡ããªãäžæ¹ã§æ¡ãæãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯åœã | ¬((Ex): ¬{A}x -> ¬(¬{AA}x & {AB}x)) | fact1: ããä»®ã«ãã®ãã¡ããã¡ã
Lv.66ã¯åãèœãšããªããªãããã®ãã¡ããã¡ã
Lv.66ã¯èš³ç¡ããšããããšã¯ãªãããããæ¡ãæãããšããããšã¯ééã£ãŠãã fact2: ãããä»®ã«ç·ã£ãœããšãããšãåã£ä»ããªãäžæ¹ã§èšè°ãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã fact3: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯æãããªãããšããããšã¯äºå®ã§ãããšããããèŠå¢ç¡ããªããããã€ãªãããšããããšã¯æãç«ããªã fact4: ããããã®ãã¡ããã¡ã
Lv.66ã¯åãèœãšããªããšããããããã¯èš³ç¡ããŠå ããŠæ¡ãæãããšããããšã¯æãç«ããªã fact5: ããããèŠå¢ç¡ããšãããšãæž©ããšããããšã¯ãªããŠèšè°ãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ãããåžžé£ããããªããªãã°åºããªããæŽã«è³ã
ãããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: ¬{A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact2: (Ex): {DH}x -> ¬(¬{CP}x & {EC}x) fact3: (x): ¬{J}x -> ¬(¬{AI}x & {U}x) fact4: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact5: (Ex): {AI}x -> ¬(¬{HQ}x & {EC}x) fact6: (Ex): ¬{IJ}x -> (¬{DA}x & {JF}x) | [
"fact1 -> hypothesis;"
] | [
"fact1 -> hypothesis;"
] | ãæãããªããšãããšãèŠå¢ç¡ããªããã©ããã€ãªãããšããããšã¯èª€ãã§ãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{J}x -> ¬(¬{AI}x & {U}x) | [
"fact7 -> int1: ãã®ã¿ã¡ã
ã¿ãLv.50ã¯æãããªããšãããããã®ã¿ã¡ã
ã¿ãLv.50ã¯èŠå¢ç¡ããªãããã©ããã€ãªãããšããããšã¯æãç«ããªã; int1 -> hypothesis;"
] | 2 | 1 | 1 | 1 | 1 | 5 | 0 | 5 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ããä»®ã«ãã®ãã¡ããã¡ã
Lv.66ã¯åãèœãšããªããªãããã®ãã¡ããã¡ã
Lv.66ã¯èš³ç¡ããšããããšã¯ãªãããããæ¡ãæãããšããããšã¯ééã£ãŠãã fact2: ãããä»®ã«ç·ã£ãœããšãããšãåã£ä»ããªãäžæ¹ã§èšè°ãããšããããšã¯ééããªãã¢ã³ã¹ã¿ãŒã¯ãã fact3: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯æãããªãããšããããšã¯äºå®ã§ãããšããããèŠå¢ç¡ããªããããã€ãªãããšããããšã¯æãç«ããªã fact4: ããããã®ãã¡ããã¡ã
Lv.66ã¯åãèœãšããªããšããããããã¯èš³ç¡ããŠå ããŠæ¡ãæãããšããããšã¯æãç«ããªã fact5: ããããèŠå¢ç¡ããšãããšãæž©ããšããããšã¯ãªããŠèšè°ãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ãããåžžé£ããããªããªãã°åºããªããæŽã«è³ã
ãããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ããããåãèœãšããªããªãã°ãèš³ç¡ããªãäžæ¹ã§æ¡ãæãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯åœã ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{aa} -> ¬(¬{AA}{aa} & {AB}{aa}) fact2: (Ex): {DH}x -> ¬(¬{CP}x & {EC}x) fact3: (x): ¬{J}x -> ¬(¬{AI}x & {U}x) fact4: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact5: (Ex): {AI}x -> ¬(¬{HQ}x & {EC}x) fact6: (Ex): ¬{IJ}x -> (¬{DA}x & {JF}x) ; $hypothesis$ = ¬((Ex): ¬{A}x -> ¬(¬{AA}x & {AB}x)) ; $proof$ = | fact1 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ãããåŒè§£ããŸãããšããããšãèµ·ãã | {B} | fact1: ãŽããŽãLv.29äºä»¶ãçºçãã | fact1: {C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããåŒè§£ããŸãããšããããšãèµ·ãã; assump1 -> int1: å°ãªããšããããšããããã¯åŒè§£ããŸãããšããããšãèµ·ãã;"
] | [
"void -> assump1: {B}; assump1 -> int1: ({A} v {B});"
] | null | null | [] | null | 5 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãŽããŽãLv.29äºä»¶ãçºçãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããåŒè§£ããŸãããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C} ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | çºçãé£ããšããããšãçããããã®äžãœã«ããœã«ãLv.78äºä»¶ãèµ·ãã | ({D} & {E}) | fact1: ãŸããŸã«ã
Lv.88äºä»¶ãèµ·ãããšããããšã¯ãã·ã¡ã
ã·ãLv.77äºä»¶ã¯èµ·ããªãããšããããšãé²ã fact2: èŒãããšããããšãèµ·ãã fact3: ãèŒãããšããããšãçããããšããããšã¯ãŸããŸã«ã
Lv.88äºä»¶ã®ãã£ãããšãªã fact4: éæãæããšããããšãèµ·ãã fact5: ã·ã¡ã
ã·ãLv.77äºä»¶ã¯ãçºçãé£ããšããããšã¯çããªãããšããããšãé»ã | fact1: {B} -> {C} fact2: {A} fact3: {A} -> {B} fact4: {JF} fact5: {C} -> {D} | [
"fact3 & fact2 -> int1: ããŸããŸã«ã
Lv.88äºä»¶ãèµ·ããããšããããšã¯æ£ãã; int1 & fact1 -> int2: ã·ã¡ã
ã·ãLv.77äºä»¶ãçºçãã; int2 & fact5 -> int3: ãçºçãé£ããšããããšãèµ·ããããšããããšã¯çå®ã ;"
] | [
"fact3 & fact2 -> int1: {B}; int1 & fact1 -> int2: {C}; int2 & fact5 -> int3: {D};"
] | null | null | [] | null | 4 | 4 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãŸããŸã«ã
Lv.88äºä»¶ãèµ·ãããšããããšã¯ãã·ã¡ã
ã·ãLv.77äºä»¶ã¯èµ·ããªãããšããããšãé²ã fact2: èŒãããšããããšãèµ·ãã fact3: ãèŒãããšããããšãçããããšããããšã¯ãŸããŸã«ã
Lv.88äºä»¶ã®ãã£ãããšãªã fact4: éæãæããšããããšãèµ·ãã fact5: ã·ã¡ã
ã·ãLv.77äºä»¶ã¯ãçºçãé£ããšããããšã¯çããªãããšããããšãé»ã ; $hypothesis$ = çºçãé£ããšããããšãçããããã®äžãœã«ããœã«ãLv.78äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} -> {C} fact2: {A} fact3: {A} -> {B} fact4: {JF} fact5: {C} -> {D} ; $hypothesis$ = ({D} & {E}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãããæžããªããå¿ å®å¿ å®ããããããã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯æ£ãããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> ¬({AA}x v ¬{AB}x) | fact1: ãã®ã¿ã¡ãã¿ã«ãLv.3ã¯ç³åããšãããšãããã¯éäžè¶³ç¡ãããšããããšã¯äºå®ã fact2: ãä»®ã«çãé£ããšãããæãæ²ããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããã銬鹿ããããšãããšãå®è¡ãæãããŸãã¯äžžãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact4: äœããã®ã¢ã³ã¹ã¿ãŒã¯æžããªããå¿ å®å¿ å®ããããŸãã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã | fact1: {FJ}{aa} -> {JH}{aa} fact2: (Ex): {JB}x -> {FN}x fact3: (Ex): {IN}x -> ¬({O}x v {FG}x) fact4: (x): {A}x -> ¬({AA}x v ¬{AB}x) | [
"fact4 -> int1: ãããã®ã¿ã¡ãã¿ã«ãLv.3ã¯æžããªãã°ããã®ã¿ã¡ãã¿ã«ãLv.3ã¯å¿ å®å¿ å®ããããããã¯ããã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã ; int1 -> hypothesis;"
] | [
"fact4 -> int1: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}); int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã¿ã¡ãã¿ã«ãLv.3ã¯ç³åããšãããšãããã¯éäžè¶³ç¡ãããšããããšã¯äºå®ã fact2: ãä»®ã«çãé£ããšãããæãæ²ããã¢ã³ã¹ã¿ãŒã¯ãã fact3: ããã銬鹿ããããšãããšãå®è¡ãæãããŸãã¯äžžãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã fact4: äœããã®ã¢ã³ã¹ã¿ãŒã¯æžããªããå¿ å®å¿ å®ããããŸãã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã ; $hypothesis$ = ãããæžããªããå¿ å®å¿ å®ããããããã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯æ£ãããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact4 -> int1: ãããã®ã¿ã¡ãã¿ã«ãLv.3ã¯æžããªãã°ããã®ã¿ã¡ãã¿ã«ãLv.3ã¯å¿ å®å¿ å®ããããããã¯ããã¯åœ¢æãæããªãããããã¯ã©ã¡ããã ããšããããšã¯ééãã ; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: {FJ}{aa} -> {JH}{aa} fact2: (Ex): {JB}x -> {FN}x fact3: (Ex): {IN}x -> ¬({O}x v {FG}x) fact4: (x): {A}x -> ¬({AA}x v ¬{AB}x) ; $hypothesis$ = (Ex): {A}x -> ¬({AA}x v ¬{AB}x) ; $proof$ = | fact4 -> int1: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}); int1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãã«ãã«ãLv.68ã¯åŸ¡èŠ§ã«æããªã | ¬{F}{b} | fact1: ããä»®ã«ãã®ãŽãªãŽãLv.93ãè²·ãæããšããããã®ãŽãªãŽãLv.93ã¯åãã fact2: ãã®ãŽãªãŽãLv.93ã¯è²·ãæã fact3: ããä»®ã«ããã®ãŽãªãŽãLv.93ã¯èããé£ããªããŠééãç¡ããªãããšããããšã¯æãç«ã€ãšããããã®ãã«ãã«ãLv.68ã¯åŸ¡èŠ§ã«æã fact4: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯è²·ãæããªããŠãã®äžå°æããªãããšããããšã¯æãç«ããªããªãè²·ãæã fact5: ä»®ã«ãã®ãŽãªãŽãLv.93ãåãããšãããšãã®ãŽãªãŽãLv.93ã¯å°æã fact6: ä»®ã«ãã®ãŽãªãŽãLv.93ãå°æããšãããšããã¯èããé£ããªããŠééãç¡ããªã | fact1: {A}{a} -> {B}{a} fact2: {A}{a} fact3: (¬{E}{a} & ¬{D}{a}) -> {F}{b} fact4: (x): ¬(¬{A}x & ¬{C}x) -> {A}x fact5: {B}{a} -> {C}{a} fact6: {C}{a} -> (¬{E}{a} & ¬{D}{a}) | [
"fact1 & fact2 -> int1: ããã®ãŽãªãŽãLv.93ã¯åããããšããããšã¯çå®ã§ãã; int1 & fact5 -> int2: ãã®ãŽãªãŽãLv.93ã¯å°æã; int2 & fact6 -> int3: ãã®ãŽãªãŽãLv.93ã¯èããé£ããšããããšã¯ãªãããã€ééãç¡ããªã; int3 & fact3 -> hypothesis;"
] | [
"fact1 & fact2 -> int1: {B}{a}; int1 & fact5 -> int2: {C}{a}; int2 & fact6 -> int3: (¬{E}{a} & ¬{D}{a}); int3 & fact3 -> hypothesis;"
] | ãã®ãã«ãããLv.75ã¯èããé£ã | {E}{es} | [
"fact7 -> int4: ãããããã®ãã«ãããLv.75ã¯è²·ãæããªããŠå°æããªãããšããããšã¯æãç«ããªããšãããšè²·ãæã;"
] | 6 | 4 | 4 | 4 | 4 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŽãªãŽãLv.93ãè²·ãæããšããããã®ãŽãªãŽãLv.93ã¯åãã fact2: ãã®ãŽãªãŽãLv.93ã¯è²·ãæã fact3: ããä»®ã«ããã®ãŽãªãŽãLv.93ã¯èããé£ããªããŠééãç¡ããªãããšããããšã¯æãç«ã€ãšããããã®ãã«ãã«ãLv.68ã¯åŸ¡èŠ§ã«æã fact4: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯è²·ãæããªããŠãã®äžå°æããªãããšããããšã¯æãç«ããªããªãè²·ãæã fact5: ä»®ã«ãã®ãŽãªãŽãLv.93ãåãããšãããšãã®ãŽãªãŽãLv.93ã¯å°æã fact6: ä»®ã«ãã®ãŽãªãŽãLv.93ãå°æããšãããšããã¯èããé£ããªããŠééãç¡ããªã ; $hypothesis$ = ãã®ãã«ãã«ãLv.68ã¯åŸ¡èŠ§ã«æããªã ; $proof$ = | fact1 & fact2 -> int1: ããã®ãŽãªãŽãLv.93ã¯åããããšããããšã¯çå®ã§ãã; int1 & fact5 -> int2: ãã®ãŽãªãŽãLv.93ã¯å°æã; int2 & fact6 -> int3: ãã®ãŽãªãŽãLv.93ã¯èããé£ããšããããšã¯ãªãããã€ééãç¡ããªã; int3 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: {A}{a} fact3: (¬{E}{a} & ¬{D}{a}) -> {F}{b} fact4: (x): ¬(¬{A}x & ¬{C}x) -> {A}x fact5: {B}{a} -> {C}{a} fact6: {C}{a} -> (¬{E}{a} & ¬{D}{a}) ; $hypothesis$ = ¬{F}{b} ; $proof$ = | fact1 & fact2 -> int1: {B}{a}; int1 & fact5 -> int2: {C}{a}; int2 & fact6 -> int3: (¬{E}{a} & ¬{D}{a}); int3 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ãããããé£è¡æ©ããã | ({C}{b} & {D}{b}) | fact1: ãã®ãŽã¡ããŽã¡ãLv.15ã¯é£è¡æ©ããã fact2: ãã®ã¿ã¡ãã¿ãLv.51ã¯åãæã fact3: ãæå±ãããæŽã«åãæããã¢ã³ã¹ã¿ãŒããããšããããã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ã fact4: ããã¢ã³ã¹ã¿ãŒã¯ç»å±±åºæ¥ã fact5: ãã®ã¿ã¡ãã¿ãLv.51ã¯æå±ãã | fact1: {D}{b} fact2: {B}{a} fact3: (x): ({A}x & {B}x) -> {C}{b} fact4: (Ex): {C}x fact5: {A}{a} | [
"fact5 & fact2 -> int1: ãã®ã¿ã¡ãã¿ãLv.51ã¯æå±ãããåãæã; int1 -> int2: ãšããã¢ã³ã¹ã¿ãŒã¯æå±ãããããã¯åãæã; int2 & fact3 -> int3: ãã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ã; int3 & fact1 -> hypothesis;"
] | [
"fact5 & fact2 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact3 -> int3: {C}{b}; int3 & fact1 -> hypothesis;"
] | ããã¢ã³ã¹ã¿ãŒã¯ãµããŒããããããŸãã«è¿ãã | (Ex): ({DN}x & {JJ}x) | [] | 5 | 4 | 4 | 4 | 4 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽã¡ããŽã¡ãLv.15ã¯é£è¡æ©ããã fact2: ãã®ã¿ã¡ãã¿ãLv.51ã¯åãæã fact3: ãæå±ãããæŽã«åãæããã¢ã³ã¹ã¿ãŒããããšããããã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ã fact4: ããã¢ã³ã¹ã¿ãŒã¯ç»å±±åºæ¥ã fact5: ãã®ã¿ã¡ãã¿ãLv.51ã¯æå±ãã ; $hypothesis$ = ãã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ãããããé£è¡æ©ããã ; $proof$ = | fact5 & fact2 -> int1: ãã®ã¿ã¡ãã¿ãLv.51ã¯æå±ãããåãæã; int1 -> int2: ãšããã¢ã³ã¹ã¿ãŒã¯æå±ãããããã¯åãæã; int2 & fact3 -> int3: ãã®ãŽã¡ããŽã¡ãLv.15ã¯ç»å±±åºæ¥ã; int3 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {D}{b} fact2: {B}{a} fact3: (x): ({A}x & {B}x) -> {C}{b} fact4: (Ex): {C}x fact5: {A}{a} ; $hypothesis$ = ({C}{b} & {D}{b}) ; $proof$ = | fact5 & fact2 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact3 -> int3: {C}{b}; int3 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ãLv.87ã¯ã²ããããªã | ¬{F}{d} | fact1: ãã®ãœã«ã
ãœãLv.90ã¯éã fact2: ãã®ãœã«ã
ãœãLv.90ã¯çãæã fact3: ä»®ã«ãã®ãŸããŸã«ãLv.90ãå¿è匷ããªããããããžã°ãä»ããªããšããã°ãã®ã·ãã·ãLv.87ã¯ã²ããããªã fact4: ããããã®ã¿ã®ã¿ã¡ã
Lv.36ãå¿è匷ããªããªãã°ãã®ãŸããŸã«ãLv.90ã¯å¿è匷ããªããŠããã«ããã¯ãžã°ãä»ããšããããšã¯ãªã fact5: éãã¢ã³ã¹ã¿ãŒã¯ã²ããã fact6: ããã®ãœã«ã
ãœãLv.90ã¯éãããšããããšã¯æ£ãããšãããæ ã | fact1: {A}{a} fact2: {C}{a} fact3: (¬{D}{c} & ¬{E}{c}) -> ¬{F}{d} fact4: ¬{D}{b} -> (¬{D}{c} & ¬{E}{c}) fact5: (x): {A}x -> {F}x fact6: {A}{a} -> {B}{a} | [
"fact6 & fact1 -> int1: ãã®ãœã«ã
ãœãLv.90ã¯æ ã; int1 & fact2 -> int2: ãã®ãœã«ã
ãœãLv.90ã¯æ ããçãæã;"
] | [
"fact6 & fact1 -> int1: {B}{a}; int1 & fact2 -> int2: ({B}{a} & {C}{a});"
] | ãã®ã·ãã·ãLv.87ã¯ã²ããã | {F}{d} | [
"fact7 -> int3: ä»®ã«ãã®ã·ãã·ãLv.87ãéããšãããšãã®ã·ãã·ãLv.87ã¯ã²ããã;"
] | 6 | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãœã«ã
ãœãLv.90ã¯éã fact2: ãã®ãœã«ã
ãœãLv.90ã¯çãæã fact3: ä»®ã«ãã®ãŸããŸã«ãLv.90ãå¿è匷ããªããããããžã°ãä»ããªããšããã°ãã®ã·ãã·ãLv.87ã¯ã²ããããªã fact4: ããããã®ã¿ã®ã¿ã¡ã
Lv.36ãå¿è匷ããªããªãã°ãã®ãŸããŸã«ãLv.90ã¯å¿è匷ããªããŠããã«ããã¯ãžã°ãä»ããšããããšã¯ãªã fact5: éãã¢ã³ã¹ã¿ãŒã¯ã²ããã fact6: ããã®ãœã«ã
ãœãLv.90ã¯éãããšããããšã¯æ£ãããšãããæ ã ; $hypothesis$ = ãã®ã·ãã·ãLv.87ã¯ã²ããããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} fact2: {C}{a} fact3: (¬{D}{c} & ¬{E}{c}) -> ¬{F}{d} fact4: ¬{D}{b} -> (¬{D}{c} & ¬{E}{c}) fact5: (x): {A}x -> {F}x fact6: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{F}{d} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœã«ããœã¡ãLv.86ã¯èŠããæããªã | ¬{A}{a} | fact1: ãã®ãœã«ããœã¡ãLv.86ã¯é£ãèŸã fact2: ããããã®ãœã«ããœã¡ãLv.86ãèŠããæããŠãŸãé£ãèŸããªãã°ãã®ãœã«ããœã¡ãLv.86ã¯è¡æ£èããšããããšã¯ãªã fact3: ãã®ã¿ãªã¿ã«ãLv.81ã¯æãã fact4: ãã®ã¿ãªã¿ã«ãLv.81ãé£ãèŸããšãããšãã®ãœã«ããœã¡ãLv.86ã¯èŠããæã fact5: ãã®ã¿ãªã¿ã«ãLv.81ãæãããšããããã®ãœã«ããœã¡ãLv.86ã¯åã fact6: ãã®ãŽããŽã¡ãLv.35ã¯ææ
šæ·±ããããã«ä¹
ãã fact7: ãã®ãŸããŸã®Lv.22ã¯é£ãèŸã | fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{a} fact3: {F}{b} fact4: {B}{b} -> {A}{a} fact5: {F}{b} -> {D}{a} fact6: ({FB}{bd} & {E}{bd}) fact7: {B}{bg} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã¡ãLv.86ã¯èŠããæã; assump1 & fact1 -> int1: ãã®ãœã«ããœã¡ãLv.86ã¯èŠããæããé£ãèŸã; int1 & fact2 -> int2: ãã®ãœã«ããœã¡ãLv.86ã¯è¡æ£èããªã;"
] | [
"void -> assump1: {A}{a}; assump1 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{a};"
] | 以äžã®ããã«ä»®å®ããããã®ãœã«ããœã¡ãLv.86ã¯èŠããæã | {A}{a} | [] | 5 | 5 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãœã«ããœã¡ãLv.86ã¯é£ãèŸã fact2: ããããã®ãœã«ããœã¡ãLv.86ãèŠããæããŠãŸãé£ãèŸããªãã°ãã®ãœã«ããœã¡ãLv.86ã¯è¡æ£èããšããããšã¯ãªã fact3: ãã®ã¿ãªã¿ã«ãLv.81ã¯æãã fact4: ãã®ã¿ãªã¿ã«ãLv.81ãé£ãèŸããšãããšãã®ãœã«ããœã¡ãLv.86ã¯èŠããæã fact5: ãã®ã¿ãªã¿ã«ãLv.81ãæãããšããããã®ãœã«ããœã¡ãLv.86ã¯åã fact6: ãã®ãŽããŽã¡ãLv.35ã¯ææ
šæ·±ããããã«ä¹
ãã fact7: ãã®ãŸããŸã®Lv.22ã¯é£ãèŸã ; $hypothesis$ = ãã®ãœã«ããœã¡ãLv.86ã¯èŠããæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{a} fact3: {F}{b} fact4: {B}{b} -> {A}{a} fact5: {F}{b} -> {D}{a} fact6: ({FB}{bd} & {E}{bd}) fact7: {B}{bg} ; $hypothesis$ = ¬{A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ãããåçŽéããããšã¯çºçããªã | ¬{A} | fact1: ã·ã¡ãã·ãLv.19äºä»¶ãèµ·ãã fact2: ããä»®ã«åçŽéããããšã¯èµ·ããªããšããã°ããŽãªãŽãLv.94äºä»¶ã§ã¯ãªããŠå¹³ã¹ã£ãããšããããšãçããããšããããšã¯èª€ãã fact3: ç©çããããšããããšã¯ãã·ã¡ãã·ãLv.19äºä»¶ãèµ·ããããã©åçŽéããããšã¯çããªãããšããããšã«é»ãŸãã fact4: ãå·®ãåºããŸãããšããããšãçºçãããããããŽããŽãLv.43äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact5: ãŽãªãŽãLv.94äºä»¶ã¯ãã·ã¡ãã·ãLv.19äºä»¶ã¯èµ·ãããªãããšããããšãåŒãèµ·ãã fact6: ããä»®ã«ããŽãªãŽãLv.94äºä»¶ã§ã¯ãªãå¹³ã¹ã£ãããšããããšãèµ·ããããšããããšã¯æãç«ããªããªãã°ã·ã¡ãã·ãLv.19äºä»¶ã¯èµ·ããªã | fact1: {B} fact2: ¬{A} -> ¬(¬{AA} & {AB}) fact3: ({B} & ¬{A}) -> ¬{EE} fact4: ¬({GL} & {FM}) fact5: {AA} -> ¬{B} fact6: ¬(¬{AA} & {AB}) -> ¬{B} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããåçŽéããããšã¯çºçããªã; fact2 & assump1 -> int1: ããŽãªãŽãLv.94äºä»¶ãçºçããªããã©å¹³ã¹ã£ãããšããããšã¯çºçããããšããããšã¯èª€ã£ãŠãã; int1 & fact6 -> int2: ã·ã¡ãã·ãLv.19äºä»¶ã¯çºçããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: ¬{A}; fact2 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact6 -> int2: ¬{B}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ç©çããããšããããšã¯çºçããªã | ¬{EE} | [] | 6 | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ã·ã¡ãã·ãLv.19äºä»¶ãèµ·ãã fact2: ããä»®ã«åçŽéããããšã¯èµ·ããªããšããã°ããŽãªãŽãLv.94äºä»¶ã§ã¯ãªããŠå¹³ã¹ã£ãããšããããšãçããããšããããšã¯èª€ãã fact3: ç©çããããšããããšã¯ãã·ã¡ãã·ãLv.19äºä»¶ãèµ·ããããã©åçŽéããããšã¯çããªãããšããããšã«é»ãŸãã fact4: ãå·®ãåºããŸãããšããããšãçºçãããããããŽããŽãLv.43äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact5: ãŽãªãŽãLv.94äºä»¶ã¯ãã·ã¡ãã·ãLv.19äºä»¶ã¯èµ·ãããªãããšããããšãåŒãèµ·ãã fact6: ããä»®ã«ããŽãªãŽãLv.94äºä»¶ã§ã¯ãªãå¹³ã¹ã£ãããšããããšãèµ·ããããšããããšã¯æãç«ããªããªãã°ã·ã¡ãã·ãLv.19äºä»¶ã¯èµ·ããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ãããåçŽéããããšã¯çºçããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããåçŽéããããšã¯çºçããªã; fact2 & assump1 -> int1: ããŽãªãŽãLv.94äºä»¶ãçºçããªããã©å¹³ã¹ã£ãããšããããšã¯çºçããããšããããšã¯èª€ã£ãŠãã; int1 & fact6 -> int2: ã·ã¡ãã·ãLv.19äºä»¶ã¯çºçããªã; int2 & fact1 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} fact2: ¬{A} -> ¬(¬{AA} & {AB}) fact3: ({B} & ¬{A}) -> ¬{EE} fact4: ¬({GL} & {FM}) fact5: {AA} -> ¬{B} fact6: ¬(¬{AA} & {AB}) -> ¬{B} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: ¬{A}; fact2 & assump1 -> int1: ¬(¬{AA} & {AB}); int1 & fact6 -> int2: ¬{B}; int2 & fact1 -> int3: #F#; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | åæ¢ããããšãèµ·ãã | {D} | fact1: ãè¿œãæãå§ããããšã¯çºçããªãããšããããšã¯ã·ã«ã·ã¡ã
Lv.91äºä»¶ãšåŸ¡ãã§ãããšããããšãçãããçãããã fact2: 埡ãã§ãããšããããšãèµ·ãã fact3: ç»é²åºæ¥ãããšãšè¿œãæãå§ããããšäž¡æ¹ãšããçºçãã fact4: ãåæ¢ããããšãçããããšããããšã¯ã埡ãã§ãããšããããšããã³åŒããšããããšäž¡æ¹ãšããèµ·ããããšããããšã«é»ãŸãã fact5: åŒããšããããšã¯ç»é²åºæ¥ãããšããã£ããã | fact1: ¬{E} -> ({IB} & {C}) fact2: {C} fact3: ({A} & {E}) fact4: ({C} & {B}) -> ¬{D} fact5: {A} -> {B} | [
"fact3 -> int1: ç»é²åºæ¥ãããšãèµ·ãã; fact5 & int1 -> int2: åŒããšããããšãçãã; int2 & fact2 -> int3: 埡ãã§ãããšããããšãèµ·ãããå ããŠåŒããšããããšãçãã; int3 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: {A}; fact5 & int1 -> int2: {B}; int2 & fact2 -> int3: ({C} & {B}); int3 & fact4 -> hypothesis;"
] | çãæããšããããšãšã·ã«ã·ã¡ã
Lv.91äºä»¶äž¡æ¹ãšããçºçãã | ({AJ} & {IB}) | [] | 4 | 4 | 4 | 4 | 4 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãè¿œãæãå§ããããšã¯çºçããªãããšããããšã¯ã·ã«ã·ã¡ã
Lv.91äºä»¶ãšåŸ¡ãã§ãããšããããšãçãããçãããã fact2: 埡ãã§ãããšããããšãèµ·ãã fact3: ç»é²åºæ¥ãããšãšè¿œãæãå§ããããšäž¡æ¹ãšããçºçãã fact4: ãåæ¢ããããšãçããããšããããšã¯ã埡ãã§ãããšããããšããã³åŒããšããããšäž¡æ¹ãšããèµ·ããããšããããšã«é»ãŸãã fact5: åŒããšããããšã¯ç»é²åºæ¥ãããšããã£ããã ; $hypothesis$ = åæ¢ããããšãèµ·ãã ; $proof$ = | fact3 -> int1: ç»é²åºæ¥ãããšãèµ·ãã; fact5 & int1 -> int2: åŒããšããããšãçãã; int2 & fact2 -> int3: 埡ãã§ãããšããããšãèµ·ãããå ããŠåŒããšããããšãçãã; int3 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{E} -> ({IB} & {C}) fact2: {C} fact3: ({A} & {E}) fact4: ({C} & {B}) -> ¬{D} fact5: {A} -> {B} ; $hypothesis$ = {D} ; $proof$ = | fact3 -> int1: {A}; fact5 & int1 -> int2: {B}; int2 & fact2 -> int3: ({C} & {B}); int3 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯èµ·ããªã | ¬{G} | fact1: ã¿ãã¿ã«Lv.30äºä»¶ãèµ·ãããªããšããããšã¯æ°é«ããšããããšãšãœããœã«ãLv.95äºä»¶ã¯çºçããããã£ããã fact2: ãã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯çããªãããšããããšã¯ã¿ãã¿ãLv.74äºä»¶ã«é²ããã fact3: ç¯ãããšããããã¯å解ããé£ããšããããšãçãã fact4: ã¿ãã¿ãLv.74äºä»¶ã¯ã¿ãã¿ã«ã
Lv.56äºä»¶ã«ç¹ãã fact5: ãåéããæããšããããšããã³äººéããããšããããšãçããããšããããšã¯èš±ãé£ããšããããšã¯èµ·ãããªããšããããšã«ãããããã fact6: ã人éããããšããããšãçãããåéããæããšããããšã¯èµ·ããªãããšããããšã¯ãåéããæããšããããšã¯çºçããªãããšããããšãå¥æ©ã§ãã fact7: åçºãæããšããããšããã³ãŸããŸã¡ãLv.39äºä»¶ãçºçããã¯ãèš±ãé£ããšããããšã¯çããªãããšããããšãçãããã fact8: ã¿ãã¿ãLv.74äºä»¶ãçºçããããããã¯ãã«ããLv.16äºä»¶ãèµ·ããããããã¯äž¡æ¹ã fact9: ã¿ãã¿ã«ã
Lv.56äºä»¶ããã«ããLv.16äºä»¶ã¯åå ã fact10: åéããæããšããããšã¯çããªããšããããšã¯ãœã®ãœãLv.77äºä»¶ããã³ã¿ãã¿ã«ã
Lv.56äºä»¶ãèµ·ããã«èµ·å ãã fact11: ãã人éããããšããããšãçºçããããããåéããæããšããããšã¯çããªããšãããã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯çããªã fact12: ãœã®ãœãLv.77äºä»¶ãèµ·ãã | fact1: ({IG} & {FM}) -> ¬{L} fact2: {A} -> {G} fact3: ({IO} v {JJ}) fact4: {A} -> {C} fact5: ¬{H} -> ({E} & {F}) fact6: ¬{E} -> ({F} & ¬{E}) fact7: ({J} & {I}) -> ¬{H} fact8: ({A} v {B}) fact9: {B} -> {C} fact10: ({D} & {C}) -> ¬{E} fact11: ({F} & ¬{E}) -> ¬{G} fact12: {D} | [
"fact8 & fact4 & fact9 -> int1: ãã¿ãã¿ã«ã
Lv.56äºä»¶ãçããããšããããšã¯åã§ãªã; int1 & fact12 -> int2: ãœã®ãœãLv.77äºä»¶ãšã¿ãã¿ã«ã
Lv.56äºä»¶ãçºçãã; int2 & fact10 -> int3: åéããæããšããããšã¯çºçããªã; int3 & fact6 -> int4: 人éããããšããããšãçºçãããåéããæããšããããšã¯èµ·ããªã; int4 & fact11 -> hypothesis;"
] | [
"fact8 & fact4 & fact9 -> int1: {C}; int1 & fact12 -> int2: ({D} & {C}); int2 & fact10 -> int3: ¬{E}; int3 & fact6 -> int4: ({F} & ¬{E}); int4 & fact11 -> hypothesis;"
] | ã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ãçãã | {G} | [] | 8 | 5 | 5 | 5 | 5 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ã¿ãã¿ã«Lv.30äºä»¶ãèµ·ãããªããšããããšã¯æ°é«ããšããããšãšãœããœã«ãLv.95äºä»¶ã¯çºçããããã£ããã fact2: ãã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯çããªãããšããããšã¯ã¿ãã¿ãLv.74äºä»¶ã«é²ããã fact3: ç¯ãããšããããã¯å解ããé£ããšããããšãçãã fact4: ã¿ãã¿ãLv.74äºä»¶ã¯ã¿ãã¿ã«ã
Lv.56äºä»¶ã«ç¹ãã fact5: ãåéããæããšããããšããã³äººéããããšããããšãçããããšããããšã¯èš±ãé£ããšããããšã¯èµ·ãããªããšããããšã«ãããããã fact6: ã人éããããšããããšãçãããåéããæããšããããšã¯èµ·ããªãããšããããšã¯ãåéããæããšããããšã¯çºçããªãããšããããšãå¥æ©ã§ãã fact7: åçºãæããšããããšããã³ãŸããŸã¡ãLv.39äºä»¶ãçºçããã¯ãèš±ãé£ããšããããšã¯çããªãããšããããšãçãããã fact8: ã¿ãã¿ãLv.74äºä»¶ãçºçããããããã¯ãã«ããLv.16äºä»¶ãèµ·ããããããã¯äž¡æ¹ã fact9: ã¿ãã¿ã«ã
Lv.56äºä»¶ããã«ããLv.16äºä»¶ã¯åå ã fact10: åéããæããšããããšã¯çããªããšããããšã¯ãœã®ãœãLv.77äºä»¶ããã³ã¿ãã¿ã«ã
Lv.56äºä»¶ãèµ·ããã«èµ·å ãã fact11: ãã人éããããšããããšãçºçããããããåéããæããšããããšã¯çããªããšãããã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯çããªã fact12: ãœã®ãœãLv.77äºä»¶ãèµ·ãã ; $hypothesis$ = ã¿ã¡ãã¿ã¡ã
Lv.44äºä»¶ã¯èµ·ããªã ; $proof$ = | fact8 & fact4 & fact9 -> int1: ãã¿ãã¿ã«ã
Lv.56äºä»¶ãçããããšããããšã¯åã§ãªã; int1 & fact12 -> int2: ãœã®ãœãLv.77äºä»¶ãšã¿ãã¿ã«ã
Lv.56äºä»¶ãçºçãã; int2 & fact10 -> int3: åéããæããšããããšã¯çºçããªã; int3 & fact6 -> int4: 人éããããšããããšãçºçãããåéããæããšããããšã¯èµ·ããªã; int4 & fact11 -> hypothesis; __PROVED__ | $facts$ = fact1: ({IG} & {FM}) -> ¬{L} fact2: {A} -> {G} fact3: ({IO} v {JJ}) fact4: {A} -> {C} fact5: ¬{H} -> ({E} & {F}) fact6: ¬{E} -> ({F} & ¬{E}) fact7: ({J} & {I}) -> ¬{H} fact8: ({A} v {B}) fact9: {B} -> {C} fact10: ({D} & {C}) -> ¬{E} fact11: ({F} & ¬{E}) -> ¬{G} fact12: {D} ; $hypothesis$ = ¬{G} ; $proof$ = | fact8 & fact4 & fact9 -> int1: {C}; int1 & fact12 -> int2: ({D} & {C}); int2 & fact10 -> int3: ¬{E}; int3 & fact6 -> int4: ({F} & ¬{E}); int4 & fact11 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã«ã
ãŸãLv.98ã¯æšããšããããšã¯ãªã | ¬{D}{a} | fact1: ãããã®ãŸã«ã
ãŸãLv.98ãçãããšãããšããã€ã fact2: ããä»®ã«ããã®ãŸã«ã
ãŸãLv.98ã¯ããã€ãããšããããšã¯æ¬åœã ãšãããšæšã fact3: ãçãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ä»®ã«ãçãããã¢ã³ã¹ã¿ãŒããããªããã®ãŸã«ã
ãŸãLv.98ã¯çãããããã«ã¢ã¡ãªã«ããã | fact1: {A}{a} -> {C}{a} fact2: {C}{a} -> {D}{a} fact3: (Ex): {A}x fact4: (x): {A}x -> ({A}{a} & {B}{a}) | [
"fact3 & fact4 -> int1: ãã®ãŸã«ã
ãŸãLv.98ã¯çãããã¢ã¡ãªã«ããã; int1 -> int2: ãããã®ãŸã«ã
ãŸãLv.98ã¯çãããªãããšããããšã¯æãç«ããªãããšããããšã¯æãç«ã€; int2 & fact1 -> int3: ãã®ãŸã«ã
ãŸãLv.98ã¯ããã€ã; int3 & fact2 -> hypothesis;"
] | [
"fact3 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {A}{a}; int2 & fact1 -> int3: {C}{a}; int3 & fact2 -> hypothesis;"
] | null | null | [] | null | 4 | 4 | 4 | 4 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããã®ãŸã«ã
ãŸãLv.98ãçãããšãããšããã€ã fact2: ããä»®ã«ããã®ãŸã«ã
ãŸãLv.98ã¯ããã€ãããšããããšã¯æ¬åœã ãšãããšæšã fact3: ãçãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ä»®ã«ãçãããã¢ã³ã¹ã¿ãŒããããªããã®ãŸã«ã
ãŸãLv.98ã¯çãããããã«ã¢ã¡ãªã«ããã ; $hypothesis$ = ãã®ãŸã«ã
ãŸãLv.98ã¯æšããšããããšã¯ãªã ; $proof$ = | fact3 & fact4 -> int1: ãã®ãŸã«ã
ãŸãLv.98ã¯çãããã¢ã¡ãªã«ããã; int1 -> int2: ãããã®ãŸã«ã
ãŸãLv.98ã¯çãããªãããšããããšã¯æãç«ããªãããšããããšã¯æãç«ã€; int2 & fact1 -> int3: ãã®ãŸã«ã
ãŸãLv.98ã¯ããã€ã; int3 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {C}{a} fact2: {C}{a} -> {D}{a} fact3: (Ex): {A}x fact4: (x): {A}x -> ({A}{a} & {B}{a}) ; $hypothesis$ = ¬{D}{a} ; $proof$ = | fact3 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: {A}{a}; int2 & fact1 -> int3: {C}{a}; int3 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ããããLv.43ã¯å¹Œããããã«è»œãããšããããšã¯èª€ãã | ¬({D}{b} & {E}{b}) | fact1: ããããã®ããããLv.9ã幌ããšããã°ãã®ããããLv.43ã¯ç
©ã fact2: ãããã®ãŸã¡ã
ãŸãLv.17ãèŠããšããããã®ãœããœãLv.47ã¯å¯ŸæŠããªãäžæ¹ã§çºéã fact3: ãã®ããããLv.9ãç
©ããšããã°ãã®ãŸããŸãLv.66ã¯çºéã fact4: ãããã®ãŸããŸãLv.66ãç
©ãããã€ããã¡ãªããšããã°ãã®ããããLv.9ã¯ç
©ããªã fact5: ããã®ããããLv.43ã¯è»œãããšããããšã¯äºå®ãšç°ãªããªã fact6: ãã®ããããLv.9ãããã¡ãªããšããããã®ãŸããŸãLv.66ã¯çºéã fact7: ãããã®ãŸããŸãLv.66ãçºéããšãããšãã®ããããLv.43ã¯å¹Œã fact8: ããããã®ããããLv.9ã¯ç
©ããªããšãããšãããã®ããããLv.43ã¯å¹Œãããã®äžè»œãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªã fact9: ããã®ããããLv.9ã¯å¯ŸæŠããªãããšããããšã¯äºå®ã§ãã fact10: ç
©ããªãã¢ã³ã¹ã¿ãŒã¯çªãè¿ããæãŠãç¡ã | fact1: {D}{a} -> {A}{b} fact2: {G}{e} -> (¬{F}{d} & {C}{d}) fact3: {A}{a} -> {C}{c} fact4: ({A}{c} & {B}{c}) -> ¬{A}{a} fact5: {E}{b} fact6: {B}{a} -> {C}{c} fact7: {C}{c} -> {D}{b} fact8: ¬{A}{a} -> ¬({D}{b} & {E}{b}) fact9: ¬{F}{a} fact10: (x): ¬{A}x -> ({ER}x v {CL}x) | [] | [] | ããã®ããããLv.43ã¯å¹Œããããã«è»œãããšããããšã¯èª€ãã | ¬({D}{b} & {E}{b}) | [] | 7 | 4 | 4 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ããããLv.9ã幌ããšããã°ãã®ããããLv.43ã¯ç
©ã fact2: ãããã®ãŸã¡ã
ãŸãLv.17ãèŠããšããããã®ãœããœãLv.47ã¯å¯ŸæŠããªãäžæ¹ã§çºéã fact3: ãã®ããããLv.9ãç
©ããšããã°ãã®ãŸããŸãLv.66ã¯çºéã fact4: ãããã®ãŸããŸãLv.66ãç
©ãããã€ããã¡ãªããšããã°ãã®ããããLv.9ã¯ç
©ããªã fact5: ããã®ããããLv.43ã¯è»œãããšããããšã¯äºå®ãšç°ãªããªã fact6: ãã®ããããLv.9ãããã¡ãªããšããããã®ãŸããŸãLv.66ã¯çºéã fact7: ãããã®ãŸããŸãLv.66ãçºéããšãããšãã®ããããLv.43ã¯å¹Œã fact8: ããããã®ããããLv.9ã¯ç
©ããªããšãããšãããã®ããããLv.43ã¯å¹Œãããã®äžè»œãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªã fact9: ããã®ããããLv.9ã¯å¯ŸæŠããªãããšããããšã¯äºå®ã§ãã fact10: ç
©ããªãã¢ã³ã¹ã¿ãŒã¯çªãè¿ããæãŠãç¡ã ; $hypothesis$ = ããã®ããããLv.43ã¯å¹Œããããã«è»œãããšããããšã¯èª€ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {D}{a} -> {A}{b} fact2: {G}{e} -> (¬{F}{d} & {C}{d}) fact3: {A}{a} -> {C}{c} fact4: ({A}{c} & {B}{c}) -> ¬{A}{a} fact5: {E}{b} fact6: {B}{a} -> {C}{c} fact7: {C}{c} -> {D}{b} fact8: ¬{A}{a} -> ¬({D}{b} & {E}{b}) fact9: ¬{F}{a} fact10: (x): ¬{A}x -> ({ER}x v {CL}x) ; $hypothesis$ = ¬({D}{b} & {E}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ãLv.75ã¯èšãã | {E}{d} | fact1: ãã®ã¿ãã¿ã¡ã
Lv.13ã¯å®ã fact2: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯çãŸãã fact3: ããã®ã¿ãã¿ã¡ã
Lv.13ã¯å®ãããšããããšã¯æ£ãããšããã°ãã®ãã«ã
ãã«ã
Lv.15ã¯çã£ããã fact4: ãã®ãœããœãLv.56ã¯å°æããããŠãã€åããæã fact5: çãŸãããŠå³ãé£ãã¢ã³ã¹ã¿ãŒã¯çã£ããããšããããšã¯ãªã fact6: çã£ããããªãã¢ã³ã¹ã¿ãŒã¯èšãããå®ã fact7: ããããã®ãã«ã
ãã«ã
Lv.15ã¯çã£ãããããšããããšã¯äºå®ã ãšããããã®ã¿ã®ã¿ã«ã
Lv.16ã¯å³ãé£ã fact8: ããããã®ã¿ã®ã¿ã«ã
Lv.16ãçãŸãããŠå ããŠå³ãé£ããªããã®ã¿ãã¿ãLv.75ã¯èšãããªã | fact1: {A}{a} fact2: {D}{c} fact3: {A}{a} -> {B}{b} fact4: ({R}{hr} & {S}{hr}) fact5: (x): ({D}x & {C}x) -> ¬{B}x fact6: (x): ¬{B}x -> ({E}x & {A}x) fact7: {B}{b} -> {C}{c} fact8: ({D}{c} & {C}{c}) -> ¬{E}{d} | [
"fact3 & fact1 -> int1: ãã®ãã«ã
ãã«ã
Lv.15ã¯çã£ããã; int1 & fact7 -> int2: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯å³ãé£ã; int2 & fact2 -> int3: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯çãŸãããå³ãé£ã; int3 & fact8 -> hypothesis;"
] | [
"fact3 & fact1 -> int1: {B}{b}; int1 & fact7 -> int2: {C}{c}; int2 & fact2 -> int3: ({D}{c} & {C}{c}); int3 & fact8 -> hypothesis;"
] | ãã®ã¿ãã¿ãLv.75ã¯èšãã | {E}{d} | [
"fact9 -> int4: ããããã®ã¿ãã¿ãLv.75ãçã£ããããªããšãããšãã®ã¿ãã¿ãLv.75ã¯èšãããããã«ããã¯å®ã; fact10 -> int5: ããããã®ã¿ãã¿ãLv.75ã¯çãŸãããŠãŸãå³ãé£ããšããã°ãçã£ããããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãã;"
] | 5 | 4 | 4 | 4 | 4 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã¿ãã¿ã¡ã
Lv.13ã¯å®ã fact2: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯çãŸãã fact3: ããã®ã¿ãã¿ã¡ã
Lv.13ã¯å®ãããšããããšã¯æ£ãããšããã°ãã®ãã«ã
ãã«ã
Lv.15ã¯çã£ããã fact4: ãã®ãœããœãLv.56ã¯å°æããããŠãã€åããæã fact5: çãŸãããŠå³ãé£ãã¢ã³ã¹ã¿ãŒã¯çã£ããããšããããšã¯ãªã fact6: çã£ããããªãã¢ã³ã¹ã¿ãŒã¯èšãããå®ã fact7: ããããã®ãã«ã
ãã«ã
Lv.15ã¯çã£ãããããšããããšã¯äºå®ã ãšããããã®ã¿ã®ã¿ã«ã
Lv.16ã¯å³ãé£ã fact8: ããããã®ã¿ã®ã¿ã«ã
Lv.16ãçãŸãããŠå ããŠå³ãé£ããªããã®ã¿ãã¿ãLv.75ã¯èšãããªã ; $hypothesis$ = ãã®ã¿ãã¿ãLv.75ã¯èšãã ; $proof$ = | fact3 & fact1 -> int1: ãã®ãã«ã
ãã«ã
Lv.15ã¯çã£ããã; int1 & fact7 -> int2: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯å³ãé£ã; int2 & fact2 -> int3: ãã®ã¿ã®ã¿ã«ã
Lv.16ã¯çãŸãããå³ãé£ã; int3 & fact8 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: {D}{c} fact3: {A}{a} -> {B}{b} fact4: ({R}{hr} & {S}{hr}) fact5: (x): ({D}x & {C}x) -> ¬{B}x fact6: (x): ¬{B}x -> ({E}x & {A}x) fact7: {B}{b} -> {C}{c} fact8: ({D}{c} & {C}{c}) -> ¬{E}{d} ; $hypothesis$ = {E}{d} ; $proof$ = | fact3 & fact1 -> int1: {B}{b}; int1 & fact7 -> int2: {C}{c}; int2 & fact2 -> int3: ({D}{c} & {C}{c}); int3 & fact8 -> hypothesis; __DISPROVED__ |
0.3 | 以äžã®ããã«ä»®å®ããããã®ãœãªãœãLv.65ã¯çºæ®ãé£ã | {A}{a} | fact1: ããã®ã·ã«ã·ãLv.19ã¯å¥ã§å§ããããšããããšã¯ç¢ºãã§ãã fact2: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯æãæããªãããããã¯å€ããæããšããããšã¯ãªãããšããããšã¯æãç«ããªããšãããšããã¯åæŽããªã fact3: ããä»®ã«ãã®ãœãªãœãLv.65ãçºæ®ãé£ããšãããšãã®ã·ã«ã·ãLv.19ã¯éžæããæããªããå¥ã§å§ãã | fact1: {AB}{b} fact2: (x): ¬(¬{D}x v ¬{C}x) -> ¬{BA}x fact3: {A}{a} -> (¬{AA}{b} & {AB}{b}) | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãœãªãœãLv.65ã¯çºæ®ãé£ã; fact3 & assump1 -> int1: ãã®ã·ã«ã·ãLv.19ã¯éžæããæããšããããšã¯ãªãããããå¥ã§å§ãã; int1 -> int2: ãã®ã·ã«ã·ãLv.19ã¯éžæããæããªã;"
] | [
"void -> assump1: {A}{a}; fact3 & assump1 -> int1: (¬{AA}{b} & {AB}{b}); int1 -> int2: ¬{AA}{b};"
] | ãã®ããããLv.72ã¯åæŽãããšããããšã¯ãªãããããçºæ®ãé£ã | (¬{BA}{eg} & {A}{eg}) | [
"fact4 -> int3: ä»®ã«ããã®ããããLv.72ã¯æãæããªãããããã¯ããã¯å€ããæããªãããšããããšã¯æãç«ããªããšãããšããã¯åæŽããªã;"
] | 4 | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®ã·ã«ã·ãLv.19ã¯å¥ã§å§ããããšããããšã¯ç¢ºãã§ãã fact2: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯æãæããªãããããã¯å€ããæããšããããšã¯ãªãããšããããšã¯æãç«ããªããšãããšããã¯åæŽããªã fact3: ããä»®ã«ãã®ãœãªãœãLv.65ãçºæ®ãé£ããšãããšãã®ã·ã«ã·ãLv.19ã¯éžæããæããªããå¥ã§å§ãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããã®ãœãªãœãLv.65ã¯çºæ®ãé£ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {AB}{b} fact2: (x): ¬(¬{D}x v ¬{C}x) -> ¬{BA}x fact3: {A}{a} -> (¬{AA}{b} & {AB}{b}) ; $hypothesis$ = {A}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽããŽã«ãLv.29ã¯é
·ããªã | ¬{F}{b} | fact1: ä»®ã«ããçãããšããããšã¯æ£ãããã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽã¡ãLv.19ã¯çãŒã fact2: ãããã®ãŽããŽã«ãLv.29ãåè«ãœããªããšããããã®ãŽããŽã«ãLv.29ã¯é
·ããšããããšã¯ãªã fact3: ãçããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããã®ãŽããŽã¡ãLv.19ãè¡ãæãããã®äžäœæäœæãããšããã°ãã®ãŽããŽã«ãLv.29ã¯åè«ãœããªã fact5: ãããçããã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽã¡ãLv.19ã¯çãŒãããããè¡ãæã fact6: ãããã®ãã«ãããªLv.79ãéç¡ãããŸãåè«ãœããšãããšãã®ãŽããŽã¡ãLv.19ã¯äœæäœæãããªã fact7: çãŒããªãã¢ã³ã¹ã¿ãŒã¯é
·ããçãããŸãã¯äž¡æ¹ãšãã§ãã fact8: ãã®ãŽããŽã¡ãLv.19ã¯çãŒã fact9: ãã®ãŽããŽã¡ãLv.19ã¯äœæäœæãã | fact1: (x): {A}x -> {B}{a} fact2: ¬{E}{b} -> ¬{F}{b} fact3: (Ex): {A}x fact4: ({C}{a} & {D}{a}) -> ¬{E}{b} fact5: (x): {A}x -> ({B}{a} & {C}{a}) fact6: ({G}{c} & {E}{c}) -> ¬{D}{a} fact7: (x): ¬{B}x -> ({F}x v {A}x) fact8: {B}{a} fact9: {D}{a} | [
"fact3 & fact5 -> int1: ãã®ãŽããŽã¡ãLv.19ã¯çãŒããããã«ããã¯è¡ãæã; int1 -> int2: ãã®ãŽããŽã¡ãLv.19ã¯è¡ãæã; int2 & fact9 -> int3: ãã®ãŽããŽã¡ãLv.19ã¯è¡ãæããŠããã¯äœæäœæãã; int3 & fact4 -> int4: ãã®ãŽããŽã«ãLv.29ã¯åè«ãœããªã; int4 & fact2 -> hypothesis;"
] | [
"fact3 & fact5 -> int1: ({B}{a} & {C}{a}); int1 -> int2: {C}{a}; int2 & fact9 -> int3: ({C}{a} & {D}{a}); int3 & fact4 -> int4: ¬{E}{b}; int4 & fact2 -> hypothesis;"
] | ãã®ãŽããŽã«ãLv.29ã¯é
·ã | {F}{b} | [
"fact10 -> int5: ããããã®ãŽããŽã¡ãLv.19ãçãŒããªããªãã°é
·ããããã¯çã;"
] | 5 | 5 | 5 | 5 | 5 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ããçãããšããããšã¯æ£ãããã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽã¡ãLv.19ã¯çãŒã fact2: ãããã®ãŽããŽã«ãLv.29ãåè«ãœããªããšããããã®ãŽããŽã«ãLv.29ã¯é
·ããšããããšã¯ãªã fact3: ãçããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããã®ãŽããŽã¡ãLv.19ãè¡ãæãããã®äžäœæäœæãããšããã°ãã®ãŽããŽã«ãLv.29ã¯åè«ãœããªã fact5: ãããçããã¢ã³ã¹ã¿ãŒãããã°ãã®ãŽããŽã¡ãLv.19ã¯çãŒãããããè¡ãæã fact6: ãããã®ãã«ãããªLv.79ãéç¡ãããŸãåè«ãœããšãããšãã®ãŽããŽã¡ãLv.19ã¯äœæäœæãããªã fact7: çãŒããªãã¢ã³ã¹ã¿ãŒã¯é
·ããçãããŸãã¯äž¡æ¹ãšãã§ãã fact8: ãã®ãŽããŽã¡ãLv.19ã¯çãŒã fact9: ãã®ãŽããŽã¡ãLv.19ã¯äœæäœæãã ; $hypothesis$ = ãã®ãŽããŽã«ãLv.29ã¯é
·ããªã ; $proof$ = | fact3 & fact5 -> int1: ãã®ãŽããŽã¡ãLv.19ã¯çãŒããããã«ããã¯è¡ãæã; int1 -> int2: ãã®ãŽããŽã¡ãLv.19ã¯è¡ãæã; int2 & fact9 -> int3: ãã®ãŽããŽã¡ãLv.19ã¯è¡ãæããŠããã¯äœæäœæãã; int3 & fact4 -> int4: ãã®ãŽããŽã«ãLv.29ã¯åè«ãœããªã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {A}x -> {B}{a} fact2: ¬{E}{b} -> ¬{F}{b} fact3: (Ex): {A}x fact4: ({C}{a} & {D}{a}) -> ¬{E}{b} fact5: (x): {A}x -> ({B}{a} & {C}{a}) fact6: ({G}{c} & {E}{c}) -> ¬{D}{a} fact7: (x): ¬{B}x -> ({F}x v {A}x) fact8: {B}{a} fact9: {D}{a} ; $hypothesis$ = ¬{F}{b} ; $proof$ = | fact3 & fact5 -> int1: ({B}{a} & {C}{a}); int1 -> int2: {C}{a}; int2 & fact9 -> int3: ({C}{a} & {D}{a}); int3 & fact4 -> int4: ¬{E}{b}; int4 & fact2 -> hypothesis; __PROVED__ |
0.3 | 䌌ããããšã¯çããªã | ¬{B} | fact1: ããä»®ã«ãã¿ãªã¿ã¡ãLv.80äºä»¶ãèµ·ããããããã¯å°œãæãŠãããšã¯çããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééã£ãŠãããšããã°äŒŒããããšã¯èµ·ãããªã fact2: ä»®ã«ãæ¥ãæããšããããšã¯èµ·ããªãããšããããšã¯æ¬åœã ãšããããã¿ãªã¿ã¡ãLv.80äºä»¶ãèµ·ããããŸãã¯å°œãæãŠãããšã¯çºçããªãããšããããšã¯ééãã§ãã fact3: æ©ãŸãããšããããšã¯èµ·ãããªããšããããšã¯äŒŒããããšãšåºãé£ããšããããšãèµ·ãããçãããã fact4: æ¥ãæããšããããšã¯èµ·ããªã | fact1: ¬({AA} v ¬{AB}) -> ¬{B} fact2: ¬{A} -> ¬({AA} v ¬{AB}) fact3: ¬{D} -> ({B} & {C}) fact4: ¬{A} | [
"fact2 & fact4 -> int1: ãã¿ãªã¿ã¡ãLv.80äºä»¶ã¯çºçãããå°œãæãŠãããšã¯èµ·ããªãããšããããšã¯ééãã§ãã; int1 & fact1 -> hypothesis;"
] | [
"fact2 & fact4 -> int1: ¬({AA} v ¬{AB}); int1 & fact1 -> hypothesis;"
] | æ©ããšããããšã¯çããªã | ¬{GJ} | [] | 6 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã¿ãªã¿ã¡ãLv.80äºä»¶ãèµ·ããããããã¯å°œãæãŠãããšã¯çããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééã£ãŠãããšããã°äŒŒããããšã¯èµ·ãããªã fact2: ä»®ã«ãæ¥ãæããšããããšã¯èµ·ããªãããšããããšã¯æ¬åœã ãšããããã¿ãªã¿ã¡ãLv.80äºä»¶ãèµ·ããããŸãã¯å°œãæãŠãããšã¯çºçããªãããšããããšã¯ééãã§ãã fact3: æ©ãŸãããšããããšã¯èµ·ãããªããšããããšã¯äŒŒããããšãšåºãé£ããšããããšãèµ·ãããçãããã fact4: æ¥ãæããšããããšã¯èµ·ããªã ; $hypothesis$ = 䌌ããããšã¯çããªã ; $proof$ = | fact2 & fact4 -> int1: ãã¿ãªã¿ã¡ãLv.80äºä»¶ã¯çºçãããå°œãæãŠãããšã¯èµ·ããªãããšããããšã¯ééãã§ãã; int1 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({AA} v ¬{AB}) -> ¬{B} fact2: ¬{A} -> ¬({AA} v ¬{AB}) fact3: ¬{D} -> ({B} & {C}) fact4: ¬{A} ; $hypothesis$ = ¬{B} ; $proof$ = | fact2 & fact4 -> int1: ¬({AA} v ¬{AB}); int1 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸã¡ãLv.95ã¯ãããç¡ããªã | ¬{F}{c} | fact1: ä»®ã«ãã®ãŸã«ããŸã«ãLv.87ãæçããšããã°ãã®ãŸããŸã¡ãLv.95ã¯é¢æ ãã fact2: ãã®ãŸããŸã¡ãLv.95ãé¢æ ãããšãããšããã¯å°ãªã fact3: ãã®ãŸã¡ããŸãLv.94ã¯åé¢ãæã fact4: ããä»®ã«ãã®ãŸããŸã¡ãLv.95ã¯å°ãªããããã¯èŠªããšããããã®ãŸããŸã¡ãLv.95ã¯ãããç¡ããªã fact5: ããä»®ã«ãã®ãŸã¡ããŸãLv.94ãåé¢ãæããªãã°ãã®ãŸã«ããŸã«ãLv.87ã¯æçã | fact1: {B}{b} -> {C}{c} fact2: {C}{c} -> {D}{c} fact3: {A}{a} fact4: ({D}{c} v {E}{c}) -> ¬{F}{c} fact5: {A}{a} -> {B}{b} | [
"fact5 & fact3 -> int1: ãã®ãŸã«ããŸã«ãLv.87ã¯æçã; int1 & fact1 -> int2: ãã®ãŸããŸã¡ãLv.95ã¯é¢æ ãã; int2 & fact2 -> int3: ãã®ãŸããŸã¡ãLv.95ã¯å°ãªã; int3 -> int4: ãã®ãŸããŸã¡ãLv.95ã¯å°ãªãããŸãã¯èŠªã; int4 & fact4 -> hypothesis;"
] | [
"fact5 & fact3 -> int1: {B}{b}; int1 & fact1 -> int2: {C}{c}; int2 & fact2 -> int3: {D}{c}; int3 -> int4: ({D}{c} v {E}{c}); int4 & fact4 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŸã«ããŸã«ãLv.87ãæçããšããã°ãã®ãŸããŸã¡ãLv.95ã¯é¢æ ãã fact2: ãã®ãŸããŸã¡ãLv.95ãé¢æ ãããšãããšããã¯å°ãªã fact3: ãã®ãŸã¡ããŸãLv.94ã¯åé¢ãæã fact4: ããä»®ã«ãã®ãŸããŸã¡ãLv.95ã¯å°ãªããããã¯èŠªããšããããã®ãŸããŸã¡ãLv.95ã¯ãããç¡ããªã fact5: ããä»®ã«ãã®ãŸã¡ããŸãLv.94ãåé¢ãæããªãã°ãã®ãŸã«ããŸã«ãLv.87ã¯æçã ; $hypothesis$ = ãã®ãŸããŸã¡ãLv.95ã¯ãããç¡ããªã ; $proof$ = | fact5 & fact3 -> int1: ãã®ãŸã«ããŸã«ãLv.87ã¯æçã; int1 & fact1 -> int2: ãã®ãŸããŸã¡ãLv.95ã¯é¢æ ãã; int2 & fact2 -> int3: ãã®ãŸããŸã¡ãLv.95ã¯å°ãªã; int3 -> int4: ãã®ãŸããŸã¡ãLv.95ã¯å°ãªãããŸãã¯èŠªã; int4 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{b} -> {C}{c} fact2: {C}{c} -> {D}{c} fact3: {A}{a} fact4: ({D}{c} v {E}{c}) -> ¬{F}{c} fact5: {A}{a} -> {B}{b} ; $hypothesis$ = ¬{F}{c} ; $proof$ = | fact5 & fact3 -> int1: {B}{b}; int1 & fact1 -> int2: {C}{c}; int2 & fact2 -> int3: {D}{c}; int3 -> int4: ({D}{c} v {E}{c}); int4 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãœãªãœã¡ã
Lv.41äºä»¶ãèµ·ãã | {A} | fact1: ãããããããLv.47äºä»¶ã¯èµ·ããªãããããã¯çã£ããããšããããšãèµ·ãããã©ã¡ããã§ããããšããããšã¯èª€ãã§ãããšããã°ã¿ãã¿ãLv.26äºä»¶ã¯èµ·ãããªã fact2: ããœããœã«Lv.80äºä»¶ã¯çããªãããšããããšã¯ãäŒè©±ããããšããããšã¯çããªãããšããããšãç·©ããšããããšãèµ·ãããšããããšããããã¯äž¡æ¹ãšãã«é»ãŸãã fact3: èã£ãœããšããããšãçºçãã fact4: ãäŒè©±ããããšããããšã¯çããªãããããã¯ç·©ããšããããšãèµ·ããããããã¯äž¡æ¹ãšãã§ããããšããããšã¯èª€ãã ãšãããããœãªãœã¡ã
Lv.41äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ fact5: ãœããœã«Lv.80äºä»¶ã¯çããªã fact6: ãŽããŽã«ãLv.9äºä»¶ãèµ·ãã | fact1: ¬(¬{HE} v {EC}) -> ¬{IS} fact2: (¬{AA} v {AB}) -> {B} fact3: {GM} fact4: ¬(¬{AA} v {AB}) -> ¬{A} fact5: ¬{B} fact6: {DM} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããäŒè©±ããããšããããšã¯èµ·ãããªãããããã¯ç·©ããšããããšãçºçãã; fact2 & assump1 -> int1: ãœããœã«Lv.80äºä»¶ãçãã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãäŒè©±ããããšããããšã¯çºçããªãããããã¯ç·©ããšããããšãèµ·ããããŸãã¯ã©ã¡ããã ããšããããšã¯äºå®ãšç°ãªã; int3 & fact4 -> hypothesis;"
] | [
"void -> assump1: (¬{AA} v {AB}); fact2 & assump1 -> int1: {B}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{AA} v {AB}); int3 & fact4 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããããããLv.47äºä»¶ã¯èµ·ããªãããããã¯çã£ããããšããããšãèµ·ãããã©ã¡ããã§ããããšããããšã¯èª€ãã§ãããšããã°ã¿ãã¿ãLv.26äºä»¶ã¯èµ·ãããªã fact2: ããœããœã«Lv.80äºä»¶ã¯çããªãããšããããšã¯ãäŒè©±ããããšããããšã¯çããªãããšããããšãç·©ããšããããšãèµ·ãããšããããšããããã¯äž¡æ¹ãšãã«é»ãŸãã fact3: èã£ãœããšããããšãçºçãã fact4: ãäŒè©±ããããšããããšã¯çããªãããããã¯ç·©ããšããããšãèµ·ããããããã¯äž¡æ¹ãšãã§ããããšããããšã¯èª€ãã ãšãããããœãªãœã¡ã
Lv.41äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ fact5: ãœããœã«Lv.80äºä»¶ã¯çããªã fact6: ãŽããŽã«ãLv.9äºä»¶ãèµ·ãã ; $hypothesis$ = ãœãªãœã¡ã
Lv.41äºä»¶ãèµ·ãã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããäŒè©±ããããšããããšã¯èµ·ãããªãããããã¯ç·©ããšããããšãçºçãã; fact2 & assump1 -> int1: ãœããœã«Lv.80äºä»¶ãçãã; int1 & fact5 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãäŒè©±ããããšããããšã¯çºçããªãããããã¯ç·©ããšããããšãèµ·ããããŸãã¯ã©ã¡ããã ããšããããšã¯äºå®ãšç°ãªã; int3 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬(¬{HE} v {EC}) -> ¬{IS} fact2: (¬{AA} v {AB}) -> {B} fact3: {GM} fact4: ¬(¬{AA} v {AB}) -> ¬{A} fact5: ¬{B} fact6: {DM} ; $hypothesis$ = {A} ; $proof$ = | void -> assump1: (¬{AA} v {AB}); fact2 & assump1 -> int1: {B}; int1 & fact5 -> int2: #F#; [assump1] & int2 -> int3: ¬(¬{AA} v {AB}); int3 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.18ã¯æç·©ã | {E}{c} | fact1: ããä»®ã«ããã®ãŽã«ããŽãLv.96ã¯æ¶ããªãããããçœã
ããããšããããšã¯åãªããæ¥è¿ãæãããšããããšã¯æ£ãã fact2: ããããåžåãæãããšããããšã¯æãç«ã€ãã¢ã³ã¹ã¿ãŒããããšããããã®ãã¡ã
ãã¡ã
Lv.30ã¯çœã
ãããªã fact3: ãããã®ãŽã«ããŽãLv.96ã¯æ¥è¿ãæããªãããã®ãŽããŽãLv.18ã¯æç·©ãããšããããšã¯æãç«ã€ fact4: ãã®ã¿ãã¿ã¡ãLv.22ã¯åžåãæã fact5: ãããããã®ãã¡ã
ãã¡ã
Lv.30ã¯çœã
ãããªãããšããããšã¯çå®ã§ãããšããã°ããã®ãŽã«ããŽãLv.96ã¯æ¶ãããããã«çœã
ããããšããããšã¯åã | fact1: ¬(¬{C}{b} & {B}{b}) -> {D}{b} fact2: (x): {A}x -> ¬{B}{a} fact3: {D}{b} -> {E}{c} fact4: {A}{aa} fact5: ¬{B}{a} -> ¬({C}{b} & {B}{b}) | [
"fact4 -> int1: ããåžåãæãããšããããšã¯äºå®ãªãã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact2 -> int2: ãã®ãã¡ã
ãã¡ã
Lv.30ã¯çœã
ãããªã;"
] | [
"fact4 -> int1: (Ex): {A}x; int1 & fact2 -> int2: ¬{B}{a};"
] | null | null | [] | null | 5 | 5 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããä»®ã«ããã®ãŽã«ããŽãLv.96ã¯æ¶ããªãããããçœã
ããããšããããšã¯åãªããæ¥è¿ãæãããšããããšã¯æ£ãã fact2: ããããåžåãæãããšããããšã¯æãç«ã€ãã¢ã³ã¹ã¿ãŒããããšããããã®ãã¡ã
ãã¡ã
Lv.30ã¯çœã
ãããªã fact3: ãããã®ãŽã«ããŽãLv.96ã¯æ¥è¿ãæããªãããã®ãŽããŽãLv.18ã¯æç·©ãããšããããšã¯æãç«ã€ fact4: ãã®ã¿ãã¿ã¡ãLv.22ã¯åžåãæã fact5: ãããããã®ãã¡ã
ãã¡ã
Lv.30ã¯çœã
ãããªãããšããããšã¯çå®ã§ãããšããã°ããã®ãŽã«ããŽãLv.96ã¯æ¶ãããããã«çœã
ããããšããããšã¯åã ; $hypothesis$ = ãã®ãŽããŽãLv.18ã¯æç·©ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{C}{b} & {B}{b}) -> {D}{b} fact2: (x): {A}x -> ¬{B}{a} fact3: {D}{b} -> {E}{c} fact4: {A}{aa} fact5: ¬{B}{a} -> ¬({C}{b} & {B}{b}) ; $hypothesis$ = {E}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããã®ãŽã«ããŽãLv.3ãäžããã°ãã®ãŸããŸãLv.14ã¯å¹
åºãããšããããšã¯æãç«ããªã | ¬({A}{a} -> {D}{c}) | fact1: ãããããã®ãŽã«ããŽãLv.3ã¯äžããããšããããšã¯æ¬åœã ãšããã°ãã®ãŽã«ããŽãLv.3ã¯è³æ¬èª¿éãã fact2: ãã®ãŸããŸãLv.14ã¯è³æ¬èª¿éãã fact3: ããä»®ã«ããã®ã·ãªã·ãLv.28ã¯æ¶Œããããšããããšã¯æãç«ã€ãªããã®ãŸããŸãLv.14ã¯å¹
åºã fact4: ããä»®ã«ãã®ãŽã«ããŽãLv.3ãè³æ¬èª¿éãããšããã°ãã®ã·ãªã·ãLv.28ã¯æ¶Œãã fact5: ãã®ãŸããŸãLv.14ã¯äžãã fact6: ãã®ãŽã«ããŽãLv.3ã¯æ¶Œãã | fact1: {A}{a} -> {B}{a} fact2: {B}{c} fact3: {C}{b} -> {D}{c} fact4: {B}{a} -> {C}{b} fact5: {A}{c} fact6: {C}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã«ããŽãLv.3ã¯äžãã; fact1 & assump1 -> int1: ããã®ãŽã«ããŽãLv.3ã¯è³æ¬èª¿éããããšããããšã¯äºå®ã ; int1 & fact4 -> int2: ãã®ã·ãªã·ãLv.28ã¯æ¶Œãã; int2 & fact3 -> int3: ããã®ãŸããŸãLv.14ã¯å¹
åºãããšããããšã¯æãç«ã€; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; [assump1] & int3 -> hypothesis;"
] | null | null | [] | null | 5 | 4 | 5 | 4 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãããããã®ãŽã«ããŽãLv.3ã¯äžããããšããããšã¯æ¬åœã ãšããã°ãã®ãŽã«ããŽãLv.3ã¯è³æ¬èª¿éãã fact2: ãã®ãŸããŸãLv.14ã¯è³æ¬èª¿éãã fact3: ããä»®ã«ããã®ã·ãªã·ãLv.28ã¯æ¶Œããããšããããšã¯æãç«ã€ãªããã®ãŸããŸãLv.14ã¯å¹
åºã fact4: ããä»®ã«ãã®ãŽã«ããŽãLv.3ãè³æ¬èª¿éãããšããã°ãã®ã·ãªã·ãLv.28ã¯æ¶Œãã fact5: ãã®ãŸããŸãLv.14ã¯äžãã fact6: ãã®ãŽã«ããŽãLv.3ã¯æ¶Œãã ; $hypothesis$ = ããããã®ãŽã«ããŽãLv.3ãäžããã°ãã®ãŸããŸãLv.14ã¯å¹
åºãããšããããšã¯æãç«ããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŽã«ããŽãLv.3ã¯äžãã; fact1 & assump1 -> int1: ããã®ãŽã«ããŽãLv.3ã¯è³æ¬èª¿éããããšããããšã¯äºå®ã ; int1 & fact4 -> int2: ãã®ã·ãªã·ãLv.28ã¯æ¶Œãã; int2 & fact3 -> int3: ããã®ãŸããŸãLv.14ã¯å¹
åºãããšããããšã¯æãç«ã€; [assump1] & int3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: {B}{c} fact3: {C}{b} -> {D}{c} fact4: {B}{a} -> {C}{b} fact5: {A}{c} fact6: {C}{a} ; $hypothesis$ = ¬({A}{a} -> {D}{c}) ; $proof$ = | void -> assump1: {A}{a}; fact1 & assump1 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{b}; int2 & fact3 -> int3: {D}{c}; [assump1] & int3 -> hypothesis; __DISPROVED__ |
0.3 | ã¿ãã¿ã¡ã
Lv.57äºä»¶ã¯çããªã | ¬{A} | fact1: ããŸããŸãLv.61äºä»¶ã¯èµ·ãããªãããšããããšã¯ã¿ãã¿ã¡ã
Lv.57äºä»¶ã«é»ãŸãã fact2: ããŸãªãŸãLv.87äºä»¶ã§ã¯ãªãã·ã«ã
ã·ãªLv.65äºä»¶ãçºçããããšããããšã¯æãç«ããªããªãã°ãã·ã«ã
ã·ãªLv.65äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã§ãã fact3: ãåãã¡é£ããšããããšããã³ææ¡ãæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯ã·ã«ã
ã·ãªLv.65äºä»¶ã¯çããªããšããããšã«ç±æ¥ãã fact4: ãåãé£ããšããããšãçããããšããããšã¯ãŸããŸãLv.61äºä»¶ãèµ·ãããšããããšãåå ã fact5: ããåãé£ããšããããšã¯çºçããããã©ãŸããŸãLv.61äºä»¶ã¯çããªãããšããããšã¯åãã¡é£ããšããããšã«ããçããããšããããšã¯æ£ãã fact6: ãã¿ãã¿ãLv.45äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ fact7: åãé£ããšããããšã¯èµ·ããªã | fact1: {A} -> {B} fact2: ¬(¬{H} & {F}) -> ¬{F} fact3: ¬{F} -> ({D} & {E}) fact4: {B} -> {C} fact5: {D} -> ({C} & ¬{B}) fact6: {GH} fact7: ¬{C} | [
"void -> assump1: 以äžã®ããã«ä»®å®ãããã¿ãã¿ã¡ã
Lv.57äºä»¶ãçºçãã; fact1 & assump1 -> int1: ãŸããŸãLv.61äºä»¶ãèµ·ãã; int1 & fact4 -> int2: åãé£ããšããããšãçºçãã; int2 & fact7 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis;"
] | [
"void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 & fact7 -> int3: #F#; [assump1] & int3 -> hypothesis;"
] | ãŽãªãŽãLv.4äºä»¶ãçãã | {EC} | [] | 8 | 5 | 4 | 5 | 4 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããŸããŸãLv.61äºä»¶ã¯èµ·ãããªãããšããããšã¯ã¿ãã¿ã¡ã
Lv.57äºä»¶ã«é»ãŸãã fact2: ããŸãªãŸãLv.87äºä»¶ã§ã¯ãªãã·ã«ã
ã·ãªLv.65äºä»¶ãçºçããããšããããšã¯æãç«ããªããªãã°ãã·ã«ã
ã·ãªLv.65äºä»¶ã¯çããªãããšããããšã¯ç¢ºãã§ãã fact3: ãåãã¡é£ããšããããšããã³ææ¡ãæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯ã·ã«ã
ã·ãªLv.65äºä»¶ã¯çããªããšããããšã«ç±æ¥ãã fact4: ãåãé£ããšããããšãçããããšããããšã¯ãŸããŸãLv.61äºä»¶ãèµ·ãããšããããšãåå ã fact5: ããåãé£ããšããããšã¯çºçããããã©ãŸããŸãLv.61äºä»¶ã¯çããªãããšããããšã¯åãã¡é£ããšããããšã«ããçããããšããããšã¯æ£ãã fact6: ãã¿ãã¿ãLv.45äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ fact7: åãé£ããšããããšã¯èµ·ããªã ; $hypothesis$ = ã¿ãã¿ã¡ã
Lv.57äºä»¶ã¯çããªã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ãããã¿ãã¿ã¡ã
Lv.57äºä»¶ãçºçãã; fact1 & assump1 -> int1: ãŸããŸãLv.61äºä»¶ãèµ·ãã; int1 & fact4 -> int2: åãé£ããšããããšãçºçãã; int2 & fact7 -> int3: ããã¯ççŸã§ãã; [assump1] & int3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} -> {B} fact2: ¬(¬{H} & {F}) -> ¬{F} fact3: ¬{F} -> ({D} & {E}) fact4: {B} -> {C} fact5: {D} -> ({C} & ¬{B}) fact6: {GH} fact7: ¬{C} ; $hypothesis$ = ¬{A} ; $proof$ = | void -> assump1: {A}; fact1 & assump1 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 & fact7 -> int3: #F#; [assump1] & int3 -> hypothesis; __PROVED__ |
0.3 | ããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ããŠé²åãæãããšããããšã¯äºå®ã | ({E}{b} & {F}{b}) | fact1: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯æ匟ããªããšãããšãããã¯äœ¿ãé£ããŠå ããŠããã¯èããããšããããšã¯ééã£ãŠãã fact2: ããããã®ããªããLv.15ãèãããšãããšãã®ãŸã«ã
ãŸãLv.63ã¯æ匟ãã fact3: ããããã®ããªããLv.15ã¯èããªããªãã°ããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ããŠãŸãããã¯é²åãæãããšããããšã¯åã§ãã fact4: ãããç¹æ®ãæãã¢ã³ã¹ã¿ãŒãæ匟ãããªããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ã fact5: ãã®ãã¡ã
ããªLv.37ã¯é²åãæã fact6: ããããã®ããªããLv.15ã䜿ãé£ããªãã°ãã®ãŸã«ã
ãŸãLv.63ã¯æ匟ãã fact7: ããä»®ã«ç§»è¡ãæãã¢ã³ã¹ã¿ãŒãç¹æ®ãæããªãæ匟ããªã fact8: ããã®ãŸã«ã
ãŸãLv.63ã¯ç¹æ®ãæãããšããããšã¯æ¬åœã§ãã fact9: ãã®ããªããLv.15ã¯èããããŸãã¯äœ¿ãé£ãããããã¯äž¡æ¹ã | fact1: (x): ¬{C}x -> ¬({B}x & {A}x) fact2: {A}{a} -> {C}{c} fact3: ¬{A}{a} -> ¬({E}{b} & {F}{b}) fact4: (x): ({D}x & {C}x) -> {E}{b} fact5: {F}{b} fact6: {B}{a} -> {C}{c} fact7: (x): ({G}x & {D}x) -> ¬{C}x fact8: {D}{c} fact9: ({A}{a} v {B}{a}) | [
"fact9 & fact2 & fact6 -> int1: ããã®ãŸã«ã
ãŸãLv.63ã¯æ匟ããããšããããšã¯äºå®ãšç°ãªããªã; int1 & fact8 -> int2: ãã®ãŸã«ã
ãŸãLv.63ã¯ç¹æ®ãæããŠæ匟ãã; int2 -> int3: ãç¹æ®ãæãã¢ã³ã¹ã¿ãŒã§ãã®äžæ匟ããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€; int3 & fact4 -> int4: ãã®ãã¡ã
ããªLv.37ã¯çŽ æ©ã; int4 & fact5 -> hypothesis;"
] | [
"fact9 & fact2 & fact6 -> int1: {C}{c}; int1 & fact8 -> int2: ({D}{c} & {C}{c}); int2 -> int3: (Ex): ({D}x & {C}x); int3 & fact4 -> int4: {E}{b}; int4 & fact5 -> hypothesis;"
] | ããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ããããã¯é²åãæãããšããããšã¯æãç«ããªã | ¬({E}{b} & {F}{b}) | [
"fact10 -> int5: ãã®ãŸã«ã
ãŸãLv.63ã¯æ匟ããªããªãã°ããã®ãŸã«ã
ãŸãLv.63ã¯äœ¿ãé£ããŠãŸãããã¯èããããšããããšã¯æ£ãããªã; fact12 -> int6: ãããã®ãŸã«ã
ãŸãLv.63ã移è¡ãæãã¢ã³ã¹ã¿ãŒã§ç¹æ®ãæããšããããã®ãŸã«ã
ãŸãLv.63ã¯æ匟ããªã;"
] | 7 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯æ匟ããªããšãããšãããã¯äœ¿ãé£ããŠå ããŠããã¯èããããšããããšã¯ééã£ãŠãã fact2: ããããã®ããªããLv.15ãèãããšãããšãã®ãŸã«ã
ãŸãLv.63ã¯æ匟ãã fact3: ããããã®ããªããLv.15ã¯èããªããªãã°ããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ããŠãŸãããã¯é²åãæãããšããããšã¯åã§ãã fact4: ãããç¹æ®ãæãã¢ã³ã¹ã¿ãŒãæ匟ãããªããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ã fact5: ãã®ãã¡ã
ããªLv.37ã¯é²åãæã fact6: ããããã®ããªããLv.15ã䜿ãé£ããªãã°ãã®ãŸã«ã
ãŸãLv.63ã¯æ匟ãã fact7: ããä»®ã«ç§»è¡ãæãã¢ã³ã¹ã¿ãŒãç¹æ®ãæããªãæ匟ããªã fact8: ããã®ãŸã«ã
ãŸãLv.63ã¯ç¹æ®ãæãããšããããšã¯æ¬åœã§ãã fact9: ãã®ããªããLv.15ã¯èããããŸãã¯äœ¿ãé£ãããããã¯äž¡æ¹ã ; $hypothesis$ = ããã®ãã¡ã
ããªLv.37ã¯çŽ æ©ããŠé²åãæãããšããããšã¯äºå®ã ; $proof$ = | fact9 & fact2 & fact6 -> int1: ããã®ãŸã«ã
ãŸãLv.63ã¯æ匟ããããšããããšã¯äºå®ãšç°ãªããªã; int1 & fact8 -> int2: ãã®ãŸã«ã
ãŸãLv.63ã¯ç¹æ®ãæããŠæ匟ãã; int2 -> int3: ãç¹æ®ãæãã¢ã³ã¹ã¿ãŒã§ãã®äžæ匟ããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ã€; int3 & fact4 -> int4: ãã®ãã¡ã
ããªLv.37ã¯çŽ æ©ã; int4 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{C}x -> ¬({B}x & {A}x) fact2: {A}{a} -> {C}{c} fact3: ¬{A}{a} -> ¬({E}{b} & {F}{b}) fact4: (x): ({D}x & {C}x) -> {E}{b} fact5: {F}{b} fact6: {B}{a} -> {C}{c} fact7: (x): ({G}x & {D}x) -> ¬{C}x fact8: {D}{c} fact9: ({A}{a} v {B}{a}) ; $hypothesis$ = ({E}{b} & {F}{b}) ; $proof$ = | fact9 & fact2 & fact6 -> int1: {C}{c}; int1 & fact8 -> int2: ({D}{c} & {C}{c}); int2 -> int3: (Ex): ({D}x & {C}x); int3 & fact4 -> int4: {E}{b}; int4 & fact5 -> hypothesis; __PROVED__ |
0.3 | ããã®ã¿ã¡ãã¿ã«ãLv.62ã¯éãé£ãããããã¯é«ããäž¡æ¹ã§ããããšããããšã¯èª€ãã§ãã | ¬({D}{d} v {E}{d}) | fact1: ãã®ã·ã¡ãã·ã¡ãLv.46ãæ©ããšããããšã¯ãªããšããããã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ã fact2: ããä»®ã«ããã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ãããšããããšã¯æ¬åœã ãšãããšãéãé£ãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã fact3: ããä»®ã«ããã®ã·ãã·ãLv.53ã¯å å·¥ãæããŠããŸãã«çºæ®ãæãããšããããšã¯æãç«ããªããšããã°ãã®ã·ã¡ãã·ã¡ãLv.46ã¯æ©ããªã fact4: ãã®ãŸã«ã
ãŸã«Lv.17ã¯è¿ããªã fact5: ããããã®ãŸã«ã
ãŸã«Lv.17ã¯è¿ããªããšãããšããã®ã·ãã·ãLv.53ãå å·¥ãæãããã®äžçºæ®ãæãããšããããšã¯æãç«ããªã fact6: ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯è¿ããããŸãã«ããã¯å¡ãããšããããšã¯æãç«ããªããšãããšããã¯è¿ããªã fact7: ããä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯è¿ããªãããšããããšã¯ç¢ºãã ãšããã°ãããã¯èº«æ¶ãããããŸãéãé£ãããšããããšã¯æãç«ããªã | fact1: ¬{B}{c} -> {C}{d} fact2: {C}{d} -> {D}{d} fact3: ¬({AA}{b} & {AB}{b}) -> ¬{B}{c} fact4: ¬{A}{a} fact5: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact6: (x): ¬({A}x & {C}x) -> ¬{A}x fact7: (x): ¬{A}x -> ¬({O}x & {D}x) | [
"fact5 & fact4 -> int1: ããã®ã·ãã·ãLv.53ã¯å å·¥ãæããæŽã«çºæ®ãæãããšããããšã¯èª€ãã§ãã; int1 & fact3 -> int2: ããã®ã·ã¡ãã·ã¡ãLv.46ã¯æ©ããšããããšã¯ãªãããšããããšã¯çå®ã ; int2 & fact1 -> int3: ãã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ã; int3 & fact2 -> int4: ãã®ã¿ã¡ãã¿ã«ãLv.62ã¯éãé£ã; int4 -> hypothesis;"
] | [
"fact5 & fact4 -> int1: ¬({AA}{b} & {AB}{b}); int1 & fact3 -> int2: ¬{B}{c}; int2 & fact1 -> int3: {C}{d}; int3 & fact2 -> int4: {D}{d}; int4 -> hypothesis;"
] | ããã®ã·ãã·ã«ãLv.97ã身æ¶ãããããã®äžããã¯éãé£ãããšããããšã¯æãç«ããªã | ¬({O}{hq} & {D}{hq}) | [
"fact8 -> int5: ããããã®ã·ãã·ã«ãLv.97ã¯è¿ããªããšããããããã¯èº«æ¶ãããããŸãéãé£ãããšããããšã¯ç¢ºãã§ãªã; fact9 -> int6: ããããã®ã·ãã·ã«ãLv.97ã¯è¿ãããŸãå¡ãããšããããšã¯æãç«ããªããªããã®ã·ãã·ã«ãLv.97ã¯è¿ããªã;"
] | 5 | 5 | 5 | 5 | 5 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ã¡ãã·ã¡ãLv.46ãæ©ããšããããšã¯ãªããšããããã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ã fact2: ããä»®ã«ããã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ãããšããããšã¯æ¬åœã ãšãããšãéãé£ãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªã fact3: ããä»®ã«ããã®ã·ãã·ãLv.53ã¯å å·¥ãæããŠããŸãã«çºæ®ãæãããšããããšã¯æãç«ããªããšããã°ãã®ã·ã¡ãã·ã¡ãLv.46ã¯æ©ããªã fact4: ãã®ãŸã«ã
ãŸã«Lv.17ã¯è¿ããªã fact5: ããããã®ãŸã«ã
ãŸã«Lv.17ã¯è¿ããªããšãããšããã®ã·ãã·ãLv.53ãå å·¥ãæãããã®äžçºæ®ãæãããšããããšã¯æãç«ããªã fact6: ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯è¿ããããŸãã«ããã¯å¡ãããšããããšã¯æãç«ããªããšãããšããã¯è¿ããªã fact7: ããä»®ã«ãäœããã®ã¢ã³ã¹ã¿ãŒã¯è¿ããªãããšããããšã¯ç¢ºãã ãšããã°ãããã¯èº«æ¶ãããããŸãéãé£ãããšããããšã¯æãç«ããªã ; $hypothesis$ = ããã®ã¿ã¡ãã¿ã«ãLv.62ã¯éãé£ãããããã¯é«ããäž¡æ¹ã§ããããšããããšã¯èª€ãã§ãã ; $proof$ = | fact5 & fact4 -> int1: ããã®ã·ãã·ãLv.53ã¯å å·¥ãæããæŽã«çºæ®ãæãããšããããšã¯èª€ãã§ãã; int1 & fact3 -> int2: ããã®ã·ã¡ãã·ã¡ãLv.46ã¯æ©ããšããããšã¯ãªãããšããããšã¯çå®ã ; int2 & fact1 -> int3: ãã®ã¿ã¡ãã¿ã«ãLv.62ã¯å¡ã; int3 & fact2 -> int4: ãã®ã¿ã¡ãã¿ã«ãLv.62ã¯éãé£ã; int4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{B}{c} -> {C}{d} fact2: {C}{d} -> {D}{d} fact3: ¬({AA}{b} & {AB}{b}) -> ¬{B}{c} fact4: ¬{A}{a} fact5: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact6: (x): ¬({A}x & {C}x) -> ¬{A}x fact7: (x): ¬{A}x -> ¬({O}x & {D}x) ; $hypothesis$ = ¬({D}{d} v {E}{d}) ; $proof$ = | fact5 & fact4 -> int1: ¬({AA}{b} & {AB}{b}); int1 & fact3 -> int2: ¬{B}{c}; int2 & fact1 -> int3: {C}{d}; int3 & fact2 -> int4: {D}{d}; int4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.50ã¯æ°åŸããã | {C}{a} | fact1: ãã®ãŸããŸãLv.50ã¯å¹Œããšããããšã¯ãªã fact2: ãããã®ãŸããŸãLv.50ãæ»æãæããšããã幌ã fact3: ãããã®ãŸããŸãLv.50ãæ»æãæããªããšããããã®ãŸããŸãLv.50ã¯æ°åŸããã fact4: ãã®ã·ã«ã
ã·ã«ã
Lv.10ã¯ä»æ¹ç¡ããªã fact5: ããããã®ãããã¡ã
Lv.90ãä»æ¹ç¡ããªãããŸããããã€ã¡ãŒãžãæããªããšãããšãã®ãããã¡ã
Lv.90ã¯æ»æãæããªã fact6: ãã®ãã«ãããLv.0ã¯æ°åŸããã | fact1: ¬{B}{a} fact2: {A}{a} -> {B}{a} fact3: ¬{A}{a} -> {C}{a} fact4: ¬{E}{c} fact5: (¬{E}{b} & ¬{D}{b}) -> ¬{A}{b} fact6: {C}{gi} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸãLv.50ã¯æ»æãæã; fact2 & assump1 -> int1: ãã®ãŸããŸãLv.50ã¯å¹Œã; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŸããŸãLv.50ã¯æ»æãæããªã; int3 & fact3 -> hypothesis;"
] | [
"void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}{a}; int3 & fact3 -> hypothesis;"
] | ãã®ãŸããŸãLv.50ã¯æ°åŸããããšããããšã¯ãªã | ¬{C}{a} | [
"fact7 -> int4: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯ä»æ¹ç¡ããªã;"
] | 6 | 5 | 4 | 5 | 4 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸãLv.50ã¯å¹Œããšããããšã¯ãªã fact2: ãããã®ãŸããŸãLv.50ãæ»æãæããšããã幌ã fact3: ãããã®ãŸããŸãLv.50ãæ»æãæããªããšããããã®ãŸããŸãLv.50ã¯æ°åŸããã fact4: ãã®ã·ã«ã
ã·ã«ã
Lv.10ã¯ä»æ¹ç¡ããªã fact5: ããããã®ãããã¡ã
Lv.90ãä»æ¹ç¡ããªãããŸããããã€ã¡ãŒãžãæããªããšãããšãã®ãããã¡ã
Lv.90ã¯æ»æãæããªã fact6: ãã®ãã«ãããLv.0ã¯æ°åŸããã ; $hypothesis$ = ãã®ãŸããŸãLv.50ã¯æ°åŸããã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããã®ãŸããŸãLv.50ã¯æ»æãæã; fact2 & assump1 -> int1: ãã®ãŸããŸãLv.50ã¯å¹Œã; int1 & fact1 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ãŸããŸãLv.50ã¯æ»æãæããªã; int3 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B}{a} fact2: {A}{a} -> {B}{a} fact3: ¬{A}{a} -> {C}{a} fact4: ¬{E}{c} fact5: (¬{E}{b} & ¬{D}{b}) -> ¬{A}{b} fact6: {C}{gi} ; $hypothesis$ = {C}{a} ; $proof$ = | void -> assump1: {A}{a}; fact2 & assump1 -> int1: {B}{a}; int1 & fact1 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}{a}; int3 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ããããLv.25ã¯èŠãé£ãããããããã¯é£²ã¿é£ããªã | ({D}{a} & ¬{A}{a}) | fact1: ããä»®ã«ãã®ããããLv.25ã¯éªéèããªãã°ãä¹
ãããšããããšã¯æ¬åœã fact2: ãã®ããããLv.25ã¯å€ããšããããšã¯ãªã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çŸå³ãããªã fact4: ãæããªãã¢ã³ã¹ã¿ãŒã¯é£²ã¿é£ããªãããããå€ã fact5: ããããã®ããããLv.25ã飲ã¿é£ããªãå€ã | fact1: {BC}{a} -> {GQ}{a} fact2: ¬{B}{a} fact3: (x): ¬{E}x fact4: (x): ¬{C}x -> (¬{A}x & {B}x) fact5: {A}{a} -> {B}{a} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããã®ããããLv.25ã¯é£²ã¿é£ã; fact5 & assump1 -> int1: ããã®ããããLv.25ã¯å€ãããšããããšã¯äºå®ãšç°ãªããªã; int1 & fact2 -> int2: ããã¯ççŸã§ãã; [assump1] & int2 -> int3: ãã®ããããLv.25ã¯é£²ã¿é£ããšããããšã¯ãªã;"
] | [
"void -> assump1: {A}{a}; fact5 & assump1 -> int1: {B}{a}; int1 & fact2 -> int2: #F#; [assump1] & int2 -> int3: ¬{A}{a};"
] | ããã®ããããLv.25ã¯èŠãé£ãããã©é£²ã¿é£ããªãããšããããšã¯ééãã§ãã | ¬({D}{a} & ¬{A}{a}) | [
"fact6 -> int4: ãã®ãœããœãªLv.30ã¯çŸå³ãããªã;"
] | 6 | 5 | 4 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ããããLv.25ã¯éªéèããªãã°ãä¹
ãããšããããšã¯æ¬åœã fact2: ãã®ããããLv.25ã¯å€ããšããããšã¯ãªã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çŸå³ãããªã fact4: ãæããªãã¢ã³ã¹ã¿ãŒã¯é£²ã¿é£ããªãããããå€ã fact5: ããããã®ããããLv.25ã飲ã¿é£ããªãå€ã ; $hypothesis$ = ãã®ããããLv.25ã¯èŠãé£ãããããããã¯é£²ã¿é£ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {BC}{a} -> {GQ}{a} fact2: ¬{B}{a} fact3: (x): ¬{E}x fact4: (x): ¬{C}x -> (¬{A}x & {B}x) fact5: {A}{a} -> {B}{a} ; $hypothesis$ = ({D}{a} & ¬{A}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããããŸããŸãLv.99äºä»¶ãèµ·ããããããã¯ç¡ããšããããšã¯èµ·ãããªãããŸãã¯äž¡æ¹ã§ãã | ({AA} v ¬{AB}) | fact1: ããŸããŸãLv.99äºä»¶ãçºçãããç¡ããšããããšã¯çããªããäž¡æ¹ãšãã§ããããšããããšã¯ã¿ãªã¿ã«Lv.92äºä»¶ãé»ã fact2: ãŸããŸãLv.99äºä»¶ãçºçãããç¡ããšããããšãèµ·ããããããã¯äž¡æ¹ãšãã fact3: ç¡ããšããããšãèµ·ãã fact4: ããä»®ã«ãããªãããããšãèµ·ããªããšãããšã²åŒ±ããšããããšã¯çºçããªããŠããŸãã«ã¿ãªã¿ã«Lv.92äºä»¶ã¯çºçããªã fact5: ã²åŒ±ããšããããšãçãã | fact1: ({AA} v ¬{AB}) -> ¬{B} fact2: ({AA} v {AB}) fact3: {AB} fact4: ¬{C} -> (¬{A} & ¬{B}) fact5: {A} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããŸããŸãLv.99äºä»¶ãèµ·ããããããã¯ç¡ããšããããšã¯èµ·ãããªãããŸãã¯äž¡æ¹ã§ãã; fact1 & assump1 -> int1: ã¿ãªã¿ã«Lv.92äºä»¶ã¯çããªã;"
] | [
"void -> assump1: ({AA} v ¬{AB}); fact1 & assump1 -> int1: ¬{B};"
] | 以äžã®ããã«ä»®å®ããããŸããŸãLv.99äºä»¶ãèµ·ããããããã¯ç¡ããšããããšã¯èµ·ãããªãããŸãã¯äž¡æ¹ã§ãã | ({AA} v ¬{AB}) | [] | 6 | 5 | 4 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããŸããŸãLv.99äºä»¶ãçºçãããç¡ããšããããšã¯çããªããäž¡æ¹ãšãã§ããããšããããšã¯ã¿ãªã¿ã«Lv.92äºä»¶ãé»ã fact2: ãŸããŸãLv.99äºä»¶ãçºçãããç¡ããšããããšãèµ·ããããããã¯äž¡æ¹ãšãã fact3: ç¡ããšããããšãèµ·ãã fact4: ããä»®ã«ãããªãããããšãèµ·ããªããšãããšã²åŒ±ããšããããšã¯çºçããªããŠããŸãã«ã¿ãªã¿ã«Lv.92äºä»¶ã¯çºçããªã fact5: ã²åŒ±ããšããããšãçãã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããããŸããŸãLv.99äºä»¶ãèµ·ããããããã¯ç¡ããšããããšã¯èµ·ãããªãããŸãã¯äž¡æ¹ã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({AA} v ¬{AB}) -> ¬{B} fact2: ({AA} v {AB}) fact3: {AB} fact4: ¬{C} -> (¬{A} & ¬{B}) fact5: {A} ; $hypothesis$ = ({AA} v ¬{AB}) ; $proof$ = | __UNKNOWN__ |
0.3 | 以äžã®ããã«ä»®å®ããã貎æ¹ããããšããããšãèµ·ãã | {A} | fact1: ã¡ããããšããããšãçºçãã fact2: ç¡ã£èŸããšããããšãèµ·ãã fact3: 霧ãä»ãããšãèµ·ãã fact4: ãœã«ããœãLv.62äºä»¶ã¯èµ·ãããªã | fact1: {B} fact2: {C} fact3: {EL} fact4: ¬{DI} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããã貎æ¹ããããšããããšãèµ·ãã; assump1 & fact1 -> int1: 貎æ¹ããããšããããšãèµ·ãããããã«ã¡ããããšããããšãèµ·ãã;"
] | [
"void -> assump1: {A}; assump1 & fact1 -> int1: ({A} & {B});"
] | null | null | [] | null | 5 | 4 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ã¡ããããšããããšãçºçãã fact2: ç¡ã£èŸããšããããšãèµ·ãã fact3: 霧ãä»ãããšãèµ·ãã fact4: ãœã«ããœãLv.62äºä»¶ã¯èµ·ãããªã ; $hypothesis$ = 以äžã®ããã«ä»®å®ããã貎æ¹ããããšããããšãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} fact2: {C} fact3: {EL} fact4: ¬{DI} ; $hypothesis$ = {A} ; $proof$ = | __UNKNOWN__ |
0.3 | ããæ±ãé£ããšããããšã§ã¯ãªããŠåŸ¡ãæããšããããšãçºçããããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬(¬{G} & {F}) | fact1: ä»®ã«ã¹ãä»ãæããšããããšã¯èµ·ãããªããªãã圹ããããšããããšãšæ±ãé£ããšããããšãçããããšããããšã¯èª€ã£ãŠãã fact2: ããä»®ã«ã圹ããããšããããšããã³æ±ãé£ããšããããšãèµ·ããããšããããšã¯èª€ãã§ãããšãããæ±ãé£ããšããããšã¯çºçããªã fact3: ããããè¡ãæããšããããšãçºçãããæŽã«ç¡ã£èŸããšããããšãçããããšããããšã¯ééã£ãŠããã°ã¹ãä»ãæããšããããšã¯èµ·ããªã fact4: ã圹ããããšããããšãèµ·ãããããŸãã«ã¹ãä»ãæããšããããšãèµ·ããããšããããšã¯ã誀解ãæããšããããšã¯èµ·ããªãããšããããšã«åž°çµãã fact5: ä»®ã«èª€è§£ãæããšããããšã¯çºçããªããšããã°ãæ±ãé£ããšããããšã¯çããªãã埡ãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact6: çŽ ã£æ°ãªããšããããšãšè² æ
ããããšã©ã¡ãããçºçãã fact7: çŽ ã£æ°ãªããšããããšã¯ã¹ãä»ãæããšããããšããããã fact8: 圹ããããšããããšãèµ·ãã | fact1: ¬{C} -> ¬({D} & {G}) fact2: ¬({D} & {G}) -> ¬{G} fact3: ¬({H} & {I}) -> ¬{C} fact4: ({D} & {C}) -> ¬{E} fact5: ¬{E} -> ¬(¬{G} & {F}) fact6: ({A} & {B}) fact7: {A} -> {C} fact8: {D} | [
"fact6 -> int1: ãçŽ ã£æ°ãªããšããããšãçããããšããããšã¯äºå®ã ; int1 & fact7 -> int2: ã¹ãä»ãæããšããããšãçãã; int2 & fact8 -> int3: 圹ããããšããããšãšã¹ãä»ãæããšããããšãçãã; int3 & fact4 -> int4: 誀解ãæããšããããšã¯çããªã; int4 & fact5 -> hypothesis;"
] | [
"fact6 -> int1: {A}; int1 & fact7 -> int2: {C}; int2 & fact8 -> int3: ({D} & {C}); int3 & fact4 -> int4: ¬{E}; int4 & fact5 -> hypothesis;"
] | æ±ãé£ããšããããšã§ã¯ãªã埡ãæããšããããšãçãã | (¬{G} & {F}) | [] | 5 | 5 | 5 | 5 | 5 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ã¹ãä»ãæããšããããšã¯èµ·ãããªããªãã圹ããããšããããšãšæ±ãé£ããšããããšãçããããšããããšã¯èª€ã£ãŠãã fact2: ããä»®ã«ã圹ããããšããããšããã³æ±ãé£ããšããããšãèµ·ããããšããããšã¯èª€ãã§ãããšãããæ±ãé£ããšããããšã¯çºçããªã fact3: ããããè¡ãæããšããããšãçºçãããæŽã«ç¡ã£èŸããšããããšãçããããšããããšã¯ééã£ãŠããã°ã¹ãä»ãæããšããããšã¯èµ·ããªã fact4: ã圹ããããšããããšãèµ·ãããããŸãã«ã¹ãä»ãæããšããããšãèµ·ããããšããããšã¯ã誀解ãæããšããããšã¯èµ·ããªãããšããããšã«åž°çµãã fact5: ä»®ã«èª€è§£ãæããšããããšã¯çºçããªããšããã°ãæ±ãé£ããšããããšã¯çããªãã埡ãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact6: çŽ ã£æ°ãªããšããããšãšè² æ
ããããšã©ã¡ãããçºçãã fact7: çŽ ã£æ°ãªããšããããšã¯ã¹ãä»ãæããšããããšããããã fact8: 圹ããããšããããšãèµ·ãã ; $hypothesis$ = ããæ±ãé£ããšããããšã§ã¯ãªããŠåŸ¡ãæããšããããšãçºçããããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact6 -> int1: ãçŽ ã£æ°ãªããšããããšãçããããšããããšã¯äºå®ã ; int1 & fact7 -> int2: ã¹ãä»ãæããšããããšãçãã; int2 & fact8 -> int3: 圹ããããšããããšãšã¹ãä»ãæããšããããšãçãã; int3 & fact4 -> int4: 誀解ãæããšããããšã¯çããªã; int4 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{C} -> ¬({D} & {G}) fact2: ¬({D} & {G}) -> ¬{G} fact3: ¬({H} & {I}) -> ¬{C} fact4: ({D} & {C}) -> ¬{E} fact5: ¬{E} -> ¬(¬{G} & {F}) fact6: ({A} & {B}) fact7: {A} -> {C} fact8: {D} ; $hypothesis$ = ¬(¬{G} & {F}) ; $proof$ = | fact6 -> int1: {A}; int1 & fact7 -> int2: {C}; int2 & fact8 -> int3: ({D} & {C}); int3 & fact4 -> int4: ¬{E}; int4 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœããœã¡ã
Lv.68ã¯èµ€é»ãããããèªããã | ({E}{b} & {F}{b}) | fact1: ä»®ã«ãã®ãŽãªãŽãLv.18ãåŸãæããšãããšãã®ãœããœã¡ã
Lv.68ã¯æ©ã¿å§ãã fact2: ãã®ãœããœã¡ã
Lv.68ã¯èªããã fact3: ãã®ãŽãªãŽãLv.18ãæ°ãŸãããšããããã®ãŽãªãŽãLv.18ã¯åŸãæã fact4: ãããã®ãœããœã¡ã
Lv.68ãæ©ã¿å§ãããšããã°ããã¯èµ€é»ã fact5: ãã®ãŽãªãŽãLv.18ã¯æåºããŠå ããŠæ°ãŸãã | fact1: {C}{a} -> {D}{b} fact2: {F}{b} fact3: {B}{a} -> {C}{a} fact4: {D}{b} -> {E}{b} fact5: ({A}{a} & {B}{a}) | [
"fact5 -> int1: ãã®ãŽãªãŽãLv.18ã¯æ°ãŸãã; int1 & fact3 -> int2: ãã®ãŽãªãŽãLv.18ã¯åŸãæã; int2 & fact1 -> int3: ãã®ãœããœã¡ã
Lv.68ã¯æ©ã¿å§ãã; int3 & fact4 -> int4: ãã®ãœããœã¡ã
Lv.68ã¯èµ€é»ã; int4 & fact2 -> hypothesis;"
] | [
"fact5 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact1 -> int3: {D}{b}; int3 & fact4 -> int4: {E}{b}; int4 & fact2 -> hypothesis;"
] | null | null | [] | null | 5 | 5 | 5 | 5 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŽãªãŽãLv.18ãåŸãæããšãããšãã®ãœããœã¡ã
Lv.68ã¯æ©ã¿å§ãã fact2: ãã®ãœããœã¡ã
Lv.68ã¯èªããã fact3: ãã®ãŽãªãŽãLv.18ãæ°ãŸãããšããããã®ãŽãªãŽãLv.18ã¯åŸãæã fact4: ãããã®ãœããœã¡ã
Lv.68ãæ©ã¿å§ãããšããã°ããã¯èµ€é»ã fact5: ãã®ãŽãªãŽãLv.18ã¯æåºããŠå ããŠæ°ãŸãã ; $hypothesis$ = ãã®ãœããœã¡ã
Lv.68ã¯èµ€é»ãããããèªããã ; $proof$ = | fact5 -> int1: ãã®ãŽãªãŽãLv.18ã¯æ°ãŸãã; int1 & fact3 -> int2: ãã®ãŽãªãŽãLv.18ã¯åŸãæã; int2 & fact1 -> int3: ãã®ãœããœã¡ã
Lv.68ã¯æ©ã¿å§ãã; int3 & fact4 -> int4: ãã®ãœããœã¡ã
Lv.68ã¯èµ€é»ã; int4 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{a} -> {D}{b} fact2: {F}{b} fact3: {B}{a} -> {C}{a} fact4: {D}{b} -> {E}{b} fact5: ({A}{a} & {B}{a}) ; $hypothesis$ = ({E}{b} & {F}{b}) ; $proof$ = | fact5 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact1 -> int3: {D}{b}; int3 & fact4 -> int4: {E}{b}; int4 & fact2 -> hypothesis; __PROVED__ |