version
stringclasses 1
value | hypothesis
stringlengths 8
84
| hypothesis_formula
stringclasses 489
values | facts
stringlengths 18
581
| facts_formula
stringlengths 10
318
| proofs
sequencelengths 0
1
| proofs_formula
sequencelengths 0
1
| negative_hypothesis
stringlengths 8
91
â | negative_hypothesis_formula
stringlengths 3
36
â | negative_proofs
sequencelengths 0
1
| negative_original_tree_depth
int64 0
11
â | original_tree_steps
int64 1
3
| original_tree_depth
int64 1
3
| steps
int64 1
3
â | depth
int64 1
3
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 75
645
| proof_serial
stringlengths 11
236
| prompt_serial_formula
stringlengths 61
365
| proof_serial_formula
stringlengths 11
147
|
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.3 | ããã®ãœã«ããœãLv.86ã¯çãèŸãããã€èéãããšããããšã¯èª€ã£ãŠãã | ¬({C}{c} & {D}{c}) | fact1: ãã®ãœã«ããœãLv.86ã¯èéã fact2: æ·±ããªãã¢ã³ã¹ã¿ãŒã¯çãèŸããããŸãã«èãæã fact3: æ·±ããªãã¢ã³ã¹ã¿ãŒãçµå¶åºæ¥ãªããšãããšããã¯èãæããªã fact4: ãããã®ãŸãªãŸã«ãLv.61ãæ·±ããªããã®ãœã«ããœãLv.86ã¯çãèŸã fact5: ãã®ããããLv.84ã¯èãæã fact6: ããä»®ã«ãã®ããããLv.84ã¯èãæããªããšãããããã®ãœã«ããœãLv.86ãçãèŸãããã®äžèéãããšããããšã¯åœã fact7: ããããšããã¢ã³ã¹ã¿ãŒã¯åãç· ãŸãããããããã¯æ¯çããªãããšããããšã¯æãç«ããªããšãããããã¯å±¯ãããšããããšã¯ãªã fact8: ãã®ããããLv.84ãèãæããšããã°ãã®ãŸãªãŸã«ãLv.61ã¯æ·±ã fact9: ãããã®ããããLv.84ã屯ããªããšãããæ·±ããªããçµå¶åºæ¥ãªã | fact1: {D}{c} fact2: (x): ¬{B}x -> ({C}x & {A}x) fact3: (x): (¬{B}x & ¬{E}x) -> ¬{A}x fact4: {B}{b} -> {C}{c} fact5: {A}{a} fact6: ¬{A}{a} -> ¬({C}{c} & {D}{c}) fact7: (x): ¬({H}x & ¬{G}x) -> ¬{F}x fact8: {A}{a} -> {B}{b} fact9: ¬{F}{a} -> (¬{B}{a} & ¬{E}{a}) | [
"fact8 & fact5 -> int1: ãã®ãŸãªãŸã«ãLv.61ã¯æ·±ã; int1 & fact4 -> int2: ãã®ãœã«ããœãLv.86ã¯çãèŸã; int2 & fact1 -> hypothesis;"
] | [
"fact8 & fact5 -> int1: {B}{b}; int1 & fact4 -> int2: {C}{c}; int2 & fact1 -> hypothesis;"
] | ããã®ãœã«ããœãLv.86ã¯çãèŸãããã€èéãããšããããšã¯èª€ã£ãŠãã | ¬({C}{c} & {D}{c}) | [
"fact10 -> int3: ãããã®ããããLv.84ãæ·±ããªãããŸããããçµå¶åºæ¥ãªããªãããã¯èãæããªã; fact11 -> int4: ããã®ããããLv.84ã¯åãç· ãŸãããã©æ¯çããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°å±¯ãããšããããšã¯ãªã;"
] | 7 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãœã«ããœãLv.86ã¯èéã fact2: æ·±ããªãã¢ã³ã¹ã¿ãŒã¯çãèŸããããŸãã«èãæã fact3: æ·±ããªãã¢ã³ã¹ã¿ãŒãçµå¶åºæ¥ãªããšãããšããã¯èãæããªã fact4: ãããã®ãŸãªãŸã«ãLv.61ãæ·±ããªããã®ãœã«ããœãLv.86ã¯çãèŸã fact5: ãã®ããããLv.84ã¯èãæã fact6: ããä»®ã«ãã®ããããLv.84ã¯èãæããªããšãããããã®ãœã«ããœãLv.86ãçãèŸãããã®äžèéãããšããããšã¯åœã fact7: ããããšããã¢ã³ã¹ã¿ãŒã¯åãç· ãŸãããããããã¯æ¯çããªãããšããããšã¯æãç«ããªããšãããããã¯å±¯ãããšããããšã¯ãªã fact8: ãã®ããããLv.84ãèãæããšããã°ãã®ãŸãªãŸã«ãLv.61ã¯æ·±ã fact9: ãããã®ããããLv.84ã屯ããªããšãããæ·±ããªããçµå¶åºæ¥ãªã ; $hypothesis$ = ããã®ãœã«ããœãLv.86ã¯çãèŸãããã€èéãããšããããšã¯èª€ã£ãŠãã ; $proof$ = | fact8 & fact5 -> int1: ãã®ãŸãªãŸã«ãLv.61ã¯æ·±ã; int1 & fact4 -> int2: ãã®ãœã«ããœãLv.86ã¯çãèŸã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{c} fact2: (x): ¬{B}x -> ({C}x & {A}x) fact3: (x): (¬{B}x & ¬{E}x) -> ¬{A}x fact4: {B}{b} -> {C}{c} fact5: {A}{a} fact6: ¬{A}{a} -> ¬({C}{c} & {D}{c}) fact7: (x): ¬({H}x & ¬{G}x) -> ¬{F}x fact8: {A}{a} -> {B}{b} fact9: ¬{F}{a} -> (¬{B}{a} & ¬{E}{a}) ; $hypothesis$ = ¬({C}{c} & {D}{c}) ; $proof$ = | fact8 & fact5 -> int1: {B}{b}; int1 & fact4 -> int2: {C}{c}; int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.15ã¯èŠãããããã«ç·ã£ãœã | ({B}{a} & {C}{a}) | fact1: ããã®ãœããœãLv.15ã¯ç·ã£ãœãããšããããšã¯æãç«ã€ fact2: ãã®ãœããœãLv.15ã¯æŽã¿æã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯æŽã¿æããªããšããã°ãããã¯èŠããããŸãç·ã£ãœãããšããããšã¯èª€ãã§ãã fact4: ããã®ãœããœãLv.15ã¯æŽã¿æãããšããããšã¯æ£ãããªãèŠãã | fact1: {C}{a} fact2: {A}{a} fact3: (x): ¬{A}x -> ¬({B}x & {C}x) fact4: {A}{a} -> {B}{a} | [
"fact4 & fact2 -> int1: ãã®ãœããœãLv.15ã¯èŠãã; int1 & fact1 -> hypothesis;"
] | [
"fact4 & fact2 -> int1: {B}{a}; int1 & fact1 -> hypothesis;"
] | ããã®ãœããœãLv.15ã¯èŠãããç·ã£ãœãããšããããšã¯æãç«ããªã | ¬({B}{a} & {C}{a}) | [
"fact5 -> int2: ä»®ã«ãã®ãœããœãLv.15ã¯æŽã¿æããªããšãããšããã®ãœããœãLv.15ã¯èŠãããå ããŠç·ã£ãœãããšããããšã¯åœã ;"
] | 4 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®ãœããœãLv.15ã¯ç·ã£ãœãããšããããšã¯æãç«ã€ fact2: ãã®ãœããœãLv.15ã¯æŽã¿æã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯æŽã¿æããªããšããã°ãããã¯èŠããããŸãç·ã£ãœãããšããããšã¯èª€ãã§ãã fact4: ããã®ãœããœãLv.15ã¯æŽã¿æãããšããããšã¯æ£ãããªãèŠãã ; $hypothesis$ = ãã®ãœããœãLv.15ã¯èŠãããããã«ç·ã£ãœã ; $proof$ = | fact4 & fact2 -> int1: ãã®ãœããœãLv.15ã¯èŠãã; int1 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{a} fact2: {A}{a} fact3: (x): ¬{A}x -> ¬({B}x & {C}x) fact4: {A}{a} -> {B}{a} ; $hypothesis$ = ({B}{a} & {C}{a}) ; $proof$ = | fact4 & fact2 -> int1: {B}{a}; int1 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ã¡ã
Lv.61ã¯å©çšãèŸããªã | ¬{D}{b} | fact1: ãã®ã·ãã·ã¡ã
Lv.61ã¯å
ãé£ã fact2: ä»®ã«ãã®ãœããœã®Lv.61ã¯ç³ãäžãããªãããã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ãããããšããããšã¯ééãã ãšããããšã¯ãªã fact3: ãã®ã¿ãã¿ãLv.3ãç¥ã
ãããªãã°ããã¯å¿å°è¯ããªã fact4: ããä»®ã«ãã®ã·ãã·ã¡ã
Lv.61ãé£è¡æ©ãããããŸãã¯ç¥ã
ããããŸãã¯ã©ã¡ããã ãšãããšãã®ã·ãã·ã¡ã
Lv.61ã¯å©çšãèŸããªã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.75ãèšãèš³ããŸãããšããããšã¯ãªããªããã®ãœããœã®Lv.61ã¯ç¥ã
ãããšããããšã¯ãªããã©ããã¯å¯æããã fact6: ç¥ã
ãããªãã¢ã³ã¹ã¿ãŒã¯ç³ãäžããããããã¯é£è¡æ©ãããããããã¯äž¡æ¹ã fact7: ããããã¢ã³ã¹ã¿ãŒã¯ç¥ã
ãããšããããããã¯é£è¡æ©ããããªãããããç³ãäžããããšããããšã¯åã fact8: ãã®ãœããœã®Lv.61ã¯ç³ãäžãã | fact1: {AQ}{b} fact2: {A}{a} -> {B}{b} fact3: {C}{ga} -> ¬{HG}{ga} fact4: ({B}{b} v {C}{b}) -> ¬{D}{b} fact5: ¬{F}{c} -> (¬{C}{a} & {E}{a}) fact6: (x): ¬{C}x -> ({A}x v {B}x) fact7: (x): {C}x -> ¬(¬{B}x & {A}x) fact8: {A}{a} | [
"fact2 & fact8 -> int1: ãã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ããã; int1 -> int2: ãã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ããããç¥ã
ãã; int2 & fact4 -> hypothesis;"
] | [
"fact2 & fact8 -> int1: {B}{b}; int1 -> int2: ({B}{b} v {C}{b}); int2 & fact4 -> hypothesis;"
] | ãã®ãœããœã®Lv.61ã¯å©çšãèŸããªã | ¬{D}{a} | [
"fact9 -> int3: ããä»®ã«ãã®ãœããœã®Lv.61ã¯ç¥ã
ãããšããã°ãããã¯é£è¡æ©ããããªããç³ãäžããããšããããšã¯ééãã§ãã;"
] | 4 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ã·ãã·ã¡ã
Lv.61ã¯å
ãé£ã fact2: ä»®ã«ãã®ãœããœã®Lv.61ã¯ç³ãäžãããªãããã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ãããããšããããšã¯ééãã ãšããããšã¯ãªã fact3: ãã®ã¿ãã¿ãLv.3ãç¥ã
ãããªãã°ããã¯å¿å°è¯ããªã fact4: ããä»®ã«ãã®ã·ãã·ã¡ã
Lv.61ãé£è¡æ©ãããããŸãã¯ç¥ã
ããããŸãã¯ã©ã¡ããã ãšãããšãã®ã·ãã·ã¡ã
Lv.61ã¯å©çšãèŸããªã fact5: ããä»®ã«ãã®ã¿ãã¿ãLv.75ãèšãèš³ããŸãããšããããšã¯ãªããªããã®ãœããœã®Lv.61ã¯ç¥ã
ãããšããããšã¯ãªããã©ããã¯å¯æããã fact6: ç¥ã
ãããªãã¢ã³ã¹ã¿ãŒã¯ç³ãäžããããããã¯é£è¡æ©ãããããããã¯äž¡æ¹ã fact7: ããããã¢ã³ã¹ã¿ãŒã¯ç¥ã
ãããšããããããã¯é£è¡æ©ããããªãããããç³ãäžããããšããããšã¯åã fact8: ãã®ãœããœã®Lv.61ã¯ç³ãäžãã ; $hypothesis$ = ãã®ã·ãã·ã¡ã
Lv.61ã¯å©çšãèŸããªã ; $proof$ = | fact2 & fact8 -> int1: ãã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ããã; int1 -> int2: ãã®ã·ãã·ã¡ã
Lv.61ã¯é£è¡æ©ããããç¥ã
ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {AQ}{b} fact2: {A}{a} -> {B}{b} fact3: {C}{ga} -> ¬{HG}{ga} fact4: ({B}{b} v {C}{b}) -> ¬{D}{b} fact5: ¬{F}{c} -> (¬{C}{a} & {E}{a}) fact6: (x): ¬{C}x -> ({A}x v {B}x) fact7: (x): {C}x -> ¬(¬{B}x & {A}x) fact8: {A}{a} ; $hypothesis$ = ¬{D}{b} ; $proof$ = | fact2 & fact8 -> int1: {B}{b}; int1 -> int2: ({B}{b} v {C}{b}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ã«ãã·ã«ãLv.35ã¯ãã£ããªããŠå ããŠæžãæã | ({D}{a} & {C}{a}) | fact1: ããä»®ã«ãã®ã·ã«ãã·ã«ãLv.35ãçæããªãã°æžãæã fact2: ãã®ã·ã«ãã·ã«ãLv.35ã¯ãã£ããªã | fact1: {B}{a} -> {C}{a} fact2: {D}{a} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããä»®ã«ãã®ã·ã«ãã·ã«ãLv.35ãçæããªãã°æžãæã fact2: ãã®ã·ã«ãã·ã«ãLv.35ã¯ãã£ããªã ; $hypothesis$ = ãã®ã·ã«ãã·ã«ãLv.35ã¯ãã£ããªããŠå ããŠæžãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} -> {C}{a} fact2: {D}{a} ; $hypothesis$ = ({D}{a} & {C}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãŽã¡ã
ãŽã«ã
Lv.64ã¯ææ
šæ·±ãäžæ¹ã§æŽçæŽé ããªãããšããããšã¯èª€ãã§ãã | ¬({AA}{a} & ¬{AB}{a}) | fact1: ææ
šæ·±ãã¢ã³ã¹ã¿ãŒã§æŽã«æŽçæŽé ããã¢ã³ã¹ã¿ãŒã¯ãªã fact2: ããã®ãŽã¡ã
ãŽã«ã
Lv.64ã¯è²°ããã©æŽçæŽé ããªãããšããããšã¯æãç«ããªã fact3: ãšããã¢ã³ã¹ã¿ãŒã¯ã·ã£ããããªããšããããããã¯éºãããæ
ãŠãããšããããšã¯æ£ãã fact4: ããã¯ç£è·ã»é€è²ããããã©æã¡äžããæããªããšããã¢ã³ã¹ã¿ãŒã¯ãªã | fact1: (x): ¬({AA}x & {AB}x) fact2: ¬({GT}{a} & ¬{AB}{a}) fact3: (x): ¬{C}x -> ({A}x & {B}x) fact4: (x): ¬({AI}x & ¬{AO}x) | [] | [] | çãããã¢ã³ã¹ã¿ãŒã§ããæŽã«åŒãåãããªãã¢ã³ã¹ã¿ãŒã¯ãªã | (x): ¬({IA}x & ¬{DS}x) | [
"fact5 -> int1: ãã®ãŽã¡ã
ãŽã«ã
Lv.64ãã·ã£ããããªããšããããã®ãŽã¡ã
ãŽã«ã
Lv.64ã¯éºãããŠããã«æ
ãŠã;"
] | 5 | 2 | 2 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ææ
šæ·±ãã¢ã³ã¹ã¿ãŒã§æŽã«æŽçæŽé ããã¢ã³ã¹ã¿ãŒã¯ãªã fact2: ããã®ãŽã¡ã
ãŽã«ã
Lv.64ã¯è²°ããã©æŽçæŽé ããªãããšããããšã¯æãç«ããªã fact3: ãšããã¢ã³ã¹ã¿ãŒã¯ã·ã£ããããªããšããããããã¯éºãããæ
ãŠãããšããããšã¯æ£ãã fact4: ããã¯ç£è·ã»é€è²ããããã©æã¡äžããæããªããšããã¢ã³ã¹ã¿ãŒã¯ãªã ; $hypothesis$ = ããã®ãŽã¡ã
ãŽã«ã
Lv.64ã¯ææ
šæ·±ãäžæ¹ã§æŽçæŽé ããªãããšããããšã¯èª€ãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬({AA}x & {AB}x) fact2: ¬({GT}{a} & ¬{AB}{a}) fact3: (x): ¬{C}x -> ({A}x & {B}x) fact4: (x): ¬({AI}x & ¬{AO}x) ; $hypothesis$ = ¬({AA}{a} & ¬{AB}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã«ãã·ãLv.54ã¯æºã蟌ã¿æã | {A}{a} | fact1: ãã®ãŸããŸã¡ãLv.7ã¯ç±ã
ãããªãããã©æããã fact2: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªã fact3: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãã fact4: ãããã®ãŸã«ããŸãLv.33ãæºã蟌ã¿æãããã©ãããç®èã£ãœããªããšãããããã¯å£çµããªã fact5: ããããã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªããšãããšæºã蟌ã¿æããšããããšã¯ãªã fact6: ããä»®ã«ãã®ã¿ã®ã¿ã®Lv.70ãç±ã
ãããšãããšãã®ãœããœãLv.6ã¯è²§ããªãäžæ¹ã§å±ãã fact7: ãæºã蟌ã¿æãã¢ã³ã¹ã¿ãŒã¯æžãäžããããã©æããããªãããšããããšã¯äºå®ã§ãã | fact1: (¬{E}{d} & {F}{d}) fact2: ({AA}{a} & ¬{AB}{a}) fact3: {AA}{a} fact4: ({A}{cd} & ¬{EH}{cd}) -> ¬{GS}{cd} fact5: ({AA}{a} & ¬{AB}{a}) -> ¬{A}{a} fact6: {E}{c} -> (¬{C}{b} & {D}{b}) fact7: (x): {A}x -> ({AA}x & ¬{F}x) | [
"fact2 -> int1: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªã; int1 & fact5 -> hypothesis;"
] | [
"fact2 -> int1: ({AA}{a} & ¬{AB}{a}); int1 & fact5 -> hypothesis;"
] | ãã®ãŽã®ãŽã¡ãLv.11ã¯æžãäžããããã©æããããªã | ({AA}{hk} & ¬{F}{hk}) | [
"fact8 -> int2: ããä»®ã«ãã®ãŽã®ãŽã¡ãLv.11ãæºã蟌ã¿æããªãã°ãã®ãŽã®ãŽã¡ãLv.11ã¯æžãäžããããã©æããããšããããšã¯ãªã;"
] | 4 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸã¡ãLv.7ã¯ç±ã
ãããªãããã©æããã fact2: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªã fact3: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãã fact4: ãããã®ãŸã«ããŸãLv.33ãæºã蟌ã¿æãããã©ãããç®èã£ãœããªããšãããããã¯å£çµããªã fact5: ããããã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªããšãããšæºã蟌ã¿æããšããããšã¯ãªã fact6: ããä»®ã«ãã®ã¿ã®ã¿ã®Lv.70ãç±ã
ãããšãããšãã®ãœããœãLv.6ã¯è²§ããªãäžæ¹ã§å±ãã fact7: ãæºã蟌ã¿æãã¢ã³ã¹ã¿ãŒã¯æžãäžããããã©æããããªãããšããããšã¯äºå®ã§ãã ; $hypothesis$ = ãã®ã·ã«ãã·ãLv.54ã¯æºã蟌ã¿æã ; $proof$ = | fact2 -> int1: ãã®ã·ã«ãã·ãLv.54ã¯æžãäžãããæ»ãé£ããªã; int1 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{E}{d} & {F}{d}) fact2: ({AA}{a} & ¬{AB}{a}) fact3: {AA}{a} fact4: ({A}{cd} & ¬{EH}{cd}) -> ¬{GS}{cd} fact5: ({AA}{a} & ¬{AB}{a}) -> ¬{A}{a} fact6: {E}{c} -> (¬{C}{b} & {D}{b}) fact7: (x): {A}x -> ({AA}x & ¬{F}x) ; $hypothesis$ = {A}{a} ; $proof$ = | fact2 -> int1: ({AA}{a} & ¬{AB}{a}); int1 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãã«ã
ãã«ãLv.92ã¯çœå¶ããããããã¿ã€ãã«ãããããšããããšã¯ééã£ãŠãã | ¬({A}{b} & {B}{b}) | fact1: ãã®ãã«ã
ãã«ãLv.92ã¯çœå¶ãã fact2: ããã®ã¿ãã¿ãLv.47ã¯æåãæãã劬ãŸãããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact3: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯çºçŸãæããªããšãããšãçœå¶ãããããã«ã¿ã€ãã«ãããããšããããšã¯æ£ãããªã fact4: ããã®ã¿ãã¿ãLv.47ã¯æåãæããããã¯åŠ¬ãŸããããšããããšã¯æãç«ããªã | fact1: {A}{b} fact2: ¬({AA}{a} & ¬{AB}{a}) fact3: (x): ¬{C}x -> ¬({A}x & {B}x) fact4: ¬({AA}{a} & {AB}{a}) | [] | [] | ããã®ãã«ã
ãã«ãLv.92ã¯çœå¶ããããããã¿ã€ãã«ãããããšããããšã¯ééã£ãŠãã | ¬({A}{b} & {B}{b}) | [
"fact5 -> int1: ãã®ãã«ã
ãã«ãLv.92ã¯çºçŸãæããªããªãã°ãããã¯çœå¶ãããã¿ã€ãã«ãããããšããããšã¯ééã£ãŠãã;"
] | 6 | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãã«ã
ãã«ãLv.92ã¯çœå¶ãã fact2: ããã®ã¿ãã¿ãLv.47ã¯æåãæãã劬ãŸãããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact3: ããäœããã®ã¢ã³ã¹ã¿ãŒã¯çºçŸãæããªããšãããšãçœå¶ãããããã«ã¿ã€ãã«ãããããšããããšã¯æ£ãããªã fact4: ããã®ã¿ãã¿ãLv.47ã¯æåãæããããã¯åŠ¬ãŸããããšããããšã¯æãç«ããªã ; $hypothesis$ = ããã®ãã«ã
ãã«ãLv.92ã¯çœå¶ããããããã¿ã€ãã«ãããããšããããšã¯ééã£ãŠãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{b} fact2: ¬({AA}{a} & ¬{AB}{a}) fact3: (x): ¬{C}x -> ¬({A}x & {B}x) fact4: ¬({AA}{a} & {AB}{a}) ; $hypothesis$ = ¬({A}{b} & {B}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ã·ã«ãã·ãªLv.65äºä»¶ãèµ·ãã | {D} | fact1: ãŽã®ãŽã«ãLv.28äºä»¶ã¯çããªã fact2: ãããéè¿ããšããããšãçãããå瀺ããããšãèµ·ãããªããªãã°ããããLv.10äºä»¶ã¯çºçããªã fact3: ä»®ã«ãééãæããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãããšãããšæ£èŠããããšã¯èµ·ããªã fact4: éè¿ããšããããšããã³å瀺ããããšäž¡æ¹ãšããèµ·ãã fact5: ã·ã«ã
ã·ã«Lv.9äºä»¶ã¯çºçããªã fact6: æ±ããããšããããšã¯èµ·ãããªã | fact1: ¬{IE} fact2: ({A} & ¬{B}) -> ¬{BM} fact3: {BH} -> ¬{EO} fact4: ({A} & {B}) fact5: ¬{EI} fact6: ¬{JB} | [
"fact4 -> int1: éè¿ããšããããšãèµ·ãã; int1 -> int2: ãèããšããããšãèµ·ããããŸãã¯éè¿ããšããããšãçºçããããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯æãç«ã€;"
] | [
"fact4 -> int1: {A}; int1 -> int2: ({C} v {A});"
] | ããããLv.10äºä»¶ã¯èµ·ããªã | ¬{BM} | [] | 6 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãŽã®ãŽã«ãLv.28äºä»¶ã¯çããªã fact2: ãããéè¿ããšããããšãçãããå瀺ããããšãèµ·ãããªããªãã°ããããLv.10äºä»¶ã¯çºçããªã fact3: ä»®ã«ãééãæããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãããšãããšæ£èŠããããšã¯èµ·ããªã fact4: éè¿ããšããããšããã³å瀺ããããšäž¡æ¹ãšããèµ·ãã fact5: ã·ã«ã
ã·ã«Lv.9äºä»¶ã¯çºçããªã fact6: æ±ããããšããããšã¯èµ·ãããªã ; $hypothesis$ = ã·ã«ãã·ãªLv.65äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{IE} fact2: ({A} & ¬{B}) -> ¬{BM} fact3: {BH} -> ¬{EO} fact4: ({A} & {B}) fact5: ¬{EI} fact6: ¬{JB} ; $hypothesis$ = {D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®ãœã¡ããœã«Lv.68ã¯åºäŒãæããŠæ¥œãããšããããšã¯ééã£ãŠããªãããšããããšã¯ééãã | ¬({B}{a} & {A}{a}) | fact1: ããããªãããã®ã¢ã³ã¹ã¿ãŒãå¯ç¬ããªããªãã°ããã¯åºäŒãæãã楜ã fact2: ãã®ãœã¡ããœã«Lv.68ã¯åºäŒãæã fact3: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æ»ãé£ããªã fact4: ãã®ãœã¡ããœã«Lv.68ã¯æ¥œã fact5: ãã®ãœã®ãœã¡ãLv.23ãæ»ãé£ããªãããŸãã¯è¿ä»ãé£ããªãããããã¯ã©ã¡ããã§ãããšããããã®ãœã®ãœã¡ãLv.23ã¯åãæããªã fact6: åãæããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯å¯ç¬ããªãããã©èšçœ®åºæ¥ã | fact1: (x): ¬{C}x -> ({B}x & {A}x) fact2: {B}{a} fact3: (x): ¬{F}x fact4: {A}{a} fact5: (¬{F}{b} v ¬{G}{b}) -> ¬{D}{b} fact6: (x): ¬{D}x -> (¬{C}x & {E}x) | [
"fact4 -> int1: ãã®ãœã¡ããœã«Lv.68ã¯æ¥œã; int1 & fact2 -> hypothesis;"
] | [
"fact4 -> int1: {A}{a}; int1 & fact2 -> hypothesis;"
] | ãããã®ãœã¡ããœã«Lv.68ã¯åºäŒãæããŠæ¥œãããšããããšã¯ééã£ãŠããªãããšããããšã¯ééãã | ¬({B}{a} & {A}{a}) | [
"fact9 -> int2: ä»®ã«ãã®ãœã®ãœã¡ãLv.23ãåãæããªããšããã°ããã¯å¯ç¬ããªãããã€èšçœ®åºæ¥ã; fact8 -> int3: ãã®ãœããœãLv.63ã¯æ»ãé£ããªã; int3 -> int4: ãã®ãœããœãLv.63ã¯æ»ãé£ããšããããšã¯ãªãããããã¯è¿ä»ãé£ããªããäž¡æ¹ãšãã ; int4 -> int5: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æ»ãé£ããªãããŸãã¯è¿ä»ãé£ããªãããããã¯äž¡æ¹ãšãã§ãã; int5 -> int6: ãã®ãœã®ãœã¡ãLv.23ã¯æ»ãé£ããªãããããã¯è¿ä»ãé£ããªã; fact7 & int6 -> int7: ãã®ãœã®ãœã¡ãLv.23ã¯åãæããªã; int2 & int7 -> int8: ãã®ãœã®ãœã¡ãLv.23ã¯å¯ç¬ããªãããã©èšçœ®åºæ¥ã;"
] | 8 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããªãããã®ã¢ã³ã¹ã¿ãŒãå¯ç¬ããªããªãã°ããã¯åºäŒãæãã楜ã fact2: ãã®ãœã¡ããœã«Lv.68ã¯åºäŒãæã fact3: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯æ»ãé£ããªã fact4: ãã®ãœã¡ããœã«Lv.68ã¯æ¥œã fact5: ãã®ãœã®ãœã¡ãLv.23ãæ»ãé£ããªãããŸãã¯è¿ä»ãé£ããªãããããã¯ã©ã¡ããã§ãããšããããã®ãœã®ãœã¡ãLv.23ã¯åãæããªã fact6: åãæããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯å¯ç¬ããªãããã©èšçœ®åºæ¥ã ; $hypothesis$ = ãããã®ãœã¡ããœã«Lv.68ã¯åºäŒãæããŠæ¥œãããšããããšã¯ééã£ãŠããªãããšããããšã¯ééãã ; $proof$ = | fact4 -> int1: ãã®ãœã¡ããœã«Lv.68ã¯æ¥œã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{C}x -> ({B}x & {A}x) fact2: {B}{a} fact3: (x): ¬{F}x fact4: {A}{a} fact5: (¬{F}{b} v ¬{G}{b}) -> ¬{D}{b} fact6: (x): ¬{D}x -> (¬{C}x & {E}x) ; $hypothesis$ = ¬({B}{a} & {A}{a}) ; $proof$ = | fact4 -> int1: {A}{a}; int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããœã®ãœãLv.48äºä»¶ãšãŽã«ã
ãŽãªLv.92äºä»¶ãçããããšããããšã¯æãç«ããªã | ¬({C} & {D}) | fact1: ãããè¯ããšããããšãèµ·ãã fact2: ãŽã«ã
ãŽãªLv.92äºä»¶ãèµ·ãã fact3: å°å¿µããããšããããè¯ããšããããšã¯ãã£ããã fact4: ã決è¡ããããšãèµ·ããããšããããšã¯æãç«ã€ fact5: ãããè¯ããšããããšãšç§»è¡ãæããšããããšãçãã fact6: ãã·ãã·ã¡ãLv.14äºä»¶ãçããããšããããšã¯ééã£ãŠãããšããããšã¯ãªã fact7: ãããããè¯ããšããããšã¯èµ·ããªããªãããœã®ãœãLv.48äºä»¶ããã³ãŽã«ã
ãŽãªLv.92äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãã fact8: ãœã®ãœãLv.48äºä»¶ã¯ç§»è¡ãæããšããããšãèµ·ãããšããããšã«èµ·å ãã | fact1: {A} fact2: {D} fact3: {A} -> {AF} fact4: {EK} fact5: ({A} & {B}) fact6: {HN} fact7: ¬{A} -> ¬({C} & {D}) fact8: {B} -> {C} | [
"fact5 -> int1: 移è¡ãæããšããããšãèµ·ãã; int1 & fact8 -> int2: ãœã®ãœãLv.48äºä»¶ãçºçãã; int2 & fact2 -> hypothesis;"
] | [
"fact5 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact2 -> hypothesis;"
] | ããœã®ãœãLv.48äºä»¶ãšãŽã«ã
ãŽãªLv.92äºä»¶ãçããããšããããšã¯æãç«ããªã | ¬({C} & {D}) | [] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããè¯ããšããããšãèµ·ãã fact2: ãŽã«ã
ãŽãªLv.92äºä»¶ãèµ·ãã fact3: å°å¿µããããšããããè¯ããšããããšã¯ãã£ããã fact4: ã決è¡ããããšãèµ·ããããšããããšã¯æãç«ã€ fact5: ãããè¯ããšããããšãšç§»è¡ãæããšããããšãçãã fact6: ãã·ãã·ã¡ãLv.14äºä»¶ãçããããšããããšã¯ééã£ãŠãããšããããšã¯ãªã fact7: ãããããè¯ããšããããšã¯èµ·ããªããªãããœã®ãœãLv.48äºä»¶ããã³ãŽã«ã
ãŽãªLv.92äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãã fact8: ãœã®ãœãLv.48äºä»¶ã¯ç§»è¡ãæããšããããšãèµ·ãããšããããšã«èµ·å ãã ; $hypothesis$ = ããœã®ãœãLv.48äºä»¶ãšãŽã«ã
ãŽãªLv.92äºä»¶ãçããããšããããšã¯æãç«ããªã ; $proof$ = | fact5 -> int1: 移è¡ãæããšããããšãèµ·ãã; int1 & fact8 -> int2: ãœã®ãœãLv.48äºä»¶ãçºçãã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A} fact2: {D} fact3: {A} -> {AF} fact4: {EK} fact5: ({A} & {B}) fact6: {HN} fact7: ¬{A} -> ¬({C} & {D}) fact8: {B} -> {C} ; $hypothesis$ = ¬({C} & {D}) ; $proof$ = | fact5 -> int1: {B}; int1 & fact8 -> int2: {C}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãŸããŸã«ã
Lv.16äºä»¶ãçããããã®äžåŸ¡ãã§ãããšããããšãçºçãã | ({A} & {B}) | fact1: ããããèãæããšããããšã¯èµ·ãããªãããšããããšã¯æ¬åœãªã絶ãé£ããšããããšãèµ·ããã埡ãã§ãããšããããšãèµ·ãã fact2: ãŸããŸã«ã
Lv.16äºä»¶ãçºçãã | fact1: ¬{D} -> ({FS} & {B}) fact2: {A} | [
"fact2 -> int1: ãŸããŸã«ã
Lv.16äºä»¶ãçºçãã;"
] | [
"fact2 -> int1: {A};"
] | 絶ãé£ããšããããšããã³ã¿ãã¿ãLv.94äºä»¶ãèµ·ãã | ({FS} & {CI}) | [] | 4 | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããèãæããšããããšã¯èµ·ãããªãããšããããšã¯æ¬åœãªã絶ãé£ããšããããšãèµ·ããã埡ãã§ãããšããããšãèµ·ãã fact2: ãŸããŸã«ã
Lv.16äºä»¶ãçºçãã ; $hypothesis$ = ãŸããŸã«ã
Lv.16äºä»¶ãçããããã®äžåŸ¡ãã§ãããšããããšãçºçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{D} -> ({FS} & {B}) fact2: {A} ; $hypothesis$ = ({A} & {B}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ã | {D}{c} | fact1: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å
¥å£ããªããšãããšãããã¯å¿ã³é£ããæŽã«å°æ±ããªãããšããããšã¯åœã fact2: ãã®ã·ãã·ãLv.62ã¯å
¥å£ãã fact3: ããããã®ã·ãã·ãLv.62ãå
¥å£ãããªãããã¯å°æ±ã fact4: ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å¿ã³é£ãããããå°æ±ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããããã¯å¿ã³é£ããªã fact5: ä»®ã«ãã®ãœããœãLv.64ã¯ç¡ããšããã°ããã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ãããšããããšã¯çå®ã§ãã fact6: ãã®ã·ãã·ãLv.62ãç¡ããšããã°ãã®ãœããœãLv.64ã¯å
¥å£ãã | fact1: (x): ¬{A}x -> ¬({D}x & ¬{B}x) fact2: {A}{a} fact3: {A}{a} -> {B}{a} fact4: (x): ¬({D}x & ¬{B}x) -> ¬{D}x fact5: {C}{b} -> {D}{c} fact6: {C}{a} -> {A}{b} | [
"fact3 & fact2 -> int1: ããã®ã·ãã·ãLv.62ã¯å°æ±ãããšããããšã¯æãç«ã€;"
] | [
"fact3 & fact2 -> int1: {B}{a};"
] | ãã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ããªã | ¬{D}{c} | [
"fact7 -> int2: ããã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ããã©å°æ±ããªãããšããããšã¯ééã£ãŠãããšãããšãã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ããªã; fact8 -> int3: ä»®ã«ãã®ã·ãã·ã«ãLv.10ã¯å
¥å£ãããšããããšã¯ãªããªãããããã¯å¿ã³é£ããŠãŸãå°æ±ããšããããšã¯ãªãããšããããšã¯æãç«ã€ããšããããšã¯èª€ãã ;"
] | 5 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å
¥å£ããªããšãããšãããã¯å¿ã³é£ããæŽã«å°æ±ããªãããšããããšã¯åœã fact2: ãã®ã·ãã·ãLv.62ã¯å
¥å£ãã fact3: ããããã®ã·ãã·ãLv.62ãå
¥å£ãããªãããã¯å°æ±ã fact4: ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å¿ã³é£ãããããå°æ±ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããããã¯å¿ã³é£ããªã fact5: ä»®ã«ãã®ãœããœãLv.64ã¯ç¡ããšããã°ããã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ãããšããããšã¯çå®ã§ãã fact6: ãã®ã·ãã·ãLv.62ãç¡ããšããã°ãã®ãœããœãLv.64ã¯å
¥å£ãã ; $hypothesis$ = ãã®ã·ãã·ã«ãLv.10ã¯å¿ã³é£ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{A}x -> ¬({D}x & ¬{B}x) fact2: {A}{a} fact3: {A}{a} -> {B}{a} fact4: (x): ¬({D}x & ¬{B}x) -> ¬{D}x fact5: {C}{b} -> {D}{c} fact6: {C}{a} -> {A}{b} ; $hypothesis$ = {D}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããããããããããªããæŽã«åããšããããšã¯ãªããšãããšããããããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã | ¬((Ex): (¬{AA}x & ¬{AB}x) -> ¬{B}x) | fact1: ä»®ã«ããã¢ã³ã¹ã¿ãŒã¯ããããããªããã©åããšããã°ããã¯ããããããªã | fact1: (x): (¬{AA}x & {AB}x) -> ¬{B}x | [] | [] | null | null | [] | null | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ã«ããã¢ã³ã¹ã¿ãŒã¯ããããããªããã©åããšããã°ããã¯ããããããªã ; $hypothesis$ = ãããããããããããªããæŽã«åããšããããšã¯ãªããšãããšããããããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): (¬{AA}x & {AB}x) -> ¬{B}x ; $hypothesis$ = ¬((Ex): (¬{AA}x & ¬{AB}x) -> ¬{B}x) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœããœãLv.32ã¯åŸ¡è¥ããã©ç·Žãå§ããªã | ({D}{c} & ¬{A}{c}) | fact1: ããã®ãœããœãLv.32ã¯ç·Žãå§ããªãããšããããšã¯åã§ãªã fact2: æãããªãã¢ã³ã¹ã¿ãŒã¯å¿æããŠããŸãã«æ±²ã¿åãã fact3: ããããã®ãããã«ã
Lv.41ãå¿æããªãã°ãã®ãŽã«ããŽãLv.18ã¯ç·Žãå§ãã fact4: ãã®ãŽã«ããŽãLv.18ãç·Žãå§ãããšããããã®ãœããœãLv.32ã¯åŸ¡è¥ããç·Žãå§ãããšããããšã¯ãªã fact5: ããããã®ãããã«ã
Lv.41ã¯åãéããããããã¯åªãããªãããŸãã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠããã°å¿æã fact6: ããã¢ã³ã¹ã¿ãŒã¯å¿æããªãã°ã埡è¥ããŠæŽã«ããã¯ç·Žãå§ããªãããšããããšã¯ééãã fact7: ããã®ãããã«ã
Lv.41ã¯åãéãããåªãããšããããšã¯ãªãããšããããšã¯åã§ãã fact8: ãã®ãããã«ã
Lv.41ã¯åãéãããªã | fact1: ¬{A}{c} fact2: (x): ¬{E}x -> ({B}x & {C}x) fact3: {B}{a} -> {A}{b} fact4: {A}{b} -> ({D}{c} & ¬{A}{c}) fact5: ¬({AA}{a} v ¬{AB}{a}) -> {B}{a} fact6: (x): {B}x -> ¬({D}x & ¬{A}x) fact7: ¬({AA}{a} v ¬{AB}{a}) fact8: ¬{AA}{a} | [
"fact5 & fact7 -> int1: ãã®ãããã«ã
Lv.41ã¯å¿æã; int1 & fact3 -> int2: ãã®ãŽã«ããŽãLv.18ã¯ç·Žãå§ãã; int2 & fact4 -> hypothesis;"
] | [
"fact5 & fact7 -> int1: {B}{a}; int1 & fact3 -> int2: {A}{b}; int2 & fact4 -> hypothesis;"
] | ããã®ãœããœãLv.32ã¯åŸ¡è¥ãããã©ç·Žãå§ããªãããšããããšã¯äºå®ãšç°ãªã | ¬({D}{c} & ¬{A}{c}) | [
"fact9 -> int3: ããããã®ãœããœãLv.32ã¯å¿æããšããã°ããã®ãœããœãLv.32ã¯åŸ¡è¥ããç·Žãå§ããªãããšããããšã¯èª€ãã ; fact10 -> int4: ä»®ã«ãã®ãœããœãLv.32ãæãããªããšãããããã¯å¿æããŠæ±²ã¿åãã;"
] | 5 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®ãœããœãLv.32ã¯ç·Žãå§ããªãããšããããšã¯åã§ãªã fact2: æãããªãã¢ã³ã¹ã¿ãŒã¯å¿æããŠããŸãã«æ±²ã¿åãã fact3: ããããã®ãããã«ã
Lv.41ãå¿æããªãã°ãã®ãŽã«ããŽãLv.18ã¯ç·Žãå§ãã fact4: ãã®ãŽã«ããŽãLv.18ãç·Žãå§ãããšããããã®ãœããœãLv.32ã¯åŸ¡è¥ããç·Žãå§ãããšããããšã¯ãªã fact5: ããããã®ãããã«ã
Lv.41ã¯åãéããããããã¯åªãããªãããŸãã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠããã°å¿æã fact6: ããã¢ã³ã¹ã¿ãŒã¯å¿æããªãã°ã埡è¥ããŠæŽã«ããã¯ç·Žãå§ããªãããšããããšã¯ééãã fact7: ããã®ãããã«ã
Lv.41ã¯åãéãããåªãããšããããšã¯ãªãããšããããšã¯åã§ãã fact8: ãã®ãããã«ã
Lv.41ã¯åãéãããªã ; $hypothesis$ = ãã®ãœããœãLv.32ã¯åŸ¡è¥ããã©ç·Žãå§ããªã ; $proof$ = | fact5 & fact7 -> int1: ãã®ãããã«ã
Lv.41ã¯å¿æã; int1 & fact3 -> int2: ãã®ãŽã«ããŽãLv.18ã¯ç·Žãå§ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{c} fact2: (x): ¬{E}x -> ({B}x & {C}x) fact3: {B}{a} -> {A}{b} fact4: {A}{b} -> ({D}{c} & ¬{A}{c}) fact5: ¬({AA}{a} v ¬{AB}{a}) -> {B}{a} fact6: (x): {B}x -> ¬({D}x & ¬{A}x) fact7: ¬({AA}{a} v ¬{AB}{a}) fact8: ¬{AA}{a} ; $hypothesis$ = ({D}{c} & ¬{A}{c}) ; $proof$ = | fact5 & fact7 -> int1: {B}{a}; int1 & fact3 -> int2: {A}{b}; int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸã¡ãLv.84ã¯çŠãèã | {A}{aa} | fact1: ããã¯ãã©ãã¹ããããªãããããã¯ããã¯æ¥ãããããŸãã¯äž¡æ¹ãšãã§ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã fact2: ããããã®ãŸããŸã¡ãLv.84ã¯ãã©ãã¹ããããšããããšã¯ãªãããããã¯ããã¯æ¥ãããããšããããšã¯äºå®ãšç°ãªãã°ãã®ãŸããŸã¡ãLv.84ã¯çŠãèããªã | fact1: (x): ¬(¬{AA}x v {AB}x) fact2: ¬(¬{AA}{aa} v {AB}{aa}) -> ¬{A}{aa} | [
"fact1 -> int1: ãããã®ãŸããŸã¡ãLv.84ã¯ãã©ãã¹ããããªããæ¥ãããããããã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠããããšããããšã¯æãç«ã€; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: ¬(¬{AA}{aa} v {AB}{aa}); int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã¯ãã©ãã¹ããããªãããããã¯ããã¯æ¥ãããããŸãã¯äž¡æ¹ãšãã§ãããšããã¢ã³ã¹ã¿ãŒã¯ãªã fact2: ããããã®ãŸããŸã¡ãLv.84ã¯ãã©ãã¹ããããšããããšã¯ãªãããããã¯ããã¯æ¥ãããããšããããšã¯äºå®ãšç°ãªãã°ãã®ãŸããŸã¡ãLv.84ã¯çŠãèããªã ; $hypothesis$ = ãã®ãŸããŸã¡ãLv.84ã¯çŠãèã ; $proof$ = | fact1 -> int1: ãããã®ãŸããŸã¡ãLv.84ã¯ãã©ãã¹ããããªããæ¥ãããããããã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠããããšããããšã¯æãç«ã€; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬(¬{AA}x v {AB}x) fact2: ¬(¬{AA}{aa} v {AB}{aa}) -> ¬{A}{aa} ; $hypothesis$ = {A}{aa} ; $proof$ = | fact1 -> int1: ¬(¬{AA}{aa} v {AB}{aa}); int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãŸããŸã®Lv.67äºä»¶ãèµ·ãã | {D} | fact1: ããŸããŸã®Lv.67äºä»¶ã¯èµ·ããªãããšããããšã¯å·Šå³ããæããšããããšã«é²ããã fact2: å·Šå³ããæããšããããšã¯é·ã£ãããããšããããšãèµ·ãããšããããšã«èµ·å ãã fact3: ãããã¡ã
Lv.36äºä»¶ãçãã fact4: ãããã¡ã
Lv.36äºä»¶ãçãããããŸãã«é·ã£ãããããšããããšãèµ·ãã | fact1: {C} -> {D} fact2: {B} -> {C} fact3: {A} fact4: ({A} & {B}) | [
"fact4 -> int1: é·ã£ãããããšããããšãèµ·ãã; int1 & fact2 -> int2: å·Šå³ããæããšããããšãçãã; int2 & fact1 -> hypothesis;"
] | [
"fact4 -> int1: {B}; int1 & fact2 -> int2: {C}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ããŸããŸã®Lv.67äºä»¶ã¯èµ·ããªãããšããããšã¯å·Šå³ããæããšããããšã«é²ããã fact2: å·Šå³ããæããšããããšã¯é·ã£ãããããšããããšãèµ·ãããšããããšã«èµ·å ãã fact3: ãããã¡ã
Lv.36äºä»¶ãçãã fact4: ãããã¡ã
Lv.36äºä»¶ãçãããããŸãã«é·ã£ãããããšããããšãèµ·ãã ; $hypothesis$ = ãŸããŸã®Lv.67äºä»¶ãèµ·ãã ; $proof$ = | fact4 -> int1: é·ã£ãããããšããããšãèµ·ãã; int1 & fact2 -> int2: å·Šå³ããæããšããããšãçãã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} -> {D} fact2: {B} -> {C} fact3: {A} fact4: ({A} & {B}) ; $hypothesis$ = {D} ; $proof$ = | fact4 -> int1: {B}; int1 & fact2 -> int2: {C}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãŽã¡ããŽãLv.82äºä»¶ãèµ·ããããããã¯ãŽããŽãLv.94äºä»¶ãçºçããããããã¯äž¡æ¹ãšãã | ({A} v {B}) | fact1: ä»®ã«å£ç
©ããšããããšã¯èµ·ãããªããªãã°ããŽã¡ããŽãLv.82äºä»¶ãçºçããããŽããŽãLv.94äºä»¶ãèµ·ããããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯èª€ãã fact2: ããŽããŽã«Lv.17äºä»¶ãšå£ç
©ããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯èª€ã£ãŠãããªãããŽããŽãLv.94äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ fact3: ãŽã¡ããŽãLv.82äºä»¶ãçºçãã | fact1: ¬{C} -> ¬({A} v {B}) fact2: ¬({D} & {C}) -> ¬{B} fact3: {A} | [
"fact3 -> int1: ãŽã¡ããŽãLv.82äºä»¶ãçºçãã; int1 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 -> hypothesis;"
] | çžé ããšããããšãèµ·ãã | {DF} | [] | 6 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«å£ç
©ããšããããšã¯èµ·ãããªããªãã°ããŽã¡ããŽãLv.82äºä»¶ãçºçããããŽããŽãLv.94äºä»¶ãèµ·ããããŸãã¯äž¡æ¹ãšãã§ããããšããããšã¯èª€ãã fact2: ããŽããŽã«Lv.17äºä»¶ãšå£ç
©ããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯èª€ã£ãŠãããªãããŽããŽãLv.94äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ fact3: ãŽã¡ããŽãLv.82äºä»¶ãçºçãã ; $hypothesis$ = ãŽã¡ããŽãLv.82äºä»¶ãèµ·ããããããã¯ãŽããŽãLv.94äºä»¶ãçºçããããããã¯äž¡æ¹ãšãã ; $proof$ = | fact3 -> int1: ãŽã¡ããŽãLv.82äºä»¶ãçºçãã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{C} -> ¬({A} v {B}) fact2: ¬({D} & {C}) -> ¬{B} fact3: {A} ; $hypothesis$ = ({A} v {B}) ; $proof$ = | fact3 -> int1: {A}; int1 -> hypothesis; __PROVED__ |
0.3 | 幌ããªããšããããšã¯èµ·ããªã | ¬{C} | fact1: ãã·ãã·ã¡ãLv.21äºä»¶ã代å
¥ããããšãèµ·ããããšããããšã¯å¹Œããªããšããããšãé»ã fact2: ãæ
£ããããšã¯çããªãããšããããšã¯åŸ¡çµå©çºããããšãšãŸãªãŸã¡ãLv.43äºä»¶ãçºçãããçºçããã fact3: ã·ãã·ã¡ãLv.21äºä»¶ãèµ·ãã fact4: åºåãããšã¯èµ·ãããªã fact5: ä»®ã«ãŸãªãŸã¡ãLv.43äºä»¶ãèµ·ãããªããŽããŽã«ãLv.71äºä»¶ãèµ·ããäžæ¹ã§ä»£å
¥ããããšã¯çºçããªã fact6: 代å
¥ããããšã¯å¹Œããªããšããããšã¯èµ·ãããªããšããããšãçãããã | fact1: ({A} v {B}) -> ¬{C} fact2: ¬{G} -> ({F} & {E}) fact3: {A} fact4: ¬{GD} fact5: {E} -> ({D} & ¬{B}) fact6: {B} -> ¬{C} | [
"fact3 -> int1: ã·ãã·ã¡ãLv.21äºä»¶ãèµ·ããã代å
¥ããããšãçºçããããããã¯äž¡æ¹ã§ãã; int1 & fact1 -> hypothesis;"
] | [
"fact3 -> int1: ({A} v {B}); int1 & fact1 -> hypothesis;"
] | 幌ããªããšããããšãèµ·ãã | {C} | [] | 7 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã·ãã·ã¡ãLv.21äºä»¶ã代å
¥ããããšãèµ·ããããšããããšã¯å¹Œããªããšããããšãé»ã fact2: ãæ
£ããããšã¯çããªãããšããããšã¯åŸ¡çµå©çºããããšãšãŸãªãŸã¡ãLv.43äºä»¶ãçºçãããçºçããã fact3: ã·ãã·ã¡ãLv.21äºä»¶ãèµ·ãã fact4: åºåãããšã¯èµ·ãããªã fact5: ä»®ã«ãŸãªãŸã¡ãLv.43äºä»¶ãèµ·ãããªããŽããŽã«ãLv.71äºä»¶ãèµ·ããäžæ¹ã§ä»£å
¥ããããšã¯çºçããªã fact6: 代å
¥ããããšã¯å¹Œããªããšããããšã¯èµ·ãããªããšããããšãçãããã ; $hypothesis$ = 幌ããªããšããããšã¯èµ·ããªã ; $proof$ = | fact3 -> int1: ã·ãã·ã¡ãLv.21äºä»¶ãèµ·ããã代å
¥ããããšãçºçããããããã¯äž¡æ¹ã§ãã; int1 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: ¬{G} -> ({F} & {E}) fact3: {A} fact4: ¬{GD} fact5: {E} -> ({D} & ¬{B}) fact6: {B} -> ¬{C} ; $hypothesis$ = ¬{C} ; $proof$ = | fact3 -> int1: ({A} v {B}); int1 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽãªãŽã«ãLv.72ã¯é倪ã | {D}{b} | fact1: ãã®ãŽãªãŽã«ãLv.72ã¯éãŸãæã fact2: ãããã®ãŽãªãŽã«ãLv.72ãç²ãæãããã®äžéãŸãæããªãã°é倪ããªã fact3: ãã®ãŽãªãŽã«ãLv.72ã¯çãé£ã fact4: ãã®ã·ã«ãã·ã¡ãLv.6ã¯åãŸãã fact5: ããä»®ã«ãã®ã·ã«ãã·ã¡ãLv.6ãåãŸãããšããã°ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæã fact6: ãã®ãŽãªãŽã«ãLv.72ãåãŸããããŸãéãŸãæããšããã°ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæããªã | fact1: {C}{b} fact2: ({B}{b} & {C}{b}) -> ¬{D}{b} fact3: {BC}{b} fact4: {A}{a} fact5: {A}{a} -> {B}{b} fact6: ({A}{b} & {C}{b}) -> ¬{B}{b} | [
"fact5 & fact4 -> int1: ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæã; int1 & fact1 -> int2: ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæããŠéãŸãæã; int2 & fact2 -> hypothesis;"
] | [
"fact5 & fact4 -> int1: {B}{b}; int1 & fact1 -> int2: ({B}{b} & {C}{b}); int2 & fact2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãŽãªãŽã«ãLv.72ã¯éãŸãæã fact2: ãããã®ãŽãªãŽã«ãLv.72ãç²ãæãããã®äžéãŸãæããªãã°é倪ããªã fact3: ãã®ãŽãªãŽã«ãLv.72ã¯çãé£ã fact4: ãã®ã·ã«ãã·ã¡ãLv.6ã¯åãŸãã fact5: ããä»®ã«ãã®ã·ã«ãã·ã¡ãLv.6ãåãŸãããšããã°ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæã fact6: ãã®ãŽãªãŽã«ãLv.72ãåãŸããããŸãéãŸãæããšããã°ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæããªã ; $hypothesis$ = ãã®ãŽãªãŽã«ãLv.72ã¯é倪ã ; $proof$ = | fact5 & fact4 -> int1: ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæã; int1 & fact1 -> int2: ãã®ãŽãªãŽã«ãLv.72ã¯ç²ãæããŠéãŸãæã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{b} fact2: ({B}{b} & {C}{b}) -> ¬{D}{b} fact3: {BC}{b} fact4: {A}{a} fact5: {A}{a} -> {B}{b} fact6: ({A}{b} & {C}{b}) -> ¬{B}{b} ; $hypothesis$ = {D}{b} ; $proof$ = | fact5 & fact4 -> int1: {B}{b}; int1 & fact1 -> int2: ({B}{b} & {C}{b}); int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããããLv.47äºä»¶ãçºçãã | {B} | fact1: ãããããŸãããšããããšãèµ·ããããšããããšã¯æãç«ã€ fact2: ããããLv.47äºä»¶ããããããŸãããšããããšãçããããšããããšã¯ãã£ããã | fact1: {A} fact2: {A} -> {B} | [
"fact1 -> int1: ãããããŸãããšããããšãèµ·ããããšããããšã¯æãç«ã€; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}; int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãããããŸãããšããããšãèµ·ããããšããããšã¯æãç«ã€ fact2: ããããLv.47äºä»¶ããããããŸãããšããããšãçããããšããããšã¯ãã£ããã ; $hypothesis$ = ããããLv.47äºä»¶ãçºçãã ; $proof$ = | fact1 -> int1: ãããããŸãããšããããšãèµ·ããããšããããšã¯æãç«ã€; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} fact2: {A} -> {B} ; $hypothesis$ = {B} ; $proof$ = | fact1 -> int1: {A}; int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ããã®ãã¡ããã«ã
Lv.75ã¯åãããããã«è³ãåããããšããããšã¯æãç«ããªã | ¬({C}{a} & {D}{a}) | fact1: ä»®ã«ãã®ãã¡ããã«ã
Lv.75ã倧差ç¡ããšããããã®ãã¡ããã«ã
Lv.75ã¯åãã fact2: ãã®ãã¡ããã«ã
Lv.75ã¯å€§å·®ç¡ããããã«åŸ¡é«ã fact3: ãã®ããªããªLv.62ã¯åŸ¡é«ã fact4: ãã®ãœããœã®Lv.53ã¯åŸ¡é«ã fact5: ãã®ãã¡ããã«ã
Lv.75ã¯è³ãåãã fact6: ãã®ãã¡ããã«ã
Lv.75ã¯å§ããã | fact1: {A}{a} -> {C}{a} fact2: ({A}{a} & {B}{a}) fact3: {B}{ep} fact4: {B}{cm} fact5: {D}{a} fact6: {EE}{a} | [
"fact2 -> int1: ãã®ãã¡ããã«ã
Lv.75ã¯å€§å·®ç¡ã; int1 & fact1 -> int2: ããã®ãã¡ããã«ã
Lv.75ã¯åããããšããããšã¯åœã ãšããããšã¯ãªã; int2 & fact5 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact5 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ãã¡ããã«ã
Lv.75ã倧差ç¡ããšããããã®ãã¡ããã«ã
Lv.75ã¯åãã fact2: ãã®ãã¡ããã«ã
Lv.75ã¯å€§å·®ç¡ããããã«åŸ¡é«ã fact3: ãã®ããªããªLv.62ã¯åŸ¡é«ã fact4: ãã®ãœããœã®Lv.53ã¯åŸ¡é«ã fact5: ãã®ãã¡ããã«ã
Lv.75ã¯è³ãåãã fact6: ãã®ãã¡ããã«ã
Lv.75ã¯å§ããã ; $hypothesis$ = ããã®ãã¡ããã«ã
Lv.75ã¯åãããããã«è³ãåããããšããããšã¯æãç«ããªã ; $proof$ = | fact2 -> int1: ãã®ãã¡ããã«ã
Lv.75ã¯å€§å·®ç¡ã; int1 & fact1 -> int2: ããã®ãã¡ããã«ã
Lv.75ã¯åããããšããããšã¯åœã ãšããããšã¯ãªã; int2 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {C}{a} fact2: ({A}{a} & {B}{a}) fact3: {B}{ep} fact4: {B}{cm} fact5: {D}{a} fact6: {EE}{a} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.13ã¯æãæã | {E}{a} | fact1: ãããã®ãŽããŽãLv.13ãå«æããããããæšããšããããšã¯ãªããšããã°åºãæã fact2: ããä»®ã«ãã®ãŸããŸãLv.76ã欲深ããªããŠå ããŠåºãæããªããšããããã®ãŸããŸãLv.76ã¯æéãã fact3: å·ä»ãæããªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å·ä»ãæã fact5: ããä»®ã«ãã®ãŽããŽãLv.13ãå«æããªããŠããã«æšããªããšãããåºãæã fact6: ããããã¢ã³ã¹ã¿ãŒãå·ä»ãæããªããªããã®ãŽããŽãLv.13ã¯å«æããªããŠãŸãæšããªã fact7: ãã®ãŽããŽãLv.13ã¯å«æãããšããããšã¯ãªã fact8: ããä»®ã«ãå·ä»ãæããªããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãŽããŽãLv.13ã¯å«æããªã | fact1: ({B}{a} & ¬{C}{a}) -> {D}{a} fact2: (¬{CB}{at} & ¬{D}{at}) -> {DQ}{at} fact3: (Ex): ¬{A}x fact4: (Ex): {A}x fact5: (¬{B}{a} & ¬{C}{a}) -> {D}{a} fact6: (x): ¬{A}x -> (¬{B}{a} & ¬{C}{a}) fact7: ¬{B}{a} fact8: (x): ¬{A}x -> ¬{B}{a} | [
"fact3 & fact6 -> int1: ãã®ãŽããŽãLv.13ã¯å«æããªãããã€æšããªã; int1 & fact5 -> int2: ãã®ãŽããŽãLv.13ã¯åºãæã;"
] | [
"fact3 & fact6 -> int1: (¬{B}{a} & ¬{C}{a}); int1 & fact5 -> int2: {D}{a};"
] | null | null | [] | null | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããã®ãŽããŽãLv.13ãå«æããããããæšããšããããšã¯ãªããšããã°åºãæã fact2: ããä»®ã«ãã®ãŸããŸãLv.76ã欲深ããªããŠå ããŠåºãæããªããšããããã®ãŸããŸãLv.76ã¯æéãã fact3: å·ä»ãæããªãã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯å·ä»ãæã fact5: ããä»®ã«ãã®ãŽããŽãLv.13ãå«æããªããŠããã«æšããªããšãããåºãæã fact6: ããããã¢ã³ã¹ã¿ãŒãå·ä»ãæããªããªããã®ãŽããŽãLv.13ã¯å«æããªããŠãŸãæšããªã fact7: ãã®ãŽããŽãLv.13ã¯å«æãããšããããšã¯ãªã fact8: ããä»®ã«ãå·ä»ãæããªããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãŽããŽãLv.13ã¯å«æããªã ; $hypothesis$ = ãã®ãŽããŽãLv.13ã¯æãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({B}{a} & ¬{C}{a}) -> {D}{a} fact2: (¬{CB}{at} & ¬{D}{at}) -> {DQ}{at} fact3: (Ex): ¬{A}x fact4: (Ex): {A}x fact5: (¬{B}{a} & ¬{C}{a}) -> {D}{a} fact6: (x): ¬{A}x -> (¬{B}{a} & ¬{C}{a}) fact7: ¬{B}{a} fact8: (x): ¬{A}x -> ¬{B}{a} ; $hypothesis$ = {E}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœããœãLv.4ã¯ç²ãé£ã | {D}{b} | fact1: ãã®ãŸããŸã«ãLv.63ã¯ããããçŸãã fact2: ä»®ã«ãã®ãŸããŸã«ãLv.63ãããããšãããšãã®ãŸããŸã«ãLv.63ã¯å€ã fact3: ãããã®ãŸããŸã«ãLv.63ãå€ããªããã®ãœããœãLv.4ã¯ç²ãé£ã | fact1: ({A}{a} & {B}{a}) fact2: {A}{a} -> {C}{a} fact3: {C}{a} -> {D}{b} | [
"fact1 -> int1: ãã®ãŸããŸã«ãLv.63ã¯ããã; int1 & fact2 -> int2: ãã®ãŸããŸã«ãLv.63ã¯å€ã; int2 & fact3 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact2 -> int2: {C}{a}; int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸããŸã«ãLv.63ã¯ããããçŸãã fact2: ä»®ã«ãã®ãŸããŸã«ãLv.63ãããããšãããšãã®ãŸããŸã«ãLv.63ã¯å€ã fact3: ãããã®ãŸããŸã«ãLv.63ãå€ããªããã®ãœããœãLv.4ã¯ç²ãé£ã ; $hypothesis$ = ãã®ãœããœãLv.4ã¯ç²ãé£ã ; $proof$ = | fact1 -> int1: ãã®ãŸããŸã«ãLv.63ã¯ããã; int1 & fact2 -> int2: ãã®ãŸããŸã«ãLv.63ã¯å€ã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: {A}{a} -> {C}{a} fact3: {C}{a} -> {D}{b} ; $hypothesis$ = {D}{b} ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact2 -> int2: {C}{a}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãšããã¢ã³ã¹ã¿ãŒã¯æŒãä»ãããŸãããããã¯éã | (Ex): ({C}x v {B}x) | fact1: ãã®ãŸããŸã«ã
Lv.83ã¯æåºããªãããã®ãŸããŸã«ã
Lv.41ã¯éãããšããããšã¯æãç«ã€ fact2: ãããã®ãŸããŸã«ã
Lv.83ã¯ä»ãé£ããšãããšããã®ãŸããŸã«ã
Lv.41ã¯ä»ãé£ãããšããããšã¯çå®ã fact3: ãã®ãŸããŸã«ã
Lv.83ã¯æåºã fact4: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æŒãä»ãããŸããããããåäŸããããªãããšããããšã¯ééããªãéããªã | fact1: {A}{a} -> {B}{b} fact2: {ID}{a} -> {ID}{b} fact3: {A}{a} fact4: (x): ¬({C}x & ¬{D}x) -> ¬{B}x | [
"fact1 & fact3 -> int1: ãã®ãŸããŸã«ã
Lv.41ã¯éã; int1 -> int2: ãã®ãŸããŸã«ã
Lv.41ã¯æŒãä»ãããŸãããéããäž¡æ¹ã ; int2 -> hypothesis;"
] | [
"fact1 & fact3 -> int1: {B}{b}; int1 -> int2: ({C}{b} v {B}{b}); int2 -> hypothesis;"
] | ãã®ãŸããŸã«ã
Lv.41ã¯ä»ãé£ã | {ID}{b} | [
"fact6 -> int3: ãããããã®ã·ã¡ãã·ãLv.12ã¯æŒãä»ãããŸããäžæ¹ã§ããã¯åäŸããããªãããšããããšã¯èª€ã£ãŠããã°ããã¯éããªã;"
] | 11 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸã«ã
Lv.83ã¯æåºããªãããã®ãŸããŸã«ã
Lv.41ã¯éãããšããããšã¯æãç«ã€ fact2: ãããã®ãŸããŸã«ã
Lv.83ã¯ä»ãé£ããšãããšããã®ãŸããŸã«ã
Lv.41ã¯ä»ãé£ãããšããããšã¯çå®ã fact3: ãã®ãŸããŸã«ã
Lv.83ã¯æåºã fact4: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯æŒãä»ãããŸããããããåäŸããããªãããšããããšã¯ééããªãéããªã ; $hypothesis$ = ãšããã¢ã³ã¹ã¿ãŒã¯æŒãä»ãããŸãããããã¯éã ; $proof$ = | fact1 & fact3 -> int1: ãã®ãŸããŸã«ã
Lv.41ã¯éã; int1 -> int2: ãã®ãŸããŸã«ã
Lv.41ã¯æŒãä»ãããŸãããéããäž¡æ¹ã ; int2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> {B}{b} fact2: {ID}{a} -> {ID}{b} fact3: {A}{a} fact4: (x): ¬({C}x & ¬{D}x) -> ¬{B}x ; $hypothesis$ = (Ex): ({C}x v {B}x) ; $proof$ = | fact1 & fact3 -> int1: {B}{b}; int1 -> int2: ({C}{b} v {B}{b}); int2 -> hypothesis; __PROVED__ |
0.3 | æã
ãããšããããšã¯èµ·ããªã | ¬{D} | fact1: ãœã¡ããœãLv.50äºä»¶ã¯ãŸããŸã¡ãLv.74äºä»¶ã®åå ãšãªã fact2: æŠãåãããšãçãã fact3: ãæã
ãããšããããšã¯èµ·ãããªãããšããããšã¯ããŸããŸã¡ãLv.74äºä»¶ãšæŠãåãããšäž¡æ¹ãçããããšããããšã«èªçºããã fact4: å
¥ãé£ããšããããšãèµ·ãã fact5: ãœã¡ããœãLv.50äºä»¶ãçãã fact6: ãœã¡ããœãLv.50äºä»¶ããããã¯ãŸããŸã¡ãLv.74äºä»¶ãçãããšããããšã¯å°ãããšããããšãé²ã fact7: ããœã«ããœãLv.78äºä»¶ã¯èµ·ãããªãããšããããšã¯ããŸããŸã¡ãLv.74äºä»¶ãèµ·ãããªããæŠãåãããšã¯çºçããããšããããšã®åå ãšãªã | fact1: {A} -> {B} fact2: {C} fact3: ({B} & {C}) -> ¬{D} fact4: {HP} fact5: {A} fact6: ({A} v {B}) -> ¬{GG} fact7: ¬{E} -> (¬{B} & {C}) | [
"fact1 & fact5 -> int1: ãŸããŸã¡ãLv.74äºä»¶ãçºçãã; int1 & fact2 -> int2: ãŸããŸã¡ãLv.74äºä»¶ãšæŠãåãããšãçºçãã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact5 -> int1: {B}; int1 & fact2 -> int2: ({B} & {C}); int2 & fact3 -> hypothesis;"
] | ãå°ãããšããããšã¯èµ·ããªãããšããããšã¯çå®ã§ãã | ¬{GG} | [] | 6 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãœã¡ããœãLv.50äºä»¶ã¯ãŸããŸã¡ãLv.74äºä»¶ã®åå ãšãªã fact2: æŠãåãããšãçãã fact3: ãæã
ãããšããããšã¯èµ·ãããªãããšããããšã¯ããŸããŸã¡ãLv.74äºä»¶ãšæŠãåãããšäž¡æ¹ãçããããšããããšã«èªçºããã fact4: å
¥ãé£ããšããããšãèµ·ãã fact5: ãœã¡ããœãLv.50äºä»¶ãçãã fact6: ãœã¡ããœãLv.50äºä»¶ããããã¯ãŸããŸã¡ãLv.74äºä»¶ãçãããšããããšã¯å°ãããšããããšãé²ã fact7: ããœã«ããœãLv.78äºä»¶ã¯èµ·ãããªãããšããããšã¯ããŸããŸã¡ãLv.74äºä»¶ãèµ·ãããªããæŠãåãããšã¯çºçããããšããããšã®åå ãšãªã ; $hypothesis$ = æã
ãããšããããšã¯èµ·ããªã ; $proof$ = | fact1 & fact5 -> int1: ãŸããŸã¡ãLv.74äºä»¶ãçºçãã; int1 & fact2 -> int2: ãŸããŸã¡ãLv.74äºä»¶ãšæŠãåãããšãçºçãã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} -> {B} fact2: {C} fact3: ({B} & {C}) -> ¬{D} fact4: {HP} fact5: {A} fact6: ({A} v {B}) -> ¬{GG} fact7: ¬{E} -> (¬{B} & {C}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact1 & fact5 -> int1: {B}; int1 & fact2 -> int2: ({B} & {C}); int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã¡ããŸãLv.17ã¯ç¶ãæã | {D}{b} | fact1: ãã®ãœã«ã
ãœãªLv.21ã¯æ±ºãé£ã fact2: ããä»®ã«ãã®ãœã«ã
ãœãªLv.21ãåãé£ããªãããã¯ã€ã¹ãã fact3: ããä»®ã«ãã®ãœã«ã
ãœãªLv.21ã決ãé£ããããŸãã«ã€ã¹ãããªããã®ãŸã¡ããŸãLv.17ã¯ç¶ãæããšããããšã¯ãªã fact4: ãã®ãœã«ã
ãœãªLv.21ã¯åãé£ã | fact1: {C}{a} fact2: {A}{a} -> {B}{a} fact3: ({C}{a} & {B}{a}) -> ¬{D}{b} fact4: {A}{a} | [
"fact2 & fact4 -> int1: ãã®ãœã«ã
ãœãªLv.21ã¯ã€ã¹ãã; int1 & fact1 -> int2: ãã®ãœã«ã
ãœãªLv.21ã¯æ±ºãé£ããŠã€ã¹ãã; int2 & fact3 -> hypothesis;"
] | [
"fact2 & fact4 -> int1: {B}{a}; int1 & fact1 -> int2: ({C}{a} & {B}{a}); int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãœã«ã
ãœãªLv.21ã¯æ±ºãé£ã fact2: ããä»®ã«ãã®ãœã«ã
ãœãªLv.21ãåãé£ããªãããã¯ã€ã¹ãã fact3: ããä»®ã«ãã®ãœã«ã
ãœãªLv.21ã決ãé£ããããŸãã«ã€ã¹ãããªããã®ãŸã¡ããŸãLv.17ã¯ç¶ãæããšããããšã¯ãªã fact4: ãã®ãœã«ã
ãœãªLv.21ã¯åãé£ã ; $hypothesis$ = ãã®ãŸã¡ããŸãLv.17ã¯ç¶ãæã ; $proof$ = | fact2 & fact4 -> int1: ãã®ãœã«ã
ãœãªLv.21ã¯ã€ã¹ãã; int1 & fact1 -> int2: ãã®ãœã«ã
ãœãªLv.21ã¯æ±ºãé£ããŠã€ã¹ãã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{a} fact2: {A}{a} -> {B}{a} fact3: ({C}{a} & {B}{a}) -> ¬{D}{b} fact4: {A}{a} ; $hypothesis$ = {D}{b} ; $proof$ = | fact2 & fact4 -> int1: {B}{a}; int1 & fact1 -> int2: ({C}{a} & {B}{a}); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ã¯ãªãã¯ããããšãšè¿æžåºæ¥ãããšãçºçãã | ({C} & {D}) | fact1: ãã¯ãªãã¯ããããšã¯èµ·ããªãããšããããšã¯ç±ã
ããšããããšã«é²ããã fact2: ãœã«ã
ãœã«ãLv.35äºä»¶ã¯çããªããšããããšã¯ãç±ã
ããšããããšã¯èµ·ããªãããã©å°œããããšãçºçããããšããããšã®ãã£ãããšãªã fact3: ããããçšãæããšããããšããã³ãœã¡ããœã«ãLv.5äºä»¶ãçããããšããããšã¯çå®ã ããšããããšã¯èª€ã£ãŠãããšããããœã«ã
ãœã«ãLv.35äºä»¶ã¯çºçããªã fact4: ããä»®ã«ç±ã
ããšããããšã¯èµ·ããªããšãããšããã¯ãªãã¯ããããšããã³è¿æžåºæ¥ãããšäž¡æ¹ãèµ·ããããšããããšã¯èª€ãã ããšããããšã¯ç¢ºãã§ãã fact5: ãç±ã
ããšããããšãšå°œããããšäž¡æ¹ãèµ·ããããšããããšã¯äºå®ã§ãã fact6: è¿æžåºæ¥ãããšãèµ·ãã | fact1: {A} -> {C} fact2: ¬{E} -> (¬{A} & {B}) fact3: ¬({F} & {G}) -> ¬{E} fact4: ¬{A} -> ¬({C} & {D}) fact5: ({A} & {B}) fact6: {D} | [
"fact5 -> int1: ç±ã
ããšããããšãèµ·ãã; int1 & fact1 -> int2: ã¯ãªãã¯ããããšãçãã; int2 & fact6 -> hypothesis;"
] | [
"fact5 -> int1: {A}; int1 & fact1 -> int2: {C}; int2 & fact6 -> hypothesis;"
] | ãã¯ãªãã¯ããããšãçããããã®äžè¿æžåºæ¥ãããšãèµ·ããããšããããšã¯èª€ã£ãŠãã | ¬({C} & {D}) | [] | 8 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã¯ãªãã¯ããããšã¯èµ·ããªãããšããããšã¯ç±ã
ããšããããšã«é²ããã fact2: ãœã«ã
ãœã«ãLv.35äºä»¶ã¯çããªããšããããšã¯ãç±ã
ããšããããšã¯èµ·ããªãããã©å°œããããšãçºçããããšããããšã®ãã£ãããšãªã fact3: ããããçšãæããšããããšããã³ãœã¡ããœã«ãLv.5äºä»¶ãçããããšããããšã¯çå®ã ããšããããšã¯èª€ã£ãŠãããšããããœã«ã
ãœã«ãLv.35äºä»¶ã¯çºçããªã fact4: ããä»®ã«ç±ã
ããšããããšã¯èµ·ããªããšãããšããã¯ãªãã¯ããããšããã³è¿æžåºæ¥ãããšäž¡æ¹ãèµ·ããããšããããšã¯èª€ãã ããšããããšã¯ç¢ºãã§ãã fact5: ãç±ã
ããšããããšãšå°œããããšäž¡æ¹ãèµ·ããããšããããšã¯äºå®ã§ãã fact6: è¿æžåºæ¥ãããšãèµ·ãã ; $hypothesis$ = ã¯ãªãã¯ããããšãšè¿æžåºæ¥ãããšãçºçãã ; $proof$ = | fact5 -> int1: ç±ã
ããšããããšãèµ·ãã; int1 & fact1 -> int2: ã¯ãªãã¯ããããšãçãã; int2 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} -> {C} fact2: ¬{E} -> (¬{A} & {B}) fact3: ¬({F} & {G}) -> ¬{E} fact4: ¬{A} -> ¬({C} & {D}) fact5: ({A} & {B}) fact6: {D} ; $hypothesis$ = ({C} & {D}) ; $proof$ = | fact5 -> int1: {A}; int1 & fact1 -> int2: {C}; int2 & fact6 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸãLv.46ã¯å€åãæããããã«æ»ãå¯ãã | ({B}{b} & {AA}{b}) | fact1: ãã®ãŸããŸãLv.46ã¯å€åãæã fact2: ä»®ã«ãã®ãŽã«ããŽãLv.43ãå°äžæ·±ããšããã°ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãããããã埡æªããšããããšã¯ãªã fact3: ãã®ãŸããŸãLv.46ã¯åŸ¡æªããªã fact4: ãã®ãŽã«ããŽãLv.43ã¯å°äžæ·±ã fact5: ãã®ãŸã¡ããŸã®Lv.75ã¯æžãŸç¡ãããã©ã³ãã³ã°ããªã | fact1: {B}{b} fact2: {A}{a} -> ({AA}{b} & ¬{AB}{b}) fact3: ¬{AB}{b} fact4: {A}{a} fact5: ({GR}{dl} & ¬{CH}{dl}) | [
"fact2 & fact4 -> int1: ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãããããã埡æªããªã; int1 -> int2: ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãã; int2 & fact1 -> hypothesis;"
] | [
"fact2 & fact4 -> int1: ({AA}{b} & ¬{AB}{b}); int1 -> int2: {AA}{b}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸããŸãLv.46ã¯å€åãæã fact2: ä»®ã«ãã®ãŽã«ããŽãLv.43ãå°äžæ·±ããšããã°ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãããããã埡æªããšããããšã¯ãªã fact3: ãã®ãŸããŸãLv.46ã¯åŸ¡æªããªã fact4: ãã®ãŽã«ããŽãLv.43ã¯å°äžæ·±ã fact5: ãã®ãŸã¡ããŸã®Lv.75ã¯æžãŸç¡ãããã©ã³ãã³ã°ããªã ; $hypothesis$ = ãã®ãŸããŸãLv.46ã¯å€åãæããããã«æ»ãå¯ãã ; $proof$ = | fact2 & fact4 -> int1: ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãããããã埡æªããªã; int1 -> int2: ãã®ãŸããŸãLv.46ã¯æ»ãå¯ãã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{b} fact2: {A}{a} -> ({AA}{b} & ¬{AB}{b}) fact3: ¬{AB}{b} fact4: {A}{a} fact5: ({GR}{dl} & ¬{CH}{dl}) ; $hypothesis$ = ({B}{b} & {AA}{b}) ; $proof$ = | fact2 & fact4 -> int1: ({AA}{b} & ¬{AB}{b}); int1 -> int2: {AA}{b}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ã«ã
ã¿ãLv.11ã¯çŽåãã | {B}{a} | fact1: ãããããã¢ã³ã¹ã¿ãŒã¯åºããšãããšãããã¯åŒãéããªããŠãŒããããšããããšã¯ééãã§ãã fact2: ãã®ã·ãã·ã«ãLv.16ã¯åºã fact3: ããä»®ã«ããã®ã·ãã·ã«ãLv.16ã¯åŒãéããªãããã®äžããã¯ãŒãããªãããšããããšã¯ééã£ãŠããã°ãã®ã¿ã«ã
ã¿ãLv.11ã¯çŽåãã fact4: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯åºããªãã°ãåŒãéãããšããããšã¯ãªãããŒãããªãããšããããšã¯æãç«ããªã | fact1: (x): {A}x -> ¬(¬{AA}x & {AB}x) fact2: {A}{aa} fact3: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{a} fact4: (x): {A}x -> ¬(¬{AA}x & ¬{AB}x) | [
"fact4 -> int1: ããä»®ã«ããã®ã·ãã·ã«ãLv.16ã¯åºãããšããããšã¯äºå®ãªããããã®ã·ãã·ã«ãLv.16ã¯åŒãéããªããŠãŒãããªãããšããããšã¯æ£ããããšããããšã¯èª€ãã ; int1 & fact2 -> int2: ããã®ã·ãã·ã«ãLv.16ã¯åŒãéãããšããããšã¯ãªããŠãŸããŒãããšããããšã¯ãªãããšããããšã¯æãç«ããªã; int2 & fact3 -> hypothesis;"
] | [
"fact4 -> int1: {A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: ¬(¬{AA}{aa} & ¬{AB}{aa}); int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãããããã¢ã³ã¹ã¿ãŒã¯åºããšãããšãããã¯åŒãéããªããŠãŒããããšããããšã¯ééãã§ãã fact2: ãã®ã·ãã·ã«ãLv.16ã¯åºã fact3: ããä»®ã«ããã®ã·ãã·ã«ãLv.16ã¯åŒãéããªãããã®äžããã¯ãŒãããªãããšããããšã¯ééã£ãŠããã°ãã®ã¿ã«ã
ã¿ãLv.11ã¯çŽåãã fact4: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯åºããªãã°ãåŒãéãããšããããšã¯ãªãããŒãããªãããšããããšã¯æãç«ããªã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ãLv.11ã¯çŽåãã ; $proof$ = | fact4 -> int1: ããä»®ã«ããã®ã·ãã·ã«ãLv.16ã¯åºãããšããããšã¯äºå®ãªããããã®ã·ãã·ã«ãLv.16ã¯åŒãéããªããŠãŒãããªãããšããããšã¯æ£ããããšããããšã¯èª€ãã ; int1 & fact2 -> int2: ããã®ã·ãã·ã«ãLv.16ã¯åŒãéãããšããããšã¯ãªããŠãŸããŒãããšããããšã¯ãªãããšããããšã¯æãç«ããªã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {A}x -> ¬(¬{AA}x & {AB}x) fact2: {A}{aa} fact3: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{a} fact4: (x): {A}x -> ¬(¬{AA}x & ¬{AB}x) ; $hypothesis$ = {B}{a} ; $proof$ = | fact4 -> int1: {A}{aa} -> ¬(¬{AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: ¬(¬{AA}{aa} & ¬{AB}{aa}); int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | äžžããšããããšã¯çããªã | ¬{D} | fact1: ãœããœã«ãLv.85äºä»¶ãèµ·ãã fact2: äžžããšããããšããã³çã
ãããšããããšãèµ·ããã¯ãç¯ãé£ããšããããšã¯çããªãããšããããšãåå ã fact3: çã
ãããšããããšãšç¯ãé£ããšããããšã©ã¡ãããèµ·ãã fact4: ããä»®ã«ç¯ãé£ããšããããšãšãœããœã«ãLv.85äºä»¶äž¡æ¹ãçºçããã°äžžããšããããšã¯èµ·ãããªã fact5: ãç
®å«ããããšãçºçããããšããããšã¯æ¬åœã§ãããšãããšç¯ãé£ããšããããšã¯çããªãããã©ãœããœã«ãLv.85äºä»¶ãçãã fact6: ããããLv.43äºä»¶ã¯çºçããªããšããã°ç
®å«ããããšããã³çŽãããããšããããšãçãã | fact1: {C} fact2: ¬{B} -> ({D} & {A}) fact3: ({A} & {B}) fact4: ({B} & {C}) -> ¬{D} fact5: {E} -> (¬{B} & {C}) fact6: ¬{G} -> ({E} & {F}) | [
"fact3 -> int1: ç¯ãé£ããšããããšãçãã; int1 & fact1 -> int2: ç¯ãé£ããšããããšãèµ·ãããããã«ãœããœã«ãLv.85äºä»¶ãèµ·ãã; int2 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: {B}; int1 & fact1 -> int2: ({B} & {C}); int2 & fact4 -> hypothesis;"
] | äžžããšããããšãèµ·ãã | {D} | [] | 8 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãœããœã«ãLv.85äºä»¶ãèµ·ãã fact2: äžžããšããããšããã³çã
ãããšããããšãèµ·ããã¯ãç¯ãé£ããšããããšã¯çããªãããšããããšãåå ã fact3: çã
ãããšããããšãšç¯ãé£ããšããããšã©ã¡ãããèµ·ãã fact4: ããä»®ã«ç¯ãé£ããšããããšãšãœããœã«ãLv.85äºä»¶äž¡æ¹ãçºçããã°äžžããšããããšã¯èµ·ãããªã fact5: ãç
®å«ããããšãçºçããããšããããšã¯æ¬åœã§ãããšãããšç¯ãé£ããšããããšã¯çããªãããã©ãœããœã«ãLv.85äºä»¶ãçãã fact6: ããããLv.43äºä»¶ã¯çºçããªããšããã°ç
®å«ããããšããã³çŽãããããšããããšãçãã ; $hypothesis$ = äžžããšããããšã¯çããªã ; $proof$ = | fact3 -> int1: ç¯ãé£ããšããããšãçãã; int1 & fact1 -> int2: ç¯ãé£ããšããããšãèµ·ãããããã«ãœããœã«ãLv.85äºä»¶ãèµ·ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: ¬{B} -> ({D} & {A}) fact3: ({A} & {B}) fact4: ({B} & {C}) -> ¬{D} fact5: {E} -> (¬{B} & {C}) fact6: ¬{G} -> ({E} & {F}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 -> int1: {B}; int1 & fact1 -> int2: ({B} & {C}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ã·ãªã·ãLv.89äºä»¶ãèµ·ããããããã¯ãŽããŽã«Lv.78äºä»¶ãçºçããããããã¯ã©ã¡ããã§ãã | ({D} v {C}) | fact1: ãçŸå³ãããšããããšãèµ·ããããšããããšã¯çå®ã§ãã fact2: ããªãã«ãLv.27äºä»¶ã¯çããªããšããã°ãçŸå³ãããšããããšãèµ·ãããè
¹ç«ããããšããããšã¯èµ·ããªãããšããããšã¯åœã fact3: ãçŸå³ãããšããããšã¯èµ·ãããªãããšããããšã¯ééãã§ãªããªããã·ãªã·ãLv.89äºä»¶ããŽããŽã«Lv.78äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact4: ãŽããŽã«Lv.78äºä»¶ãçºçãããšããããšã¯ããªãã«ãLv.27äºä»¶ã¯åå ã§ãã fact5: ãããçŸå³ãããšããããšãèµ·ãããè
¹ç«ããããšããããšã¯çºçããªãããšããããšã¯æãç«ããªããšããã°è
¹ç«ããããšããããšãçºçãã | fact1: {A} fact2: ¬{B} -> ¬({A} & ¬{CD}) fact3: ¬{A} -> ¬({D} v {C}) fact4: {B} -> {C} fact5: ¬({A} & ¬{CD}) -> {CD} | [] | [] | è
¹ç«ããããšããããšãèµ·ããããããã¯çžé ããšããããšãçºçãã | ({CD} v {GO}) | [] | 7 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãçŸå³ãããšããããšãèµ·ããããšããããšã¯çå®ã§ãã fact2: ããªãã«ãLv.27äºä»¶ã¯çããªããšããã°ãçŸå³ãããšããããšãèµ·ãããè
¹ç«ããããšããããšã¯èµ·ããªãããšããããšã¯åœã fact3: ãçŸå³ãããšããããšã¯èµ·ãããªãããšããããšã¯ééãã§ãªããªããã·ãªã·ãLv.89äºä»¶ããŽããŽã«Lv.78äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact4: ãŽããŽã«Lv.78äºä»¶ãçºçãããšããããšã¯ããªãã«ãLv.27äºä»¶ã¯åå ã§ãã fact5: ãããçŸå³ãããšããããšãèµ·ãããè
¹ç«ããããšããããšã¯çºçããªãããšããããšã¯æãç«ããªããšããã°è
¹ç«ããããšããããšãçºçãã ; $hypothesis$ = ã·ãªã·ãLv.89äºä»¶ãèµ·ããããããã¯ãŽããŽã«Lv.78äºä»¶ãçºçããããããã¯ã©ã¡ããã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: ¬{B} -> ¬({A} & ¬{CD}) fact3: ¬{A} -> ¬({D} v {C}) fact4: {B} -> {C} fact5: ¬({A} & ¬{CD}) -> {CD} ; $hypothesis$ = ({D} v {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ã·ãã·ã«Lv.12äºä»¶ããã³ãŸããŸãLv.84äºä»¶ãçãã | ({D} & {C}) | fact1: æãã£ãœããšããããšãçºçãã fact2: ãã·ãã·ã«Lv.12äºä»¶ã¯çºçããªãããšããããšã¯ãœã¡ããœã«ãLv.98äºä»¶ã¯çºçããªããšããããšã«ããçºçãã fact3: å€ããšããããšãçºçãã fact4: æ·±ããšããããšãçãããšããããšã¯ãŸããŸãLv.84äºä»¶ãçãããã fact5: ã·ãã·ã«Lv.12äºä»¶ãèµ·ãã fact6: ããä»®ã«ãŽããŽã«ãLv.94äºä»¶ããŸãã¯æŒæºããããšãçãããšãããšãœã¡ããœã«ãLv.98äºä»¶ã¯çããªã | fact1: {DR} fact2: ¬{E} -> ¬{D} fact3: {A} fact4: {B} -> {C} fact5: {D} fact6: ({G} v {F}) -> ¬{E} | [] | [] | ã¿ã¡ãã¿ã«ã
Lv.90äºä»¶ãèµ·ãã | {HK} | [] | 7 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: æãã£ãœããšããããšãçºçãã fact2: ãã·ãã·ã«Lv.12äºä»¶ã¯çºçããªãããšããããšã¯ãœã¡ããœã«ãLv.98äºä»¶ã¯çºçããªããšããããšã«ããçºçãã fact3: å€ããšããããšãçºçãã fact4: æ·±ããšããããšãçãããšããããšã¯ãŸããŸãLv.84äºä»¶ãçãããã fact5: ã·ãã·ã«Lv.12äºä»¶ãèµ·ãã fact6: ããä»®ã«ãŽããŽã«ãLv.94äºä»¶ããŸãã¯æŒæºããããšãçãããšãããšãœã¡ããœã«ãLv.98äºä»¶ã¯çããªã ; $hypothesis$ = ã·ãã·ã«Lv.12äºä»¶ããã³ãŸããŸãLv.84äºä»¶ãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {DR} fact2: ¬{E} -> ¬{D} fact3: {A} fact4: {B} -> {C} fact5: {D} fact6: ({G} v {F}) -> ¬{E} ; $hypothesis$ = ({D} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã¡ãã¿ãLv.89ã¯è¢«èŠãããéæ¬ãã | ({A}{aa} v {B}{aa}) | fact1: ããããã®ãŽã«ããŽãªLv.22ã¯è¿ããªããªãããã®ãŽã«ããŽãªLv.22ã¯è©®ç¡ããªãããã©æ±ãå¯ããããšããããšã¯èª€ã£ãŠãã fact2: ãããã®ã¿ã¡ãã¿ãLv.89ã¯æ©èœåºæ¥ãªããŠãã®äžãã©ã³ã¹è¯ããªãããšããããšã¯äºå®ã§ããããšããããšã¯åœã§ãã fact3: ããä»®ã«ãã®ã¿ã¡ãã¿ãLv.89ããã©ã³ã¹è¯ããšããããã®ã¿ã¡ãã¿ãLv.89ã¯éæ¬ãã fact4: ããã®ã¿ã«ãã¿ãªLv.56ã¯æããªãããŸã埡å®ãããªãããšããããšã¯èª€ã£ãŠãã | fact1: ¬{E}{b} -> ¬(¬{D}{b} & {C}{b}) fact2: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact3: {AB}{aa} -> {B}{aa} fact4: ¬(¬{BB}{bp} & ¬{ES}{bp}) | [] | [] | ããã®ã¿ã¡ãã¿ãLv.89ã¯è¢«èŠããããŸãã¯éæ¬ããããšããããšã¯èª€ãã§ãã | ¬({A}{aa} v {B}{aa}) | [] | 6 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã®ãŽã«ããŽãªLv.22ã¯è¿ããªããªãããã®ãŽã«ããŽãªLv.22ã¯è©®ç¡ããªãããã©æ±ãå¯ããããšããããšã¯èª€ã£ãŠãã fact2: ãããã®ã¿ã¡ãã¿ãLv.89ã¯æ©èœåºæ¥ãªããŠãã®äžãã©ã³ã¹è¯ããªãããšããããšã¯äºå®ã§ããããšããããšã¯åœã§ãã fact3: ããä»®ã«ãã®ã¿ã¡ãã¿ãLv.89ããã©ã³ã¹è¯ããšããããã®ã¿ã¡ãã¿ãLv.89ã¯éæ¬ãã fact4: ããã®ã¿ã«ãã¿ãªLv.56ã¯æããªãããŸã埡å®ãããªãããšããããšã¯èª€ã£ãŠãã ; $hypothesis$ = ãã®ã¿ã¡ãã¿ãLv.89ã¯è¢«èŠãããéæ¬ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{E}{b} -> ¬(¬{D}{b} & {C}{b}) fact2: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact3: {AB}{aa} -> {B}{aa} fact4: ¬(¬{BB}{bp} & ¬{ES}{bp}) ; $hypothesis$ = ({A}{aa} v {B}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã¡ã
ã·ãLv.72ã¯åã | {D}{a} | fact1: ãã®ã·ã¡ã
ã·ãLv.72ã¯äŒãæããæãé£ã fact2: ããä»®ã«ãã®ã·ã¡ã
ã·ãLv.72ãæãé£ããªããšãããšãã®ãããã«ãLv.36ã¯å°äžæ·±ããããã«ããã¯äŒãæã fact3: ä»®ã«ãã®ã·ã¡ã
ã·ãLv.72ãäŒãæããªããã®ã·ã¡ã
ã·ãLv.72ã¯å°äžæ·±ã | fact1: ({A}{a} & {B}{a}) fact2: ¬{B}{a} -> ({C}{hi} & {A}{hi}) fact3: {A}{a} -> {C}{a} | [
"fact1 -> int1: ãã®ã·ã¡ã
ã·ãLv.72ã¯äŒãæã; int1 & fact3 -> int2: ãã®ã·ã¡ã
ã·ãLv.72ã¯å°äžæ·±ã;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact3 -> int2: {C}{a};"
] | ãã®ãããã«ãLv.36ã¯å°äžæ·±ã | {C}{hi} | [] | 6 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ã·ã¡ã
ã·ãLv.72ã¯äŒãæããæãé£ã fact2: ããä»®ã«ãã®ã·ã¡ã
ã·ãLv.72ãæãé£ããªããšãããšãã®ãããã«ãLv.36ã¯å°äžæ·±ããããã«ããã¯äŒãæã fact3: ä»®ã«ãã®ã·ã¡ã
ã·ãLv.72ãäŒãæããªããã®ã·ã¡ã
ã·ãLv.72ã¯å°äžæ·±ã ; $hypothesis$ = ãã®ã·ã¡ã
ã·ãLv.72ã¯åã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: ¬{B}{a} -> ({C}{hi} & {A}{hi}) fact3: {A}{a} -> {C}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã¿ã¡ãã¿ã®Lv.39ã¯çºçãæãããããã¯ç¬ãããããããã¯ã©ã¡ããã ããšããããšã¯èª€ãã§ãã | ¬({D}{c} v {C}{c}) | fact1: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãå®ããªãã°ããã¯å¢ãé£ããªã fact2: è³¢ãããªãã¢ã³ã¹ã¿ãŒã¯å®ã fact3: ãã®ãœã«ããœãLv.6ã¯çºçãæã fact4: ãããã®ãã«ãããLv.72ãå¢ãé£ããšããããã®ã¿ãã¿ãLv.14ã¯å®ã fact5: ãã®ã¿ãã¿ãLv.14ã¯å®ããšãããšããã®ã¿ã¡ãã¿ã®Lv.39ã¯ç¬ãããããšããããšã¯äºå®ã fact6: ãããã®ãã«ãããLv.72ã¯æ±ãæããªããªããããã®ãã«ãããLv.72ã¯è³¢ãããŠããã¯è¯ãããšããããšã¯ééãã§ããããšããããšã¯äºå®ã§ãã fact7: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å¢ãé£ããªããªããããã¯çºçãæãããããã¯ããã¯ç¬ãããããšããããšã¯æãç«ããªã fact8: ãã®ãã«ãããLv.72ã¯å¢ãé£ã | fact1: (x): {B}x -> ¬{A}x fact2: (x): ¬{E}x -> {B}x fact3: {D}{fa} fact4: {A}{a} -> {B}{b} fact5: {B}{b} -> {C}{c} fact6: ¬{F}{a} -> ¬({E}{a} & {G}{a}) fact7: (x): ¬{A}x -> ¬({D}x v {C}x) fact8: {A}{a} | [
"fact4 & fact8 -> int1: ãã®ã¿ãã¿ãLv.14ã¯å®ã; int1 & fact5 -> int2: ãã®ã¿ã¡ãã¿ã®Lv.39ã¯ç¬ããã; int2 -> hypothesis;"
] | [
"fact4 & fact8 -> int1: {B}{b}; int1 & fact5 -> int2: {C}{c}; int2 -> hypothesis;"
] | ããã®ã¿ã¡ãã¿ã®Lv.39ã¯çºçãæãããããã¯ç¬ãããããããã¯ã©ã¡ããã ããšããããšã¯èª€ãã§ãã | ¬({D}{c} v {C}{c}) | [
"fact9 -> int3: ãã®ã¿ã¡ãã¿ã®Lv.39ã¯å¢ãé£ããªããšãããšããã®ã¿ã¡ãã¿ã®Lv.39ã¯çºçãæãããããã¯ç¬ãããããŸãã¯ã©ã¡ããã ããšããããšã¯æãç«ããªã; fact10 -> int4: ããã®ã¿ã¡ãã¿ã®Lv.39ã¯å®ããªãããšããããšã¯èª€ãã ãšãããããã®ã¿ã¡ãã¿ã®Lv.39ã¯å¢ãé£ããšããããšã¯ãªãããšããããšã¯æ¬åœã ; fact11 -> int5: ä»®ã«ãã®ã¿ã¡ãã¿ã®Lv.39ãè³¢ãããªããªãã°ãã®ã¿ã¡ãã¿ã®Lv.39ã¯å®ã;"
] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒãå®ããªãã°ããã¯å¢ãé£ããªã fact2: è³¢ãããªãã¢ã³ã¹ã¿ãŒã¯å®ã fact3: ãã®ãœã«ããœãLv.6ã¯çºçãæã fact4: ãããã®ãã«ãããLv.72ãå¢ãé£ããšããããã®ã¿ãã¿ãLv.14ã¯å®ã fact5: ãã®ã¿ãã¿ãLv.14ã¯å®ããšãããšããã®ã¿ã¡ãã¿ã®Lv.39ã¯ç¬ãããããšããããšã¯äºå®ã fact6: ãããã®ãã«ãããLv.72ã¯æ±ãæããªããªããããã®ãã«ãããLv.72ã¯è³¢ãããŠããã¯è¯ãããšããããšã¯ééãã§ããããšããããšã¯äºå®ã§ãã fact7: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å¢ãé£ããªããªããããã¯çºçãæãããããã¯ããã¯ç¬ãããããšããããšã¯æãç«ããªã fact8: ãã®ãã«ãããLv.72ã¯å¢ãé£ã ; $hypothesis$ = ããã®ã¿ã¡ãã¿ã®Lv.39ã¯çºçãæãããããã¯ç¬ãããããããã¯ã©ã¡ããã ããšããããšã¯èª€ãã§ãã ; $proof$ = | fact4 & fact8 -> int1: ãã®ã¿ãã¿ãLv.14ã¯å®ã; int1 & fact5 -> int2: ãã®ã¿ã¡ãã¿ã®Lv.39ã¯ç¬ããã; int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {B}x -> ¬{A}x fact2: (x): ¬{E}x -> {B}x fact3: {D}{fa} fact4: {A}{a} -> {B}{b} fact5: {B}{b} -> {C}{c} fact6: ¬{F}{a} -> ¬({E}{a} & {G}{a}) fact7: (x): ¬{A}x -> ¬({D}x v {C}x) fact8: {A}{a} ; $hypothesis$ = ¬({D}{c} v {C}{c}) ; $proof$ = | fact4 & fact8 -> int1: {B}{b}; int1 & fact5 -> int2: {C}{c}; int2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã·ã«ãã·ãLv.27ã¯èŠè©°ãããå ããŠæå³æ·±ãããšããããšã¯æãç«ããªã | ¬({C}{b} & {D}{b}) | fact1: ãããã®ã·ã«ãã·ãLv.27ãæ±ããªãããã¯èŠè©°ãã fact2: ãã®ã¿ã¡ã
ã¿ã¡ãLv.32ã¯é·ã
ãã fact3: ããããã¢ã³ã¹ã¿ãŒã¯é·ã
ãããªããšããã°ãããã¯èŠè©°ããããã€æå³æ·±ãããšããããšã¯æãç«ããªã fact4: ããã®ã·ã«ãã·ãLv.27ã¯æå³æ·±ãããšããããšã¯çå®ã fact5: ãã®ãŸããŸã¡ãLv.68ã¯é·ã
ãã fact6: ããä»®ã«ãã®ã¿ã¡ã
ã¿ã¡ãLv.32ãæ±ããªããªãã°ãã®ãŽããŽã®Lv.21ã¯æå³æ·±ããããã¯é·ã
ãã | fact1: {B}{b} -> {C}{b} fact2: {A}{a} fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: {D}{b} fact5: {A}{bg} fact6: ¬{B}{a} -> ({D}{ht} & {A}{ht}) | [] | [] | ãã®ãŽããŽã®Lv.21ã¯æå³æ·±ããå¯ã
ãã | ({D}{ht} & {ER}{ht}) | [] | 5 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ã·ã«ãã·ãLv.27ãæ±ããªãããã¯èŠè©°ãã fact2: ãã®ã¿ã¡ã
ã¿ã¡ãLv.32ã¯é·ã
ãã fact3: ããããã¢ã³ã¹ã¿ãŒã¯é·ã
ãããªããšããã°ãããã¯èŠè©°ããããã€æå³æ·±ãããšããããšã¯æãç«ããªã fact4: ããã®ã·ã«ãã·ãLv.27ã¯æå³æ·±ãããšããããšã¯çå®ã fact5: ãã®ãŸããŸã¡ãLv.68ã¯é·ã
ãã fact6: ããä»®ã«ãã®ã¿ã¡ã
ã¿ã¡ãLv.32ãæ±ããªããªãã°ãã®ãŽããŽã®Lv.21ã¯æå³æ·±ããããã¯é·ã
ãã ; $hypothesis$ = ããã®ã·ã«ãã·ãLv.27ã¯èŠè©°ãããå ããŠæå³æ·±ãããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{b} -> {C}{b} fact2: {A}{a} fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: {D}{b} fact5: {A}{bg} fact6: ¬{B}{a} -> ({D}{ht} & {A}{ht}) ; $hypothesis$ = ¬({C}{b} & {D}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã¿ãªã¿ãLv.3ã¯æãé£ããªããŠããã«ããã¯æœ°ããªãããšããããšã¯ééãã§ãã | ¬(¬{C}{c} & ¬{E}{c}) | fact1: ãã®ã·ãã·ãªLv.59ã¯æé
·ã fact2: ããä»®ã«ãã®ã·ãã·ãªLv.59ãç
§ãããŸãæé
·ããšãããšãã®ãŽããŽã¡ãLv.15ã¯æãé£ããšããããšã¯ãªã fact3: ãã®ã·ãã·ãªLv.59ã¯ç
§ã fact4: ãã®ã·ãã·ãªLv.59ã¯å¥³æ§ããã fact5: ãã®ã¿ãªã¿ãLv.3ã¯æé
·ããªããŠãã€æãé£ããªã fact6: ãã®ãŽããŽã¡ãLv.15ã¯ç
§ã fact7: ããä»®ã«ãã®ãŽããŽã¡ãLv.15ãæé
·ãã朰ãããšãããšãã®ã·ãã·ãªLv.59ã¯æãé£ããªã | fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: {A}{a} fact4: {JI}{a} fact5: (¬{B}{c} & ¬{C}{c}) fact6: {A}{b} fact7: ({B}{b} & {E}{b}) -> ¬{C}{a} | [
"fact3 & fact1 -> int1: ãã®ã·ãã·ãªLv.59ã¯ç
§ãããã€æé
·ã; int1 & fact2 -> int2: ãã®ãŽããŽã¡ãLv.15ã¯æãé£ããªã;"
] | [
"fact3 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{b};"
] | null | null | [] | null | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ã·ãã·ãªLv.59ã¯æé
·ã fact2: ããä»®ã«ãã®ã·ãã·ãªLv.59ãç
§ãããŸãæé
·ããšãããšãã®ãŽããŽã¡ãLv.15ã¯æãé£ããšããããšã¯ãªã fact3: ãã®ã·ãã·ãªLv.59ã¯ç
§ã fact4: ãã®ã·ãã·ãªLv.59ã¯å¥³æ§ããã fact5: ãã®ã¿ãªã¿ãLv.3ã¯æé
·ããªããŠãã€æãé£ããªã fact6: ãã®ãŽããŽã¡ãLv.15ã¯ç
§ã fact7: ããä»®ã«ãã®ãŽããŽã¡ãLv.15ãæé
·ãã朰ãããšãããšãã®ã·ãã·ãªLv.59ã¯æãé£ããªã ; $hypothesis$ = ããã®ã¿ãªã¿ãLv.3ã¯æãé£ããªããŠããã«ããã¯æœ°ããªãããšããããšã¯ééãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: {A}{a} fact4: {JI}{a} fact5: (¬{B}{c} & ¬{C}{c}) fact6: {A}{b} fact7: ({B}{b} & {E}{b}) -> ¬{C}{a} ; $hypothesis$ = ¬(¬{C}{c} & ¬{E}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æããŠå ããŠããã¯åã | ({C}{b} & {D}{b}) | fact1: ãã®ã¿ãã¿ã¡ã
Lv.17ã¯ããè¥ã fact2: ããä»®ã«ããã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæãããšããããšã¯æ¬åœã§ãããªããã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æã fact3: ãã®ãŽããŽãLv.18ã¯æãé£ããããã¯æã£ãã fact4: ãã®ã¿ãã¿ã¡ãLv.79ã¯ããè¥ã fact5: ããã®ã¿ãã¿ã¡ã
Lv.17ã¯åãããšããããšã¯æ£ãã fact6: ãã®ãœã®ãœãLv.90ã¯æã¡æã fact7: ãã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæããããè¥ã | fact1: {B}{b} fact2: {A}{a} -> {C}{b} fact3: ({BQ}{fo} & {GK}{fo}) fact4: {B}{a} fact5: {D}{b} fact6: {C}{ej} fact7: ({A}{a} & {B}{a}) | [
"fact7 -> int1: ãã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæã; int1 & fact2 -> int2: ãã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æã; int2 & fact5 -> hypothesis;"
] | [
"fact7 -> int1: {A}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact5 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã¿ãã¿ã¡ã
Lv.17ã¯ããè¥ã fact2: ããä»®ã«ããã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæãããšããããšã¯æ¬åœã§ãããªããã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æã fact3: ãã®ãŽããŽãLv.18ã¯æãé£ããããã¯æã£ãã fact4: ãã®ã¿ãã¿ã¡ãLv.79ã¯ããè¥ã fact5: ããã®ã¿ãã¿ã¡ã
Lv.17ã¯åãããšããããšã¯æ£ãã fact6: ãã®ãœã®ãœãLv.90ã¯æã¡æã fact7: ãã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæããããè¥ã ; $hypothesis$ = ãã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æããŠå ããŠããã¯åã ; $proof$ = | fact7 -> int1: ãã®ã¿ãã¿ã¡ãLv.79ã¯ç±ãæã; int1 & fact2 -> int2: ãã®ã¿ãã¿ã¡ã
Lv.17ã¯æã¡æã; int2 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{b} fact2: {A}{a} -> {C}{b} fact3: ({BQ}{fo} & {GK}{fo}) fact4: {B}{a} fact5: {D}{b} fact6: {C}{ej} fact7: ({A}{a} & {B}{a}) ; $hypothesis$ = ({C}{b} & {D}{b}) ; $proof$ = | fact7 -> int1: {A}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact5 -> hypothesis; __PROVED__ |
0.3 | çãæ·±ããšããããšã¯çºçããªã | ¬{D} | fact1: 埡èšãããšãèµ·ãã fact2: ãåã¡æããšããããšã¯èµ·ããªãããšããããšã¯çãæ·±ããšããããšãšãœã«ã
ãœã«ãLv.35äºä»¶ãèµ·ããããããã fact3: ã倧ç¹çããããšãèµ·ããããŸãæããããšããããšãçºçããããšããããšã¯ããŸããŸã«ãLv.60äºä»¶ã¯èµ·ããªãããšããããšã«èªçºããã fact4: ãŽã®ãŽãLv.45äºä»¶ãçãããªãæ¥æ¬äººããããšããããšãçãããã©åã¡æããšããããšã¯èµ·ãããªã fact5: 倧ç¹çããããšã¯ãŽã®ãŽãLv.45äºä»¶ããããã fact6: ããœã«ã
ãœã«ãLv.35äºä»¶ãèµ·ããããŸãåã¡æããšããããšãçããããšããããšã¯æãç«ã€ | fact1: {GA} fact2: ¬{B} -> ({D} & {A}) fact3: ¬{H} -> ({F} & {G}) fact4: {E} -> ({C} & ¬{B}) fact5: {F} -> {E} fact6: ({A} & {B}) | [
"fact6 -> int1: åã¡æããšããããšãçãã; int1 -> int2: åã¡æããšããããšãèµ·ããããããã¯æ¥æ¬äººããããšããããšãèµ·ããããããã¯ã©ã¡ããã ;"
] | [
"fact6 -> int1: {B}; int1 -> int2: ({B} v {C});"
] | çãæ·±ããšããããšãçºçãã | {D} | [] | 9 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: 埡èšãããšãèµ·ãã fact2: ãåã¡æããšããããšã¯èµ·ããªãããšããããšã¯çãæ·±ããšããããšãšãœã«ã
ãœã«ãLv.35äºä»¶ãèµ·ããããããã fact3: ã倧ç¹çããããšãèµ·ããããŸãæããããšããããšãçºçããããšããããšã¯ããŸããŸã«ãLv.60äºä»¶ã¯èµ·ããªãããšããããšã«èªçºããã fact4: ãŽã®ãŽãLv.45äºä»¶ãçãããªãæ¥æ¬äººããããšããããšãçãããã©åã¡æããšããããšã¯èµ·ãããªã fact5: 倧ç¹çããããšã¯ãŽã®ãŽãLv.45äºä»¶ããããã fact6: ããœã«ã
ãœã«ãLv.35äºä»¶ãèµ·ããããŸãåã¡æããšããããšãçããããšããããšã¯æãç«ã€ ; $hypothesis$ = çãæ·±ããšããããšã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {GA} fact2: ¬{B} -> ({D} & {A}) fact3: ¬{H} -> ({F} & {G}) fact4: {E} -> ({C} & ¬{B}) fact5: {F} -> {E} fact6: ({A} & {B}) ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸããŸãLv.14ã¯è²ã¡åããããããæ··åãæã | ({B}{a} & {C}{a}) | fact1: ãã®ãŸããŸãLv.14ã¯æ··åãæã fact2: ããä»®ã«ããã®ãœããœã¡ã
Lv.89ã¯ä¿¡ãé£ããªãããšããããšã¯æãç«ã€ãªããã®ãœã«ããœãLv.18ã¯ç¬ããšããããšã¯ãªãããããã¯ååãããªããã©ã¡ããã§ãã fact3: ããããã®ã¿ãã¿ãLv.44ã¯ç¬ããªããšãããããã®ãŸããŸãLv.14ã¯è²ã¡åãããããã«æ··åãæãããšããããšã¯äºå®ãšç°ãªã fact4: ãã®ãœããœã«ãLv.4ã¯ç¬ãã軜ãŒã | fact1: {C}{a} fact2: ¬{E}{d} -> (¬{A}{c} v ¬{D}{c}) fact3: ¬{A}{b} -> ¬({B}{a} & {C}{a}) fact4: ({A}{fp} & {EP}{fp}) | [] | [] | ããã®ãŸããŸãLv.14ã¯è²ã¡åããããããæ··åãæãããšããããšã¯èª€ã£ãŠãã | ¬({B}{a} & {C}{a}) | [] | 7 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãŸããŸãLv.14ã¯æ··åãæã fact2: ããä»®ã«ããã®ãœããœã¡ã
Lv.89ã¯ä¿¡ãé£ããªãããšããããšã¯æãç«ã€ãªããã®ãœã«ããœãLv.18ã¯ç¬ããšããããšã¯ãªãããããã¯ååãããªããã©ã¡ããã§ãã fact3: ããããã®ã¿ãã¿ãLv.44ã¯ç¬ããªããšãããããã®ãŸããŸãLv.14ã¯è²ã¡åãããããã«æ··åãæãããšããããšã¯äºå®ãšç°ãªã fact4: ãã®ãœããœã«ãLv.4ã¯ç¬ãã軜ãŒã ; $hypothesis$ = ãã®ãŸããŸãLv.14ã¯è²ã¡åããããããæ··åãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{a} fact2: ¬{E}{d} -> (¬{A}{c} v ¬{D}{c}) fact3: ¬{A}{b} -> ¬({B}{a} & {C}{a}) fact4: ({A}{fp} & {EP}{fp}) ; $hypothesis$ = ({B}{a} & {C}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ã¡ãã·ã®Lv.1ã¯æå·ããã女ã£ãœãããšããããšã¯ééã£ãŠãã | ¬({D}{b} & {C}{b}) | fact1: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯å·ãæããªãããšããããšã¯ç¢ºãã§ãããšããã°ãããã¯æå·ãããããã女ã£ãœãããšããããšã¯äºå®ãšç°ãªã fact2: ãã®ã·ã¡ãã·ã®Lv.1ã¯æå·ãã fact3: ãã®ãŽã«ããŽã®Lv.32ã¯è¹Žæ£ãã fact4: ãããã®ã·ã¡ãã·ã®Lv.1ãå·ãæããªããã®ãŽã«ããŽã®Lv.32ã¯å¥³ã£ãœã fact5: ããããã®ãŽã«ããŽã®Lv.32ãå·ãæããšããã°ãã®ã·ã¡ãã·ã®Lv.1ã¯å¥³ã£ãœã fact6: ãã®ãŽã«ããŽã®Lv.32ã¯å·ãæãããã€è¹Žæ£ãã | fact1: (x): ¬{A}x -> ¬({D}x & {C}x) fact2: {D}{b} fact3: {B}{a} fact4: {A}{b} -> {C}{a} fact5: {A}{a} -> {C}{b} fact6: ({A}{a} & {B}{a}) | [
"fact6 -> int1: ãã®ãŽã«ããŽã®Lv.32ã¯å·ãæã; int1 & fact5 -> int2: ãã®ã·ã¡ãã·ã®Lv.1ã¯å¥³ã£ãœã; int2 & fact2 -> hypothesis;"
] | [
"fact6 -> int1: {A}{a}; int1 & fact5 -> int2: {C}{b}; int2 & fact2 -> hypothesis;"
] | ããã®ã·ã¡ãã·ã®Lv.1ã¯æå·ããã女ã£ãœãããšããããšã¯ééã£ãŠãã | ¬({D}{b} & {C}{b}) | [
"fact7 -> int3: ä»®ã«ãã®ã·ã¡ãã·ã®Lv.1ã¯å·ãæããªããªãããããã¯æå·ããã女ã£ãœãããšããããšã¯äºå®ã§ããããšããããšã¯æãç«ããªã;"
] | 5 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯å·ãæããªãããšããããšã¯ç¢ºãã§ãããšããã°ãããã¯æå·ãããããã女ã£ãœãããšããããšã¯äºå®ãšç°ãªã fact2: ãã®ã·ã¡ãã·ã®Lv.1ã¯æå·ãã fact3: ãã®ãŽã«ããŽã®Lv.32ã¯è¹Žæ£ãã fact4: ãããã®ã·ã¡ãã·ã®Lv.1ãå·ãæããªããã®ãŽã«ããŽã®Lv.32ã¯å¥³ã£ãœã fact5: ããããã®ãŽã«ããŽã®Lv.32ãå·ãæããšããã°ãã®ã·ã¡ãã·ã®Lv.1ã¯å¥³ã£ãœã fact6: ãã®ãŽã«ããŽã®Lv.32ã¯å·ãæãããã€è¹Žæ£ãã ; $hypothesis$ = ããã®ã·ã¡ãã·ã®Lv.1ã¯æå·ããã女ã£ãœãããšããããšã¯ééã£ãŠãã ; $proof$ = | fact6 -> int1: ãã®ãŽã«ããŽã®Lv.32ã¯å·ãæã; int1 & fact5 -> int2: ãã®ã·ã¡ãã·ã®Lv.1ã¯å¥³ã£ãœã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{A}x -> ¬({D}x & {C}x) fact2: {D}{b} fact3: {B}{a} fact4: {A}{b} -> {C}{a} fact5: {A}{a} -> {C}{b} fact6: ({A}{a} & {B}{a}) ; $hypothesis$ = ¬({D}{b} & {C}{b}) ; $proof$ = | fact6 -> int1: {A}{a}; int1 & fact5 -> int2: {C}{b}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸããŸãªLv.70ã¯å®¹ããããšããããšã¯æ¬åœã | {B}{a} | fact1: ãã®ãããã«Lv.60ã¯éãæã fact2: ãããã®ãããã«Lv.60ãç¯ãæããšãããšãã®ãŸããŸãªLv.70ã¯å®¹ãã | fact1: {A}{aa} fact2: {C}{aa} -> {B}{a} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãããã«Lv.60ã¯éãæã fact2: ãããã®ãããã«Lv.60ãç¯ãæããšãããšãã®ãŸããŸãªLv.70ã¯å®¹ãã ; $hypothesis$ = ããã®ãŸããŸãªLv.70ã¯å®¹ããããšããããšã¯æ¬åœã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{aa} fact2: {C}{aa} -> {B}{a} ; $hypothesis$ = {B}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ã¿ã¡ãã¿ã¡ãLv.81äºä»¶ãçºçãã | {D} | fact1: ãŸã«ã
ãŸã«ã
Lv.88äºä»¶ãèµ·ããããã€ã¿ã«ã
ã¿ãLv.75äºä»¶ãèµ·ãã fact2: ã¿ã¡ãã¿ã¡ãLv.81äºä»¶ã¯èµ·ãããªããšããããšã¯ããœã¡ããœã«Lv.78äºä»¶ãèµ·ããããããã¯ã¿ã«ã
ã¿ãLv.75äºä»¶ãèµ·ããããšããããšã«ç±æ¥ãã | fact1: ({A} & {B}) fact2: ({C} v {B}) -> ¬{D} | [
"fact1 -> int1: ã¿ã«ã
ã¿ãLv.75äºä»¶ãçãã; int1 -> int2: ãœã¡ããœã«Lv.78äºä»¶ããããã¯ã¿ã«ã
ã¿ãLv.75äºä»¶ããŸãã¯ã©ã¡ãããçºçãã; int2 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {B}; int1 -> int2: ({C} v {B}); int2 & fact2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãŸã«ã
ãŸã«ã
Lv.88äºä»¶ãèµ·ããããã€ã¿ã«ã
ã¿ãLv.75äºä»¶ãèµ·ãã fact2: ã¿ã¡ãã¿ã¡ãLv.81äºä»¶ã¯èµ·ãããªããšããããšã¯ããœã¡ããœã«Lv.78äºä»¶ãèµ·ããããããã¯ã¿ã«ã
ã¿ãLv.75äºä»¶ãèµ·ããããšããããšã«ç±æ¥ãã ; $hypothesis$ = ã¿ã¡ãã¿ã¡ãLv.81äºä»¶ãçºçãã ; $proof$ = | fact1 -> int1: ã¿ã«ã
ã¿ãLv.75äºä»¶ãçãã; int1 -> int2: ãœã¡ããœã«Lv.78äºä»¶ããããã¯ã¿ã«ã
ã¿ãLv.75äºä»¶ããŸãã¯ã©ã¡ãããçºçãã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) fact2: ({C} v {B}) -> ¬{D} ; $hypothesis$ = {D} ; $proof$ = | fact1 -> int1: {B}; int1 -> int2: ({C} v {B}); int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãŸããŸã¡ãLv.82äºä»¶ãçããããŸãã¯æããããšããããšãçããããããã¯äž¡æ¹ã§ãã | ({A} v {C}) | fact1: ã·ãã·ãLv.80äºä»¶ããããã¯çŠã
ãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ãé²ã fact2: ããåãå€ããããšãèµ·ãããã¢ããŒã«åºæ¥ãããšã¯çºçããªãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ã¯èµ·ãããªããšããããšãé²ãããšããããšã¯èª€ã£ãŠããªã fact3: è¿·ä¿¡æ·±ããšããããšãçãã fact4: ããä»®ã«ããœã¡ã
ãœãLv.33äºä»¶ã¯çºçããªãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªããšãããããŸããŸã¡ãLv.82äºä»¶ãçºçããããããã¯æããããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact5: ãœã¡ã
ãœãLv.33äºä»¶ã¯ããŸããŸã¡ãLv.82äºä»¶ãçºçããããšããããšãçºçããã fact6: ãåãå€ããããšãçºçããªããã¢ããŒã«åºæ¥ãããšã¯çºçããªãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ãçãããã | fact1: ({E} v {D}) -> ¬{B} fact2: ({AA} & ¬{AB}) -> {B} fact3: {GQ} fact4: ¬{B} -> ¬({A} v {C}) fact5: {B} -> {A} fact6: (¬{AA} & ¬{AB}) -> {B} | [] | [] | ããŸããŸã¡ãLv.82äºä»¶ããããã¯æããããšããããšããããã¯ã©ã¡ãããçããããšããããšã¯æãç«ããªã | ¬({A} v {C}) | [] | 7 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã·ãã·ãLv.80äºä»¶ããããã¯çŠã
ãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ãé²ã fact2: ããåãå€ããããšãèµ·ãããã¢ããŒã«åºæ¥ãããšã¯çºçããªãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ã¯èµ·ãããªããšããããšãé²ãããšããããšã¯èª€ã£ãŠããªã fact3: è¿·ä¿¡æ·±ããšããããšãçãã fact4: ããä»®ã«ããœã¡ã
ãœãLv.33äºä»¶ã¯çºçããªãããšããããšã¯èª€ã£ãŠãããšããããšã¯ãªããšãããããŸããŸã¡ãLv.82äºä»¶ãçºçããããããã¯æããããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact5: ãœã¡ã
ãœãLv.33äºä»¶ã¯ããŸããŸã¡ãLv.82äºä»¶ãçºçããããšããããšãçºçããã fact6: ãåãå€ããããšãçºçããªããã¢ããŒã«åºæ¥ãããšã¯çºçããªãããšããããšã¯ãœã¡ã
ãœãLv.33äºä»¶ãçãããã ; $hypothesis$ = ãŸããŸã¡ãLv.82äºä»¶ãçããããŸãã¯æããããšããããšãçããããããã¯äž¡æ¹ã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({E} v {D}) -> ¬{B} fact2: ({AA} & ¬{AB}) -> {B} fact3: {GQ} fact4: ¬{B} -> ¬({A} v {C}) fact5: {B} -> {A} fact6: (¬{AA} & ¬{AB}) -> {B} ; $hypothesis$ = ({A} v {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããããç¡ããšããããšãèµ·ããããŽããŽã¡ãLv.63äºä»¶ãçããããšããããšã¯ééãã | ¬({B} & {C}) | fact1: ãŽã¡ããŽãLv.38äºä»¶ãçãã fact2: å¡©ã£èŸããšããããšãèµ·ãã fact3: ããããªLv.85äºä»¶ãçãã fact4: ããŽããŽã¡ãLv.63äºä»¶ãçããããšããããšã¯äºå®ã§ãã fact5: ã¿ãã¿ã«Lv.95äºä»¶ãèµ·ãã | fact1: {A} fact2: {BS} fact3: {U} fact4: {C} fact5: {IQ} | [] | [] | null | null | [] | null | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãŽã¡ããŽãLv.38äºä»¶ãçãã fact2: å¡©ã£èŸããšããããšãèµ·ãã fact3: ããããªLv.85äºä»¶ãçãã fact4: ããŽããŽã¡ãLv.63äºä»¶ãçããããšããããšã¯äºå®ã§ãã fact5: ã¿ãã¿ã«Lv.95äºä»¶ãèµ·ãã ; $hypothesis$ = ããããç¡ããšããããšãèµ·ããããŽããŽã¡ãLv.63äºä»¶ãçããããšããããšã¯ééãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: {BS} fact3: {U} fact4: {C} fact5: {IQ} ; $hypothesis$ = ¬({B} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | èãèŸããšããããšãçãã | {D} | fact1: ãœãªãœãLv.59äºä»¶ãèµ·ãããæŽã«ãŽã«ããŽãLv.80äºä»¶ãèµ·ãã fact2: ãããããé¢ãéããããšã¯èµ·ãããªãããããã¯èãèŸããšããããšã¯èµ·ãããªãããããã¯äž¡æ¹ã ããšããããšã¯äºå®ã ããšããããšã¯åã§ãããšããããè
ç²æç¡ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact3: çŽ äººã£ãœããšããããšã¯ãœããœã«ã
Lv.81äºä»¶ãçºçãããšããããšããããã fact4: èãèŸããšããããšã¯ãè
ç²æç¡ããšããããšããã³ãããã¡ãLv.80äºä»¶äž¡æ¹ãšããçºçããããšããããšã«é²ããã fact5: è
ç²æç¡ããšããããšãçãã fact6: è
ç²æç¡ããšããããšã¯çºçããªããšããããšã¯ããããã¡ãLv.80äºä»¶ããã³çŽ 人ã£ãœããšããããšäž¡æ¹ãšããèµ·ããããšããããšãçãããã fact7: çŽ äººã£ãœããšããããšãçãã fact8: çŽ äººã£ãœããšããããšãšãããã¡ãLv.80äºä»¶ãèµ·ãã | fact1: ({BN} & {HQ}) fact2: ¬(¬{E} v ¬{D}) -> ¬{C} fact3: {A} -> {T} fact4: ({C} & {B}) -> ¬{D} fact5: {C} fact6: ¬{C} -> ({B} & {A}) fact7: {A} fact8: ({A} & {B}) | [
"fact8 -> int1: ãããã¡ãLv.80äºä»¶ãèµ·ãã; int1 & fact5 -> int2: è
ç²æç¡ããšããããšããã³ãããã¡ãLv.80äºä»¶ãçºçãã; int2 & fact4 -> hypothesis;"
] | [
"fact8 -> int1: {B}; int1 & fact5 -> int2: ({C} & {B}); int2 & fact4 -> hypothesis;"
] | ãœããœã«ã
Lv.81äºä»¶ãèµ·ãã | {T} | [] | 8 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãœãªãœãLv.59äºä»¶ãèµ·ãããæŽã«ãŽã«ããŽãLv.80äºä»¶ãèµ·ãã fact2: ãããããé¢ãéããããšã¯èµ·ãããªãããããã¯èãèŸããšããããšã¯èµ·ãããªãããããã¯äž¡æ¹ã ããšããããšã¯äºå®ã ããšããããšã¯åã§ãããšããããè
ç²æç¡ããšããããšã¯èµ·ããªãããšããããšã¯æãç«ã€ fact3: çŽ äººã£ãœããšããããšã¯ãœããœã«ã
Lv.81äºä»¶ãçºçãããšããããšããããã fact4: èãèŸããšããããšã¯ãè
ç²æç¡ããšããããšããã³ãããã¡ãLv.80äºä»¶äž¡æ¹ãšããçºçããããšããããšã«é²ããã fact5: è
ç²æç¡ããšããããšãçãã fact6: è
ç²æç¡ããšããããšã¯çºçããªããšããããšã¯ããããã¡ãLv.80äºä»¶ããã³çŽ 人ã£ãœããšããããšäž¡æ¹ãšããèµ·ããããšããããšãçãããã fact7: çŽ äººã£ãœããšããããšãçãã fact8: çŽ äººã£ãœããšããããšãšãããã¡ãLv.80äºä»¶ãèµ·ãã ; $hypothesis$ = èãèŸããšããããšãçãã ; $proof$ = | fact8 -> int1: ãããã¡ãLv.80äºä»¶ãèµ·ãã; int1 & fact5 -> int2: è
ç²æç¡ããšããããšããã³ãããã¡ãLv.80äºä»¶ãçºçãã; int2 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({BN} & {HQ}) fact2: ¬(¬{E} v ¬{D}) -> ¬{C} fact3: {A} -> {T} fact4: ({C} & {B}) -> ¬{D} fact5: {C} fact6: ¬{C} -> ({B} & {A}) fact7: {A} fact8: ({A} & {B}) ; $hypothesis$ = {D} ; $proof$ = | fact8 -> int1: {B}; int1 & fact5 -> int2: ({C} & {B}); int2 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽã®Lv.41ã¯åŒå¿ãåããªã | ¬{A}{a} | fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯äžå·¡ãã fact2: ãã®ãœã®ãœã¡ã
Lv.84ã¯åŒå¿ãåã fact3: ããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåã fact4: ããããã¢ã³ã¹ã¿ãŒã¯å·®ãæ¯ãæã fact5: ããä»®ã«åãããªãã¢ã³ã¹ã¿ãŒãäžå·¡ããã°èããªã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåããèãããšããããšã¯èª€ã£ãŠãããªãåŒå¿ãåããªã | fact1: (x): {D}x fact2: {A}{hu} fact3: (x): {A}x fact4: (x): {CN}x fact5: (x): (¬{C}x & {D}x) -> ¬{B}x fact6: (x): ¬({A}x & {B}x) -> ¬{A}x | [
"fact3 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåã; int1 -> hypothesis;"
] | [
"fact3 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã®ãŽããŽã®Lv.41ã¯åŒå¿ãåããªã | ¬{A}{a} | [
"fact7 -> int2: ãããããã®ãŽããŽã®Lv.41ã¯åŒå¿ãåããèãããšããããšã¯ééã£ãŠãããªãããã®ãŽããŽã®Lv.41ã¯åŒå¿ãåããšããããšã¯ãªãããšããããšã¯äºå®ã ;"
] | 4 | 2 | 2 | 2 | 2 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯äžå·¡ãã fact2: ãã®ãœã®ãœã¡ã
Lv.84ã¯åŒå¿ãåã fact3: ããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåã fact4: ããããã¢ã³ã¹ã¿ãŒã¯å·®ãæ¯ãæã fact5: ããä»®ã«åãããªãã¢ã³ã¹ã¿ãŒãäžå·¡ããã°èããªã fact6: ããããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåããèãããšããããšã¯èª€ã£ãŠãããªãåŒå¿ãåããªã ; $hypothesis$ = ãã®ãŽããŽã®Lv.41ã¯åŒå¿ãåããªã ; $proof$ = | fact3 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯åŒå¿ãåã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {D}x fact2: {A}{hu} fact3: (x): {A}x fact4: (x): {CN}x fact5: (x): (¬{C}x & {D}x) -> ¬{B}x fact6: (x): ¬({A}x & {B}x) -> ¬{A}x ; $hypothesis$ = ¬{A}{a} ; $proof$ = | fact3 -> int1: (x): {A}x; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.31ã¯éã | {E}{b} | fact1: ä»®ã«ãã®ããããLv.92ãå
±é³Žãæããªããã®ãŽããŽãLv.31ã¯æãŸãã fact2: ããããã®ã·ã«ã·ã¡ãLv.80ã¯å®ããšãããšããã®ããããLv.92ã¯å
±é³Žãæãããšããããšã¯æ¬åœã fact3: å
±é³Žãæããªãã¢ã³ã¹ã¿ãŒã¯å®ããæãç¡ã fact4: ãã®ã·ã«ã·ã¡ãLv.80ã¯å®ããæãç¡ã fact5: ãã®ã·ã«ã·ã¡ãLv.80ãæãç¡ããšããããã®ããããLv.92ã¯å
±é³Žãæã fact6: ããããã®ãŽããŽãLv.31ã¯æãŸããããšããããšã¯äºå®ãšç°ãªããšããããšã¯ãªããšããããã®ãŽããŽãLv.31ã¯éã fact7: ããä»®ã«ããã®ããããLv.92ã¯åäŸã£ãœãäžæ¹ã§æãŸãããªãããšããããšã¯æãç«ããªããªãã°ããã®ã·ã«ã·ã¡ãLv.80ã¯å
±é³Žãæããªãããšããããšã¯æãç«ã€ | fact1: {C}{c} -> {D}{b} fact2: {A}{a} -> {C}{c} fact3: (x): ¬{C}x -> ({A}x & {B}x) fact4: ({A}{a} v {B}{a}) fact5: {B}{a} -> {C}{c} fact6: {D}{b} -> {E}{b} fact7: ¬({F}{c} & ¬{D}{c}) -> ¬{C}{a} | [
"fact4 & fact2 & fact5 -> int1: ãã®ããããLv.92ã¯å
±é³Žãæã; int1 & fact1 -> int2: ãã®ãŽããŽãLv.31ã¯æãŸãã; int2 & fact6 -> hypothesis;"
] | [
"fact4 & fact2 & fact5 -> int1: {C}{c}; int1 & fact1 -> int2: {D}{b}; int2 & fact6 -> hypothesis;"
] | ããã®ãŽããŽãLv.31ã¯éããšããããšã¯ãªãããšããããšã¯æ£ãã | ¬{E}{b} | [
"fact9 -> int3: ãããã®ã·ã«ã·ã¡ãLv.80ãå
±é³Žãæããªããšããã°ãã®ã·ã«ã·ã¡ãLv.80ã¯å®ããããã¯æãç¡ã;"
] | 6 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ããããLv.92ãå
±é³Žãæããªããã®ãŽããŽãLv.31ã¯æãŸãã fact2: ããããã®ã·ã«ã·ã¡ãLv.80ã¯å®ããšãããšããã®ããããLv.92ã¯å
±é³Žãæãããšããããšã¯æ¬åœã fact3: å
±é³Žãæããªãã¢ã³ã¹ã¿ãŒã¯å®ããæãç¡ã fact4: ãã®ã·ã«ã·ã¡ãLv.80ã¯å®ããæãç¡ã fact5: ãã®ã·ã«ã·ã¡ãLv.80ãæãç¡ããšããããã®ããããLv.92ã¯å
±é³Žãæã fact6: ããããã®ãŽããŽãLv.31ã¯æãŸããããšããããšã¯äºå®ãšç°ãªããšããããšã¯ãªããšããããã®ãŽããŽãLv.31ã¯éã fact7: ããä»®ã«ããã®ããããLv.92ã¯åäŸã£ãœãäžæ¹ã§æãŸãããªãããšããããšã¯æãç«ããªããªãã°ããã®ã·ã«ã·ã¡ãLv.80ã¯å
±é³Žãæããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ãŽããŽãLv.31ã¯éã ; $proof$ = | fact4 & fact2 & fact5 -> int1: ãã®ããããLv.92ã¯å
±é³Žãæã; int1 & fact1 -> int2: ãã®ãŽããŽãLv.31ã¯æãŸãã; int2 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: {C}{c} -> {D}{b} fact2: {A}{a} -> {C}{c} fact3: (x): ¬{C}x -> ({A}x & {B}x) fact4: ({A}{a} v {B}{a}) fact5: {B}{a} -> {C}{c} fact6: {D}{b} -> {E}{b} fact7: ¬({F}{c} & ¬{D}{c}) -> ¬{C}{a} ; $hypothesis$ = {E}{b} ; $proof$ = | fact4 & fact2 & fact5 -> int1: {C}{c}; int1 & fact1 -> int2: {D}{b}; int2 & fact6 -> hypothesis; __PROVED__ |
0.3 | ããã®ãœã«ããœãLv.13ã¯çãŸãããããã«å·ããããšããããšã¯æãç«ããªã | ¬({C}{a} & {D}{a}) | fact1: ãã®ãŸã«ãŸã«ãLv.72ã¯èšããããŸãã«é¢é£ãã fact2: èœã¡æãã¢ã³ã¹ã¿ãŒã¯ãããããã fact3: ãã®ãœã«ããœãLv.13ã¯ãããããã fact4: ãããã®ãã«ããã®Lv.78ã¯ãããããããšããããšã¯ãªããšããã°ãèœã¡æããªããŠããã«äžå³ããªãããšããããšã¯ééãã§ãã fact5: ãã®ãœã«ããœãLv.13ã¯å·ãã fact6: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èœã¡æããªããããã¯äžå³ããªãããšããããšã¯ééãã ãšãããèœã¡æã fact7: ãã®ãœã«ããœãLv.13ãèœã¡æãããã®äžããã¯ãããããã fact8: ããä»®ã«ãã®ãœã«ããœãLv.13ãèœã¡æããšãããšãã®ãœã«ããœãLv.13ã¯çãŸãã | fact1: ({FH}{hd} & {IQ}{hd}) fact2: (x): {A}x -> {B}x fact3: {B}{a} fact4: ¬{B}{b} -> ¬(¬{A}{b} & ¬{E}{b}) fact5: {D}{a} fact6: (x): ¬(¬{A}x & ¬{E}x) -> {A}x fact7: ({A}{a} & {B}{a}) fact8: {A}{a} -> {C}{a} | [
"fact7 -> int1: ãã®ãœã«ããœãLv.13ã¯èœã¡æã; int1 & fact8 -> int2: ãã®ãœã«ããœãLv.13ã¯çãŸãã; int2 & fact5 -> hypothesis;"
] | [
"fact7 -> int1: {A}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact5 -> hypothesis;"
] | ããã®ã·ãã·ãLv.16ã¯ããããããããšããããšã¯æãç«ã€ | {B}{gi} | [
"fact9 -> int3: ããããã®ã·ãã·ãLv.16ãèœã¡æããšããã°ãããããã;"
] | 5 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸã«ãŸã«ãLv.72ã¯èšããããŸãã«é¢é£ãã fact2: èœã¡æãã¢ã³ã¹ã¿ãŒã¯ãããããã fact3: ãã®ãœã«ããœãLv.13ã¯ãããããã fact4: ãããã®ãã«ããã®Lv.78ã¯ãããããããšããããšã¯ãªããšããã°ãèœã¡æããªããŠããã«äžå³ããªãããšããããšã¯ééãã§ãã fact5: ãã®ãœã«ããœãLv.13ã¯å·ãã fact6: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èœã¡æããªããããã¯äžå³ããªãããšããããšã¯ééãã ãšãããèœã¡æã fact7: ãã®ãœã«ããœãLv.13ãèœã¡æãããã®äžããã¯ãããããã fact8: ããä»®ã«ãã®ãœã«ããœãLv.13ãèœã¡æããšãããšãã®ãœã«ããœãLv.13ã¯çãŸãã ; $hypothesis$ = ããã®ãœã«ããœãLv.13ã¯çãŸãããããã«å·ããããšããããšã¯æãç«ããªã ; $proof$ = | fact7 -> int1: ãã®ãœã«ããœãLv.13ã¯èœã¡æã; int1 & fact8 -> int2: ãã®ãœã«ããœãLv.13ã¯çãŸãã; int2 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({FH}{hd} & {IQ}{hd}) fact2: (x): {A}x -> {B}x fact3: {B}{a} fact4: ¬{B}{b} -> ¬(¬{A}{b} & ¬{E}{b}) fact5: {D}{a} fact6: (x): ¬(¬{A}x & ¬{E}x) -> {A}x fact7: ({A}{a} & {B}{a}) fact8: {A}{a} -> {C}{a} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact7 -> int1: {A}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ãããã«ãLv.95äºä»¶ãšçºãŸãæããšããããšãçãã | ({E} & {D}) | fact1: ãæ±ãæããšããããšã¯çããªãããšããããšã¯ããŽããŽãLv.41äºä»¶ãèµ·ãããããã«ãŸããŸãLv.51äºä»¶ãèµ·ããããšããããšãå¥æ©ã fact2: ãçºãŸãæããšããããšã¯èµ·ããªããŠãã€ãããã«ãLv.95äºä»¶ã¯èµ·ãããªãããšããããšã¯èµ€ããšããããšã¯çããªããšããããšã«åŒãèµ·ãããã fact3: é»è²ã£ãœããšããããšãçããããããã¯åºãŸãæããããšãçãã fact4: ãŸããŸãLv.51äºä»¶ãèµ·ãã fact5: ãæ°Žèããšããããšãèµ·ããããšããããšã¯äºå®ã§ããã°ãŸããŸãLv.51äºä»¶ã¯çºçããªãããããã¯æ±ãæããšããããšã¯çºçããªãããããã¯äž¡æ¹ã fact6: ããä»®ã«æ±ãæããšããããšã¯èµ·ããªããªãã°ããããã«ãLv.95äºä»¶ãèµ·ããããã€çºãŸãæããšããããšãçããããšããããšã¯åã§ãã fact7: ããä»®ã«çºãŸãæããšããããšã¯èµ·ãããªããšããããæ±ãæããšããããšã¯çããªããããããŸããŸãLv.51äºä»¶ãçºçããããšããããšã¯ééãã§ãã fact8: ããä»®ã«ãŸããŸãLv.51äºä»¶ã¯çºçããªããªããããã«ãLv.95äºä»¶ãèµ·ããããã€ãŽããŽãLv.41äºä»¶ãèµ·ãã fact9: ãŽããŽãLv.41äºä»¶ãèµ·ãã | fact1: ({A} & {B}) -> ¬{C} fact2: ¬{F} -> (¬{D} & ¬{E}) fact3: ({J} v {K}) fact4: {B} fact5: {H} -> (¬{B} v ¬{C}) fact6: ¬{C} -> ¬({E} & {D}) fact7: ¬{D} -> ¬(¬{C} & {B}) fact8: ¬{B} -> ({E} & {A}) fact9: {A} | [
"fact9 & fact4 -> int1: ããŽããŽãLv.41äºä»¶ããã³ãŸããŸãLv.51äºä»¶ãçããããšããããšã¯æãç«ã€; int1 & fact1 -> int2: æ±ãæããšããããšã¯çºçããªã; int2 & fact6 -> hypothesis;"
] | [
"fact9 & fact4 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact6 -> hypothesis;"
] | ãããã«ãLv.95äºä»¶ãšçºãŸãæããšããããšãçãã | ({E} & {D}) | [] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãæ±ãæããšããããšã¯çããªãããšããããšã¯ããŽããŽãLv.41äºä»¶ãèµ·ãããããã«ãŸããŸãLv.51äºä»¶ãèµ·ããããšããããšãå¥æ©ã fact2: ãçºãŸãæããšããããšã¯èµ·ããªããŠãã€ãããã«ãLv.95äºä»¶ã¯èµ·ãããªãããšããããšã¯èµ€ããšããããšã¯çããªããšããããšã«åŒãèµ·ãããã fact3: é»è²ã£ãœããšããããšãçããããããã¯åºãŸãæããããšãçãã fact4: ãŸããŸãLv.51äºä»¶ãèµ·ãã fact5: ãæ°Žèããšããããšãèµ·ããããšããããšã¯äºå®ã§ããã°ãŸããŸãLv.51äºä»¶ã¯çºçããªãããããã¯æ±ãæããšããããšã¯çºçããªãããããã¯äž¡æ¹ã fact6: ããä»®ã«æ±ãæããšããããšã¯èµ·ããªããªãã°ããããã«ãLv.95äºä»¶ãèµ·ããããã€çºãŸãæããšããããšãçããããšããããšã¯åã§ãã fact7: ããä»®ã«çºãŸãæããšããããšã¯èµ·ãããªããšããããæ±ãæããšããããšã¯çããªããããããŸããŸãLv.51äºä»¶ãçºçããããšããããšã¯ééãã§ãã fact8: ããä»®ã«ãŸããŸãLv.51äºä»¶ã¯çºçããªããªããããã«ãLv.95äºä»¶ãèµ·ããããã€ãŽããŽãLv.41äºä»¶ãèµ·ãã fact9: ãŽããŽãLv.41äºä»¶ãèµ·ãã ; $hypothesis$ = ãããã«ãLv.95äºä»¶ãšçºãŸãæããšããããšãçãã ; $proof$ = | fact9 & fact4 -> int1: ããŽããŽãLv.41äºä»¶ããã³ãŸããŸãLv.51äºä»¶ãçããããšããããšã¯æãç«ã€; int1 & fact1 -> int2: æ±ãæããšããããšã¯çºçããªã; int2 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} & {B}) -> ¬{C} fact2: ¬{F} -> (¬{D} & ¬{E}) fact3: ({J} v {K}) fact4: {B} fact5: {H} -> (¬{B} v ¬{C}) fact6: ¬{C} -> ¬({E} & {D}) fact7: ¬{D} -> ¬(¬{C} & {B}) fact8: ¬{B} -> ({E} & {A}) fact9: {A} ; $hypothesis$ = ({E} & {D}) ; $proof$ = | fact9 & fact4 -> int1: ({A} & {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ãã·ã«ã
Lv.21ã¯ææ¡ãèŸã | {D}{b} | fact1: ããä»®ã«ãã®ã¿ãã¿ãLv.2ãåªãããªãã°ãã®ã¿ãã¿ãLv.2ã¯èªèŠã fact2: ãã®ã¿ãã¿ãLv.2ã¯åªãã fact3: ãããã®ã¿ãã¿ãLv.2ã¯èªèŠããå¯ç¬ãããã©ã¡ããã§ãããšãããšããã®ã·ãã·ã«ã
Lv.21ã¯ææ¡ãèŸããªãããšããããšã¯æ¬åœã | fact1: {A}{a} -> {B}{a} fact2: {A}{a} fact3: ({B}{a} v {C}{a}) -> ¬{D}{b} | [
"fact1 & fact2 -> int1: ãã®ã¿ãã¿ãLv.2ã¯èªèŠã; int1 -> int2: ãã®ã¿ãã¿ãLv.2ã¯èªèŠãããããã¯å¯ç¬ãã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact2 -> int1: {B}{a}; int1 -> int2: ({B}{a} v {C}{a}); int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããä»®ã«ãã®ã¿ãã¿ãLv.2ãåªãããªãã°ãã®ã¿ãã¿ãLv.2ã¯èªèŠã fact2: ãã®ã¿ãã¿ãLv.2ã¯åªãã fact3: ãããã®ã¿ãã¿ãLv.2ã¯èªèŠããå¯ç¬ãããã©ã¡ããã§ãããšãããšããã®ã·ãã·ã«ã
Lv.21ã¯ææ¡ãèŸããªãããšããããšã¯æ¬åœã ; $hypothesis$ = ãã®ã·ãã·ã«ã
Lv.21ã¯ææ¡ãèŸã ; $proof$ = | fact1 & fact2 -> int1: ãã®ã¿ãã¿ãLv.2ã¯èªèŠã; int1 -> int2: ãã®ã¿ãã¿ãLv.2ã¯èªèŠãããããã¯å¯ç¬ãã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {B}{a} fact2: {A}{a} fact3: ({B}{a} v {C}{a}) -> ¬{D}{b} ; $hypothesis$ = {D}{b} ; $proof$ = | fact1 & fact2 -> int1: {B}{a}; int1 -> int2: ({B}{a} v {C}{a}); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœã®Lv.39ã¯åŸ®ç¬ãŸãã | {C}{b} | fact1: ããã¢ã³ã¹ã¿ãŒãæµããæãããŸãã¯æŽ»åãé£ãããŸãã¯äž¡æ¹ã§ãããªãã°ãã®ãœããœã®Lv.39ã¯åŸ®ç¬ãŸãããªã fact2: ãã®ãŸããŸã«ãLv.66ã¯æŽ»åãé£ã fact3: ããã®ãŸããŸã«ãLv.66ã¯åŸ®ç¬ãŸããããŸãã¯æŽ»åãé£ãããããã¯äž¡æ¹ãšãã ããšããããšã¯æ¬åœã fact4: ãã®ãœããœã®Lv.39ã¯æŽ»åãé£ãããããã¯åŸ®ç¬ãŸããããããã¯ã©ã¡ããã§ãã | fact1: (x): ({A}x v {B}x) -> ¬{C}{b} fact2: {B}{a} fact3: ({C}{a} v {B}{a}) fact4: ({B}{b} v {C}{b}) | [
"fact2 -> int1: ãã®ãŸããŸã«ãLv.66ã¯æµããæãããããã¯æŽ»åãé£ã; int1 -> int2: ãæµããæãããŸãã¯æŽ»åãé£ãããŸãã¯ã©ã¡ããã§ãããã¢ã³ã¹ã¿ãŒã¯ãã; int2 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: ({A}{a} v {B}{a}); int1 -> int2: (Ex): ({A}x v {B}x); int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã¢ã³ã¹ã¿ãŒãæµããæãããŸãã¯æŽ»åãé£ãããŸãã¯äž¡æ¹ã§ãããªãã°ãã®ãœããœã®Lv.39ã¯åŸ®ç¬ãŸãããªã fact2: ãã®ãŸããŸã«ãLv.66ã¯æŽ»åãé£ã fact3: ããã®ãŸããŸã«ãLv.66ã¯åŸ®ç¬ãŸããããŸãã¯æŽ»åãé£ãããããã¯äž¡æ¹ãšãã ããšããããšã¯æ¬åœã fact4: ãã®ãœããœã®Lv.39ã¯æŽ»åãé£ãããããã¯åŸ®ç¬ãŸããããããã¯ã©ã¡ããã§ãã ; $hypothesis$ = ãã®ãœããœã®Lv.39ã¯åŸ®ç¬ãŸãã ; $proof$ = | fact2 -> int1: ãã®ãŸããŸã«ãLv.66ã¯æµããæãããããã¯æŽ»åãé£ã; int1 -> int2: ãæµããæãããŸãã¯æŽ»åãé£ãããŸãã¯ã©ã¡ããã§ãããã¢ã³ã¹ã¿ãŒã¯ãã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ({A}x v {B}x) -> ¬{C}{b} fact2: {B}{a} fact3: ({C}{a} v {B}{a}) fact4: ({B}{b} v {C}{b}) ; $hypothesis$ = {C}{b} ; $proof$ = | fact2 -> int1: ({A}{a} v {B}{a}); int1 -> int2: (Ex): ({A}x v {B}x); int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãŸã¡ã
ãŸãªLv.99äºä»¶ãçãã | {C} | fact1: ä»®ã«å¿æããšããããšãèµ·ãããšããã°ã¿ã¡ãã¿ãªLv.58äºä»¶ãèµ·ããããœã«ãœãLv.99äºä»¶ã¯èµ·ãããªã fact2: ãããœã«ãœãLv.99äºä»¶ã¯èµ·ãããªããªãããŸã¡ã
ãŸãªLv.99äºä»¶ãèµ·ãããæŽã«ãœã®ãœã«ã
Lv.14äºä»¶ãèµ·ããããšããããšã¯åã fact3: ä»®ã«ããŸã¡ã
ãŸãªLv.99äºä»¶ãšãœã®ãœã«ã
Lv.14äºä»¶ãçºçããããšããããšã¯ééãã§ãããšããããŸã¡ã
ãŸãªLv.99äºä»¶ã¯çããªã fact4: ããŸã¡ã
ãŸãªLv.99äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœã®ãœã«ã
Lv.14äºä»¶ã«é»æ¢ããã fact5: ããœã®ãœã«ã
Lv.14äºä»¶ã¯èµ·ããªãããšããããšã¯ãœã«ãœãLv.99äºä»¶ã«é»ãŸãã | fact1: {E} -> ({D} & ¬{A}) fact2: ¬{A} -> ¬({C} & {B}) fact3: ¬({C} & {B}) -> ¬{C} fact4: {B} -> {C} fact5: {A} -> {B} | [] | [] | ãŸã¡ã
ãŸãªLv.99äºä»¶ã¯çºçããªã | ¬{C} | [] | 8 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«å¿æããšããããšãèµ·ãããšããã°ã¿ã¡ãã¿ãªLv.58äºä»¶ãèµ·ããããœã«ãœãLv.99äºä»¶ã¯èµ·ãããªã fact2: ãããœã«ãœãLv.99äºä»¶ã¯èµ·ãããªããªãããŸã¡ã
ãŸãªLv.99äºä»¶ãèµ·ãããæŽã«ãœã®ãœã«ã
Lv.14äºä»¶ãèµ·ããããšããããšã¯åã fact3: ä»®ã«ããŸã¡ã
ãŸãªLv.99äºä»¶ãšãœã®ãœã«ã
Lv.14äºä»¶ãçºçããããšããããšã¯ééãã§ãããšããããŸã¡ã
ãŸãªLv.99äºä»¶ã¯çããªã fact4: ããŸã¡ã
ãŸãªLv.99äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœã®ãœã«ã
Lv.14äºä»¶ã«é»æ¢ããã fact5: ããœã®ãœã«ã
Lv.14äºä»¶ã¯èµ·ããªãããšããããšã¯ãœã«ãœãLv.99äºä»¶ã«é»ãŸãã ; $hypothesis$ = ãŸã¡ã
ãŸãªLv.99äºä»¶ãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {E} -> ({D} & ¬{A}) fact2: ¬{A} -> ¬({C} & {B}) fact3: ¬({C} & {B}) -> ¬{C} fact4: {B} -> {C} fact5: {A} -> {B} ; $hypothesis$ = {C} ; $proof$ = | __UNKNOWN__ |
0.3 | èŠå¢ç¡ããšããããšãèµ·ããããŸã空æããããšããããšãèµ·ãã | ({B} & {A}) | fact1: 空æããããšããããšãçãã fact2: èŠå¢ç¡ããšããããšãèµ·ãã | fact1: {A} fact2: {B} | [
"fact1 -> int1: 空æããããšããããšãçãã; int1 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}; int1 & fact2 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: 空æããããšããããšãçãã fact2: èŠå¢ç¡ããšããããšãèµ·ãã ; $hypothesis$ = èŠå¢ç¡ããšããããšãèµ·ããããŸã空æããããšããããšãèµ·ãã ; $proof$ = | fact1 -> int1: 空æããããšããããšãçãã; int1 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A} fact2: {B} ; $hypothesis$ = ({B} & {A}) ; $proof$ = | fact1 -> int1: {A}; int1 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã¿ãã¿ã¡ãLv.37äºä»¶ã¯çããªãããšããããšã¯èª€ãã§ãã | {B} | fact1: çŸããæããšããããšãçãã fact2: ãããçŸããæããšããããšãèµ·ãããªããœããœãªLv.32äºä»¶ã¯çããªã fact3: ããä»®ã«ãçŸããæããšããããšããã³ç¶æ管çããããšäž¡æ¹ãçããããšããããšã¯æãç«ããªããšãããã¿ãã¿ã¡ãLv.37äºä»¶ã¯çããªã fact4: ãœããœãªLv.32äºä»¶ã¯èµ·ãããªã fact5: ããœããœãªLv.32äºä»¶ãèµ·ãããªãããã©ç©åãŒããšããããšã¯çºçããããšããããšã¯çŸããæããšããããšã«ãããããã | fact1: {A} fact2: {A} -> ¬{AA} fact3: ¬({A} & {C}) -> ¬{B} fact4: ¬{AA} fact5: {A} -> (¬{AA} & {AB}) | [
"fact5 & fact1 -> int1: ãœããœãªLv.32äºä»¶ã¯èµ·ããªãããããç©åãŒããšããããšãèµ·ãã; int1 -> int2: ç©åãŒããšããããšãçºçãã;"
] | [
"fact5 & fact1 -> int1: (¬{AA} & {AB}); int1 -> int2: {AB};"
] | ã¿ãã¿ã¡ãLv.37äºä»¶ã¯çããªã | ¬{B} | [] | 6 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: çŸããæããšããããšãçãã fact2: ãããçŸããæããšããããšãèµ·ãããªããœããœãªLv.32äºä»¶ã¯çããªã fact3: ããä»®ã«ãçŸããæããšããããšããã³ç¶æ管çããããšäž¡æ¹ãçããããšããããšã¯æãç«ããªããšãããã¿ãã¿ã¡ãLv.37äºä»¶ã¯çããªã fact4: ãœããœãªLv.32äºä»¶ã¯èµ·ãããªã fact5: ããœããœãªLv.32äºä»¶ãèµ·ãããªãããã©ç©åãŒããšããããšã¯çºçããããšããããšã¯çŸããæããšããããšã«ãããããã ; $hypothesis$ = ãã¿ãã¿ã¡ãLv.37äºä»¶ã¯çããªãããšããããšã¯èª€ãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} fact2: {A} -> ¬{AA} fact3: ¬({A} & {C}) -> ¬{B} fact4: ¬{AA} fact5: {A} -> (¬{AA} & {AB}) ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | æ¶åãæããšããããšã¯çããªã | ¬{D} | fact1: ç³åçŽä»ããããšãèµ·ãã fact2: éãŸãæããšããããšã¯çããªããšããããšã¯è»œããšããããšã«é»ãŸãã fact3: ããã䟵å
¥ãæããšããããšã¯çºçããªããªãéãŸãæããšããããšãçºçããããŸãã¯è»œããšããããšãçãã fact4: ããåä»»ããããšãèµ·ãããšããã°ã·ãã·ã«ãLv.5äºä»¶ãçºçãã fact5: 䟵å
¥ãæããšããããšãèµ·ãã fact6: éåŠããããšã話ãæããšããããšã¯å¥æ©ã§ãã fact7: ããä»®ã«éãŸãæããšããããšãšäŸµå
¥ãæããšããããšã©ã¡ãããçºçãããšãããšæ¶åãæããšããããšã¯èµ·ãããªã | fact1: {JD} fact2: {A} -> {B} fact3: ¬{C} -> ({B} v {A}) fact4: {L} -> {ID} fact5: {C} fact6: {U} -> {K} fact7: ({B} & {C}) -> ¬{D} | [] | [] | ããœã«ãœã¡ãLv.78äºä»¶ãèµ·ããããšããããšã¯ç¢ºãã | {JB} | [] | 6 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ç³åçŽä»ããããšãèµ·ãã fact2: éãŸãæããšããããšã¯çããªããšããããšã¯è»œããšããããšã«é»ãŸãã fact3: ããã䟵å
¥ãæããšããããšã¯çºçããªããªãéãŸãæããšããããšãçºçããããŸãã¯è»œããšããããšãçãã fact4: ããåä»»ããããšãèµ·ãããšããã°ã·ãã·ã«ãLv.5äºä»¶ãçºçãã fact5: 䟵å
¥ãæããšããããšãèµ·ãã fact6: éåŠããããšã話ãæããšããããšã¯å¥æ©ã§ãã fact7: ããä»®ã«éãŸãæããšããããšãšäŸµå
¥ãæããšããããšã©ã¡ãããçºçãããšãããšæ¶åãæããšããããšã¯èµ·ãããªã ; $hypothesis$ = æ¶åãæããšããããšã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {JD} fact2: {A} -> {B} fact3: ¬{C} -> ({B} v {A}) fact4: {L} -> {ID} fact5: {C} fact6: {U} -> {K} fact7: ({B} & {C}) -> ¬{D} ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽã®ãŽã«Lv.21ã¯ããŠãè¯ããªã | ¬{D}{c} | fact1: ããä»®ã«ãã®ãŽã®ãŽã«Lv.21ã匱ããšãããšãã®ãŽã®ãŽã«Lv.21ã¯ããŠãè¯ã fact2: ããã®ã¿ã¡ãã¿ãLv.94ã¯å
¥ãèŸããªãããšããããšã¯æãç«ããªã fact3: ããŠãè¯ãããã€æ³åãé£ããªãã¢ã³ã¹ã¿ãŒã¯é¿ãé£ããªã fact4: ãã®ããªããLv.13ãé¿ãé£ããªããšãããšãã®ããªããLv.13ã¯å
¥ãèŸããŠæŽã«åŒ±ã fact5: ããä»®ã«ãã®ãŸã®ãŸãLv.52ãé¿ãé£ããšããããã®ãŽã®ãŽã«Lv.21ã¯åŒ±ã fact6: ããä»®ã«ãã®ã¿ã¡ãã¿ãLv.94ãå
¥ãèŸããªããã®ãŸã®ãŸãLv.52ã¯é¿ãé£ã | fact1: {C}{c} -> {D}{c} fact2: {A}{a} fact3: (x): ({D}x & ¬{E}x) -> ¬{B}x fact4: ¬{B}{af} -> ({A}{af} & {C}{af}) fact5: {B}{b} -> {C}{c} fact6: {A}{a} -> {B}{b} | [
"fact6 & fact2 -> int1: ããã®ãŸã®ãŸãLv.52ã¯é¿ãé£ãããšããããšã¯æ¬åœã§ãã; int1 & fact5 -> int2: ãã®ãŽã®ãŽã«Lv.21ã¯åŒ±ã; int2 & fact1 -> hypothesis;"
] | [
"fact6 & fact2 -> int1: {B}{b}; int1 & fact5 -> int2: {C}{c}; int2 & fact1 -> hypothesis;"
] | ãã®ããªããLv.13ã¯åŒ±ã | {C}{af} | [
"fact8 -> int3: ããããã®ããªããLv.13ã¯ããŠãè¯ãããã©æ³åãé£ããšããããšã¯ãªããªãããã¯é¿ãé£ããªã;"
] | 6 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãŽã®ãŽã«Lv.21ã匱ããšãããšãã®ãŽã®ãŽã«Lv.21ã¯ããŠãè¯ã fact2: ããã®ã¿ã¡ãã¿ãLv.94ã¯å
¥ãèŸããªãããšããããšã¯æãç«ããªã fact3: ããŠãè¯ãããã€æ³åãé£ããªãã¢ã³ã¹ã¿ãŒã¯é¿ãé£ããªã fact4: ãã®ããªããLv.13ãé¿ãé£ããªããšãããšãã®ããªããLv.13ã¯å
¥ãèŸããŠæŽã«åŒ±ã fact5: ããä»®ã«ãã®ãŸã®ãŸãLv.52ãé¿ãé£ããšããããã®ãŽã®ãŽã«Lv.21ã¯åŒ±ã fact6: ããä»®ã«ãã®ã¿ã¡ãã¿ãLv.94ãå
¥ãèŸããªããã®ãŸã®ãŸãLv.52ã¯é¿ãé£ã ; $hypothesis$ = ãã®ãŽã®ãŽã«Lv.21ã¯ããŠãè¯ããªã ; $proof$ = | fact6 & fact2 -> int1: ããã®ãŸã®ãŸãLv.52ã¯é¿ãé£ãããšããããšã¯æ¬åœã§ãã; int1 & fact5 -> int2: ãã®ãŽã®ãŽã«Lv.21ã¯åŒ±ã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C}{c} -> {D}{c} fact2: {A}{a} fact3: (x): ({D}x & ¬{E}x) -> ¬{B}x fact4: ¬{B}{af} -> ({A}{af} & {C}{af}) fact5: {B}{b} -> {C}{c} fact6: {A}{a} -> {B}{b} ; $hypothesis$ = ¬{D}{c} ; $proof$ = | fact6 & fact2 -> int1: {B}{b}; int1 & fact5 -> int2: {C}{c}; int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãœã¡ã
ãœãLv.53ã¯ç·ã£ãœãããšããããšã¯æãç«ã€ | {A}{a} | fact1: è»ããããªãã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããŠããã«è²«åŸ¹ãã fact2: çœããªãã¢ã³ã¹ã¿ãŒã¯è»ããããªã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããšããããšã¯ãªã | fact1: (x): ¬{C}x -> ({A}x & {B}x) fact2: (x): ¬{D}x -> ¬{C}x fact3: (x): ¬{A}x | [
"fact3 -> int1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããšããããšã¯ãªã; int1 -> hypothesis;"
] | [
"fact3 -> int1: (x): ¬{A}x; int1 -> hypothesis;"
] | ããã®ãœã¡ã
ãœãLv.53ã¯ç·ã£ãœãããšããããšã¯æãç«ã€ | {A}{a} | [
"fact4 -> int2: ãã®ãœã¡ã
ãœãLv.53ãè»ããããšããããšã¯ãªããªãã°ç·ã£ãœããŠå ããŠè²«åŸ¹ãã; fact5 -> int3: ããä»®ã«ãã®ãœã¡ã
ãœãLv.53ãçœããªããªããã®ãœã¡ã
ãœãLv.53ã¯è»ããããªã;"
] | 5 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: è»ããããªãã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããŠããã«è²«åŸ¹ãã fact2: çœããªãã¢ã³ã¹ã¿ãŒã¯è»ããããªã fact3: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããšããããšã¯ãªã ; $hypothesis$ = ããã®ãœã¡ã
ãœãLv.53ã¯ç·ã£ãœãããšããããšã¯æãç«ã€ ; $proof$ = | fact3 -> int1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯ç·ã£ãœããšããããšã¯ãªã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{C}x -> ({A}x & {B}x) fact2: (x): ¬{D}x -> ¬{C}x fact3: (x): ¬{A}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact3 -> int1: (x): ¬{A}x; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãŸã¡ããŸãLv.62äºä»¶ãšæ¥ãæããšããããšãèµ·ãã | ({D} & {C}) | fact1: æ°ãããšããããšãçãã fact2: ä»®ã«é£ã¹æããšããããšã¯çããªããšãããããŸã¡ããŸãLv.62äºä»¶ããã³æ¥ãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact3: ãŸã¡ããŸãLv.62äºä»¶ãçãã fact4: åºè¡ãæããšããããšã¯èµ·ããªããšããããšã¯é£ã¹æããšããããšã«é»æ¢ããã fact5: ãœã¡ã
ãœã¡ãLv.49äºä»¶ã¯çããªããªãã°ãåºè¡ãæããšããããšãçºçãããéããšããããšã¯èµ·ãããªãããšããããšã¯æ£ãããªã fact6: é£ã¹æããšããããšãçãã fact7: åºè¡ãæããšããããšã¯ãæ¥ãæããšããããšã¯çããªãããšããããšãé»æ¢ãã | fact1: {JH} fact2: ¬{A} -> ¬({D} & {C}) fact3: {D} fact4: {A} -> {B} fact5: ¬{F} -> ¬({B} & ¬{E}) fact6: {A} fact7: {B} -> {C} | [
"fact4 & fact6 -> int1: åºè¡ãæããšããããšãçºçãã; int1 & fact7 -> int2: æ¥ãæããšããããšãçãã; int2 & fact3 -> hypothesis;"
] | [
"fact4 & fact6 -> int1: {B}; int1 & fact7 -> int2: {C}; int2 & fact3 -> hypothesis;"
] | ããŸã¡ããŸãLv.62äºä»¶ããã³æ¥ãæããšããããšãçºçããããšããããšã¯æãç«ããªã | ¬({D} & {C}) | [] | 7 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: æ°ãããšããããšãçãã fact2: ä»®ã«é£ã¹æããšããããšã¯çããªããšãããããŸã¡ããŸãLv.62äºä»¶ããã³æ¥ãæããšããããšãèµ·ããããšããããšã¯æãç«ããªã fact3: ãŸã¡ããŸãLv.62äºä»¶ãçãã fact4: åºè¡ãæããšããããšã¯èµ·ããªããšããããšã¯é£ã¹æããšããããšã«é»æ¢ããã fact5: ãœã¡ã
ãœã¡ãLv.49äºä»¶ã¯çããªããªãã°ãåºè¡ãæããšããããšãçºçãããéããšããããšã¯èµ·ãããªãããšããããšã¯æ£ãããªã fact6: é£ã¹æããšããããšãçãã fact7: åºè¡ãæããšããããšã¯ãæ¥ãæããšããããšã¯çããªãããšããããšãé»æ¢ãã ; $hypothesis$ = ãŸã¡ããŸãLv.62äºä»¶ãšæ¥ãæããšããããšãèµ·ãã ; $proof$ = | fact4 & fact6 -> int1: åºè¡ãæããšããããšãçºçãã; int1 & fact7 -> int2: æ¥ãæããšããããšãçãã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {JH} fact2: ¬{A} -> ¬({D} & {C}) fact3: {D} fact4: {A} -> {B} fact5: ¬{F} -> ¬({B} & ¬{E}) fact6: {A} fact7: {B} -> {C} ; $hypothesis$ = ({D} & {C}) ; $proof$ = | fact4 & fact6 -> int1: {B}; int1 & fact7 -> int2: {C}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸã®ãŸãLv.29ã¯èãå¯ããªã | ¬{B}{b} | fact1: ããã®ã·ãªã·ã®Lv.20ã¯æ³å®ãé£ãããšããããšã¯çå®ã fact2: ãã®ãŸã®ãŸãLv.29ã¯æ³å®ãé£ã fact3: ãããããšããã¢ã³ã¹ã¿ãŒã巡瀌ããªããªãããã¯èãå¯ããŠæ³å®ãé£ãããšããããšã¯ç¢ºãã§ãã fact4: ããä»®ã«ãã®ã·ãªã·ã®Lv.20ãèãå¯ããšãããšãã®ãŸã®ãŸãLv.29ã¯æ³å®ãé£ã fact5: ãã®ã·ãªã·ã®Lv.20ãæ³å®ãé£ããªããã®ãŸã®ãŸãLv.29ã¯èãå¯ã fact6: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯æ³å®ãé£ããªãããããã¯èãå¯ããªããã©ã¡ãããªãã°èãå¯ããªã | fact1: {A}{a} fact2: {A}{b} fact3: (x): ¬{C}x -> ({B}x & {A}x) fact4: {B}{a} -> {A}{b} fact5: {A}{a} -> {B}{b} fact6: (x): (¬{A}x v ¬{B}x) -> ¬{B}x | [
"fact1 -> int1: ããã®ã·ãªã·ã®Lv.20ã¯æ³å®ãé£ãããšããããšã¯çå®ã ; int1 & fact5 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact5 -> hypothesis;"
] | ãã®ãŸã®ãŸãLv.29ã¯èãå¯ããªã | ¬{B}{b} | [
"fact7 -> int2: ããä»®ã«ãã®ãŸã®ãŸãLv.29ãæ³å®ãé£ããªãããããã¯ãããèãå¯ããšããããšã¯ãªããªãã°ãã®ãŸã®ãŸãLv.29ã¯èãå¯ããªã;"
] | 4 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããã®ã·ãªã·ã®Lv.20ã¯æ³å®ãé£ãããšããããšã¯çå®ã fact2: ãã®ãŸã®ãŸãLv.29ã¯æ³å®ãé£ã fact3: ãããããšããã¢ã³ã¹ã¿ãŒã巡瀌ããªããªãããã¯èãå¯ããŠæ³å®ãé£ãããšããããšã¯ç¢ºãã§ãã fact4: ããä»®ã«ãã®ã·ãªã·ã®Lv.20ãèãå¯ããšãããšãã®ãŸã®ãŸãLv.29ã¯æ³å®ãé£ã fact5: ãã®ã·ãªã·ã®Lv.20ãæ³å®ãé£ããªããã®ãŸã®ãŸãLv.29ã¯èãå¯ã fact6: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯æ³å®ãé£ããªãããããã¯èãå¯ããªããã©ã¡ãããªãã°èãå¯ããªã ; $hypothesis$ = ãã®ãŸã®ãŸãLv.29ã¯èãå¯ããªã ; $proof$ = | fact1 -> int1: ããã®ã·ãªã·ã®Lv.20ã¯æ³å®ãé£ãããšããããšã¯çå®ã ; int1 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: {A}{b} fact3: (x): ¬{C}x -> ({B}x & {A}x) fact4: {B}{a} -> {A}{b} fact5: {A}{a} -> {B}{b} fact6: (x): (¬{A}x v ¬{B}x) -> ¬{B}x ; $hypothesis$ = ¬{B}{b} ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽã«ã
Lv.14ã¯ç©æããªã | ¬{D}{c} | fact1: ããä»®ã«ãã®ãŽããŽã«ãLv.32ãç©æããšããããã®ãŽããŽã«ãLv.32ã¯æŽ»åãæã fact2: ããä»®ã«ãã®ãŽããŽã«ãLv.32ãçŽåŸãæããªãã°ãã®ãŽããŽã«ãLv.32ã¯æãããã fact3: ããä»®ã«ããã®ãŽããŽã«ãLv.32ã¯æããããããšããããšã¯æ£ãããªãã°ãã®ãŽããŽã«ã
Lv.14ã¯ç©æã fact4: ãã®ãŸããŸãLv.6ã誀ããšããããã®ãŽããŽã«ãLv.32ã¯çŽåŸãæã fact5: ãã®ãŸããŸãLv.6ã¯èª€ã | fact1: {D}{b} -> {GM}{b} fact2: {B}{b} -> {C}{b} fact3: {C}{b} -> {D}{c} fact4: {A}{a} -> {B}{b} fact5: {A}{a} | [
"fact4 & fact5 -> int1: ãã®ãŽããŽã«ãLv.32ã¯çŽåŸãæã; int1 & fact2 -> int2: ãã®ãŽããŽã«ãLv.32ã¯æãããã; int2 & fact3 -> hypothesis;"
] | [
"fact4 & fact5 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããä»®ã«ãã®ãŽããŽã«ãLv.32ãç©æããšããããã®ãŽããŽã«ãLv.32ã¯æŽ»åãæã fact2: ããä»®ã«ãã®ãŽããŽã«ãLv.32ãçŽåŸãæããªãã°ãã®ãŽããŽã«ãLv.32ã¯æãããã fact3: ããä»®ã«ããã®ãŽããŽã«ãLv.32ã¯æããããããšããããšã¯æ£ãããªãã°ãã®ãŽããŽã«ã
Lv.14ã¯ç©æã fact4: ãã®ãŸããŸãLv.6ã誀ããšããããã®ãŽããŽã«ãLv.32ã¯çŽåŸãæã fact5: ãã®ãŸããŸãLv.6ã¯èª€ã ; $hypothesis$ = ãã®ãŽããŽã«ã
Lv.14ã¯ç©æããªã ; $proof$ = | fact4 & fact5 -> int1: ãã®ãŽããŽã«ãLv.32ã¯çŽåŸãæã; int1 & fact2 -> int2: ãã®ãŽããŽã«ãLv.32ã¯æãããã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{b} -> {GM}{b} fact2: {B}{b} -> {C}{b} fact3: {C}{b} -> {D}{c} fact4: {A}{a} -> {B}{b} fact5: {A}{a} ; $hypothesis$ = ¬{D}{c} ; $proof$ = | fact4 & fact5 -> int1: {B}{b}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœã«ã
Lv.34ã¯é»ã£ãœããªã | ¬{B}{aa} | fact1: ããããªãããã®ã¢ã³ã¹ã¿ãŒãéé£ããŸãããšãããšç·©ã¿æããšããããšã¯ãªããåããèŸããªã fact2: ãã®ãœããœã«ã
Lv.34ã¯éé£ããŸãã fact3: ãã®ã·ã¡ãã·ã«ãLv.6ã¯éé£ããŸãã fact4: ããã®ãœã¡ããœãLv.21ã¯éé£ããŸããããšããããšã¯äºå®ã fact5: ãã®ãœããœã«ã
Lv.34ã¯é ã fact6: ãã®ãœããœã«ã
Lv.34ã¯ç·©ã¿æããªããŠãã€åããèŸããªããªãã°ããã¯é»ã£ãœã | fact1: (x): {A}x -> (¬{AA}x & ¬{AB}x) fact2: {A}{aa} fact3: {A}{en} fact4: {A}{bl} fact5: {FJ}{aa} fact6: (¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} | [
"fact1 -> int1: ããããã®ãœããœã«ã
Lv.34ãéé£ããŸãããªãã°ç·©ã¿æããªããããã«ããã¯åããèŸããšããããšã¯ãªã; int1 & fact2 -> int2: ãã®ãœããœã«ã
Lv.34ã¯ç·©ã¿æããªããŠæŽã«åããèŸããšããããšã¯ãªã; int2 & fact6 -> hypothesis;"
] | [
"fact1 -> int1: {A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: (¬{AA}{aa} & ¬{AB}{aa}); int2 & fact6 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 3 | 0 | 3 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããªãããã®ã¢ã³ã¹ã¿ãŒãéé£ããŸãããšãããšç·©ã¿æããšããããšã¯ãªããåããèŸããªã fact2: ãã®ãœããœã«ã
Lv.34ã¯éé£ããŸãã fact3: ãã®ã·ã¡ãã·ã«ãLv.6ã¯éé£ããŸãã fact4: ããã®ãœã¡ããœãLv.21ã¯éé£ããŸããããšããããšã¯äºå®ã fact5: ãã®ãœããœã«ã
Lv.34ã¯é ã fact6: ãã®ãœããœã«ã
Lv.34ã¯ç·©ã¿æããªããŠãã€åããèŸããªããªãã°ããã¯é»ã£ãœã ; $hypothesis$ = ãã®ãœããœã«ã
Lv.34ã¯é»ã£ãœããªã ; $proof$ = | fact1 -> int1: ããããã®ãœããœã«ã
Lv.34ãéé£ããŸãããªãã°ç·©ã¿æããªããããã«ããã¯åããèŸããšããããšã¯ãªã; int1 & fact2 -> int2: ãã®ãœããœã«ã
Lv.34ã¯ç·©ã¿æããªããŠæŽã«åããèŸããšããããšã¯ãªã; int2 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {A}x -> (¬{AA}x & ¬{AB}x) fact2: {A}{aa} fact3: {A}{en} fact4: {A}{bl} fact5: {FJ}{aa} fact6: (¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa} ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | fact1 -> int1: {A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: (¬{AA}{aa} & ¬{AB}{aa}); int2 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŽããŽã®Lv.59ã¯èã
ãæãããããããã¯æãé£ãããšããããšã¯åã§ãã | ¬({C}{a} & {D}{a}) | fact1: ãã®ã¿ãã¿ã«ãLv.13ã¯æãé£ãããã€ããã¯ç«ãŠé£ã fact2: ããã®ãŽããŽã®Lv.59ã¯æãé£ãããšããããšã¯ç¢ºãã§ãã fact3: ããšããã¢ã³ã¹ã¿ãŒã¯ææ
®æ·±ããªãããšããããšã¯äºå®ãªããããã¯èã
ãæããæŽã«æãé£ãããšããããšã¯çå®ã§ãªã fact4: ææ
®æ·±ãã¢ã³ã¹ã¿ãŒã¯å©ãé£ã fact5: ä»®ã«ãã®ãŽããŽã®Lv.59ãææ
®æ·±ããšããã°ãã®ãŽããŽã®Lv.59ã¯å解ããé£ã fact6: ãã®ãŽããŽã®Lv.59ã¯ææ
®æ·±ã fact7: ä»®ã«ãã®ãŽããŽã®Lv.59ãå解ããé£ããšãããããã¯èã
ãæã | fact1: ({D}{ci} & {BA}{ci}) fact2: {D}{a} fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: (x): {A}x -> {JD}x fact5: {A}{a} -> {B}{a} fact6: {A}{a} fact7: {B}{a} -> {C}{a} | [
"fact5 & fact6 -> int1: ãã®ãŽããŽã®Lv.59ã¯å解ããé£ã; int1 & fact7 -> int2: ãã®ãŽããŽã®Lv.59ã¯èã
ãæã; int2 & fact2 -> hypothesis;"
] | [
"fact5 & fact6 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{a}; int2 & fact2 -> hypothesis;"
] | ãã®ã·ãªã·ãLv.92ã¯å©ãé£ããŠããã¯åæ£åãã | ({JD}{de} & {HG}{de}) | [
"fact8 -> int3: ãããã®ã·ãªã·ãLv.92ãææ
®æ·±ããšãããããã¯å©ãé£ã;"
] | 4 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã¿ãã¿ã«ãLv.13ã¯æãé£ãããã€ããã¯ç«ãŠé£ã fact2: ããã®ãŽããŽã®Lv.59ã¯æãé£ãããšããããšã¯ç¢ºãã§ãã fact3: ããšããã¢ã³ã¹ã¿ãŒã¯ææ
®æ·±ããªãããšããããšã¯äºå®ãªããããã¯èã
ãæããæŽã«æãé£ãããšããããšã¯çå®ã§ãªã fact4: ææ
®æ·±ãã¢ã³ã¹ã¿ãŒã¯å©ãé£ã fact5: ä»®ã«ãã®ãŽããŽã®Lv.59ãææ
®æ·±ããšããã°ãã®ãŽããŽã®Lv.59ã¯å解ããé£ã fact6: ãã®ãŽããŽã®Lv.59ã¯ææ
®æ·±ã fact7: ä»®ã«ãã®ãŽããŽã®Lv.59ãå解ããé£ããšãããããã¯èã
ãæã ; $hypothesis$ = ããã®ãŽããŽã®Lv.59ã¯èã
ãæãããããããã¯æãé£ãããšããããšã¯åã§ãã ; $proof$ = | fact5 & fact6 -> int1: ãã®ãŽããŽã®Lv.59ã¯å解ããé£ã; int1 & fact7 -> int2: ãã®ãŽããŽã®Lv.59ã¯èã
ãæã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({D}{ci} & {BA}{ci}) fact2: {D}{a} fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: (x): {A}x -> {JD}x fact5: {A}{a} -> {B}{a} fact6: {A}{a} fact7: {B}{a} -> {C}{a} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact5 & fact6 -> int1: {B}{a}; int1 & fact7 -> int2: {C}{a}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ããããLv.28ã¯èªãã£ãœããªãããããã¯åãçµããããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã | ¬(¬{E}{a} v {D}{a}) | fact1: ãã®ããããLv.28ã¯æãç¶ãããšããããšã¯ãªããšããã°ãããã¯èªãã£ãœããªãããŸãã¯åãçµããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ã£ãŠãã fact2: ãã®ããããLv.28ã¯é¡°ãã fact3: ãã®ããããLv.28ã¯åã fact4: ä»®ã«ãã®ããããLv.28ã¯é¡°ãããå ããŠåããšããã°ããã¯æãç¶ããªã fact5: ãã®ã¿ãã¿ãLv.81ã¯èªãã£ãœããªã | fact1: ¬{C}{a} -> ¬(¬{E}{a} v {D}{a}) fact2: {A}{a} fact3: {B}{a} fact4: ({A}{a} & {B}{a}) -> ¬{C}{a} fact5: ¬{E}{at} | [
"fact2 & fact3 -> int1: ãã®ããããLv.28ã¯é¡°ãããããŸãã«åã; int1 & fact4 -> int2: ãã®ããããLv.28ã¯æãç¶ããªã; int2 & fact1 -> hypothesis;"
] | [
"fact2 & fact3 -> int1: ({A}{a} & {B}{a}); int1 & fact4 -> int2: ¬{C}{a}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ããããLv.28ã¯æãç¶ãããšããããšã¯ãªããšããã°ãããã¯èªãã£ãœããªãããŸãã¯åãçµããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ã£ãŠãã fact2: ãã®ããããLv.28ã¯é¡°ãã fact3: ãã®ããããLv.28ã¯åã fact4: ä»®ã«ãã®ããããLv.28ã¯é¡°ãããå ããŠåããšããã°ããã¯æãç¶ããªã fact5: ãã®ã¿ãã¿ãLv.81ã¯èªãã£ãœããªã ; $hypothesis$ = ããã®ããããLv.28ã¯èªãã£ãœããªãããããã¯åãçµããããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã ; $proof$ = | fact2 & fact3 -> int1: ãã®ããããLv.28ã¯é¡°ãããããŸãã«åã; int1 & fact4 -> int2: ãã®ããããLv.28ã¯æãç¶ããªã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{C}{a} -> ¬(¬{E}{a} v {D}{a}) fact2: {A}{a} fact3: {B}{a} fact4: ({A}{a} & {B}{a}) -> ¬{C}{a} fact5: ¬{E}{at} ; $hypothesis$ = ¬(¬{E}{a} v {D}{a}) ; $proof$ = | fact2 & fact3 -> int1: ({A}{a} & {B}{a}); int1 & fact4 -> int2: ¬{C}{a}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæãããŸãããã¯åèµããããšããããšã¯æãç«ããªã | ¬({A}{a} & {B}{a}) | fact1: ãã®ã¿ãã¿ãªLv.4ã¯è¿·ãæã fact2: ãã®ã¿ã®ã¿ã«ãLv.63ã¯åèµãã fact3: 眪深ãã¢ã³ã¹ã¿ãŒã¯æããããªã fact4: ãã®ã¿ã®ã¿ã«ãLv.63ã¯ç±ã
ãããŠãã€èŠåºã ãé£ã fact5: ãã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæã fact6: ãããã®ãœããœãLv.0ã¯æããããªããšãããšãããã¯èãåãæãããããããã¯è¿·ãæãããšããããšã¯æãç«ã€ | fact1: {A}{dp} fact2: {B}{a} fact3: (x): {E}x -> ¬{C}x fact4: ({IG}{a} & {AP}{a}) fact5: {A}{a} fact6: ¬{C}{ce} -> ({FO}{ce} & {A}{ce}) | [
"fact5 -> int1: ãã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæã; int1 & fact2 -> hypothesis;"
] | [
"fact5 -> int1: {A}{a}; int1 & fact2 -> hypothesis;"
] | ãã®ãœããœãLv.0ã¯èãåãæãããã€åèµãã | ({FO}{ce} & {B}{ce}) | [
"fact8 -> int2: ããããã®ãœããœãLv.0ã眪深ããšãããæããããªã;"
] | 5 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã¿ãã¿ãªLv.4ã¯è¿·ãæã fact2: ãã®ã¿ã®ã¿ã«ãLv.63ã¯åèµãã fact3: 眪深ãã¢ã³ã¹ã¿ãŒã¯æããããªã fact4: ãã®ã¿ã®ã¿ã«ãLv.63ã¯ç±ã
ãããŠãã€èŠåºã ãé£ã fact5: ãã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæã fact6: ãããã®ãœããœãLv.0ã¯æããããªããšãããšãããã¯èãåãæãããããããã¯è¿·ãæãããšããããšã¯æãç«ã€ ; $hypothesis$ = ããã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæãããŸãããã¯åèµããããšããããšã¯æãç«ããªã ; $proof$ = | fact5 -> int1: ãã®ã¿ã®ã¿ã«ãLv.63ã¯è¿·ãæã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{dp} fact2: {B}{a} fact3: (x): {E}x -> ¬{C}x fact4: ({IG}{a} & {AP}{a}) fact5: {A}{a} fact6: ¬{C}{ce} -> ({FO}{ce} & {A}{ce}) ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | fact5 -> int1: {A}{a}; int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãæ¡ãæããšããããšãçºçããããŸãã¯ãã©ããããšããããšã¯çºçããªãããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãã | ¬({D} v ¬{E}) | fact1: ã·ãã·ã®Lv.80äºä»¶ããŸããŸãLv.82äºä»¶ã¯èµ·ãããªããšããããšãé²ã fact2: ãŸããŸãLv.82äºä»¶ã¯ãŸã«ããŸã¡ãLv.16äºä»¶ã«ç±æ¥ãã fact3: æ¡ãæããšããããšãèµ·ããããŸãã¯ãã©ããããšããããšãèµ·ãã fact4: ä»®ã«ããŸã«ããŸã¡ãLv.16äºä»¶ãçããããšããããšã¯ç¢ºãã§ãããšããã°ãæ¡ãæããšããããšãèµ·ããããã©ããããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ãšç°ãªã fact5: ãŽããŽãLv.59äºä»¶ã¯çºçããªããšããããšã¯ã·ãã·ã®Lv.80äºä»¶ãšãŸããŸãLv.82äºä»¶ãçãããçºçããã fact6: ã·ã¡ã
ã·ã®Lv.73äºä»¶ããŸã«ããŸã¡ãLv.16äºä»¶ã¯ãã£ããã§ãã fact7: ãŸã«ããŸã¡ãLv.16äºä»¶ãçããããããã¯ã·ãã·ã®Lv.80äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã§ãã fact8: ç§èµããããšãèµ·ããããŸãã¯ã¿ãã¿ãLv.1äºä»¶ã¯èµ·ããªã | fact1: {B} -> {C} fact2: {A} -> {C} fact3: ({D} v {E}) fact4: {A} -> ¬({D} v ¬{E}) fact5: ¬{F} -> ({B} & {C}) fact6: {A} -> {IT} fact7: ({A} v {B}) fact8: ({CF} v ¬{BU}) | [
"fact7 & fact2 & fact1 -> int1: ããŸããŸãLv.82äºä»¶ãçºçããããšããããšã¯çå®ã§ãã;"
] | [
"fact7 & fact2 & fact1 -> int1: {C};"
] | ãæ¡ãæããšããããšãçºçããããŸãã¯ãã©ããããšããããšã¯çºçããªãããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãã | ¬({D} v ¬{E}) | [] | 7 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã·ãã·ã®Lv.80äºä»¶ããŸããŸãLv.82äºä»¶ã¯èµ·ãããªããšããããšãé²ã fact2: ãŸããŸãLv.82äºä»¶ã¯ãŸã«ããŸã¡ãLv.16äºä»¶ã«ç±æ¥ãã fact3: æ¡ãæããšããããšãèµ·ããããŸãã¯ãã©ããããšããããšãèµ·ãã fact4: ä»®ã«ããŸã«ããŸã¡ãLv.16äºä»¶ãçããããšããããšã¯ç¢ºãã§ãããšããã°ãæ¡ãæããšããããšãèµ·ããããã©ããããšããããšã¯èµ·ãããªãããšããããšã¯äºå®ãšç°ãªã fact5: ãŽããŽãLv.59äºä»¶ã¯çºçããªããšããããšã¯ã·ãã·ã®Lv.80äºä»¶ãšãŸããŸãLv.82äºä»¶ãçãããçºçããã fact6: ã·ã¡ã
ã·ã®Lv.73äºä»¶ããŸã«ããŸã¡ãLv.16äºä»¶ã¯ãã£ããã§ãã fact7: ãŸã«ããŸã¡ãLv.16äºä»¶ãçããããããã¯ã·ãã·ã®Lv.80äºä»¶ãèµ·ããããããã¯äž¡æ¹ãšãã§ãã fact8: ç§èµããããšãèµ·ããããŸãã¯ã¿ãã¿ãLv.1äºä»¶ã¯èµ·ããªã ; $hypothesis$ = ãæ¡ãæããšããããšãçºçããããŸãã¯ãã©ããããšããããšã¯çºçããªãããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} -> {C} fact2: {A} -> {C} fact3: ({D} v {E}) fact4: {A} -> ¬({D} v ¬{E}) fact5: ¬{F} -> ({B} & {C}) fact6: {A} -> {IT} fact7: ({A} v {B}) fact8: ({CF} v ¬{BU}) ; $hypothesis$ = ¬({D} v ¬{E}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã«ããŸãLv.49ã¯å¯èµ·ããã | {C}{b} | fact1: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯å€±èžªããªãããã£ãããªãããšããããšã¯ééããªãããã¯å¯èµ·ãããªã fact2: ãã®ãã¡ã
ãã«Lv.91ã¯å€±èžªãã fact3: ãã®ãã¡ã
ãã«Lv.91ã¯ãã£ãããŠããã«å€±èžªãã fact4: ããä»®ã«ãã®ãã¡ã
ãã«Lv.91ããã£ãããªããã®ãŸã«ããŸãLv.49ã¯å¯èµ·ããã fact5: ãã®ãŸã«ããŸãLv.49ã¯ãã£ãã | fact1: (x): ¬(¬{B}x v ¬{A}x) -> ¬{C}x fact2: {B}{a} fact3: ({A}{a} & {B}{a}) fact4: {A}{a} -> {C}{b} fact5: {A}{b} | [
"fact3 -> int1: ãã®ãã¡ã
ãã«Lv.91ã¯ãã£ãã; int1 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: {A}{a}; int1 & fact4 -> hypothesis;"
] | ããã®ãŸã«ããŸãLv.49ã¯å¯èµ·ãããªãããšããããšã¯æ¬åœã | ¬{C}{b} | [
"fact6 -> int2: ããä»®ã«ããã®ãŸã«ããŸãLv.49ã¯å€±èžªããªãããããã¯ãã£ãããªãããšããããšã¯åãªãããã¯å¯èµ·ãããªã;"
] | 5 | 2 | 2 | 2 | 2 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯å€±èžªããªãããã£ãããªãããšããããšã¯ééããªãããã¯å¯èµ·ãããªã fact2: ãã®ãã¡ã
ãã«Lv.91ã¯å€±èžªãã fact3: ãã®ãã¡ã
ãã«Lv.91ã¯ãã£ãããŠããã«å€±èžªãã fact4: ããä»®ã«ãã®ãã¡ã
ãã«Lv.91ããã£ãããªããã®ãŸã«ããŸãLv.49ã¯å¯èµ·ããã fact5: ãã®ãŸã«ããŸãLv.49ã¯ãã£ãã ; $hypothesis$ = ãã®ãŸã«ããŸãLv.49ã¯å¯èµ·ããã ; $proof$ = | fact3 -> int1: ãã®ãã¡ã
ãã«Lv.91ã¯ãã£ãã; int1 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬(¬{B}x v ¬{A}x) -> ¬{C}x fact2: {B}{a} fact3: ({A}{a} & {B}{a}) fact4: {A}{a} -> {C}{b} fact5: {A}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | fact3 -> int1: {A}{a}; int1 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã£ããããããšãšãŸãªãŸã¡ãLv.23äºä»¶äž¡æ¹ãèµ·ãã | ({B} & {C}) | fact1: çãæããšããããšãèµ·ãã fact2: ããä»®ã«åŸ®ç¬ãŸãããšããããšã¯çºçããªããšãããããã£ããããããšãçããããŸãªãŸã¡ãLv.23äºä»¶ãçºçããããšããããšã¯èª€ã£ãŠãã fact3: 埮ç¬ãŸãããšããããšãèµ·ãã fact4: ããããŽã«ããŽãªLv.76äºä»¶ãèµ·ãããªããªãçãé£ããšããããšãšæ°æã¡è¯ããšããããšäž¡æ¹ã¯çºçãã fact5: ãŽããŽã«ãLv.0äºä»¶ããã³ã·ãã·ãLv.91äºä»¶ãçãã fact6: ãäœã¿è¯ããšããããšãèµ·ããããšããããšã¯çå®ã§ãã fact7: ããã£ããããããšã¯èµ·ãããªãããšããããšã¯åŸ®ç¬ãŸãããšããããšã«é»æ¢ããã | fact1: {GB} fact2: ¬{A} -> ¬({B} & {C}) fact3: {A} fact4: ¬{F} -> ({AN} & {E}) fact5: ({FE} & {I}) fact6: {AT} fact7: {A} -> {B} | [
"fact7 & fact3 -> int1: ãã£ããããããšãçºçãã;"
] | [
"fact7 & fact3 -> int1: {B};"
] | ããã£ããããããšãšãŸãªãŸã¡ãLv.23äºä»¶ã©ã¡ãããèµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({B} & {C}) | [] | 6 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: çãæããšããããšãèµ·ãã fact2: ããä»®ã«åŸ®ç¬ãŸãããšããããšã¯çºçããªããšãããããã£ããããããšãçããããŸãªãŸã¡ãLv.23äºä»¶ãçºçããããšããããšã¯èª€ã£ãŠãã fact3: 埮ç¬ãŸãããšããããšãèµ·ãã fact4: ããããŽã«ããŽãªLv.76äºä»¶ãèµ·ãããªããªãçãé£ããšããããšãšæ°æã¡è¯ããšããããšäž¡æ¹ã¯çºçãã fact5: ãŽããŽã«ãLv.0äºä»¶ããã³ã·ãã·ãLv.91äºä»¶ãçãã fact6: ãäœã¿è¯ããšããããšãèµ·ããããšããããšã¯çå®ã§ãã fact7: ããã£ããããããšã¯èµ·ãããªãããšããããšã¯åŸ®ç¬ãŸãããšããããšã«é»æ¢ããã ; $hypothesis$ = ãã£ããããããšãšãŸãªãŸã¡ãLv.23äºä»¶äž¡æ¹ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {GB} fact2: ¬{A} -> ¬({B} & {C}) fact3: {A} fact4: ¬{F} -> ({AN} & {E}) fact5: ({FE} & {I}) fact6: {AT} fact7: {A} -> {B} ; $hypothesis$ = ({B} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | å°æããšããããšã¯çºçãããã¿ã¡ãã¿ã«ãLv.30äºä»¶ã¯çºçãã | ({C} & {D}) | fact1: ãããããLv.81äºä»¶ãšå»ºèšããããšäž¡æ¹ãçããããšããããšã¯ããœããœãLv.46äºä»¶ã¯çºçããªãããšããããšã«ãããããã fact2: ãã¿ã¡ãã¿ã«ãLv.30äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ fact3: ãŽããŽãLv.52äºä»¶ã¯ãå°æããšããããšã¯èµ·ããªããŠããã«ãœããœãLv.46äºä»¶ã¯èµ·ãããªãããšããããšã«åž°çµãã fact4: 建èšããããšã¯èµ·ãããªããšããã°ãå°æããšããããšãšã¿ã¡ãã¿ã«ãLv.30äºä»¶ã©ã¡ãããèµ·ããããšããããšã¯æ£ãããšããããšã¯ãªã fact5: ãŽããŽãLv.52äºä»¶ããã³æ瞊åºæ¥ãããšãçºçããã¯ãæ
å ±åéããããšã¯èµ·ããªãããšããããšã¯ãã£ããã§ãã fact6: ãœããœãLv.46äºä»¶ã¯ãå°æããšããããšã¯çããªãããšããããšãé²ã fact7: 建èšããããšãšãœããœãLv.46äºä»¶ã©ã¡ãããçãã fact8: æããããšãèµ·ãã | fact1: ¬{B} -> ({DL} & {A}) fact2: {D} fact3: {E} -> (¬{C} & ¬{B}) fact4: ¬{A} -> ¬({C} & {D}) fact5: ¬{G} -> ({E} & {F}) fact6: {B} -> {C} fact7: ({A} & {B}) fact8: {EO} | [
"fact7 -> int1: ãœããœãLv.46äºä»¶ãçãã; int1 & fact6 -> int2: å°æããšããããšãçºçãã; int2 & fact2 -> hypothesis;"
] | [
"fact7 -> int1: {B}; int1 & fact6 -> int2: {C}; int2 & fact2 -> hypothesis;"
] | èããšããããšãšããããLv.81äºä»¶äž¡æ¹ãšããèµ·ãã | ({JH} & {DL}) | [] | 7 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããããLv.81äºä»¶ãšå»ºèšããããšäž¡æ¹ãçããããšããããšã¯ããœããœãLv.46äºä»¶ã¯çºçããªãããšããããšã«ãããããã fact2: ãã¿ã¡ãã¿ã«ãLv.30äºä»¶ãèµ·ããããšããããšã¯æãç«ã€ fact3: ãŽããŽãLv.52äºä»¶ã¯ãå°æããšããããšã¯èµ·ããªããŠããã«ãœããœãLv.46äºä»¶ã¯èµ·ãããªãããšããããšã«åž°çµãã fact4: 建èšããããšã¯èµ·ãããªããšããã°ãå°æããšããããšãšã¿ã¡ãã¿ã«ãLv.30äºä»¶ã©ã¡ãããèµ·ããããšããããšã¯æ£ãããšããããšã¯ãªã fact5: ãŽããŽãLv.52äºä»¶ããã³æ瞊åºæ¥ãããšãçºçããã¯ãæ
å ±åéããããšã¯èµ·ããªãããšããããšã¯ãã£ããã§ãã fact6: ãœããœãLv.46äºä»¶ã¯ãå°æããšããããšã¯çããªãããšããããšãé²ã fact7: 建èšããããšãšãœããœãLv.46äºä»¶ã©ã¡ãããçãã fact8: æããããšãèµ·ãã ; $hypothesis$ = å°æããšããããšã¯çºçãããã¿ã¡ãã¿ã«ãLv.30äºä»¶ã¯çºçãã ; $proof$ = | fact7 -> int1: ãœããœãLv.46äºä»¶ãçãã; int1 & fact6 -> int2: å°æããšããããšãçºçãã; int2 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B} -> ({DL} & {A}) fact2: {D} fact3: {E} -> (¬{C} & ¬{B}) fact4: ¬{A} -> ¬({C} & {D}) fact5: ¬{G} -> ({E} & {F}) fact6: {B} -> {C} fact7: ({A} & {B}) fact8: {EO} ; $hypothesis$ = ({C} & {D}) ; $proof$ = | fact7 -> int1: {B}; int1 & fact6 -> int2: {C}; int2 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãœããœãLv.41äºä»¶ãèµ·ãã | {D} | fact1: ããä»®ã«ãããŸã«ããŸãªLv.23äºä»¶ãçºçããªããããŸãã«ãœã®ãœãLv.69äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ããªããªãã°ãŽã¡ããŽã¡ãLv.58äºä»¶ã¯èµ·ããªã fact2: ãŽã¡ããŽã¡ãLv.58äºä»¶ãçºçãã fact3: ãŽããŽãLv.73äºä»¶ã¯ããããŸãããšããããšãçãããã fact4: ããä»®ã«ãŽã¡ããŽã¡ãLv.58äºä»¶ãçãããããŸãã«ããããŸãããšããããšãçãããšããããœããœãLv.41äºä»¶ã¯çããªã fact5: ããããœã®ãœãLv.69äºä»¶ãèµ·ãããšããã°ããŽã¡ããŽã¡ãLv.58äºä»¶ãçºçããªãããŸããŸã«ããŸãªLv.23äºä»¶ã¯èµ·ããªãããšããããšã¯ééãã | fact1: ¬(¬{E} & ¬{F}) -> ¬{C} fact2: {C} fact3: {A} -> {B} fact4: ({C} & {B}) -> ¬{D} fact5: {F} -> ¬(¬{C} & ¬{E}) | [] | [] | å¯ããšããããšãçºçãã | {DF} | [] | 6 | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãããŸã«ããŸãªLv.23äºä»¶ãçºçããªããããŸãã«ãœã®ãœãLv.69äºä»¶ã¯çºçããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ããªããªãã°ãŽã¡ããŽã¡ãLv.58äºä»¶ã¯èµ·ããªã fact2: ãŽã¡ããŽã¡ãLv.58äºä»¶ãçºçãã fact3: ãŽããŽãLv.73äºä»¶ã¯ããããŸãããšããããšãçãããã fact4: ããä»®ã«ãŽã¡ããŽã¡ãLv.58äºä»¶ãçãããããŸãã«ããããŸãããšããããšãçãããšããããœããœãLv.41äºä»¶ã¯çããªã fact5: ããããœã®ãœãLv.69äºä»¶ãèµ·ãããšããã°ããŽã¡ããŽã¡ãLv.58äºä»¶ãçºçããªãããŸããŸã«ããŸãªLv.23äºä»¶ã¯èµ·ããªãããšããããšã¯ééãã ; $hypothesis$ = ãœããœãLv.41äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{E} & ¬{F}) -> ¬{C} fact2: {C} fact3: {A} -> {B} fact4: ({C} & {B}) -> ¬{D} fact5: {F} -> ¬(¬{C} & ¬{E}) ; $hypothesis$ = {D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã©èããªãã°ãå©çšãé£ãããããã¯è²ã£ãœããªãããŸãã¯ã©ã¡ããã§ããããšããããšã¯ééãã§ãããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): {A}x -> ¬({AA}x v ¬{AB}x) | fact1: ãããæãå€ããšããã°äŒããæããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãã®ãœã«ããœã®Lv.24ã¯ããã©èããšãããšãå©çšãé£ãããããã¯è²ã£ãœããªãããããã¯äž¡æ¹ã ããšããããšã¯åã§ãã fact3: ä»®ã«ãã®ãœã«ããœã®Lv.24ãããã©èããšããããã®ãœã«ããœã®Lv.24ã¯è²ã£ãœã fact4: ããããããã©èããšããã°å©çšãé£ãããããã¯è²ã£ãœããšããããšã¯ãªããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: (Ex): {DA}x -> {HG}x fact2: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact3: {A}{aa} -> {AB}{aa} fact4: (Ex): {A}x -> ({AA}x v ¬{AB}x) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | null | null | [] | null | 1 | 1 | 1 | 1 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ãããæãå€ããšããã°äŒããæããã¢ã³ã¹ã¿ãŒã¯ãã fact2: ãã®ãœã«ããœã®Lv.24ã¯ããã©èããšãããšãå©çšãé£ãããããã¯è²ã£ãœããªãããããã¯äž¡æ¹ã ããšããããšã¯åã§ãã fact3: ä»®ã«ãã®ãœã«ããœã®Lv.24ãããã©èããšããããã®ãœã«ããœã®Lv.24ã¯è²ã£ãœã fact4: ããããããã©èããšããã°å©çšãé£ãããããã¯è²ã£ãœããšããããšã¯ãªããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ãããã©èããªãã°ãå©çšãé£ãããããã¯è²ã£ãœããªãããŸãã¯ã©ã¡ããã§ããããšããããšã¯ééãã§ãããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): {DA}x -> {HG}x fact2: {A}{aa} -> ¬({AA}{aa} v ¬{AB}{aa}) fact3: {A}{aa} -> {AB}{aa} fact4: (Ex): {A}x -> ({AA}x v ¬{AB}x) ; $hypothesis$ = (Ex): {A}x -> ¬({AA}x v ¬{AB}x) ; $proof$ = | fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ã«ã
ã¿ãLv.51ã¯é©åããããããã¯å»æ£ããªãããããã¯äž¡æ¹ã§ãã | ({E}{b} v ¬{C}{b}) | fact1: ããããããã®ãŽããŽã«ã
Lv.49ã¯é©åãããå ããŠããã¯ããæ°ç¡ãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªããªãã°ãã®ã¿ã«ã
ã¿ãLv.51ã¯ããæ°ç¡ããªã fact2: ããä»®ã«ããã®ãŽããŽã«ã
Lv.49ã¯åŸ¡å¿ãããªãããšããããšã¯æãç«ã€ãšããã°ãé©åãããããŸãã«ããæ°ç¡ãããšããããšã¯äºå®ãšç°ãªã fact3: ãã®ãŽããŽã«ã
Lv.49ãéããããããã¯ããã¯èªãããããããã¯äž¡æ¹ã ãšããã°å»æ£ããªã fact4: ãã®ãŽããŽã«ã
Lv.49ã¯éãã fact5: ããæ°ç¡ããªãã¢ã³ã¹ã¿ãŒã¯å»æ£ããããããã¯èªããããã©ã¡ããã fact6: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯è¿ä»ãé£ããããã¯æããããšããããšã¯ãªãããšããããšã¯ééã£ãŠããã°åŸ¡å¿ãããªã fact7: ãããã®ãŽããŽã«ã
Lv.49ãèªããããšãããšãã®ãŽããŽã«ã
Lv.49ã¯ããæ°ç¡ããªããã©éãã | fact1: ¬({E}{a} & {D}{a}) -> ¬{D}{b} fact2: ¬{F}{a} -> ¬({E}{a} & {D}{a}) fact3: ({A}{a} v {B}{a}) -> ¬{C}{a} fact4: {A}{a} fact5: (x): ¬{D}x -> ({C}x v {B}x) fact6: (x): ¬({G}x v ¬{H}x) -> ¬{F}x fact7: {B}{a} -> (¬{D}{a} & {A}{a}) | [
"fact4 -> int1: ãã®ãŽããŽã«ã
Lv.49ã¯éããããããã¯ããã¯èªããã; int1 & fact3 -> int2: ãã®ãŽããŽã«ã
Lv.49ã¯å»æ£ããªã;"
] | [
"fact4 -> int1: ({A}{a} v {B}{a}); int1 & fact3 -> int2: ¬{C}{a};"
] | ããã®ã¿ã«ã
ã¿ãLv.51ã¯é©åããããããã¯å»æ£ããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({E}{b} v ¬{C}{b}) | [] | 5 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããããã®ãŽããŽã«ã
Lv.49ã¯é©åãããå ããŠããã¯ããæ°ç¡ãããšããããšã¯çå®ã ããšããããšã¯æãç«ããªããªãã°ãã®ã¿ã«ã
ã¿ãLv.51ã¯ããæ°ç¡ããªã fact2: ããä»®ã«ããã®ãŽããŽã«ã
Lv.49ã¯åŸ¡å¿ãããªãããšããããšã¯æãç«ã€ãšããã°ãé©åãããããŸãã«ããæ°ç¡ãããšããããšã¯äºå®ãšç°ãªã fact3: ãã®ãŽããŽã«ã
Lv.49ãéããããããã¯ããã¯èªãããããããã¯äž¡æ¹ã ãšããã°å»æ£ããªã fact4: ãã®ãŽããŽã«ã
Lv.49ã¯éãã fact5: ããæ°ç¡ããªãã¢ã³ã¹ã¿ãŒã¯å»æ£ããããããã¯èªããããã©ã¡ããã fact6: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯è¿ä»ãé£ããããã¯æããããšããããšã¯ãªãããšããããšã¯ééã£ãŠããã°åŸ¡å¿ãããªã fact7: ãããã®ãŽããŽã«ã
Lv.49ãèªããããšãããšãã®ãŽããŽã«ã
Lv.49ã¯ããæ°ç¡ããªããã©éãã ; $hypothesis$ = ãã®ã¿ã«ã
ã¿ãLv.51ã¯é©åããããããã¯å»æ£ããªãããããã¯äž¡æ¹ã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({E}{a} & {D}{a}) -> ¬{D}{b} fact2: ¬{F}{a} -> ¬({E}{a} & {D}{a}) fact3: ({A}{a} v {B}{a}) -> ¬{C}{a} fact4: {A}{a} fact5: (x): ¬{D}x -> ({C}x v {B}x) fact6: (x): ¬({G}x v ¬{H}x) -> ¬{F}x fact7: {B}{a} -> (¬{D}{a} & {A}{a}) ; $hypothesis$ = ({E}{b} v ¬{C}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãã«ã
ããLv.13ã¯ç«ã¡å
¥ã | {B}{aa} | fact1: ä»®ã«ãã®ãã«ã
ããLv.13ãåºãé£ãããããææãæããªããšããã°ããã®ãã«ã
ããLv.13ã¯ç«ã¡å
¥ããªãããšããããšã¯åã§ãã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãåãèŸããšããã°åºãé£ãããã©ææãæããªã fact3: ãã®ãã«ã
ããLv.13ã¯åºãé£ã fact4: ãã®ãã«ã
ããLv.13ã¯åãèŸã fact5: ä»®ã«ãã®ãã«ã
ããLv.13ã¯åãèŸããªããåºãé£ãããšããããšã¯æãç«ã€ | fact1: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact2: (x): {A}x -> ({AA}x & ¬{AB}x) fact3: {AA}{aa} fact4: {A}{aa} fact5: {A}{aa} -> {AA}{aa} | [
"fact2 -> int1: ããä»®ã«ãã®ãã«ã
ããLv.13ãåãèŸããªãããã¯åºãé£ãäžæ¹ã§ææãæããªã; int1 & fact4 -> int2: ãã®ãã«ã
ããLv.13ã¯åºãé£ããææãæããšããããšã¯ãªã; int2 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}); int1 & fact4 -> int2: ({AA}{aa} & ¬{AB}{aa}); int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«ãã®ãã«ã
ããLv.13ãåºãé£ãããããææãæããªããšããã°ããã®ãã«ã
ããLv.13ã¯ç«ã¡å
¥ããªãããšããããšã¯åã§ãã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãåãèŸããšããã°åºãé£ãããã©ææãæããªã fact3: ãã®ãã«ã
ããLv.13ã¯åºãé£ã fact4: ãã®ãã«ã
ããLv.13ã¯åãèŸã fact5: ä»®ã«ãã®ãã«ã
ããLv.13ã¯åãèŸããªããåºãé£ãããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ãã«ã
ããLv.13ã¯ç«ã¡å
¥ã ; $proof$ = | fact2 -> int1: ããä»®ã«ãã®ãã«ã
ããLv.13ãåãèŸããªãããã¯åºãé£ãäžæ¹ã§ææãæããªã; int1 & fact4 -> int2: ãã®ãã«ã
ããLv.13ã¯åºãé£ããææãæããšããããšã¯ãªã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA}{aa} & ¬{AB}{aa}) -> {B}{aa} fact2: (x): {A}x -> ({AA}x & ¬{AB}x) fact3: {AA}{aa} fact4: {A}{aa} fact5: {A}{aa} -> {AA}{aa} ; $hypothesis$ = {B}{aa} ; $proof$ = | fact2 -> int1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}); int1 & fact4 -> int2: ({AA}{aa} & ¬{AB}{aa}); int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ã®ã·ãªLv.1ã¯æ£æ©ãã | {D}{b} | fact1: ãã®ãœã«ãœã¡ã
Lv.61ã¯æžã fact2: ããããã®ãœã«ãœã¡ã
Lv.61ããããç¡ããšããã°ãã®ã·ã®ã·ãªLv.1ã¯èªãé£ã fact3: ããããã®ã·ã®ã·ãªLv.1ãèªãé£ããªãã°æ£æ©ãã fact4: ãã®ãœã«ãœã¡ã
Lv.61ã¯æžãããŸããããç¡ã fact5: ãã®ãœã«ãœã¡ã
Lv.61ã¯ãããç¡ããªããšãããšãã®ã¿ã¡ãã¿ã¡ãLv.33ã¯æ£æ©ãããããã«æžã | fact1: {A}{a} fact2: {B}{a} -> {C}{b} fact3: {C}{b} -> {D}{b} fact4: ({A}{a} & {B}{a}) fact5: ¬{B}{a} -> ({D}{dt} & {A}{dt}) | [
"fact4 -> int1: ãã®ãœã«ãœã¡ã
Lv.61ã¯ãããç¡ã; int1 & fact2 -> int2: ãã®ã·ã®ã·ãªLv.1ã¯èªãé£ã; int2 & fact3 -> hypothesis;"
] | [
"fact4 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> hypothesis;"
] | ãã®ã¿ã¡ãã¿ã¡ãLv.33ã¯æ£æ©ãã | {D}{dt} | [] | 6 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãœã«ãœã¡ã
Lv.61ã¯æžã fact2: ããããã®ãœã«ãœã¡ã
Lv.61ããããç¡ããšããã°ãã®ã·ã®ã·ãªLv.1ã¯èªãé£ã fact3: ããããã®ã·ã®ã·ãªLv.1ãèªãé£ããªãã°æ£æ©ãã fact4: ãã®ãœã«ãœã¡ã
Lv.61ã¯æžãããŸããããç¡ã fact5: ãã®ãœã«ãœã¡ã
Lv.61ã¯ãããç¡ããªããšãããšãã®ã¿ã¡ãã¿ã¡ãLv.33ã¯æ£æ©ãããããã«æžã ; $hypothesis$ = ãã®ã·ã®ã·ãªLv.1ã¯æ£æ©ãã ; $proof$ = | fact4 -> int1: ãã®ãœã«ãœã¡ã
Lv.61ã¯ãããç¡ã; int1 & fact2 -> int2: ãã®ã·ã®ã·ãªLv.1ã¯èªãé£ã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: {B}{a} -> {C}{b} fact3: {C}{b} -> {D}{b} fact4: ({A}{a} & {B}{a}) fact5: ¬{B}{a} -> ({D}{dt} & {A}{dt}) ; $hypothesis$ = {D}{b} ; $proof$ = | fact4 -> int1: {B}{a}; int1 & fact2 -> int2: {C}{b}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | åããšããããšãçºçãã | {C} | fact1: ã¿ã«ã¿ãLv.18äºä»¶ãšåããšããããšãçºçããã¯ãçã¿é£ããšããããšã¯çºçããªãããšããããšã«ããçãã fact2: ã¿ã«ã¿ãLv.18äºä»¶ãšçã¿é£ããšããããšãçºçãã fact3: ããä»®ã«æµãåãããšãçãããšãããšåºäŒãæããšããããšã¯èµ·ãããªãããŽã«ããŽãLv.77äºä»¶ãçãã | fact1: ¬{B} -> ({A} & {C}) fact2: ({A} & {B}) fact3: {BS} -> (¬{IR} & {J}) | [
"fact2 -> int1: çã¿é£ããšããããšãçºçãã;"
] | [
"fact2 -> int1: {B};"
] | åããšããããšãçºçãã | {C} | [] | 6 | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ã¿ã«ã¿ãLv.18äºä»¶ãšåããšããããšãçºçããã¯ãçã¿é£ããšããããšã¯çºçããªãããšããããšã«ããçãã fact2: ã¿ã«ã¿ãLv.18äºä»¶ãšçã¿é£ããšããããšãçºçãã fact3: ããä»®ã«æµãåãããšãçãããšãããšåºäŒãæããšããããšã¯èµ·ãããªãããŽã«ããŽãLv.77äºä»¶ãçãã ; $hypothesis$ = åããšããããšãçºçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{B} -> ({A} & {C}) fact2: ({A} & {B}) fact3: {BS} -> (¬{IR} & {J}) ; $hypothesis$ = {C} ; $proof$ = | __UNKNOWN__ |
0.3 | 女ã
ãããšããããšã¯èµ·ãããªã | ¬{D} | fact1: å¿ç¡ããšããããšãèµ·ãã fact2: ããä»®ã«ç¡å£°åãæããšããããšã¯çããªããšããã°å¥³ã
ãããšããããšããã³æ»ãæããšããããšã©ã¡ãããçãã fact3: ãç¡å£°åãæããšããããšãšå¿ç¡ããšããããšãçããããšããããšã¯å¥³ã
ãããšããããšãé»ã fact4: ã¿ã«ã
ã¿ã¡ãLv.51äºä»¶ã¯èµ·ããªã fact5: ãœã«ããœãLv.16äºä»¶ããã³åãããšããããšãçãã fact6: ãæ»ãæããšããããšãèµ·ãããæŽã«ç¡å£°åãæããšããããšãçããããšããããšã¯æ£ãã | fact1: {C} fact2: ¬{B} -> ({D} & {A}) fact3: ({B} & {C}) -> ¬{D} fact4: ¬{HA} fact5: ({GE} & {O}) fact6: ({A} & {B}) | [
"fact6 -> int1: ç¡å£°åãæããšããããšãçãã; int1 & fact1 -> int2: ç¡å£°åãæããšããããšããã³å¿ç¡ããšããããšãèµ·ãã; int2 & fact3 -> hypothesis;"
] | [
"fact6 -> int1: {B}; int1 & fact1 -> int2: ({B} & {C}); int2 & fact3 -> hypothesis;"
] | 女ã
ãããšããããšãèµ·ãã | {D} | [] | 6 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: å¿ç¡ããšããããšãèµ·ãã fact2: ããä»®ã«ç¡å£°åãæããšããããšã¯çããªããšããã°å¥³ã
ãããšããããšããã³æ»ãæããšããããšã©ã¡ãããçãã fact3: ãç¡å£°åãæããšããããšãšå¿ç¡ããšããããšãçããããšããããšã¯å¥³ã
ãããšããããšãé»ã fact4: ã¿ã«ã
ã¿ã¡ãLv.51äºä»¶ã¯èµ·ããªã fact5: ãœã«ããœãLv.16äºä»¶ããã³åãããšããããšãçãã fact6: ãæ»ãæããšããããšãèµ·ãããæŽã«ç¡å£°åãæããšããããšãçããããšããããšã¯æ£ãã ; $hypothesis$ = 女ã
ãããšããããšã¯èµ·ãããªã ; $proof$ = | fact6 -> int1: ç¡å£°åãæããšããããšãçãã; int1 & fact1 -> int2: ç¡å£°åãæããšããããšããã³å¿ç¡ããšããããšãèµ·ãã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: ¬{B} -> ({D} & {A}) fact3: ({B} & {C}) -> ¬{D} fact4: ¬{HA} fact5: ({GE} & {O}) fact6: ({A} & {B}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact6 -> int1: {B}; int1 & fact1 -> int2: ({B} & {C}); int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ã«ãã¿ã«ãLv.93ã¯æ¶ããªã | ¬{B}{aa} | fact1: ããã¢ã³ã¹ã¿ãŒã¯åããèŸããšããããšã¯ãªããšããã°ãããã¯æã¡äžããæããå°ç¡ãããšããããšã¯èª€ã£ãŠãã fact2: æãã¢ã³ã¹ã¿ãŒã¯åããèŸããªããããã«æ¶ããªã fact3: ããããã®ã¿ã«ãã¿ã«ãLv.93ã¯æã¡äžããæãããããå°ç¡ãããšããããšã¯æãç«ããªããªãæ¶ããªã fact4: ããä»®ã«ãã®ã¿ã¡ã
ã¿ãªLv.32ãåããèŸããªããããã«æ¶ããªããšããã°ãã®ããªããLv.70ã¯å°ç¡ããªã fact5: ä»®ã«ãã®ã¿ã¡ã
ã¿ãªLv.32ãæããªããšããããã®ã¿ã«ãã¿ã«ãLv.93ã¯æ¶ãããã€åããèŸã fact6: 京éœããããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ãã°ããããæã | fact1: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact2: (x): {C}x -> (¬{A}x & ¬{B}x) fact3: ¬({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact4: (¬{A}{a} & ¬{B}{a}) -> ¬{AB}{cd} fact5: ¬{C}{a} -> ({B}{aa} & {A}{aa}) fact6: (x): ¬{E}x -> ({D}x & {C}x) | [
"fact1 -> int1: ããããã®ã¿ã«ãã¿ã«ãLv.93ã¯åããèŸããšããããšã¯ãªããšããã°ãããã¯æã¡äžããæãããã®äžå°ç¡ãããšããããšã¯ééã£ãŠãã;"
] | [
"fact1 -> int1: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa});"
] | ãã®ã¿ã«ãã¿ã«ãLv.93ã¯æ¶ã | {B}{aa} | [] | 6 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã¢ã³ã¹ã¿ãŒã¯åããèŸããšããããšã¯ãªããšããã°ãããã¯æã¡äžããæããå°ç¡ãããšããããšã¯èª€ã£ãŠãã fact2: æãã¢ã³ã¹ã¿ãŒã¯åããèŸããªããããã«æ¶ããªã fact3: ããããã®ã¿ã«ãã¿ã«ãLv.93ã¯æã¡äžããæãããããå°ç¡ãããšããããšã¯æãç«ããªããªãæ¶ããªã fact4: ããä»®ã«ãã®ã¿ã¡ã
ã¿ãªLv.32ãåããèŸããªããããã«æ¶ããªããšããã°ãã®ããªããLv.70ã¯å°ç¡ããªã fact5: ä»®ã«ãã®ã¿ã¡ã
ã¿ãªLv.32ãæããªããšããããã®ã¿ã«ãã¿ã«ãLv.93ã¯æ¶ãããã€åããèŸã fact6: 京éœããããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ãã°ããããæã ; $hypothesis$ = ãã®ã¿ã«ãã¿ã«ãLv.93ã¯æ¶ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{A}x -> ¬({AA}x & {AB}x) fact2: (x): {C}x -> (¬{A}x & ¬{B}x) fact3: ¬({AA}{aa} & {AB}{aa}) -> ¬{B}{aa} fact4: (¬{A}{a} & ¬{B}{a}) -> ¬{AB}{cd} fact5: ¬{C}{a} -> ({B}{aa} & {A}{aa}) fact6: (x): ¬{E}x -> ({D}x & {C}x) ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãã«ãããªLv.64ã¯è¡åè¯ããããã€ãããã | ({B}{b} & {C}{b}) | fact1: ãã®ã¿ã«ãã¿ã¡ã
Lv.23ã¯çŽ æŽãã fact2: ãããã®ã¿ã«ãã¿ã¡ã
Lv.23ãçŽ æŽãããªãã°ãã®ãã«ãããªLv.64ã¯å®ãæããããã¯ææ
šæ·±ããªã fact3: ããããã®ã¿ã«ãã¿ã¡ã
Lv.23ãçŽ æŽãããšããã°ãã®ãã«ãããªLv.64ã¯å®ãæããªãããããã¯ææ
šæ·±ããªã fact4: ããä»®ã«ãã®ãã«ãããªLv.64ã¯å®ãæããªããææ
šæ·±ããªãããŸãã¯äž¡æ¹ãšãã§ãããšãããšè¡åè¯ã fact5: ãã®ãã«ãããªLv.64ã¯ããã€ãããã | fact1: {A}{a} fact2: {A}{a} -> ({AA}{b} v ¬{AB}{b}) fact3: {A}{a} -> (¬{AA}{b} v ¬{AB}{b}) fact4: (¬{AA}{b} v ¬{AB}{b}) -> {B}{b} fact5: {C}{b} | [
"fact3 & fact1 -> int1: ãã®ãã«ãããªLv.64ã¯å®ãæããªãããŸãã¯ææ
šæ·±ããªãããŸãã¯äž¡æ¹ãšãã§ãã; int1 & fact4 -> int2: ãã®ãã«ãããªLv.64ã¯è¡åè¯ã; int2 & fact5 -> hypothesis;"
] | [
"fact3 & fact1 -> int1: (¬{AA}{b} v ¬{AB}{b}); int1 & fact4 -> int2: {B}{b}; int2 & fact5 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã¿ã«ãã¿ã¡ã
Lv.23ã¯çŽ æŽãã fact2: ãããã®ã¿ã«ãã¿ã¡ã
Lv.23ãçŽ æŽãããªãã°ãã®ãã«ãããªLv.64ã¯å®ãæããããã¯ææ
šæ·±ããªã fact3: ããããã®ã¿ã«ãã¿ã¡ã
Lv.23ãçŽ æŽãããšããã°ãã®ãã«ãããªLv.64ã¯å®ãæããªãããããã¯ææ
šæ·±ããªã fact4: ããä»®ã«ãã®ãã«ãããªLv.64ã¯å®ãæããªããææ
šæ·±ããªãããŸãã¯äž¡æ¹ãšãã§ãããšãããšè¡åè¯ã fact5: ãã®ãã«ãããªLv.64ã¯ããã€ãããã ; $hypothesis$ = ãã®ãã«ãããªLv.64ã¯è¡åè¯ããããã€ãããã ; $proof$ = | fact3 & fact1 -> int1: ãã®ãã«ãããªLv.64ã¯å®ãæããªãããŸãã¯ææ
šæ·±ããªãããŸãã¯äž¡æ¹ãšãã§ãã; int1 & fact4 -> int2: ãã®ãã«ãããªLv.64ã¯è¡åè¯ã; int2 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: {A}{a} -> ({AA}{b} v ¬{AB}{b}) fact3: {A}{a} -> (¬{AA}{b} v ¬{AB}{b}) fact4: (¬{AA}{b} v ¬{AB}{b}) -> {B}{b} fact5: {C}{b} ; $hypothesis$ = ({B}{b} & {C}{b}) ; $proof$ = | fact3 & fact1 -> int1: (¬{AA}{b} v ¬{AB}{b}); int1 & fact4 -> int2: {B}{b}; int2 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãœã®ãœã«Lv.15äºä»¶ãçºçãã | {C} | fact1: ãŸã¡ããŸã¡ãLv.32äºä»¶ãã¿ã¡ãã¿ã«ãLv.31äºä»¶ãçãããšããããšãäž¡æ¹ã¯ãœã®ãœã«Lv.15äºä»¶ãé»ã fact2: ãããã¡ãLv.18äºä»¶ã¯èµ·ãããªã fact3: ããœã®ãœã«Lv.15äºä»¶ãèµ·ãããã¿ã¡ãã¿ã«ãLv.31äºä»¶ã¯èµ·ããªãããšããããšã¯èŠãæããšããããšãåå ã fact4: ãŸã«ããŸã«ãLv.66äºä»¶ããããã¯æãç¥ããããšãèµ·ãã fact5: ãŸã¡ããŸã¡ãLv.32äºä»¶ãçºçãã | fact1: ({A} v {B}) -> ¬{C} fact2: ¬{BJ} fact3: {D} -> ({C} & ¬{B}) fact4: ({HA} v {FF}) fact5: {A} | [
"fact5 -> int1: ãŸã¡ããŸã¡ãLv.32äºä»¶ããããã¯ã¿ã¡ãã¿ã«ãLv.31äºä»¶ããŸãã¯äž¡æ¹ãèµ·ãã; int1 & fact1 -> hypothesis;"
] | [
"fact5 -> int1: ({A} v {B}); int1 & fact1 -> hypothesis;"
] | çžå¿ãããšããããšãæ©ãŸãããšããããšããŸãã¯ã©ã¡ãããçºçãã | ({EK} v {CO}) | [] | 6 | 2 | 2 | 2 | 2 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãŸã¡ããŸã¡ãLv.32äºä»¶ãã¿ã¡ãã¿ã«ãLv.31äºä»¶ãçãããšããããšãäž¡æ¹ã¯ãœã®ãœã«Lv.15äºä»¶ãé»ã fact2: ãããã¡ãLv.18äºä»¶ã¯èµ·ãããªã fact3: ããœã®ãœã«Lv.15äºä»¶ãèµ·ãããã¿ã¡ãã¿ã«ãLv.31äºä»¶ã¯èµ·ããªãããšããããšã¯èŠãæããšããããšãåå ã fact4: ãŸã«ããŸã«ãLv.66äºä»¶ããããã¯æãç¥ããããšãèµ·ãã fact5: ãŸã¡ããŸã¡ãLv.32äºä»¶ãçºçãã ; $hypothesis$ = ãœã®ãœã«Lv.15äºä»¶ãçºçãã ; $proof$ = | fact5 -> int1: ãŸã¡ããŸã¡ãLv.32äºä»¶ããããã¯ã¿ã¡ãã¿ã«ãLv.31äºä»¶ããŸãã¯äž¡æ¹ãèµ·ãã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: ¬{BJ} fact3: {D} -> ({C} & ¬{B}) fact4: ({HA} v {FF}) fact5: {A} ; $hypothesis$ = {C} ; $proof$ = | fact5 -> int1: ({A} v {B}); int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã¿ãã¿ã«Lv.97ã¯é€ããããŸãã¯ããã¯æ
ãŸããããããã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠãã | ¬({C}{a} v {D}{a}) | fact1: ãã®ã¿ãã¿ã«Lv.97ã¯æ
ãŸãããªã fact2: ãã®ã¿ãã¿ã«Lv.97ãéãæããšãããããã¯é€ãã | fact1: ¬{D}{a} fact2: {A}{a} -> {C}{a} | [] | [] | ãã®ãŸã¡ããŸã®Lv.85ã¯åœ±é¿ããæã | {B}{jf} | [] | 5 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ã¿ãã¿ã«Lv.97ã¯æ
ãŸãããªã fact2: ãã®ã¿ãã¿ã«Lv.97ãéãæããšãããããã¯é€ãã ; $hypothesis$ = ããã®ã¿ãã¿ã«Lv.97ã¯é€ããããŸãã¯ããã¯æ
ãŸããããããã¯ã©ã¡ããã ããšããããšã¯ééã£ãŠãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{D}{a} fact2: {A}{a} -> {C}{a} ; $hypothesis$ = ¬({C}{a} v {D}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ããããªLv.6ã¯åŸãæããªãããããã¯ããã¯å£²ãå§ããªãããããã¯ã©ã¡ããã | (¬{AA}{aa} v ¬{AB}{aa}) | fact1: ããã®ããããªLv.6ã¯å®çŸãæããšããããšã¯ãªãããšããããšã¯çå®ã fact2: ããããã®ããããªLv.6ãå®çŸãæããªããªããã®ããããªLv.6ã¯åŸãæãããããã¯å£²ãå§ãããšããããšã¯ãªãããããã¯äž¡æ¹ã | fact1: ¬{A}{aa} fact2: ¬{A}{aa} -> ({AA}{aa} v ¬{AB}{aa}) | [] | [] | null | null | [] | null | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããã®ããããªLv.6ã¯å®çŸãæããšããããšã¯ãªãããšããããšã¯çå®ã fact2: ããããã®ããããªLv.6ãå®çŸãæããªããªããã®ããããªLv.6ã¯åŸãæãããããã¯å£²ãå§ãããšããããšã¯ãªãããããã¯äž¡æ¹ã ; $hypothesis$ = ãã®ããããªLv.6ã¯åŸãæããªãããããã¯ããã¯å£²ãå§ããªãããããã¯ã©ã¡ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{aa} fact2: ¬{A}{aa} -> ({AA}{aa} v ¬{AB}{aa}) ; $hypothesis$ = (¬{AA}{aa} v ¬{AB}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãæ»ãæããšããããšã§ã¯ãªããŠãœããœãLv.55äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã | ¬(¬{E} & {D}) | fact1: ä»®ã«æ±ãé£ããšããããšã¯çããªããšããã°ãæ»ãæããšããããšã¯çããªãããœããœãLv.55äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact2: 軜ããšããããšã¯èµ·ãããªããšããããšã¯åŸé£ããšããããšãå¥æ©ã fact3: ä»®ã«æœããšããããšã¯èµ·ããªããªãã°ããã·ãã·ãLv.86äºä»¶ã§ã¯ãªããŠäŸ®èŸ±ããããšãçºçããããšããããšã¯æ£ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: æ±ãé£ããšããããšã¯ããããLv.10äºä»¶ã«é»æ¢ããã fact5: æ±ãé£ããšããããšã¯ãçœã£ãœããšããããšãçºçããããšããããšããããããLv.10äºä»¶ãçããããšããããšããããã¯äž¡æ¹ãšãã«é»ãŸãã fact6: çœã£ãœããšããããšãçãã | fact1: ¬{C} -> ¬(¬{E} & {D}) fact2: {EC} -> ¬{P} fact3: ¬{EP} -> ¬(¬{U} & {GO}) fact4: {B} -> ¬{C} fact5: ({A} v {B}) -> ¬{C} fact6: {A} | [
"fact6 -> int1: çœã£ãœããšããããšããŸãã¯ããããLv.10äºä»¶ããããã¯ã©ã¡ãããèµ·ãã; int1 & fact5 -> int2: æ±ãé£ããšããããšã¯èµ·ããªã; int2 & fact1 -> hypothesis;"
] | [
"fact6 -> int1: ({A} v {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«æ±ãé£ããšããããšã¯çããªããšããã°ãæ»ãæããšããããšã¯çããªãããœããœãLv.55äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact2: 軜ããšããããšã¯èµ·ãããªããšããããšã¯åŸé£ããšããããšãå¥æ©ã fact3: ä»®ã«æœããšããããšã¯èµ·ããªããªãã°ããã·ãã·ãLv.86äºä»¶ã§ã¯ãªããŠäŸ®èŸ±ããããšãçºçããããšããããšã¯æ£ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: æ±ãé£ããšããããšã¯ããããLv.10äºä»¶ã«é»æ¢ããã fact5: æ±ãé£ããšããããšã¯ãçœã£ãœããšããããšãçºçããããšããããšããããããLv.10äºä»¶ãçããããšããããšããããã¯äž¡æ¹ãšãã«é»ãŸãã fact6: çœã£ãœããšããããšãçãã ; $hypothesis$ = ãæ»ãæããšããããšã§ã¯ãªããŠãœããœãLv.55äºä»¶ãèµ·ããããšããããšã¯äºå®ãšç°ãªã ; $proof$ = | fact6 -> int1: çœã£ãœããšããããšããŸãã¯ããããLv.10äºä»¶ããããã¯ã©ã¡ãããèµ·ãã; int1 & fact5 -> int2: æ±ãé£ããšããããšã¯èµ·ããªã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{C} -> ¬(¬{E} & {D}) fact2: {EC} -> ¬{P} fact3: ¬{EP} -> ¬(¬{U} & {GO}) fact4: {B} -> ¬{C} fact5: ({A} v {B}) -> ¬{C} fact6: {A} ; $hypothesis$ = ¬(¬{E} & {D}) ; $proof$ = | fact6 -> int1: ({A} v {B}); int1 & fact5 -> int2: ¬{C}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽããŽãLv.89ã¯ãããããããªã | ¬{D}{d} | fact1: ãããã®ã¿ãã¿ã«ã
Lv.73ãéãé£ããšããããã®ãŸã¡ããŸã«Lv.43ã¯æå°åãã fact2: ãã®ãŸã¡ããŸã«Lv.43ãæå°åãããšããããã®ãŽããŽãLv.89ã¯ãããããã fact3: ãã®ãœãªãœãLv.53ãæå°åããã°ãã®ãœãªãœãLv.53ã¯éãé£ã fact4: ãæãã¢ã³ã¹ã¿ãŒã¯æå°åãã fact5: ãã®ãœãªãœãLv.53ã¯èŠå¢ç¡ã fact6: ãã®ã·ã¡ãã·ãªLv.71ã¯æå°åãã fact7: ããä»®ã«ãã®ãœãªãœãLv.53ãèŠå¢ç¡ããšãããšãã®ã¿ãã¿ã«ã
Lv.73ã¯éãé£ã fact8: ããä»®ã«ãã®ã¿ãã¿ã«ã
Lv.73ãçãé£ããšããã°ãã®ãœãªãœãLv.53ã¯ãæã fact9: ããä»®ã«ãã®ãœãªãœãLv.53ãéãé£ããšãããšãã®ãŽããŽãLv.89ã¯ãããããããªãäžæ¹ã§èŠå¢ç¡ã | fact1: {B}{b} -> {C}{c} fact2: {C}{c} -> {D}{d} fact3: {C}{a} -> {B}{a} fact4: (x): {E}x -> {C}x fact5: {A}{a} fact6: {C}{is} fact7: {A}{a} -> {B}{b} fact8: {F}{b} -> {E}{a} fact9: {B}{a} -> (¬{D}{d} & {A}{d}) | [
"fact7 & fact5 -> int1: ãã®ã¿ãã¿ã«ã
Lv.73ã¯éãé£ã; int1 & fact1 -> int2: ãã®ãŸã¡ããŸã«Lv.43ã¯æå°åãã; int2 & fact2 -> hypothesis;"
] | [
"fact7 & fact5 -> int1: {B}{b}; int1 & fact1 -> int2: {C}{c}; int2 & fact2 -> hypothesis;"
] | ãã®ãŽããŽãLv.89ã¯ãããããããªã | ¬{D}{d} | [
"fact10 -> int3: ãããã®ãœãªãœãLv.53ããæããšãããããã¯æå°åãã;"
] | 8 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããã®ã¿ãã¿ã«ã
Lv.73ãéãé£ããšããããã®ãŸã¡ããŸã«Lv.43ã¯æå°åãã fact2: ãã®ãŸã¡ããŸã«Lv.43ãæå°åãããšããããã®ãŽããŽãLv.89ã¯ãããããã fact3: ãã®ãœãªãœãLv.53ãæå°åããã°ãã®ãœãªãœãLv.53ã¯éãé£ã fact4: ãæãã¢ã³ã¹ã¿ãŒã¯æå°åãã fact5: ãã®ãœãªãœãLv.53ã¯èŠå¢ç¡ã fact6: ãã®ã·ã¡ãã·ãªLv.71ã¯æå°åãã fact7: ããä»®ã«ãã®ãœãªãœãLv.53ãèŠå¢ç¡ããšãããšãã®ã¿ãã¿ã«ã
Lv.73ã¯éãé£ã fact8: ããä»®ã«ãã®ã¿ãã¿ã«ã
Lv.73ãçãé£ããšããã°ãã®ãœãªãœãLv.53ã¯ãæã fact9: ããä»®ã«ãã®ãœãªãœãLv.53ãéãé£ããšãããšãã®ãŽããŽãLv.89ã¯ãããããããªãäžæ¹ã§èŠå¢ç¡ã ; $hypothesis$ = ãã®ãŽããŽãLv.89ã¯ãããããããªã ; $proof$ = | fact7 & fact5 -> int1: ãã®ã¿ãã¿ã«ã
Lv.73ã¯éãé£ã; int1 & fact1 -> int2: ãã®ãŸã¡ããŸã«Lv.43ã¯æå°åãã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{b} -> {C}{c} fact2: {C}{c} -> {D}{d} fact3: {C}{a} -> {B}{a} fact4: (x): {E}x -> {C}x fact5: {A}{a} fact6: {C}{is} fact7: {A}{a} -> {B}{b} fact8: {F}{b} -> {E}{a} fact9: {B}{a} -> (¬{D}{d} & {A}{d}) ; $hypothesis$ = ¬{D}{d} ; $proof$ = | fact7 & fact5 -> int1: {B}{b}; int1 & fact1 -> int2: {C}{c}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã·ãã·ãLv.73ã¯å°ããããšããããšã¯æãç«ã€ | {D}{a} | fact1: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæããŠããŸãã«ããã¯ãªã¯ã fact2: ããã®ã·ãã·ãLv.73ã¯åã£ä»ãããšããããšã¯æ¬åœã§ãã fact3: ããä»®ã«ãã®ã·ãã·ãLv.73ãå®è¡ãæããŠåã£ä»ãã°ãã®ã·ãã·ãLv.73ã¯å°ãããªã | fact1: ({A}{a} & {B}{a}) fact2: {C}{a} fact3: ({A}{a} & {C}{a}) -> ¬{D}{a} | [
"fact1 -> int1: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæã; int1 & fact2 -> int2: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæããããã¯åã£ä»ã; int2 & fact3 -> hypothesis;"
] | [
"fact1 -> int1: {A}{a}; int1 & fact2 -> int2: ({A}{a} & {C}{a}); int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæããŠããŸãã«ããã¯ãªã¯ã fact2: ããã®ã·ãã·ãLv.73ã¯åã£ä»ãããšããããšã¯æ¬åœã§ãã fact3: ããä»®ã«ãã®ã·ãã·ãLv.73ãå®è¡ãæããŠåã£ä»ãã°ãã®ã·ãã·ãLv.73ã¯å°ãããªã ; $hypothesis$ = ããã®ã·ãã·ãLv.73ã¯å°ããããšããããšã¯æãç«ã€ ; $proof$ = | fact1 -> int1: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæã; int1 & fact2 -> int2: ãã®ã·ãã·ãLv.73ã¯å®è¡ãæããããã¯åã£ä»ã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: {C}{a} fact3: ({A}{a} & {C}{a}) -> ¬{D}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | fact1 -> int1: {A}{a}; int1 & fact2 -> int2: ({A}{a} & {C}{a}); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã«ã
ãã«ãLv.22ã¯ç ãã | {D}{a} | fact1: ãã®ãã«ã
ãã«ãLv.22ã¯çããã fact2: ãããã®ãã«ã
ãã«ãLv.22ãçããããšããããã®ãã«ã
ãã«ãLv.22ã¯å¬éãã fact3: ããããã®ãã«ã
ãã«ãLv.22ãåºããšããã°ãã®ãã«ã
ãã«ãLv.22ã¯ç ãã fact4: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯çããããã©å¬éããªããšãããç ãããšããããšã¯ãªã fact5: äœããã®ã¢ã³ã¹ã¿ãŒãäžãæããªãæ²¹ã£ãœã fact6: ä»®ã«ãã®ã·ãã·ã«ã
Lv.64ãç ãããªããã®ã·ãã·ã«ã
Lv.64ã¯åãé£ã fact7: ä»®ã«ãã®ãã«ã
ãã«ãLv.22ãå·ä»ãæããšããããã®ãã«ã
ãã«ãLv.22ã¯å¬éãã fact8: ãããããã®ãã«ã
ãã«ãLv.22ã¯å¬éããããšããããšã¯äºå®ã§ãããšããããåºãããšããããšã¯ç¢ºãã§ãã | fact1: {A}{a} fact2: {A}{a} -> {B}{a} fact3: {C}{a} -> {D}{a} fact4: (x): ({A}x & ¬{B}x) -> ¬{D}x fact5: (x): {AA}x -> {GM}x fact6: {D}{im} -> {BF}{im} fact7: {JI}{a} -> {B}{a} fact8: {B}{a} -> {C}{a} | [
"fact2 & fact1 -> int1: ãã®ãã«ã
ãã«ãLv.22ã¯å¬éãã; int1 & fact8 -> int2: ãã®ãã«ã
ãã«ãLv.22ã¯åºã; int2 & fact3 -> hypothesis;"
] | [
"fact2 & fact1 -> int1: {B}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact3 -> hypothesis;"
] | ä»®ã«ãã®ãã«ã
ãã«ãLv.22ãäžãæããšãããããã¯æ²¹ã£ãœã | {AA}{a} -> {GM}{a} | [
"fact9 -> hypothesis;"
] | 1 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãã®ãã«ã
ãã«ãLv.22ã¯çããã fact2: ãããã®ãã«ã
ãã«ãLv.22ãçããããšããããã®ãã«ã
ãã«ãLv.22ã¯å¬éãã fact3: ããããã®ãã«ã
ãã«ãLv.22ãåºããšããã°ãã®ãã«ã
ãã«ãLv.22ã¯ç ãã fact4: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯çããããã©å¬éããªããšãããç ãããšããããšã¯ãªã fact5: äœããã®ã¢ã³ã¹ã¿ãŒãäžãæããªãæ²¹ã£ãœã fact6: ä»®ã«ãã®ã·ãã·ã«ã
Lv.64ãç ãããªããã®ã·ãã·ã«ã
Lv.64ã¯åãé£ã fact7: ä»®ã«ãã®ãã«ã
ãã«ãLv.22ãå·ä»ãæããšããããã®ãã«ã
ãã«ãLv.22ã¯å¬éãã fact8: ãããããã®ãã«ã
ãã«ãLv.22ã¯å¬éããããšããããšã¯äºå®ã§ãããšããããåºãããšããããšã¯ç¢ºãã§ãã ; $hypothesis$ = ãã®ãã«ã
ãã«ãLv.22ã¯ç ãã ; $proof$ = | fact2 & fact1 -> int1: ãã®ãã«ã
ãã«ãLv.22ã¯å¬éãã; int1 & fact8 -> int2: ãã®ãã«ã
ãã«ãLv.22ã¯åºã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: {A}{a} -> {B}{a} fact3: {C}{a} -> {D}{a} fact4: (x): ({A}x & ¬{B}x) -> ¬{D}x fact5: (x): {AA}x -> {GM}x fact6: {D}{im} -> {BF}{im} fact7: {JI}{a} -> {B}{a} fact8: {B}{a} -> {C}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | fact2 & fact1 -> int1: {B}{a}; int1 & fact8 -> int2: {C}{a}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããªãããããã¯éçŒããããŸãã¯äž¡æ¹ãšãã§ãã | (¬{C}{b} v {D}{b}) | fact1: ä»®ã«ããã®ãŽã«ããŽãªLv.7ã¯äºãããããããåããªãããšããããšã¯æ£ãããªããªãã°ãããã¯çãæ·±ããªãããšããããšã¯ç¢ºãã§ãã fact2: ä»®ã«ãã®ãŽã«ããŽãªLv.7ãåãããšããã°ãã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããšããããšã¯ãªã fact3: ããããã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããªããšãããããã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããªããããã¯éçŒããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ã£ãŠãã fact4: ä»®ã«ãã®ã¿ãªã¿ã¡ãLv.79ã¯çãæ·±ããªãã°ãããã®ãŽã«ããŽãªLv.7ã¯ã ã ã£åºããªããŠããããã©ããªããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªãããšããããšã¯æãç«ã€ fact5: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ã ã ã£åºããªããŠãã©ããªããªãããšããããšã¯èª€ã£ãŠãããšãããšãã©ããªã fact6: ããä»®ã«ããã¢ã³ã¹ã¿ãŒããã©ããªããšãããšããã¯é¢ä¿æ·±ããªãããããã¯ããã¯éçŒããããããã¯ã©ã¡ããã§ãã fact7: ããä»®ã«ãã®ã¿ãªã¿ã¡ãLv.79ã¯ãã©ããªããšãããšããã®ãŽã«ããŽãªLv.7ã¯äºãããããã©ããã¯åãããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãªã fact8: ãã®ã¿ãªã¿ã¡ãLv.79ã¯ãã©ããªã | fact1: ¬({AA}{b} & ¬{AB}{b}) -> ¬{B}{b} fact2: {AB}{b} -> ¬{B}{b} fact3: ¬{B}{b} -> ¬(¬{C}{b} v {D}{b}) fact4: {B}{a} -> ¬(¬{E}{b} & ¬{A}{b}) fact5: (x): ¬(¬{E}x & ¬{A}x) -> {A}x fact6: (x): {A}x -> (¬{C}x v {D}x) fact7: {A}{a} -> ¬({AA}{b} & ¬{AB}{b}) fact8: {A}{a} | [
"fact7 & fact8 -> int1: ããã®ãŽã«ããŽãªLv.7ã¯äºããããåããªãããšããããšã¯åœã ; int1 & fact1 -> int2: ãã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããªã; int2 & fact3 -> hypothesis;"
] | [
"fact7 & fact8 -> int1: ¬({AA}{b} & ¬{AB}{b}); int1 & fact1 -> int2: ¬{B}{b}; int2 & fact3 -> hypothesis;"
] | ãã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããªãããããã¯éçŒããããŸãã¯äž¡æ¹ãšãã§ãã | (¬{C}{b} v {D}{b}) | [
"fact11 -> int3: ä»®ã«ãã®ãŽã«ããŽãªLv.7ããã©ããªããªãã°ãã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããšããããšã¯ãªããéçŒããããŸãã¯äž¡æ¹ã§ãã; fact9 -> int4: ããä»®ã«ããã®ãŽã«ããŽãªLv.7ã¯ã ã ã£åºããªãããã©ããªããªãããšããããšã¯æãç«ããªããªããã®ãŽã«ããŽãªLv.7ã¯ãã©ããªã;"
] | 5 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ããã®ãŽã«ããŽãªLv.7ã¯äºãããããããåããªãããšããããšã¯æ£ãããªããªãã°ãããã¯çãæ·±ããªãããšããããšã¯ç¢ºãã§ãã fact2: ä»®ã«ãã®ãŽã«ããŽãªLv.7ãåãããšããã°ãã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããšããããšã¯ãªã fact3: ããããã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããªããšãããããã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããªããããã¯éçŒããããŸãã¯äž¡æ¹ã§ããããšããããšã¯èª€ã£ãŠãã fact4: ä»®ã«ãã®ã¿ãªã¿ã¡ãLv.79ã¯çãæ·±ããªãã°ãããã®ãŽã«ããŽãªLv.7ã¯ã ã ã£åºããªããŠããããã©ããªããšããããšã¯ãªãããšããããšã¯äºå®ã§ãªãããšããããšã¯æãç«ã€ fact5: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ã ã ã£åºããªããŠãã©ããªããªãããšããããšã¯èª€ã£ãŠãããšãããšãã©ããªã fact6: ããä»®ã«ããã¢ã³ã¹ã¿ãŒããã©ããªããšãããšããã¯é¢ä¿æ·±ããªãããããã¯ããã¯éçŒããããããã¯ã©ã¡ããã§ãã fact7: ããä»®ã«ãã®ã¿ãªã¿ã¡ãLv.79ã¯ãã©ããªããšãããšããã®ãŽã«ããŽãªLv.7ã¯äºãããããã©ããã¯åãããšããããšã¯ãªãããšããããšã¯ç¢ºãã§ãªã fact8: ãã®ã¿ãªã¿ã¡ãLv.79ã¯ãã©ããªã ; $hypothesis$ = ãã®ãŽã«ããŽãªLv.7ã¯é¢ä¿æ·±ããªãããããã¯éçŒããããŸãã¯äž¡æ¹ãšãã§ãã ; $proof$ = | fact7 & fact8 -> int1: ããã®ãŽã«ããŽãªLv.7ã¯äºããããåããªãããšããããšã¯åœã ; int1 & fact1 -> int2: ãã®ãŽã«ããŽãªLv.7ã¯çãæ·±ããªã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA}{b} & ¬{AB}{b}) -> ¬{B}{b} fact2: {AB}{b} -> ¬{B}{b} fact3: ¬{B}{b} -> ¬(¬{C}{b} v {D}{b}) fact4: {B}{a} -> ¬(¬{E}{b} & ¬{A}{b}) fact5: (x): ¬(¬{E}x & ¬{A}x) -> {A}x fact6: (x): {A}x -> (¬{C}x v {D}x) fact7: {A}{a} -> ¬({AA}{b} & ¬{AB}{b}) fact8: {A}{a} ; $hypothesis$ = (¬{C}{b} v {D}{b}) ; $proof$ = | fact7 & fact8 -> int1: ¬({AA}{b} & ¬{AB}{b}); int1 & fact1 -> int2: ¬{B}{b}; int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | 匱ããšããããšãèµ·ãã | {C} | fact1: ãããèæ§åããããšããã³æ
ææ·±ããšããããšã©ã¡ãããèµ·ããããšããããšã¯äºå®ã§ãªããšãããæ
ææ·±ããšããããšã¯èµ·ããªã fact2: èæ§åããããšãèµ·ãã fact3: ããããLv.5äºä»¶ãèµ·ãã fact4: å§æããããšãçºçãã fact5: 匱ããšããããšã¯å§æããããšãšèæ§åããããšãèµ·ããã«é»æ¢ããã | fact1: ¬({B} & {CA}) -> ¬{CA} fact2: {B} fact3: {JH} fact4: {A} fact5: ({A} & {B}) -> ¬{C} | [
"fact4 & fact2 -> int1: å§æããããšãšèæ§åããããšã©ã¡ãããèµ·ãã; int1 & fact5 -> hypothesis;"
] | [
"fact4 & fact2 -> int1: ({A} & {B}); int1 & fact5 -> hypothesis;"
] | æ
ææ·±ããšããããšã¯çããªã | ¬{CA} | [] | 5 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããèæ§åããããšããã³æ
ææ·±ããšããããšã©ã¡ãããèµ·ããããšããããšã¯äºå®ã§ãªããšãããæ
ææ·±ããšããããšã¯èµ·ããªã fact2: èæ§åããããšãèµ·ãã fact3: ããããLv.5äºä»¶ãèµ·ãã fact4: å§æããããšãçºçãã fact5: 匱ããšããããšã¯å§æããããšãšèæ§åããããšãèµ·ããã«é»æ¢ããã ; $hypothesis$ = 匱ããšããããšãèµ·ãã ; $proof$ = | fact4 & fact2 -> int1: å§æããããšãšèæ§åããããšã©ã¡ãããèµ·ãã; int1 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({B} & {CA}) -> ¬{CA} fact2: {B} fact3: {JH} fact4: {A} fact5: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {C} ; $proof$ = | fact4 & fact2 -> int1: ({A} & {B}); int1 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | åé«ããšããããšã¯èµ·ãããªã | ¬{D} | fact1: åé«ããšããããšãçºçãããšããããšã¯åæããããšããã³æ°Žæº¶åããããšãèµ·ããã«é²ããã fact2: ã氎溶åããããšãçºçããããšããããšã¯çå®ã§ãã fact3: åé«ããšããããšããã³ããæããšããããšãçããã¯åæããããšã¯çããªããšããããšã«ç±æ¥ãã | fact1: ({B} & {C}) -> ¬{D} fact2: {C} fact3: ¬{B} -> ({D} & {A}) | [] | [] | åé«ããšããããšãçãã | {D} | [] | 6 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: åé«ããšããããšãçºçãããšããããšã¯åæããããšããã³æ°Žæº¶åããããšãèµ·ããã«é²ããã fact2: ã氎溶åããããšãçºçããããšããããšã¯çå®ã§ãã fact3: åé«ããšããããšããã³ããæããšããããšãçããã¯åæããããšã¯çããªããšããããšã«ç±æ¥ãã ; $hypothesis$ = åé«ããšããããšã¯èµ·ãããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({B} & {C}) -> ¬{D} fact2: {C} fact3: ¬{B} -> ({D} & {A}) ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã«ã·ã¡ãLv.60ã¯ããããšããããšã¯ãªã | ¬{D}{c} | fact1: ããããã®ã¿ã®ã¿ã«ãLv.36ãæ³ãŸããæã¡æããšããããã®ãœã¡ã
ãœãLv.14ã¯è¿œç©¶ãããšããããšã¯ãªã fact2: ãã®ããããLv.41ã¯ããããå ããŠé²åãæã fact3: ãã®ã¿ã®ã¿ã«ãLv.36ã¯æã¡æã fact4: ãã®ãœã¡ã
ãœãLv.14ã远究ããªããšããã°ãã®ã·ã«ã·ã¡ãLv.60ã¯ããã | fact1: ({A}{a} & {B}{a}) -> ¬{C}{b} fact2: ({D}{es} & {AL}{es}) fact3: {B}{a} fact4: ¬{C}{b} -> {D}{c} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããã®ã¿ã®ã¿ã«ãLv.36ãæ³ãŸããæã¡æããšããããã®ãœã¡ã
ãœãLv.14ã¯è¿œç©¶ãããšããããšã¯ãªã fact2: ãã®ããããLv.41ã¯ããããå ããŠé²åãæã fact3: ãã®ã¿ã®ã¿ã«ãLv.36ã¯æã¡æã fact4: ãã®ãœã¡ã
ãœãLv.14ã远究ããªããšããã°ãã®ã·ã«ã·ã¡ãLv.60ã¯ããã ; $hypothesis$ = ãã®ã·ã«ã·ã¡ãLv.60ã¯ããããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A}{a} & {B}{a}) -> ¬{C}{b} fact2: ({D}{es} & {AL}{es}) fact3: {B}{a} fact4: ¬{C}{b} -> {D}{c} ; $hypothesis$ = ¬{D}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ããLv.14äºä»¶ãšæ¡é²ããããšäž¡æ¹ãèµ·ãã | ({C} & {A}) | fact1: ãã®ããLv.14äºä»¶ãèµ·ãã fact2: ä»®ã«ãã®ããLv.14äºä»¶ãçºçãããšãããšãœã¡ããœãLv.22äºä»¶ãèµ·ãã fact3: ããœããœãLv.53äºä»¶ãçããªãããããã·ãã·ãLv.79äºä»¶ã¯çºçããããšããããšã¯äºå®ãšç°ãªããªã fact4: ããœã¡ããœãLv.22äºä»¶ã¯çºçããªãããšããããšã¯ããªãã¡ãLv.72äºä»¶ã«é»ãŸãã fact5: ãã®ããLv.14äºä»¶ããããã¯ããªãã¡ãLv.72äºä»¶ããããã¯äž¡æ¹ããœããœãLv.53äºä»¶ãçããªããšããããšã¯ãã£ããã§ãã fact6: ããªãã¡ãLv.72äºä»¶ãèµ·ãã | fact1: {C} fact2: {C} -> {ID} fact3: (¬{D} & {F}) fact4: {B} -> {ID} fact5: ¬{D} -> ({C} v {B}) fact6: {B} | [] | [] | ãœã¡ããœãLv.22äºä»¶ãšç· ãã£ãœããšããããšäž¡æ¹ãšããèµ·ãã | ({ID} & {AA}) | [
"fact8 -> int1: ãœããœãLv.53äºä»¶ã¯çºçããªã; fact9 & int1 -> int2: ãã®ããLv.14äºä»¶ããããã¯ããªãã¡ãLv.72äºä»¶ããŸãã¯äž¡æ¹ãçºçãã; int2 & fact7 & fact10 -> int3: ãœã¡ããœãLv.22äºä»¶ãçºçãã;"
] | 6 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ããLv.14äºä»¶ãèµ·ãã fact2: ä»®ã«ãã®ããLv.14äºä»¶ãçºçãããšãããšãœã¡ããœãLv.22äºä»¶ãèµ·ãã fact3: ããœããœãLv.53äºä»¶ãçããªãããããã·ãã·ãLv.79äºä»¶ã¯çºçããããšããããšã¯äºå®ãšç°ãªããªã fact4: ããœã¡ããœãLv.22äºä»¶ã¯çºçããªãããšããããšã¯ããªãã¡ãLv.72äºä»¶ã«é»ãŸãã fact5: ãã®ããLv.14äºä»¶ããããã¯ããªãã¡ãLv.72äºä»¶ããããã¯äž¡æ¹ããœããœãLv.53äºä»¶ãçããªããšããããšã¯ãã£ããã§ãã fact6: ããªãã¡ãLv.72äºä»¶ãèµ·ãã ; $hypothesis$ = ãã®ããLv.14äºä»¶ãšæ¡é²ããããšäž¡æ¹ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C} fact2: {C} -> {ID} fact3: (¬{D} & {F}) fact4: {B} -> {ID} fact5: ¬{D} -> ({C} v {B}) fact6: {B} ; $hypothesis$ = ({C} & {A}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ããªã | ¬{C}{b} | fact1: ãã®ãœããœãLv.23ã¯çžå¿ãã fact2: ããçžå¿ããããšããããšã¯æãç«ã€ãã¢ã³ã¹ã¿ãŒã¯ãã fact3: ä»®ã«çžå¿ããã¢ã³ã¹ã¿ãŒãæããšãããšãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ã fact4: ãã®ãœããœãLv.23ã¯æã fact5: ããä»®ã«ãããã¢ã³ã¹ã¿ãŒãæå
ãããã®äžããã¯æãããšããããšã¯ééãã ãšãããšæå
ããªã | fact1: {A}{a} fact2: (Ex): {A}x fact3: (x): ({A}x & {B}x) -> {C}{b} fact4: {B}{a} fact5: (x): ¬({C}x & {B}x) -> ¬{C}x | [
"fact1 & fact4 -> int1: ãã®ãœããœãLv.23ã¯çžå¿ãããŠãŸãæã; int1 -> int2: äœããã®ã¢ã³ã¹ã¿ãŒã¯çžå¿ãããæŽã«æã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact3 -> hypothesis;"
] | ãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ããªã | ¬{C}{b} | [
"fact6 -> int3: ãããããã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ããŠãŸãããã¯æãããšããããšã¯ééã£ãŠããã°ãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ããªã;"
] | 4 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãœããœãLv.23ã¯çžå¿ãã fact2: ããçžå¿ããããšããããšã¯æãç«ã€ãã¢ã³ã¹ã¿ãŒã¯ãã fact3: ä»®ã«çžå¿ããã¢ã³ã¹ã¿ãŒãæããšãããšãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ã fact4: ãã®ãœããœãLv.23ã¯æã fact5: ããä»®ã«ãããã¢ã³ã¹ã¿ãŒãæå
ãããã®äžããã¯æãããšããããšã¯ééãã ãšãããšæå
ããªã ; $hypothesis$ = ãã®ã¿ã«ãã¿ã«Lv.80ã¯æå
ããªã ; $proof$ = | fact1 & fact4 -> int1: ãã®ãœããœãLv.23ã¯çžå¿ãããŠãŸãæã; int1 -> int2: äœããã®ã¢ã³ã¹ã¿ãŒã¯çžå¿ãããæŽã«æã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: (Ex): {A}x fact3: (x): ({A}x & {B}x) -> {C}{b} fact4: {B}{a} fact5: (x): ¬({C}x & {B}x) -> ¬{C}x ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact1 & fact4 -> int1: ({A}{a} & {B}{a}); int1 -> int2: (Ex): ({A}x & {B}x); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.15ã¯å¥³ã
ãã | {D}{a} | fact1: ãã®ãœããœãLv.15ã¯éæ¢ãã fact2: ãã®ãœããœãLv.15ãå¿å°è¯ããŠãã€éèŠãããšããã°ãã®ãœããœãLv.15ã¯å¥³ã
ãããªã fact3: ä»®ã«ãã®ãœããœãLv.15ãéæ¢ãããšãããšãã®ãœããœãLv.15ã¯å¿å°è¯ã | fact1: {A}{a} fact2: ({B}{a} & {C}{a}) -> ¬{D}{a} fact3: {A}{a} -> {B}{a} | [
"fact3 & fact1 -> int1: ãã®ãœããœãLv.15ã¯å¿å°è¯ã;"
] | [
"fact3 & fact1 -> int1: {B}{a};"
] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãœããœãLv.15ã¯éæ¢ãã fact2: ãã®ãœããœãLv.15ãå¿å°è¯ããŠãã€éèŠãããšããã°ãã®ãœããœãLv.15ã¯å¥³ã
ãããªã fact3: ä»®ã«ãã®ãœããœãLv.15ãéæ¢ãããšãããšãã®ãœããœãLv.15ã¯å¿å°è¯ã ; $hypothesis$ = ãã®ãœããœãLv.15ã¯å¥³ã
ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} fact2: ({B}{a} & {C}{a}) -> ¬{D}{a} fact3: {A}{a} -> {B}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã«ãLv.26äºä»¶ã¯èµ·ãããªã | ¬{D} | fact1: ãã¡ããã¡ãLv.24äºä»¶ãèµ·ãã fact2: çãæããšããããšãçºçãããä¿¡ä»°æ·±ããšããããšãçãã fact3: ãããã«ãLv.26äºä»¶ã¯ã眰ãããšãèµ·ãããæŽã«ãã¡ããã¡ãLv.24äºä»¶ãçããããšããããšã«é»ãŸãã fact4: ãå¯ããšããããšã¯èµ·ãããªãäžæ¹ã§ãŸã«ããŸãLv.21äºä»¶ãçããããšããããšã¯èª€ã£ãŠããã°å¯ããšããããšãèµ·ãã fact5: 眰ãããšãšãŸã«ããŸãLv.21äºä»¶ã©ã¡ãããçãã fact6: ããããã«ãLv.26äºä»¶ãçºçãããããã眰ãããšãèµ·ããããšããããšã¯ãŸã«ããŸãLv.21äºä»¶ã¯èµ·ãããªããšããããšã«èµ·å ãã | fact1: {C} fact2: ({AG} & {DK}) fact3: ({A} & {C}) -> ¬{D} fact4: ¬(¬{AS} & {B}) -> {AS} fact5: ({A} & {B}) fact6: ¬{B} -> ({D} & {A}) | [
"fact5 -> int1: 眰ãããšãèµ·ãã; int1 & fact1 -> int2: 眰ãããšãçºçããããã¡ããã¡ãLv.24äºä»¶ãèµ·ãã; int2 & fact3 -> hypothesis;"
] | [
"fact5 -> int1: {A}; int1 & fact1 -> int2: ({A} & {C}); int2 & fact3 -> hypothesis;"
] | å¯ããšããããšãšã¿ãã¿ãLv.33äºä»¶ã©ã¡ãããèµ·ãã | ({AS} & {IS}) | [] | 4 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã¡ããã¡ãLv.24äºä»¶ãèµ·ãã fact2: çãæããšããããšãçºçãããä¿¡ä»°æ·±ããšããããšãçãã fact3: ãããã«ãLv.26äºä»¶ã¯ã眰ãããšãèµ·ãããæŽã«ãã¡ããã¡ãLv.24äºä»¶ãçããããšããããšã«é»ãŸãã fact4: ãå¯ããšããããšã¯èµ·ãããªãäžæ¹ã§ãŸã«ããŸãLv.21äºä»¶ãçããããšããããšã¯èª€ã£ãŠããã°å¯ããšããããšãèµ·ãã fact5: 眰ãããšãšãŸã«ããŸãLv.21äºä»¶ã©ã¡ãããçãã fact6: ããããã«ãLv.26äºä»¶ãçºçãããããã眰ãããšãèµ·ããããšããããšã¯ãŸã«ããŸãLv.21äºä»¶ã¯èµ·ãããªããšããããšã«èµ·å ãã ; $hypothesis$ = ãããã«ãLv.26äºä»¶ã¯èµ·ãããªã ; $proof$ = | fact5 -> int1: 眰ãããšãèµ·ãã; int1 & fact1 -> int2: 眰ãããšãçºçããããã¡ããã¡ãLv.24äºä»¶ãèµ·ãã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: ({AG} & {DK}) fact3: ({A} & {C}) -> ¬{D} fact4: ¬(¬{AS} & {B}) -> {AS} fact5: ({A} & {B}) fact6: ¬{B} -> ({D} & {A}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact5 -> int1: {A}; int1 & fact1 -> int2: ({A} & {C}); int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ããä»®ã«èµ·ããæããªããªããçšè¯ããŠããŸãã«ãªããããšããããšã¯åãªãã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã | ¬((Ex): ¬{A}x -> ¬({AA}x & {AB}x)) | fact1: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯èªãåããªããªããããã¯èžãããæŽã«ããã¯ã匱ãããšããããšã¯æãç«ããªã fact2: ãããã®ã¿ãã¿ãLv.48ã¯èµ·ããæããªããšãããšããã®ã¿ãã¿ãLv.48ã¯çšè¯ããæŽã«ãªããããšããããšã¯èª€ã£ãŠãã fact3: ãããä»®ã«èµ·ããæããšããã°ãçšè¯ããããã«ãªããããšããããšã¯åœã§ãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ä»®ã«ãã®ã¿ãã¿ãLv.48ã¯çŸšãŸãããšããããç¡ã£èŸãããããäžãé£ãããšããããšã¯åœã§ãã fact5: ããããæ¶å»ããªããšããã°ããç·çµãããé通ããããšããããšã¯ç¢ºãã ããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã | fact1: (x): ¬{HB}x -> ¬({CK}x & {BE}x) fact2: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact3: (Ex): {A}x -> ¬({AA}x & {AB}x) fact4: {CT}{aa} -> ¬({IU}{aa} & {HI}{aa}) fact5: (Ex): ¬{AT}x -> ¬({HD}x & {BC}x) | [
"fact2 -> hypothesis;"
] | [
"fact2 -> hypothesis;"
] | ãããä»®ã«èªãåããšããããšã¯ãªããšããããèžãããæŽã«ã匱ãããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{HB}x -> ¬({CK}x & {BE}x) | [
"fact6 -> int1: ãããã®ãã«ããªLv.42ã¯èªãåããšããããšã¯ãªããšããã°ããã®ãã«ããªLv.42ã¯èžããããŸãã匱ãããšããããšã¯æãç«ããªã; int1 -> hypothesis;"
] | 2 | 1 | 1 | 1 | 1 | 4 | 0 | 4 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãããªãããã®ã¢ã³ã¹ã¿ãŒã¯èªãåããªããªããããã¯èžãããæŽã«ããã¯ã匱ãããšããããšã¯æãç«ããªã fact2: ãããã®ã¿ãã¿ãLv.48ã¯èµ·ããæããªããšãããšããã®ã¿ãã¿ãLv.48ã¯çšè¯ããæŽã«ãªããããšããããšã¯èª€ã£ãŠãã fact3: ãããä»®ã«èµ·ããæããšããã°ãçšè¯ããããã«ãªããããšããããšã¯åœã§ãããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ä»®ã«ãã®ã¿ãã¿ãLv.48ã¯çŸšãŸãããšããããç¡ã£èŸãããããäžãé£ãããšããããšã¯åœã§ãã fact5: ããããæ¶å»ããªããšããã°ããç·çµãããé通ããããšããããšã¯ç¢ºãã ããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ããä»®ã«èµ·ããæããªããªããçšè¯ããŠããŸãã«ãªããããšããããšã¯åãªãã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æãç«ããªã ; $proof$ = | fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬{HB}x -> ¬({CK}x & {BE}x) fact2: ¬{A}{aa} -> ¬({AA}{aa} & {AB}{aa}) fact3: (Ex): {A}x -> ¬({AA}x & {AB}x) fact4: {CT}{aa} -> ¬({IU}{aa} & {HI}{aa}) fact5: (Ex): ¬{AT}x -> ¬({HD}x & {BC}x) ; $hypothesis$ = ¬((Ex): ¬{A}x -> ¬({AA}x & {AB}x)) ; $proof$ = | fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãäœããã®ã¢ã³ã¹ã¿ãŒã¯èŠãé£ããããã«åå±ããããšããããšã¯æ¬åœã§ãªã | ¬((Ex): ({B}x & {C}x)) | fact1: ããã®ãœã®ãœãLv.42ã¯æãããããšããããšã¯æãç«ã€ fact2: ãã®ã·ã®ã·ãLv.79ã¯èŠãé£ã fact3: ããã¢ã³ã¹ã¿ãŒã¯åå±ãã fact4: ãã®ãœã®ãœãLv.42ã¯åå±ãã fact5: ããããã®ãœã®ãœãLv.42ãåå±ããªããšããããã®ãœã«ã
ãœãLv.91ã¯åŸ¡ä»ãç³ããèŠãé£ã fact6: ãã®ãœã®ãœãLv.42ã¯è¶ã£ãœããããã«èéã fact7: ãã®ãœã®ãœãLv.42ã¯åŸ¡ä»ãç³ããæŽã«èŠãé£ã | fact1: {DB}{a} fact2: {B}{bi} fact3: (Ex): {C}x fact4: {C}{a} fact5: ¬{C}{a} -> ({A}{dh} & {B}{dh}) fact6: ({HM}{a} & {FB}{a}) fact7: ({A}{a} & {B}{a}) | [
"fact7 -> int1: ãã®ãœã®ãœãLv.42ã¯èŠãé£ã; int1 & fact4 -> int2: ãã®ãœã®ãœãLv.42ã¯èŠãé£ããŠããã«ããã¯åå±ãã; int2 -> hypothesis;"
] | [
"fact7 -> int1: {B}{a}; int1 & fact4 -> int2: ({B}{a} & {C}{a}); int2 -> hypothesis;"
] | ãã®ãœã«ã
ãœãLv.91ã¯åŸ¡ä»ãç³ã | {A}{dh} | [] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããã®ãœã®ãœãLv.42ã¯æãããããšããããšã¯æãç«ã€ fact2: ãã®ã·ã®ã·ãLv.79ã¯èŠãé£ã fact3: ããã¢ã³ã¹ã¿ãŒã¯åå±ãã fact4: ãã®ãœã®ãœãLv.42ã¯åå±ãã fact5: ããããã®ãœã®ãœãLv.42ãåå±ããªããšããããã®ãœã«ã
ãœãLv.91ã¯åŸ¡ä»ãç³ããèŠãé£ã fact6: ãã®ãœã®ãœãLv.42ã¯è¶ã£ãœããããã«èéã fact7: ãã®ãœã®ãœãLv.42ã¯åŸ¡ä»ãç³ããæŽã«èŠãé£ã ; $hypothesis$ = ãäœããã®ã¢ã³ã¹ã¿ãŒã¯èŠãé£ããããã«åå±ããããšããããšã¯æ¬åœã§ãªã ; $proof$ = | fact7 -> int1: ãã®ãœã®ãœãLv.42ã¯èŠãé£ã; int1 & fact4 -> int2: ãã®ãœã®ãœãLv.42ã¯èŠãé£ããŠããã«ããã¯åå±ãã; int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {DB}{a} fact2: {B}{bi} fact3: (Ex): {C}x fact4: {C}{a} fact5: ¬{C}{a} -> ({A}{dh} & {B}{dh}) fact6: ({HM}{a} & {FB}{a}) fact7: ({A}{a} & {B}{a}) ; $hypothesis$ = ¬((Ex): ({B}x & {C}x)) ; $proof$ = | fact7 -> int1: {B}{a}; int1 & fact4 -> int2: ({B}{a} & {C}{a}); int2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸã«ããŸãLv.84ã¯åŸ¡å¯ãã | {D}{a} | fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯åœŒããããªãããã®äžèŒãããªã fact2: ãããã®ãŽããŽãLv.65ã圌ãããäžæ¹ã§èŒãããªããªãã°ãã®ãŸã«ããŸãLv.84ã¯ç±ã
ã fact3: ä»®ã«ãã®ãŽããŽãLv.65ãç±ã
ãäžæ¹ã§åŸ¡å¯ãããšããããšã¯ãªããšããã°ãã®ãŸã«ããŸãLv.84ã¯èŒãã fact4: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯ããã°ã£ããããšããã°ãããã¯ç±ã
ããæŽã«ããã¯æåºãããªãããšããããšã¯åã fact5: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èŒãããšããããšã¯ãªããæŽã«åœŒããããªãããšããããšã¯æãç«ããªããšãããšç®ããªã fact6: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åŸ¡å¯ãããããã圌ããããªãããšããããšã¯ééãã§ãããšããã埡å¯ãããªã fact7: ä»®ã«ãã®ãŽããŽãLv.65ã圌ããããšããããšã¯ãªããŠãããèŒãããªããªããã®ãŸã«ããŸãLv.84ã¯ç±ã
ã fact8: ãããã®ãŸã«ããŸãLv.84ãç±ã
ããªãã°åŸ¡å¯ãã | fact1: (x): (¬{A}x & ¬{B}x) fact2: ({A}{aa} & ¬{B}{aa}) -> {C}{a} fact3: ({C}{aa} & ¬{D}{aa}) -> {B}{a} fact4: (x): {F}x -> ¬({C}x & ¬{E}x) fact5: (x): ¬(¬{B}x & ¬{A}x) -> ¬{AM}x fact6: (x): ¬({D}x & ¬{A}x) -> ¬{D}x fact7: (¬{A}{aa} & ¬{B}{aa}) -> {C}{a} fact8: {C}{a} -> {D}{a} | [
"fact1 -> int1: ãã®ãŽããŽãLv.65ã¯åœŒããããªããæŽã«èŒãããªã; int1 & fact7 -> int2: ãã®ãŸã«ããŸãLv.84ã¯ç±ã
ã; int2 & fact8 -> hypothesis;"
] | [
"fact1 -> int1: (¬{A}{aa} & ¬{B}{aa}); int1 & fact7 -> int2: {C}{a}; int2 & fact8 -> hypothesis;"
] | ãã®ãŸããŸãLv.33ã¯åŸ¡å¯ãããªããããŸãã«ç®ãããšããããšã¯ãªã | (¬{D}{ce} & ¬{AM}{ce}) | [
"fact9 -> int3: ããããã®ãŸããŸãLv.33ã¯èŒãããªãããã€åœŒããããªãããšããããšã¯æãç«ããªããšããã°ãã®ãŸããŸãLv.33ã¯ç®ããªã; fact10 -> int4: ãããã®ãŸã«ããŸãLv.84ã¯ããã°ã£ããããšãããšãç±ã
ããã©æåºãããªãããšããããšã¯æãç«ããªã;"
] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯åœŒããããªãããã®äžèŒãããªã fact2: ãããã®ãŽããŽãLv.65ã圌ãããäžæ¹ã§èŒãããªããªãã°ãã®ãŸã«ããŸãLv.84ã¯ç±ã
ã fact3: ä»®ã«ãã®ãŽããŽãLv.65ãç±ã
ãäžæ¹ã§åŸ¡å¯ãããšããããšã¯ãªããšããã°ãã®ãŸã«ããŸãLv.84ã¯èŒãã fact4: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯ããã°ã£ããããšããã°ãããã¯ç±ã
ããæŽã«ããã¯æåºãããªãããšããããšã¯åã fact5: ããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èŒãããšããããšã¯ãªããæŽã«åœŒããããªãããšããããšã¯æãç«ããªããšãããšç®ããªã fact6: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åŸ¡å¯ãããããã圌ããããªãããšããããšã¯ééãã§ãããšããã埡å¯ãããªã fact7: ä»®ã«ãã®ãŽããŽãLv.65ã圌ããããšããããšã¯ãªããŠãããèŒãããªããªããã®ãŸã«ããŸãLv.84ã¯ç±ã
ã fact8: ãããã®ãŸã«ããŸãLv.84ãç±ã
ããªãã°åŸ¡å¯ãã ; $hypothesis$ = ãã®ãŸã«ããŸãLv.84ã¯åŸ¡å¯ãã ; $proof$ = | fact1 -> int1: ãã®ãŽããŽãLv.65ã¯åœŒããããªããæŽã«èŒãããªã; int1 & fact7 -> int2: ãã®ãŸã«ããŸãLv.84ã¯ç±ã
ã; int2 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): (¬{A}x & ¬{B}x) fact2: ({A}{aa} & ¬{B}{aa}) -> {C}{a} fact3: ({C}{aa} & ¬{D}{aa}) -> {B}{a} fact4: (x): {F}x -> ¬({C}x & ¬{E}x) fact5: (x): ¬(¬{B}x & ¬{A}x) -> ¬{AM}x fact6: (x): ¬({D}x & ¬{A}x) -> ¬{D}x fact7: (¬{A}{aa} & ¬{B}{aa}) -> {C}{a} fact8: {C}{a} -> {D}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | fact1 -> int1: (¬{A}{aa} & ¬{B}{aa}); int1 & fact7 -> int2: {C}{a}; int2 & fact8 -> hypothesis; __PROVED__ |
0.3 | ãŸã«ããŸã«ãLv.65äºä»¶ãèµ·ãã | {C} | fact1: 軜ããšããããšãèµ·ãã fact2: ãçŸããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact3: ä»®ã«çŸããšããããšãšè»œããšããããšäž¡æ¹ãšããèµ·ãããšãããšãŸã«ããŸã«ãLv.65äºä»¶ã¯èµ·ããªã | fact1: {B} fact2: {A} fact3: ({A} & {B}) -> ¬{C} | [
"fact2 & fact1 -> int1: çŸããšããããšãèµ·ãããããŸãã«è»œããšããããšãèµ·ãã; int1 & fact3 -> hypothesis;"
] | [
"fact2 & fact1 -> int1: ({A} & {B}); int1 & fact3 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: 軜ããšããããšãèµ·ãã fact2: ãçŸããšããããšãèµ·ããããšããããšã¯æ¬åœã§ãã fact3: ä»®ã«çŸããšããããšãšè»œããšããããšäž¡æ¹ãšããèµ·ãããšãããšãŸã«ããŸã«ãLv.65äºä»¶ã¯èµ·ããªã ; $hypothesis$ = ãŸã«ããŸã«ãLv.65äºä»¶ãèµ·ãã ; $proof$ = | fact2 & fact1 -> int1: çŸããšããããšãèµ·ãããããŸãã«è»œããšããããšãèµ·ãã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} fact2: {A} fact3: ({A} & {B}) -> ¬{C} ; $hypothesis$ = {C} ; $proof$ = | fact2 & fact1 -> int1: ({A} & {B}); int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ã«ã¿ã«Lv.35ã¯æãããããã¯åãæ²ããã©ã¡ããã§ãã | ({D}{b} v {E}{b}) | fact1: ãã®ãŽã®ãŽã¡ãLv.86ãåæµ®äžãããšããã°ãã®ã·ã¡ã
ã·ãªLv.2ã¯èœå¹ã fact2: ãããã®ã·ã¡ã
ã·ãªLv.2ãèœå¹ããšãããšãã®ã¿ã«ã¿ã«Lv.35ã¯æã fact3: ãããã®ãŽã®ãŽã¡ãLv.86ãæããªããšããã°ãã®ãŽã®ãŽã¡ãLv.86ã¯èœå¹ããæž
ã fact4: ãã®ãŽã®ãŽã¡ãLv.86ã¯åæµ®äžããããŸãã¯æž
ããäž¡æ¹ãšãã | fact1: {A}{a} -> {C}{c} fact2: {C}{c} -> {D}{b} fact3: ¬{D}{a} -> ({C}{a} & {B}{a}) fact4: ({A}{a} v {B}{a}) | [] | [] | ãã®ã¿ãã¿ã«ãLv.9ã¯æ Œå¥œè¯ãããŸãã¯éå¥ããããããã¯äž¡æ¹ãšãã | ({DN}{p} v {IG}{p}) | [] | 6 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ãŽã®ãŽã¡ãLv.86ãåæµ®äžãããšããã°ãã®ã·ã¡ã
ã·ãªLv.2ã¯èœå¹ã fact2: ãããã®ã·ã¡ã
ã·ãªLv.2ãèœå¹ããšãããšãã®ã¿ã«ã¿ã«Lv.35ã¯æã fact3: ãããã®ãŽã®ãŽã¡ãLv.86ãæããªããšããã°ãã®ãŽã®ãŽã¡ãLv.86ã¯èœå¹ããæž
ã fact4: ãã®ãŽã®ãŽã¡ãLv.86ã¯åæµ®äžããããŸãã¯æž
ããäž¡æ¹ãšãã ; $hypothesis$ = ãã®ã¿ã«ã¿ã«Lv.35ã¯æãããããã¯åãæ²ããã©ã¡ããã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{a} -> {C}{c} fact2: {C}{c} -> {D}{b} fact3: ¬{D}{a} -> ({C}{a} & {B}{a}) fact4: ({A}{a} v {B}{a}) ; $hypothesis$ = ({D}{b} v {E}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã«ã
Lv.93ã¯ä»ãæã | {A}{a} | fact1: ããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ããããã匷å¶ä¹³åããªãããšããããšã¯æãç«ããªã fact2: ããã®ã¿ãã¿ãLv.81ã¯åæããªããã©åŒ·å¶ä¹³åããããšããããšã¯åœã fact3: ããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ãªããŠããã«åŒ·å¶ä¹³åããªãããšããããšã¯äºå®ãšç°ãªã fact4: ãããããã®ãŽããŽã«ãLv.1ã¯åŒ·å¶ä¹³åãããšããããšã¯ãªããŠãããèªçµŠåºæ¥ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãããã¯ä»ãæã fact5: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ããããããªããŠãã®äžããã¯èªçµŠåºæ¥ããšããããšã¯ãªãããšããããšã¯åã ãšãããããã¯ä»ãæã fact6: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯èªçµŠåºæ¥ãªããŠåŒ·å¶ä¹³åããªãããšããããšã¯èª€ã£ãŠãããšããã°ããã¯ããããã fact7: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãèªçµŠåºæ¥ããšããã°ããã¯ããããã fact8: ãããã®ãŽããŽã«ãLv.1ãããããããšããããã®ã¿ãã¿ã«ã
Lv.93ã¯ä»ãæã | fact1: ¬({AA}{aa} & ¬{AB}{aa}) fact2: ¬(¬{HD}{il} & {AB}{il}) fact3: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact4: ¬(¬{AB}{aa} & ¬{AA}{aa}) -> {A}{aa} fact5: (x): ¬(¬{B}x & ¬{AA}x) -> {A}x fact6: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact7: (x): {AA}x -> {B}x fact8: {B}{aa} -> {A}{a} | [
"fact6 -> int1: ãããããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ãªãã匷å¶ä¹³åããªãããšããããšã¯æãç«ããªãããšããããšã¯çå®ã ãšããã°ãã®ãŽããŽã«ãLv.1ã¯ããããã; int1 & fact3 -> int2: ãã®ãŽããŽã«ãLv.1ã¯ããããã; int2 & fact8 -> hypothesis;"
] | [
"fact6 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa}; int1 & fact3 -> int2: {B}{aa}; int2 & fact8 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | null | PROVED | null | $facts$ = fact1: ããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ããããã匷å¶ä¹³åããªãããšããããšã¯æãç«ããªã fact2: ããã®ã¿ãã¿ãLv.81ã¯åæããªããã©åŒ·å¶ä¹³åããããšããããšã¯åœã fact3: ããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ãªããŠããã«åŒ·å¶ä¹³åããªãããšããããšã¯äºå®ãšç°ãªã fact4: ãããããã®ãŽããŽã«ãLv.1ã¯åŒ·å¶ä¹³åãããšããããšã¯ãªããŠãããèªçµŠåºæ¥ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãããã¯ä»ãæã fact5: ããä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯ããããããªããŠãã®äžããã¯èªçµŠåºæ¥ããšããããšã¯ãªãããšããããšã¯åã ãšãããããã¯ä»ãæã fact6: ãäœããã®ã¢ã³ã¹ã¿ãŒã¯èªçµŠåºæ¥ãªããŠåŒ·å¶ä¹³åããªãããšããããšã¯èª€ã£ãŠãããšããã°ããã¯ããããã fact7: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒãèªçµŠåºæ¥ããšããã°ããã¯ããããã fact8: ãããã®ãŽããŽã«ãLv.1ãããããããšããããã®ã¿ãã¿ã«ã
Lv.93ã¯ä»ãæã ; $hypothesis$ = ãã®ã¿ãã¿ã«ã
Lv.93ã¯ä»ãæã ; $proof$ = | fact6 -> int1: ãããããã®ãŽããŽã«ãLv.1ã¯èªçµŠåºæ¥ãªãã匷å¶ä¹³åããªãããšããããšã¯æãç«ããªãããšããããšã¯çå®ã ãšããã°ãã®ãŽããŽã«ãLv.1ã¯ããããã; int1 & fact3 -> int2: ãã®ãŽããŽã«ãLv.1ã¯ããããã; int2 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({AA}{aa} & ¬{AB}{aa}) fact2: ¬(¬{HD}{il} & {AB}{il}) fact3: ¬(¬{AA}{aa} & ¬{AB}{aa}) fact4: ¬(¬{AB}{aa} & ¬{AA}{aa}) -> {A}{aa} fact5: (x): ¬(¬{B}x & ¬{AA}x) -> {A}x fact6: (x): ¬(¬{AA}x & ¬{AB}x) -> {B}x fact7: (x): {AA}x -> {B}x fact8: {B}{aa} -> {A}{a} ; $hypothesis$ = {A}{a} ; $proof$ = | fact6 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> {B}{aa}; int1 & fact3 -> int2: {B}{aa}; int2 & fact8 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŽããŽã«Lv.97ã¯é
èããŠåŸ¡è©³ããããšããããšã¯èª€ãã | ¬({B}{a} & {C}{a}) | fact1: ãã®ãŽããŽã«Lv.97ã¯å解ããé£ã fact2: ãããã®ãŸããŸãLv.43ã¯å解ããé£ããªããªãã°ããã®ãŽããŽã«Lv.97ã¯é
èãã埡詳ããããšããããšã¯åœã fact3: ããä»®ã«ãã®ãŽããŽã«Lv.97ãå解ããé£ããšãããšããã¯é
èã fact4: ãã®ãŸããŸãLv.43ã¯åŸ¡è©³ãããããã¯å解ããé£ã fact5: ããããã®ãŽããŽã«Lv.97ã埡詳ãããªããšããããã®ãŽã¡ããŽã¡ãLv.80ã¯åŸ¡è©³ãã fact6: ãã®ãŽããŽã«Lv.97ã¯åŸ¡è©³ãã | fact1: {A}{a} fact2: ¬{A}{b} -> ¬({B}{a} & {C}{a}) fact3: {A}{a} -> {B}{a} fact4: ({C}{b} & {A}{b}) fact5: ¬{C}{a} -> {C}{s} fact6: {C}{a} | [
"fact3 & fact1 -> int1: ããã®ãŽããŽã«Lv.97ã¯é
èãããšããããšã¯æ¬åœã ; int1 & fact6 -> hypothesis;"
] | [
"fact3 & fact1 -> int1: {B}{a}; int1 & fact6 -> hypothesis;"
] | ãã®ãŽã¡ããŽã¡ãLv.80ã¯åŸ¡è©³ãã | {C}{s} | [
"fact8 -> int2: ãã®ãŸããŸãLv.43ã¯åŸ¡è©³ãã;"
] | 6 | 2 | 2 | 2 | 2 | 3 | 0 | 3 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽããŽã«Lv.97ã¯å解ããé£ã fact2: ãããã®ãŸããŸãLv.43ã¯å解ããé£ããªããªãã°ããã®ãŽããŽã«Lv.97ã¯é
èãã埡詳ããããšããããšã¯åœã fact3: ããä»®ã«ãã®ãŽããŽã«Lv.97ãå解ããé£ããšãããšããã¯é
èã fact4: ãã®ãŸããŸãLv.43ã¯åŸ¡è©³ãããããã¯å解ããé£ã fact5: ããããã®ãŽããŽã«Lv.97ã埡詳ãããªããšããããã®ãŽã¡ããŽã¡ãLv.80ã¯åŸ¡è©³ãã fact6: ãã®ãŽããŽã«Lv.97ã¯åŸ¡è©³ãã ; $hypothesis$ = ããã®ãŽããŽã«Lv.97ã¯é
èããŠåŸ¡è©³ããããšããããšã¯èª€ãã ; $proof$ = | fact3 & fact1 -> int1: ããã®ãŽããŽã«Lv.97ã¯é
èãããšããããšã¯æ¬åœã ; int1 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: ¬{A}{b} -> ¬({B}{a} & {C}{a}) fact3: {A}{a} -> {B}{a} fact4: ({C}{b} & {A}{b}) fact5: ¬{C}{a} -> {C}{s} fact6: {C}{a} ; $hypothesis$ = ¬({B}{a} & {C}{a}) ; $proof$ = | fact3 & fact1 -> int1: {B}{a}; int1 & fact6 -> hypothesis; __DISPROVED__ |