version
stringclasses 1
value | hypothesis
stringlengths 9
71
| hypothesis_formula
stringlengths 3
36
| facts
stringlengths 19
572
| facts_formula
stringlengths 13
324
| proofs
sequencelengths 0
1
| proofs_formula
sequencelengths 0
1
| negative_hypothesis
stringlengths 9
87
â | negative_hypothesis_formula
stringlengths 3
36
â | negative_proofs
sequencelengths 0
1
| negative_original_tree_depth
int64 1
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
630
| proof_serial
stringlengths 11
199
| prompt_serial_formula
stringlengths 61
373
| proof_serial_formula
stringlengths 11
141
|
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.3 | å£è«ããããšããã³ãã¡ãããLv.32äºä»¶ãçãã | ({D} & {C}) | fact1: ä»®ã«ããœããœãLv.23äºä»¶ã¯çºçãããã·ãã·ãªLv.91äºä»¶ã¯çããªãããšããããšã¯äºå®ãšç°ãªãã°ã·ãã·ãªLv.91äºä»¶ãçãã fact2: ä»®ã«ã·ãã·ãªLv.91äºä»¶ãçºçããã°ãã¡ãããLv.32äºä»¶ãèµ·ããäžæ¹ã§å£è«ããããšã¯çããªã fact3: ããããLv.97äºä»¶ãšçºçãé£ããšããããšäž¡æ¹ãèµ·ãã fact4: çºçãé£ããšããããšã¯èµ·ãããªããšããããšã¯ãããããLv.21äºä»¶ããã³ããããLv.97äºä»¶ãèµ·ããããšããããšãæã fact5: å£è«ããããšãçãã fact6: çºçãé£ããšããããšãèµ·ãã | fact1: ¬({G} & ¬{E}) -> {E} fact2: {E} -> ({C} & ¬{D}) fact3: ({A} & {B}) fact4: ¬{B} -> ({BQ} & {A}) fact5: {D} fact6: {B} | [
"fact3 -> int1: ããããLv.97äºä»¶ãçºçãã;"
] | [
"fact3 -> int1: {A};"
] | ããããLv.21äºä»¶ãèµ·ãã | {BQ} | [] | 8 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ããœããœãLv.23äºä»¶ã¯çºçãããã·ãã·ãªLv.91äºä»¶ã¯çããªãããšããããšã¯äºå®ãšç°ãªãã°ã·ãã·ãªLv.91äºä»¶ãçãã fact2: ä»®ã«ã·ãã·ãªLv.91äºä»¶ãçºçããã°ãã¡ãããLv.32äºä»¶ãèµ·ããäžæ¹ã§å£è«ããããšã¯çããªã fact3: ããããLv.97äºä»¶ãšçºçãé£ããšããããšäž¡æ¹ãèµ·ãã fact4: çºçãé£ããšããããšã¯èµ·ãããªããšããããšã¯ãããããLv.21äºä»¶ããã³ããããLv.97äºä»¶ãèµ·ããããšããããšãæã fact5: å£è«ããããšãçãã fact6: çºçãé£ããšããããšãèµ·ãã ; $hypothesis$ = å£è«ããããšããã³ãã¡ãããLv.32äºä»¶ãçãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({G} & ¬{E}) -> {E} fact2: {E} -> ({C} & ¬{D}) fact3: ({A} & {B}) fact4: ¬{B} -> ({BQ} & {A}) fact5: {D} fact6: {B} ; $hypothesis$ = ({D} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ã«ãLv.48ã¯éã©ã | {B}{a} | fact1: 埡å®ãã¢ã³ã¹ã¿ãŒã¯è²æãã fact2: ãã®ãŸã«ããŸã«ã
Lv.92ã¯åŸ¡å®ã fact3: ããä»®ã«ãã®ãŸã«ããŸã«ã
Lv.92ã埡å®ããšããã°ããã¯è²æãã fact4: ããä»®ã«ãã®ãŸã«ããŸã«ã
Lv.92ãè²æããããã©ééãæããªããªãã°ãã®ã·ãã·ã«ãLv.48ã¯éã©ããªã fact5: ãã®ã·ãã·ã«ãLv.48ã¯è²æãã fact6: ããããšããã¢ã³ã¹ã¿ãŒã埡å®ããªãã°è²æããããããééãæããªã fact7: éã©ããŠèç©ããæãã¢ã³ã¹ã¿ãŒã¯ãã fact8: ããã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããšããããšã¯æãç«ã€ | fact1: (x): {A}x -> {AA}x fact2: {A}{aa} fact3: {A}{aa} -> {AA}{aa} fact4: ({AA}{aa} & ¬{AB}{aa}) -> ¬{B}{a} fact5: {AA}{a} fact6: (x): {A}x -> ({AA}x & ¬{AB}x) fact7: (Ex): ({B}x & {E}x) fact8: {AA}{aa} | [
"fact6 -> int1: ãã®ãŸã«ããŸã«ã
Lv.92ã¯åŸ¡å®ããšãããããã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããããééãæããªãããšããããšã¯æãç«ã€; int1 & fact2 -> int2: ãã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããããééãæããªã; int2 & fact4 -> hypothesis;"
] | [
"fact6 -> int1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: ({AA}{aa} & ¬{AB}{aa}); int2 & fact4 -> hypothesis;"
] | ãã®ã·ãã·ã®Lv.38ã¯åŸ¡å®ããªã | ¬{A}{ib} | [] | 5 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: 埡å®ãã¢ã³ã¹ã¿ãŒã¯è²æãã fact2: ãã®ãŸã«ããŸã«ã
Lv.92ã¯åŸ¡å®ã fact3: ããä»®ã«ãã®ãŸã«ããŸã«ã
Lv.92ã埡å®ããšããã°ããã¯è²æãã fact4: ããä»®ã«ãã®ãŸã«ããŸã«ã
Lv.92ãè²æããããã©ééãæããªããªãã°ãã®ã·ãã·ã«ãLv.48ã¯éã©ããªã fact5: ãã®ã·ãã·ã«ãLv.48ã¯è²æãã fact6: ããããšããã¢ã³ã¹ã¿ãŒã埡å®ããªãã°è²æããããããééãæããªã fact7: éã©ããŠèç©ããæãã¢ã³ã¹ã¿ãŒã¯ãã fact8: ããã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ã·ãã·ã«ãLv.48ã¯éã©ã ; $proof$ = | fact6 -> int1: ãã®ãŸã«ããŸã«ã
Lv.92ã¯åŸ¡å®ããšãããããã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããããééãæããªãããšããããšã¯æãç«ã€; int1 & fact2 -> int2: ãã®ãŸã«ããŸã«ã
Lv.92ã¯è²æããããããééãæããªã; int2 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): {A}x -> {AA}x fact2: {A}{aa} fact3: {A}{aa} -> {AA}{aa} fact4: ({AA}{aa} & ¬{AB}{aa}) -> ¬{B}{a} fact5: {AA}{a} fact6: (x): {A}x -> ({AA}x & ¬{AB}x) fact7: (Ex): ({B}x & {E}x) fact8: {AA}{aa} ; $hypothesis$ = {B}{a} ; $proof$ = | fact6 -> int1: {A}{aa} -> ({AA}{aa} & ¬{AB}{aa}); int1 & fact2 -> int2: ({AA}{aa} & ¬{AB}{aa}); int2 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŸããŸãLv.19ã¯çžåãããšããããšã¯æ¬åœã | {A}{a} | fact1: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒãè¬èããªããªãããã¯çžåããªã fact2: ããããã¢ã³ã¹ã¿ãŒã¯çžåã | fact1: (x): ¬{B}x -> ¬{A}x fact2: (x): {A}x | [
"fact2 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯çžåã; int1 -> hypothesis;"
] | [
"fact2 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã®ãŸããŸãLv.19ã¯çžåããªã | ¬{A}{a} | [
"fact3 -> int2: ãããã®ãŸããŸãLv.19ãè¬èããšããããšã¯ãªããšããããã®ãŸããŸãLv.19ã¯çžåããªã;"
] | 4 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãšããã¢ã³ã¹ã¿ãŒãè¬èããªããªãããã¯çžåããªã fact2: ããããã¢ã³ã¹ã¿ãŒã¯çžåã ; $hypothesis$ = ããã®ãŸããŸãLv.19ã¯çžåãããšããããšã¯æ¬åœã ; $proof$ = | fact2 -> int1: ããããã¢ã³ã¹ã¿ãŒã¯çžåã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{B}x -> ¬{A}x fact2: (x): {A}x ; $hypothesis$ = {A}{a} ; $proof$ = | fact2 -> int1: (x): {A}x; int1 -> hypothesis; __PROVED__ |
0.3 | ãã¿ã®ã¿ã¡ãLv.16äºä»¶ãçããªããŠæã¡æ®ããããšã¯çããªãããšããããšã¯æãç«ããªã | ¬(¬{B} & ¬{AA}) | fact1: ãããŸããŸãLv.44äºä»¶ãèµ·ãããªãæã¡æ®ããããšã¯èµ·ãããªãããœã«ã
ãœã«ãLv.77äºä»¶ãçãã fact2: ãã¿ã®ã¿ã¡ãLv.16äºä»¶ã¯çºçããªãããšããããšã¯ç¢ºãã | fact1: {A} -> (¬{AA} & {AB}) fact2: ¬{B} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããŸããŸãLv.44äºä»¶ãèµ·ãããªãæã¡æ®ããããšã¯èµ·ãããªãããœã«ã
ãœã«ãLv.77äºä»¶ãçãã fact2: ãã¿ã®ã¿ã¡ãLv.16äºä»¶ã¯çºçããªãããšããããšã¯ç¢ºãã ; $hypothesis$ = ãã¿ã®ã¿ã¡ãLv.16äºä»¶ãçããªããŠæã¡æ®ããããšã¯çããªãããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A} -> (¬{AA} & {AB}) fact2: ¬{B} ; $hypothesis$ = ¬(¬{B} & ¬{AA}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽããŽãªLv.51ã¯ä»æç¡ããªã | ¬{C}{b} | fact1: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãã°ããã fact2: ããããã®ãŽããŽãªLv.51ãè¡ããããšãããšãã®ãŽããŽãªLv.51ã¯çã£æã fact3: ããä»®ã«ãã®ã·ãã·ã¡ãLv.34ãå¯ããšããããšã¯ãªããã©ãã£ããªããªããã®ãŽããŽãªLv.51ã¯è¡ããã fact4: ãã®ã·ãã·ã¡ãLv.34ã¯ãã£ããªããªã fact5: ãã®ã·ãã·ã¡ãLv.34ã¯å¯ããªããŠå ããŠãã£ããªããªã fact6: ããä»®ã«ãã®ãŽããŽãªLv.51ãçã£æããªãã°ããã¯ä»æç¡ã fact7: ãã®ã·ãã·ã¡ãLv.34ã¯ä»æç¡ã | fact1: (Ex): {E}x fact2: {B}{b} -> {A}{b} fact3: (¬{AA}{a} & {AB}{a}) -> {B}{b} fact4: ¬{AB}{a} fact5: (¬{AA}{a} & ¬{AB}{a}) fact6: {A}{b} -> {C}{b} fact7: {C}{a} | [] | [] | ãã®ã·ã¡ãã·ã«ãLv.61ã¯ä»æç¡ã | {C}{it} | [] | 5 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ãã°ããã fact2: ããããã®ãŽããŽãªLv.51ãè¡ããããšãããšãã®ãŽããŽãªLv.51ã¯çã£æã fact3: ããä»®ã«ãã®ã·ãã·ã¡ãLv.34ãå¯ããšããããšã¯ãªããã©ãã£ããªããªããã®ãŽããŽãªLv.51ã¯è¡ããã fact4: ãã®ã·ãã·ã¡ãLv.34ã¯ãã£ããªããªã fact5: ãã®ã·ãã·ã¡ãLv.34ã¯å¯ããªããŠå ããŠãã£ããªããªã fact6: ããä»®ã«ãã®ãŽããŽãªLv.51ãçã£æããªãã°ããã¯ä»æç¡ã fact7: ãã®ã·ãã·ã¡ãLv.34ã¯ä»æç¡ã ; $hypothesis$ = ãã®ãŽããŽãªLv.51ã¯ä»æç¡ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (Ex): {E}x fact2: {B}{b} -> {A}{b} fact3: (¬{AA}{a} & {AB}{a}) -> {B}{b} fact4: ¬{AB}{a} fact5: (¬{AA}{a} & ¬{AB}{a}) fact6: {A}{b} -> {C}{b} fact7: {C}{a} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶ãèµ·ãã | {C} | fact1: ä»®ã«ã·ãã·ãªLv.42äºä»¶ã¯çºçããªããšããã°ãçµåãæããšããããšããã³ãœããœã«Lv.61äºä»¶ãçããããšããããšã¯ç¢ºãã§ãªã fact2: ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶ã¯ãã·ãã·ã«Lv.1äºä»¶ããã³ãœããœã«Lv.61äºä»¶ãçããããšããããšã«é»æ¢ããã fact3: ããä»®ã«ãœããœã«Lv.61äºä»¶ã¯çããªããªãã°ã·ãã·ã«Lv.1äºä»¶ããã³ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶äž¡æ¹ãšããçãã fact4: ã·ãã·ã«Lv.1äºä»¶ãçºçãã fact5: ãããããäžãé£ããšããããšãèµ·ãããå ããŠã·ãã·ã«Lv.1äºä»¶ãèµ·ããããšããããšã¯æ¬åœã§ãªãããšããããšã¯äºå®ãªãã°äžãé£ããšããããšã¯èµ·ãããªã fact6: ãçµåãæããšããããšãèµ·ãããããŸãã«ãœããœã«Lv.61äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãããªããœããœã«Lv.61äºä»¶ã¯çºçããªã fact7: ãœããœã«Lv.61äºä»¶ãèµ·ãã | fact1: ¬{E} -> ¬({D} & {B}) fact2: ({A} & {B}) -> ¬{C} fact3: ¬{B} -> ({A} & {C}) fact4: {A} fact5: ¬({FI} & {A}) -> ¬{FI} fact6: ¬({D} & {B}) -> ¬{B} fact7: {B} | [
"fact4 & fact7 -> int1: ã·ãã·ã«Lv.1äºä»¶ãèµ·ããããœããœã«Lv.61äºä»¶ãèµ·ãã; int1 & fact2 -> hypothesis;"
] | [
"fact4 & fact7 -> int1: ({A} & {B}); int1 & fact2 -> hypothesis;"
] | ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶ãèµ·ãã | {C} | [] | 8 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ã·ãã·ãªLv.42äºä»¶ã¯çºçããªããšããã°ãçµåãæããšããããšããã³ãœããœã«Lv.61äºä»¶ãçããããšããããšã¯ç¢ºãã§ãªã fact2: ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶ã¯ãã·ãã·ã«Lv.1äºä»¶ããã³ãœããœã«Lv.61äºä»¶ãçããããšããããšã«é»æ¢ããã fact3: ããä»®ã«ãœããœã«Lv.61äºä»¶ã¯çããªããªãã°ã·ãã·ã«Lv.1äºä»¶ããã³ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶äž¡æ¹ãšããçãã fact4: ã·ãã·ã«Lv.1äºä»¶ãçºçãã fact5: ãããããäžãé£ããšããããšãèµ·ãããå ããŠã·ãã·ã«Lv.1äºä»¶ãèµ·ããããšããããšã¯æ¬åœã§ãªãããšããããšã¯äºå®ãªãã°äžãé£ããšããããšã¯èµ·ãããªã fact6: ãçµåãæããšããããšãèµ·ãããããŸãã«ãœããœã«Lv.61äºä»¶ãèµ·ããããšããããšã¯ééã£ãŠãããªããœããœã«Lv.61äºä»¶ã¯çºçããªã fact7: ãœããœã«Lv.61äºä»¶ãèµ·ãã ; $hypothesis$ = ã¿ã¡ãã¿ã¡ã
Lv.69äºä»¶ãèµ·ãã ; $proof$ = | fact4 & fact7 -> int1: ã·ãã·ã«Lv.1äºä»¶ãèµ·ããããœããœã«Lv.61äºä»¶ãèµ·ãã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{E} -> ¬({D} & {B}) fact2: ({A} & {B}) -> ¬{C} fact3: ¬{B} -> ({A} & {C}) fact4: {A} fact5: ¬({FI} & {A}) -> ¬{FI} fact6: ¬({D} & {B}) -> ¬{B} fact7: {B} ; $hypothesis$ = {C} ; $proof$ = | fact4 & fact7 -> int1: ({A} & {B}); int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããœã¡ããœãLv.35äºä»¶ãèµ·ãããªãäžæ¹ã§ãŽã«ããŽãLv.15äºä»¶ã¯çºçããããšããããšã¯æãç«ããªã | ¬(¬{C} & {B}) | fact1: ãããœã¡ããœãLv.35äºä»¶ã¯çããªããŠãŽã«ããŽãLv.15äºä»¶ã¯çºçããããšããããšã¯æãç«ã€ããšããããšã¯åé¡ããããšã¯çããªããšããããšã«ç±æ¥ãã fact2: ããä»®ã«èãåŸãããšã¯çºçããªããšãããããœã¡ããœãLv.35äºä»¶ã§ã¯ãªããŠãŽã«ããŽãLv.15äºä»¶ãçºçããããšããããšã¯åœã§ãã fact3: ããä»®ã«èãåŸãããšãçãããªããåé¡ããããšã¯çºçããªããããã«åŠäœããããšããããšã¯çããªãããšããããšã¯çå®ã§ãã fact4: ããä»®ã«ããŽããŽãªLv.89äºä»¶ãšæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯æãç«ããªããšãããšèãåŸãããšã¯çºçããªã fact5: èãåŸãããšãèµ·ãã | fact1: ¬{AA} -> (¬{C} & {B}) fact2: ¬{A} -> ¬(¬{C} & {B}) fact3: {A} -> (¬{AA} & ¬{AB}) fact4: ¬({D} & {E}) -> ¬{A} fact5: {A} | [
"fact3 & fact5 -> int1: åé¡ããããšã¯èµ·ããªããŠåŠäœããããšããããšã¯çºçããªã; int1 -> int2: åé¡ããããšã¯çããªã; int2 & fact1 -> hypothesis;"
] | [
"fact3 & fact5 -> int1: (¬{AA} & ¬{AB}); int1 -> int2: ¬{AA}; int2 & fact1 -> hypothesis;"
] | ããœã¡ããœãLv.35äºä»¶ãèµ·ãããªãäžæ¹ã§ãŽã«ããŽãLv.15äºä»¶ã¯çºçããããšããããšã¯æãç«ããªã | ¬(¬{C} & {B}) | [] | 7 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããœã¡ããœãLv.35äºä»¶ã¯çããªããŠãŽã«ããŽãLv.15äºä»¶ã¯çºçããããšããããšã¯æãç«ã€ããšããããšã¯åé¡ããããšã¯çããªããšããããšã«ç±æ¥ãã fact2: ããä»®ã«èãåŸãããšã¯çºçããªããšãããããœã¡ããœãLv.35äºä»¶ã§ã¯ãªããŠãŽã«ããŽãLv.15äºä»¶ãçºçããããšããããšã¯åœã§ãã fact3: ããä»®ã«èãåŸãããšãçãããªããåé¡ããããšã¯çºçããªããããã«åŠäœããããšããããšã¯çããªãããšããããšã¯çå®ã§ãã fact4: ããä»®ã«ããŽããŽãªLv.89äºä»¶ãšæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯æãç«ããªããšãããšèãåŸãããšã¯çºçããªã fact5: èãåŸãããšãèµ·ãã ; $hypothesis$ = ããœã¡ããœãLv.35äºä»¶ãèµ·ãããªãäžæ¹ã§ãŽã«ããŽãLv.15äºä»¶ã¯çºçããããšããããšã¯æãç«ããªã ; $proof$ = | fact3 & fact5 -> int1: åé¡ããããšã¯èµ·ããªããŠåŠäœããããšããããšã¯çºçããªã; int1 -> int2: åé¡ããããšã¯çããªã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{AA} -> (¬{C} & {B}) fact2: ¬{A} -> ¬(¬{C} & {B}) fact3: {A} -> (¬{AA} & ¬{AB}) fact4: ¬({D} & {E}) -> ¬{A} fact5: {A} ; $hypothesis$ = ¬(¬{C} & {B}) ; $proof$ = | fact3 & fact5 -> int1: (¬{AA} & ¬{AB}); int1 -> int2: ¬{AA}; int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœããœãLv.99ã¯å°ã¢ããŸãããªã | ¬{C}{c} | fact1: ããä»®ã«ãã®ã¿ã«ãã¿ãLv.15ãããã£ããããšããããã®ãœããœãLv.99ã¯æã¡åœãŠã fact2: ããã®ãããã¡ã
Lv.92ã¯é¢æ ãããã©æ ããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact3: ããä»®ã«ããã®ãããã¡ã
Lv.92ã¯é¢æ ããäžæ¹ã§æ ãããªãããšããããšã¯ééãã ãšããã°ãã®ã¿ã«ãã¿ãLv.15ã¯ããã£ããã fact4: ãããããã®ãœããœãLv.99ã¯æã¡åœãŠãããšããããšã¯æãç«ã€ãšããã°ãã®ãœããœãLv.99ã¯å°ã¢ããŸããã fact5: ããã®ãããã¡ã
Lv.92ã¯é¢æ ããããŸãæ ãããšããããšã¯äºå®ãšç°ãªã | fact1: {B}{b} -> {A}{c} fact2: ¬({AA}{a} & ¬{AB}{a}) fact3: ¬({AA}{a} & ¬{AB}{a}) -> {B}{b} fact4: {A}{c} -> {C}{c} fact5: ¬({AA}{a} & {AB}{a}) | [
"fact3 & fact2 -> int1: ããã®ã¿ã«ãã¿ãLv.15ã¯ããã£ãããããšããããšã¯èª€ã£ãŠããªã; int1 & fact1 -> int2: ãã®ãœããœãLv.99ã¯æã¡åœãŠã; int2 & fact4 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: {B}{b}; int1 & fact1 -> int2: {A}{c}; int2 & fact4 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããä»®ã«ãã®ã¿ã«ãã¿ãLv.15ãããã£ããããšããããã®ãœããœãLv.99ã¯æã¡åœãŠã fact2: ããã®ãããã¡ã
Lv.92ã¯é¢æ ãããã©æ ããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact3: ããä»®ã«ããã®ãããã¡ã
Lv.92ã¯é¢æ ããäžæ¹ã§æ ãããªãããšããããšã¯ééãã ãšããã°ãã®ã¿ã«ãã¿ãLv.15ã¯ããã£ããã fact4: ãããããã®ãœããœãLv.99ã¯æã¡åœãŠãããšããããšã¯æãç«ã€ãšããã°ãã®ãœããœãLv.99ã¯å°ã¢ããŸããã fact5: ããã®ãããã¡ã
Lv.92ã¯é¢æ ããããŸãæ ãããšããããšã¯äºå®ãšç°ãªã ; $hypothesis$ = ãã®ãœããœãLv.99ã¯å°ã¢ããŸãããªã ; $proof$ = | fact3 & fact2 -> int1: ããã®ã¿ã«ãã¿ãLv.15ã¯ããã£ãããããšããããšã¯èª€ã£ãŠããªã; int1 & fact1 -> int2: ãã®ãœããœãLv.99ã¯æã¡åœãŠã; int2 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{b} -> {A}{c} fact2: ¬({AA}{a} & ¬{AB}{a}) fact3: ¬({AA}{a} & ¬{AB}{a}) -> {B}{b} fact4: {A}{c} -> {C}{c} fact5: ¬({AA}{a} & {AB}{a}) ; $hypothesis$ = ¬{C}{c} ; $proof$ = | fact3 & fact2 -> int1: {B}{b}; int1 & fact1 -> int2: {A}{c}; int2 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãœã«ããœãªLv.99ã¯éžæãããããã©ã¢ã¡ãªã«ããããªã | ({C}{b} & ¬{B}{b}) | fact1: ãã®ãœã«ããœãªLv.99ã¯éžæããã fact2: ãã®ããããLv.93ã¯æŒãæãããããããã¯é£ãåºããªã fact3: ãããã®ãœã«ããœãªLv.99ãã©ãããŠã欲ããããããæãåºããªããªããã®ãœã«ããœãªLv.99ã¯ã¢ã¡ãªã«ããããªã fact4: ããããã®ãŽã«ã
ãŽã¡ãLv.97ãçºçŸãæããªããªãã°ãã®ãœã«ããœãªLv.99ã¯ã©ãããŠã欲ãããããã¯æãåºããªã | fact1: {C}{b} fact2: ({CD}{fh} & ¬{FN}{fh}) fact3: ({AA}{b} & ¬{AB}{b}) -> ¬{B}{b} fact4: ¬{A}{a} -> ({AA}{b} & ¬{AB}{b}) | [] | [] | null | null | [] | null | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãœã«ããœãªLv.99ã¯éžæããã fact2: ãã®ããããLv.93ã¯æŒãæãããããããã¯é£ãåºããªã fact3: ãããã®ãœã«ããœãªLv.99ãã©ãããŠã欲ããããããæãåºããªããªããã®ãœã«ããœãªLv.99ã¯ã¢ã¡ãªã«ããããªã fact4: ããããã®ãŽã«ã
ãŽã¡ãLv.97ãçºçŸãæããªããªãã°ãã®ãœã«ããœãªLv.99ã¯ã©ãããŠã欲ãããããã¯æãåºããªã ; $hypothesis$ = ãã®ãœã«ããœãªLv.99ã¯éžæãããããã©ã¢ã¡ãªã«ããããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{b} fact2: ({CD}{fh} & ¬{FN}{fh}) fact3: ({AA}{b} & ¬{AB}{b}) -> ¬{B}{b} fact4: ¬{A}{a} -> ({AA}{b} & ¬{AB}{b}) ; $hypothesis$ = ({C}{b} & ¬{B}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãã«ãããLv.65ã¯æãããã©ã¡ããæããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | ¬({D}{b} & ¬{E}{b}) | fact1: ãã®ãŸããŸãLv.49ã¯å¿æã fact2: ãããããã®ãŸããŸãLv.49ãåŒãå
¥ãããããã¯å¿æããšãããšããã®ãã«ãããLv.65ã¯ã€ã¹ãããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ fact3: ãã®ãŸããŸãLv.49ã¯åŒãå
¥ãã fact4: ããä»®ã«ãã®ãã«ãããLv.65ã¯ã€ã¹ãããªããšãããšãæãããããã¯ã¡ããæããªãããšããããšã¯åã§ãã | fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: {A}{a} fact4: ¬{C}{b} -> ¬({D}{b} & ¬{E}{b}) | [
"fact3 & fact1 -> int1: ãã®ãŸããŸãLv.49ã¯åŒãå
¥ãããå¿æã; int1 & fact2 -> int2: ãã®ãã«ãããLv.65ã¯ã€ã¹ãããšããããšã¯ãªã; int2 & fact4 -> hypothesis;"
] | [
"fact3 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{b}; int2 & fact4 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ãŸããŸãLv.49ã¯å¿æã fact2: ãããããã®ãŸããŸãLv.49ãåŒãå
¥ãããããã¯å¿æããšãããšããã®ãã«ãããLv.65ã¯ã€ã¹ãããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ fact3: ãã®ãŸããŸãLv.49ã¯åŒãå
¥ãã fact4: ããä»®ã«ãã®ãã«ãããLv.65ã¯ã€ã¹ãããªããšãããšãæãããããã¯ã¡ããæããªãããšããããšã¯åã§ãã ; $hypothesis$ = ããã®ãã«ãããLv.65ã¯æãããã©ã¡ããæããšããããšã¯ãªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $proof$ = | fact3 & fact1 -> int1: ãã®ãŸããŸãLv.49ã¯åŒãå
¥ãããå¿æã; int1 & fact2 -> int2: ãã®ãã«ãããLv.65ã¯ã€ã¹ãããšããããšã¯ãªã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{b} fact3: {A}{a} fact4: ¬{C}{b} -> ¬({D}{b} & ¬{E}{b}) ; $hypothesis$ = ¬({D}{b} & ¬{E}{b}) ; $proof$ = | fact3 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{b}; int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã | {D}{c} | fact1: ä»®ã«ãã®ãŽããŽã«ãLv.91ãåãåããªããšããããã®ããããLv.23ã¯äžç®åããªããŠæŽã«æ¥æã¡ãããšããããšã¯ãªã fact2: ä»®ã«ãã®ãŽããŽã«ãLv.91ãåãåãã溶ãé£ããšãããšãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ããªã fact3: ãããã®ããããLv.23ãäžç®åãããã©ãããæ¥æã¡ããªããšãããšãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã fact4: ããããã®ããããLv.23ãæå°ãããªããšããããã®ãŽããŽã«ãLv.91ã¯äžç®åããªãããã©åãåã fact5: ããã®ãŽããŽã«ãLv.91ã¯æžãŸç¡ããªãäžæ¹ã§ããã¯å ãæ··ããããšããããšã¯èª€ãã fact6: ããã®ãŽããŽã«ãLv.91ã¯æžãŸç¡ããªããã©å ãæ··ããããšããããšã¯èª€ããªãã°ãã®ãŽããŽã«ãLv.91ã¯åãåããªã fact7: ä»®ã«ããã®ããããLv.23ã¯æå°ããæãããããšããããšã¯æ£ãããªããªãã°æå°ãããªã fact8: ããä»®ã«ãã®ããããLv.23ãäžç®åããªããŠæ¥æã¡ããªããšããã°ãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã fact9: 銎æã¿é£ããªãã¢ã³ã¹ã¿ãŒã¯æº¶ãé£ããŠãŸãæ¥æã¡ãã | fact1: ¬{B}{a} -> (¬{C}{b} & ¬{A}{b}) fact2: ({B}{a} & {D}{a}) -> ¬{D}{c} fact3: ({C}{b} & ¬{A}{b}) -> {D}{c} fact4: ¬{F}{b} -> (¬{C}{a} & {B}{a}) fact5: ¬(¬{AA}{a} & {AB}{a}) fact6: ¬(¬{AA}{a} & {AB}{a}) -> ¬{B}{a} fact7: ¬({F}{b} & {H}{b}) -> ¬{F}{b} fact8: (¬{C}{b} & ¬{A}{b}) -> {D}{c} fact9: (x): ¬{E}x -> ({D}x & {A}x) | [
"fact6 & fact5 -> int1: ãã®ãŽããŽã«ãLv.91ã¯åãåããªã; int1 & fact1 -> int2: ãã®ããããLv.23ã¯äžç®åããªããããŸãã«æ¥æã¡ããªã; int2 & fact8 -> hypothesis;"
] | [
"fact6 & fact5 -> int1: ¬{B}{a}; int1 & fact1 -> int2: (¬{C}{b} & ¬{A}{b}); int2 & fact8 -> hypothesis;"
] | ãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ããªã | ¬{D}{c} | [
"fact11 -> int3: ä»®ã«ãã®ãŽããŽã«ãLv.91ã銎æã¿é£ããªããªã溶ãé£ããæ¥æã¡ãã;"
] | 5 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãŽããŽã«ãLv.91ãåãåããªããšããããã®ããããLv.23ã¯äžç®åããªããŠæŽã«æ¥æã¡ãããšããããšã¯ãªã fact2: ä»®ã«ãã®ãŽããŽã«ãLv.91ãåãåãã溶ãé£ããšãããšãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ããªã fact3: ãããã®ããããLv.23ãäžç®åãããã©ãããæ¥æã¡ããªããšãããšãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã fact4: ããããã®ããããLv.23ãæå°ãããªããšããããã®ãŽããŽã«ãLv.91ã¯äžç®åããªãããã©åãåã fact5: ããã®ãŽããŽã«ãLv.91ã¯æžãŸç¡ããªãäžæ¹ã§ããã¯å ãæ··ããããšããããšã¯èª€ãã fact6: ããã®ãŽããŽã«ãLv.91ã¯æžãŸç¡ããªããã©å ãæ··ããããšããããšã¯èª€ããªãã°ãã®ãŽããŽã«ãLv.91ã¯åãåããªã fact7: ä»®ã«ããã®ããããLv.23ã¯æå°ããæãããããšããããšã¯æ£ãããªããªãã°æå°ãããªã fact8: ããä»®ã«ãã®ããããLv.23ãäžç®åããªããŠæ¥æã¡ããªããšããã°ãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã fact9: 銎æã¿é£ããªãã¢ã³ã¹ã¿ãŒã¯æº¶ãé£ããŠãŸãæ¥æã¡ãã ; $hypothesis$ = ãã®ãœãªãœã«Lv.76ã¯æº¶ãé£ã ; $proof$ = | fact6 & fact5 -> int1: ãã®ãŽããŽã«ãLv.91ã¯åãåããªã; int1 & fact1 -> int2: ãã®ããããLv.23ã¯äžç®åããªããããŸãã«æ¥æã¡ããªã; int2 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B}{a} -> (¬{C}{b} & ¬{A}{b}) fact2: ({B}{a} & {D}{a}) -> ¬{D}{c} fact3: ({C}{b} & ¬{A}{b}) -> {D}{c} fact4: ¬{F}{b} -> (¬{C}{a} & {B}{a}) fact5: ¬(¬{AA}{a} & {AB}{a}) fact6: ¬(¬{AA}{a} & {AB}{a}) -> ¬{B}{a} fact7: ¬({F}{b} & {H}{b}) -> ¬{F}{b} fact8: (¬{C}{b} & ¬{A}{b}) -> {D}{c} fact9: (x): ¬{E}x -> ({D}x & {A}x) ; $hypothesis$ = {D}{c} ; $proof$ = | fact6 & fact5 -> int1: ¬{B}{a}; int1 & fact1 -> int2: (¬{C}{b} & ¬{A}{b}); int2 & fact8 -> hypothesis; __PROVED__ |
0.3 | ããã®ãœã«ãœãªLv.31ã¯å²ã蟌ãŸãªãããšããããšã¯çå®ã | ¬{E}{b} | fact1: ãããã®ãœã«ãœãªLv.31ãé¿ãé£ããªããŠãããåããé£ããªããšãããšããã¯å²ã蟌ã fact2: ãããã®ã¿ã«ãã¿ã¡ãLv.86ãç¯ãç¶ããªããŠé¿ãé£ããªããªãã°åã fact3: ãããã®ãŸã«ã
ãŸã¡ã
Lv.12ãæãèµ·ãããªããã®ãœã«ãœãªLv.31ã¯é¬±é¶ãã fact4: ãã®ã¿ã¡ã
ã¿ã«ãLv.68ã¯åããé£ããšãããšããã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯é¬±é¶ãããªããŠããã«ããã¯æãèµ·ãããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact5: ãã®ã¿ã«ã
ã¿ã¡ã
Lv.20ãé¿ãé£ããªããã®ã¿ã¡ã
ã¿ã«ãLv.68ã¯åããé£ã fact6: ãã®ãœã«ã
ãœã«Lv.49ã¯é¬±é¶ãã fact7: ãã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯æãèµ·ãã fact8: ãã®ãŸã«ã
ãŸã¡ã
Lv.12ãç
ããäžæ¹ã§å¹ãéããªããªããã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯å²ã蟌ã fact9: ããä»®ã«ãã®ãœã«ãœãªLv.31ã鬱é¶ãããšãããšããã¯é¿ãé£ããªããããŸãã«åããé£ããšããããšã¯ãªã | fact1: (¬{D}{b} & ¬{C}{b}) -> {E}{b} fact2: (¬{FI}{iq} & ¬{D}{iq}) -> {GD}{iq} fact3: {A}{a} -> {B}{b} fact4: {C}{c} -> ¬(¬{B}{a} & ¬{A}{a}) fact5: {D}{d} -> {C}{c} fact6: {B}{ia} fact7: {A}{a} fact8: ({HM}{a} & ¬{IJ}{a}) -> {E}{a} fact9: {B}{b} -> (¬{D}{b} & ¬{C}{b}) | [
"fact3 & fact7 -> int1: ãã®ãœã«ãœãªLv.31ã¯é¬±é¶ãã; int1 & fact9 -> int2: ãã®ãœã«ãœãªLv.31ã¯é¿ãé£ããªããããŸãã«åããé£ããªã; int2 & fact1 -> hypothesis;"
] | [
"fact3 & fact7 -> int1: {B}{b}; int1 & fact9 -> int2: (¬{D}{b} & ¬{C}{b}); int2 & fact1 -> hypothesis;"
] | ããã®ãœã«ãœãªLv.31ã¯å²ã蟌ãŸãªãããšããããšã¯çå®ã | ¬{E}{b} | [] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããã®ãœã«ãœãªLv.31ãé¿ãé£ããªããŠãããåããé£ããªããšãããšããã¯å²ã蟌ã fact2: ãããã®ã¿ã«ãã¿ã¡ãLv.86ãç¯ãç¶ããªããŠé¿ãé£ããªããªãã°åã fact3: ãããã®ãŸã«ã
ãŸã¡ã
Lv.12ãæãèµ·ãããªããã®ãœã«ãœãªLv.31ã¯é¬±é¶ãã fact4: ãã®ã¿ã¡ã
ã¿ã«ãLv.68ã¯åããé£ããšãããšããã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯é¬±é¶ãããªããŠããã«ããã¯æãèµ·ãããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact5: ãã®ã¿ã«ã
ã¿ã¡ã
Lv.20ãé¿ãé£ããªããã®ã¿ã¡ã
ã¿ã«ãLv.68ã¯åããé£ã fact6: ãã®ãœã«ã
ãœã«Lv.49ã¯é¬±é¶ãã fact7: ãã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯æãèµ·ãã fact8: ãã®ãŸã«ã
ãŸã¡ã
Lv.12ãç
ããäžæ¹ã§å¹ãéããªããªããã®ãŸã«ã
ãŸã¡ã
Lv.12ã¯å²ã蟌ã fact9: ããä»®ã«ãã®ãœã«ãœãªLv.31ã鬱é¶ãããšãããšããã¯é¿ãé£ããªããããŸãã«åããé£ããšããããšã¯ãªã ; $hypothesis$ = ããã®ãœã«ãœãªLv.31ã¯å²ã蟌ãŸãªãããšããããšã¯çå®ã ; $proof$ = | fact3 & fact7 -> int1: ãã®ãœã«ãœãªLv.31ã¯é¬±é¶ãã; int1 & fact9 -> int2: ãã®ãœã«ãœãªLv.31ã¯é¿ãé£ããªããããŸãã«åããé£ããªã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{D}{b} & ¬{C}{b}) -> {E}{b} fact2: (¬{FI}{iq} & ¬{D}{iq}) -> {GD}{iq} fact3: {A}{a} -> {B}{b} fact4: {C}{c} -> ¬(¬{B}{a} & ¬{A}{a}) fact5: {D}{d} -> {C}{c} fact6: {B}{ia} fact7: {A}{a} fact8: ({HM}{a} & ¬{IJ}{a}) -> {E}{a} fact9: {B}{b} -> (¬{D}{b} & ¬{C}{b}) ; $hypothesis$ = ¬{E}{b} ; $proof$ = | fact3 & fact7 -> int1: {B}{b}; int1 & fact9 -> int2: (¬{D}{b} & ¬{C}{b}); int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ããããLv.3ã¯åŸ¡å®ãããŠåãé£ã | ({B}{aa} & {A}{aa}) | fact1: ãã®ããããLv.3ã¯åç£ç¢ç£šããªããåãæããäž¡æ¹ã fact2: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯é¡§ã¿ãªããšãããšã埡å®ãããåãé£ãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ãã®ãŽã«ããŽãLv.85ã¯çŽ æŽãããããã埡å®ãã fact4: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯ç¡è³¢ããšããã°ãå
±ååºæ¥ãªãããšããããšã¯æãç«ããªã fact5: ãããšããã¢ã³ã¹ã¿ãŒã¯åç£ç¢ç£šããªããåãæããã©ã¡ããã§ãããšããã°ããã¯åŸ¡å®ãã fact6: ä»®ã«ããã®ã·ã¡ã
ã·ãªLv.68ã¯é¡§ã¿ãªããŠä»ãæããªãããšããããšã¯ééã£ãŠããã°ãã®ããããLv.3ã¯é¡§ã¿ãªã fact7: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯å
±ååºæ¥ããšããã°ãã顧ã¿ãªãããããä»ãæããªãããšããããšã¯äºå®ãšç°ãªããªãããšããããšã¯äºå®ãšç°ãªã | fact1: (¬{AA}{aa} v {AB}{aa}) fact2: (x): ¬{C}x -> ¬({B}x & {A}x) fact3: ({CO}{bq} & {B}{bq}) fact4: (x): {F}x -> {D}x fact5: (x): (¬{AA}x v {AB}x) -> {B}x fact6: ¬(¬{C}{a} & ¬{E}{a}) -> ¬{C}{aa} fact7: (x): {D}x -> ¬(¬{C}x & ¬{E}x) | [
"fact5 -> int1: ãã®ããããLv.3ãåç£ç¢ç£šããªãããããã¯ãããåãæãããããã¯ã©ã¡ããã§ãããšããããã®ããããLv.3ã¯åŸ¡å®ãã; int1 & fact1 -> int2: ãã®ããããLv.3ã¯åŸ¡å®ãã;"
] | [
"fact5 -> int1: (¬{AA}{aa} v {AB}{aa}) -> {B}{aa}; int1 & fact1 -> int2: {B}{aa};"
] | ããã®ããããLv.3ã埡å®ããããã®äžåãé£ãããšããããšã¯æ¬åœã§ãªã | ¬({B}{aa} & {A}{aa}) | [
"fact9 -> int3: ä»®ã«ãã®ããããLv.3ã¯é¡§ã¿ãªããšãããšããã®ããããLv.3ã¯åŸ¡å®ãããŠãŸãåãé£ãããšããããšã¯æ£ãããªã; fact8 -> int4: ããããã®ã·ã¡ã
ã·ãªLv.68ã¯å
±ååºæ¥ããªãããã®ã·ã¡ã
ã·ãªLv.68ã¯é¡§ã¿ãªããŠãŸãä»ãæããªãããšããããšã¯ééã£ãŠãã; fact11 -> int5: ããã®ã·ã¡ã
ã·ãªLv.68ã¯ç¡è³¢ãããšããããšã¯æãç«ã€ãšããã°å
±ååºæ¥ã;"
] | 6 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ããããLv.3ã¯åç£ç¢ç£šããªããåãæããäž¡æ¹ã fact2: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯é¡§ã¿ãªããšãããšã埡å®ãããåãé£ãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact3: ãã®ãŽã«ããŽãLv.85ã¯çŽ æŽãããããã埡å®ãã fact4: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯ç¡è³¢ããšããã°ãå
±ååºæ¥ãªãããšããããšã¯æãç«ããªã fact5: ãããšããã¢ã³ã¹ã¿ãŒã¯åç£ç¢ç£šããªããåãæããã©ã¡ããã§ãããšããã°ããã¯åŸ¡å®ãã fact6: ä»®ã«ããã®ã·ã¡ã
ã·ãªLv.68ã¯é¡§ã¿ãªããŠä»ãæããªãããšããããšã¯ééã£ãŠããã°ãã®ããããLv.3ã¯é¡§ã¿ãªã fact7: ããä»®ã«ãªãããã®ã¢ã³ã¹ã¿ãŒã¯å
±ååºæ¥ããšããã°ãã顧ã¿ãªãããããä»ãæããªãããšããããšã¯äºå®ãšç°ãªããªãããšããããšã¯äºå®ãšç°ãªã ; $hypothesis$ = ãã®ããããLv.3ã¯åŸ¡å®ãããŠåãé£ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{AA}{aa} v {AB}{aa}) fact2: (x): ¬{C}x -> ¬({B}x & {A}x) fact3: ({CO}{bq} & {B}{bq}) fact4: (x): {F}x -> {D}x fact5: (x): (¬{AA}x v {AB}x) -> {B}x fact6: ¬(¬{C}{a} & ¬{E}{a}) -> ¬{C}{aa} fact7: (x): {D}x -> ¬(¬{C}x & ¬{E}x) ; $hypothesis$ = ({B}{aa} & {A}{aa}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã®ãŸãLv.64ã¯çºçãæããªã | ¬{B}{aa} | fact1: ããä»®ã«ãã®ããããLv.34ã幌ããšããã°ãã®ããããLv.34ã¯è©°ã蟌ãã fact2: ããä»®ã«ãã®ããããLv.34ãå±ãŸãªããšããããã®ããããLv.34ã¯å¹ŒããŠéç±ãã fact3: ä»®ã«ãã®ãããã«ãLv.5ã¯æ¯èŒãé£ããšãããšããã®ãããã«Lv.54ã¯çºçãæããªãäžæ¹ã§èŠéããé£ãããšããããšã¯æãç«ããªã fact4: ããããã®ãŸã®ãŸãLv.64ãå°ããªããããã決è¡ããªããšããããã®ãŸã®ãŸãLv.64ã¯çºçãæããªã fact5: ãããšããã¢ã³ã¹ã¿ãŒã競ãåããªããšãããšå°ããªãããã€æ±ºè¡ããªã fact6: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯çºçãé£ããšããããšã¯ãªã fact7: ãã®ãŸã®ãŸãLv.64ã¯ç«¶ãåããªã fact8: çºçãé£ããªãã¢ã³ã¹ã¿ãŒã¯å±ãŸãªããæŽã«æšæ²ããªã | fact1: {F}{b} -> {E}{b} fact2: ¬{H}{b} -> ({F}{b} & {G}{b}) fact3: {D}{a} -> ¬(¬{B}{ch} & {C}{ch}) fact4: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} fact5: (x): ¬{A}x -> (¬{AA}x & ¬{AB}x) fact6: (x): ¬{J}x fact7: ¬{A}{aa} fact8: (x): ¬{J}x -> (¬{H}x & ¬{I}x) | [
"fact5 -> int1: ããããã®ãŸã®ãŸãLv.64ã¯ç«¶ãåããªãããšããããšã¯æãç«ã€ãªããã®ãŸã®ãŸãLv.64ã¯å°ããªããŠããã«ããã¯æ±ºè¡ããªã; int1 & fact7 -> int2: ãã®ãŸã®ãŸãLv.64ã¯å°ããšããããšã¯ãªããããã«ããã¯æ±ºè¡ããªã; int2 & fact4 -> hypothesis;"
] | [
"fact5 -> int1: ¬{A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}); int1 & fact7 -> int2: (¬{AA}{aa} & ¬{AB}{aa}); int2 & fact4 -> hypothesis;"
] | ãã®ãããã«Lv.54ã¯ç«¶ãåããªã | ¬{A}{ch} | [
"fact12 -> int3: ãããã®ãŽããŽã¡ãLv.68ãçºçãé£ããšããããšã¯ãªããšããã°ãã®ãŽããŽã¡ãLv.68ã¯å±ãŸãªããŠãŸãæšæ²ãããšããããšã¯ãªã; fact11 -> int4: ãã®ãŽããŽã¡ãLv.68ã¯çºçãé£ããªã; int3 & int4 -> int5: ãã®ãŽããŽã¡ãLv.68ã¯å±ãŸãªããæšæ²ããªã; int5 -> int6: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯å±ãŸãªããŠå ããŠããã¯æšæ²ããªã; int6 -> int7: ãã®ããããLv.34ã¯å±ãŸãªããŠæšæ²ããªã; int7 -> int8: ãã®ããããLv.34ã¯å±ãŸãªã; int8 & fact10 -> int9: ãã®ããããLv.34ã¯å¹ŒããããŸãã«éç±ãã; int9 -> int10: ãã®ããããLv.34ã¯å¹Œã; int10 & fact13 -> int11: ãã®ããããLv.34ã¯è©°ã蟌ãã;"
] | 11 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ããããLv.34ã幌ããšããã°ãã®ããããLv.34ã¯è©°ã蟌ãã fact2: ããä»®ã«ãã®ããããLv.34ãå±ãŸãªããšããããã®ããããLv.34ã¯å¹ŒããŠéç±ãã fact3: ä»®ã«ãã®ãããã«ãLv.5ã¯æ¯èŒãé£ããšãããšããã®ãããã«Lv.54ã¯çºçãæããªãäžæ¹ã§èŠéããé£ãããšããããšã¯æãç«ããªã fact4: ããããã®ãŸã®ãŸãLv.64ãå°ããªããããã決è¡ããªããšããããã®ãŸã®ãŸãLv.64ã¯çºçãæããªã fact5: ãããšããã¢ã³ã¹ã¿ãŒã競ãåããªããšãããšå°ããªãããã€æ±ºè¡ããªã fact6: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯çºçãé£ããšããããšã¯ãªã fact7: ãã®ãŸã®ãŸãLv.64ã¯ç«¶ãåããªã fact8: çºçãé£ããªãã¢ã³ã¹ã¿ãŒã¯å±ãŸãªããæŽã«æšæ²ããªã ; $hypothesis$ = ãã®ãŸã®ãŸãLv.64ã¯çºçãæããªã ; $proof$ = | fact5 -> int1: ããããã®ãŸã®ãŸãLv.64ã¯ç«¶ãåããªãããšããããšã¯æãç«ã€ãªããã®ãŸã®ãŸãLv.64ã¯å°ããªããŠããã«ããã¯æ±ºè¡ããªã; int1 & fact7 -> int2: ãã®ãŸã®ãŸãLv.64ã¯å°ããšããããšã¯ãªããããã«ããã¯æ±ºè¡ããªã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {F}{b} -> {E}{b} fact2: ¬{H}{b} -> ({F}{b} & {G}{b}) fact3: {D}{a} -> ¬(¬{B}{ch} & {C}{ch}) fact4: (¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa} fact5: (x): ¬{A}x -> (¬{AA}x & ¬{AB}x) fact6: (x): ¬{J}x fact7: ¬{A}{aa} fact8: (x): ¬{J}x -> (¬{H}x & ¬{I}x) ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | fact5 -> int1: ¬{A}{aa} -> (¬{AA}{aa} & ¬{AB}{aa}); int1 & fact7 -> int2: (¬{AA}{aa} & ¬{AB}{aa}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœã¡ã
ãœãLv.49ã¯é¡ãããã©ã¯ãããªããªã | ({AA}{a} & ¬{AB}{a}) | fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¡ããããããã¯ãããªããªã | fact1: (x): ({AA}x & ¬{AB}x) | [
"fact1 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¡ããããããã¯ãããªããªã; int1 -> hypothesis;"
] | [
"fact1 -> int1: (x): ({AA}x & ¬{AB}x); int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¡ããããããã¯ãããªããªã ; $hypothesis$ = ãã®ãœã¡ã
ãœãLv.49ã¯é¡ãããã©ã¯ãããªããªã ; $proof$ = | fact1 -> int1: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯é¡ããããããã¯ãããªããªã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ({AA}x & ¬{AB}x) ; $hypothesis$ = ({AA}{a} & ¬{AB}{a}) ; $proof$ = | fact1 -> int1: (x): ({AA}x & ¬{AB}x); int1 -> hypothesis; __PROVED__ |
0.3 | ããœããœãLv.76äºä»¶ã¯èµ·ãããªããå°äžæ·±ããšããããšãèµ·ããããšããããšã¯åã | ¬(¬{E} v {D}) | fact1: èŠé£ããšããããšãèµ·ããããŸãã¯é·ããšããããšãçºçããããŸãã¯äž¡æ¹ãšãã fact2: ãœã¡ããœãLv.79äºä»¶ã¯ãœã¡ããœã¡ã
Lv.85äºä»¶ã®åå ãšãªã fact3: ãœããœã¡ãLv.50äºä»¶ã¯ãŸã«ããŸãLv.67äºä»¶ã«åŒãèµ·ãããã fact4: ãœããœã¡ãLv.50äºä»¶ã¯åŒ·ããšããããšã¯çºçããªããšããããšãåé¿ãã fact5: æ
ããªããšããããšãèµ·ãã fact6: ãŸã«ããŸãLv.67äºä»¶ãèµ·ãã fact7: 匷ããšããããšãçºçãããªããœããœãLv.76äºä»¶ãçããªãããããã¯å°äžæ·±ããšããããšã¯çºçããããããã¯äž¡æ¹ãšãã fact8: ãœã¡ããœãLv.90äºä»¶ããŸãã¯ããããLv.46äºä»¶ãèµ·ãã | fact1: ({JI} v {AN}) fact2: {CI} -> {FG} fact3: {A} -> {B} fact4: {B} -> {C} fact5: {HM} fact6: {A} fact7: {C} -> (¬{E} v {D}) fact8: ({DU} v {DM}) | [
"fact3 & fact6 -> int1: ãœããœã¡ãLv.50äºä»¶ãèµ·ãã; int1 & fact4 -> int2: 匷ããšããããšãèµ·ãã; int2 & fact7 -> hypothesis;"
] | [
"fact3 & fact6 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 & fact7 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: èŠé£ããšããããšãèµ·ããããŸãã¯é·ããšããããšãçºçããããŸãã¯äž¡æ¹ãšãã fact2: ãœã¡ããœãLv.79äºä»¶ã¯ãœã¡ããœã¡ã
Lv.85äºä»¶ã®åå ãšãªã fact3: ãœããœã¡ãLv.50äºä»¶ã¯ãŸã«ããŸãLv.67äºä»¶ã«åŒãèµ·ãããã fact4: ãœããœã¡ãLv.50äºä»¶ã¯åŒ·ããšããããšã¯çºçããªããšããããšãåé¿ãã fact5: æ
ããªããšããããšãèµ·ãã fact6: ãŸã«ããŸãLv.67äºä»¶ãèµ·ãã fact7: 匷ããšããããšãçºçãããªããœããœãLv.76äºä»¶ãçããªãããããã¯å°äžæ·±ããšããããšã¯çºçããããããã¯äž¡æ¹ãšãã fact8: ãœã¡ããœãLv.90äºä»¶ããŸãã¯ããããLv.46äºä»¶ãèµ·ãã ; $hypothesis$ = ããœããœãLv.76äºä»¶ã¯èµ·ãããªããå°äžæ·±ããšããããšãèµ·ããããšããããšã¯åã ; $proof$ = | fact3 & fact6 -> int1: ãœããœã¡ãLv.50äºä»¶ãèµ·ãã; int1 & fact4 -> int2: 匷ããšããããšãèµ·ãã; int2 & fact7 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({JI} v {AN}) fact2: {CI} -> {FG} fact3: {A} -> {B} fact4: {B} -> {C} fact5: {HM} fact6: {A} fact7: {C} -> (¬{E} v {D}) fact8: ({DU} v {DM}) ; $hypothesis$ = ¬(¬{E} v {D}) ; $proof$ = | fact3 & fact6 -> int1: {B}; int1 & fact4 -> int2: {C}; int2 & fact7 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãŽã«ã
ãŽã®Lv.73ã¯çŒçœãããåŸãæããšããããšã¯ãªãããšããããšã¯çå®ã§ãªã | ¬({E}{a} & ¬{D}{a}) | fact1: ããããã®ãŽã«ã
ãŽã®Lv.73ãçµã³ä»ãé£ããšããã°çã
ãã fact2: ä»®ã«ãã®ãŽã«ã
ãŽã®Lv.73ãçã
ãããšãããšçŒçœãããåŸãæããªã fact3: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çµã³ä»ãé£ããã©ããã¯å¹
åºããªã | fact1: {A}{a} -> {C}{a} fact2: {C}{a} -> ({E}{a} & ¬{D}{a}) fact3: ({A}{a} & ¬{B}{a}) | [
"fact3 -> int1: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çµã³ä»ãé£ã; int1 & fact1 -> int2: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çã
ãã; int2 & fact2 -> hypothesis;"
] | [
"fact3 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããã®ãŽã«ã
ãŽã®Lv.73ãçµã³ä»ãé£ããšããã°çã
ãã fact2: ä»®ã«ãã®ãŽã«ã
ãŽã®Lv.73ãçã
ãããšãããšçŒçœãããåŸãæããªã fact3: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çµã³ä»ãé£ããã©ããã¯å¹
åºããªã ; $hypothesis$ = ããã®ãŽã«ã
ãŽã®Lv.73ã¯çŒçœãããåŸãæããšããããšã¯ãªãããšããããšã¯çå®ã§ãªã ; $proof$ = | fact3 -> int1: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çµã³ä»ãé£ã; int1 & fact1 -> int2: ãã®ãŽã«ã
ãŽã®Lv.73ã¯çã
ãã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {C}{a} fact2: {C}{a} -> ({E}{a} & ¬{D}{a}) fact3: ({A}{a} & ¬{B}{a}) ; $hypothesis$ = ¬({E}{a} & ¬{D}{a}) ; $proof$ = | fact3 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãçŽåŸãæããªããã¢ã³ã¹ã¿ãŒã¯ãã | (Ex): ¬{B}x | fact1: ããä»®ã«çŽåŸãæããªãã¢ã³ã¹ã¿ãŒãå°æããããªãã°ããã¯æ
ã¿æ·±ããªã fact2: ãã®ã·ãã·ãLv.1ã¯å°æããããªã fact3: ãããããã®ã·ãã·ãLv.1ã¯æ
ã¿æ·±ãããŸãæžãé£ãããšããããšã¯åœãªããã®ã·ãã·ãLv.1ã¯çŽåŸãæããªã fact4: ãã®ã·ãã·ãLv.1ãæ
ã¿æ·±ããªããšããã°ãã®ã·ãã·ãLv.1ã¯çŽåŸãæããªã fact5: å°æããªãã¢ã³ã¹ã¿ãŒã¯çŽåŸãæããªããã©å°æããã fact6: ãå°æããããªããã¢ã³ã¹ã¿ãŒã¯ãã fact7: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çŽåŸãæã | fact1: (x): (¬{B}x & {A}x) -> ¬{AA}x fact2: ¬{A}{a} fact3: ¬({AA}{a} & {AB}{a}) -> ¬{B}{a} fact4: ¬{AA}{a} -> ¬{B}{a} fact5: (x): ¬{C}x -> (¬{B}x & {A}x) fact6: (Ex): ¬{A}x fact7: (Ex): {B}x | [] | [] | ãã®ãœããœãLv.95ã¯æ
ã¿æ·±ããªã | ¬{AA}{cu} | [
"fact9 -> int1: ãããã®ãœããœãLv.95ãçŽåŸãæããªãããããå°æããããšããããã®ãœããœãLv.95ã¯æ
ã¿æ·±ããªã; fact8 -> int2: ãããã®ãœããœãLv.95ãå°æããªããšãããšãã®ãœããœãLv.95ã¯çŽåŸãæããšããããšã¯ãªãäžæ¹ã§å°æããã;"
] | 5 | 3 | 3 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«çŽåŸãæããªãã¢ã³ã¹ã¿ãŒãå°æããããªãã°ããã¯æ
ã¿æ·±ããªã fact2: ãã®ã·ãã·ãLv.1ã¯å°æããããªã fact3: ãããããã®ã·ãã·ãLv.1ã¯æ
ã¿æ·±ãããŸãæžãé£ãããšããããšã¯åœãªããã®ã·ãã·ãLv.1ã¯çŽåŸãæããªã fact4: ãã®ã·ãã·ãLv.1ãæ
ã¿æ·±ããªããšããã°ãã®ã·ãã·ãLv.1ã¯çŽåŸãæããªã fact5: å°æããªãã¢ã³ã¹ã¿ãŒã¯çŽåŸãæããªããã©å°æããã fact6: ãå°æããããªããã¢ã³ã¹ã¿ãŒã¯ãã fact7: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çŽåŸãæã ; $hypothesis$ = ãçŽåŸãæããªããã¢ã³ã¹ã¿ãŒã¯ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): (¬{B}x & {A}x) -> ¬{AA}x fact2: ¬{A}{a} fact3: ¬({AA}{a} & {AB}{a}) -> ¬{B}{a} fact4: ¬{AA}{a} -> ¬{B}{a} fact5: (x): ¬{C}x -> (¬{B}x & {A}x) fact6: (Ex): ¬{A}x fact7: (Ex): {B}x ; $hypothesis$ = (Ex): ¬{B}x ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœã¡ãLv.13äºä»¶ã¯èµ·ããªã | ¬{D} | fact1: ããä»®ã«äžè»¢ããããšã§ã¯ãªãå®è³ªåããããšãçºçãããšããã°ãœããœã¡ãLv.13äºä»¶ã¯çºçãã fact2: ãœããœã¡ãLv.10äºä»¶ãšç²åŸããããšãèµ·ãã fact3: ãæãããããšããããšã¯çããªãããšããããšã¯ãäžè»¢ããããšã§ã¯ãªãå®è³ªåããããšãçããããšããããšã®åå ãšãªã fact4: ãæãããããšããããšã¯çããªãããšããããšã¯äžè»¢ããããšã¯çããªããšããããšã«ç¹ãã fact5: ããäžè»¢ããããšã¯çããªããšãããããæãããããšããããšãèµ·ããããã©å®è³ªåããããšã¯çºçããªãããšããããšã¯ééãã§ããããšããããšã¯æãç«ã€ fact6: æãããããšããããšã¯æœããšããããšãšãŽããŽãLv.9äºä»¶ãèµ·ããã«é»æ¢ããã | fact1: (¬{C} & {A}) -> {D} fact2: ({EB} & {JG}) fact3: ¬{B} -> (¬{C} & {A}) fact4: ¬{B} -> ¬{C} fact5: ¬{C} -> ¬({B} & ¬{A}) fact6: ({AA} & {AB}) -> ¬{B} | [] | [] | ãœããœã¡ãLv.13äºä»¶ã¯èµ·ããªã | ¬{D} | [] | 6 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«äžè»¢ããããšã§ã¯ãªãå®è³ªåããããšãçºçãããšããã°ãœããœã¡ãLv.13äºä»¶ã¯çºçãã fact2: ãœããœã¡ãLv.10äºä»¶ãšç²åŸããããšãèµ·ãã fact3: ãæãããããšããããšã¯çããªãããšããããšã¯ãäžè»¢ããããšã§ã¯ãªãå®è³ªåããããšãçããããšããããšã®åå ãšãªã fact4: ãæãããããšããããšã¯çããªãããšããããšã¯äžè»¢ããããšã¯çããªããšããããšã«ç¹ãã fact5: ããäžè»¢ããããšã¯çããªããšãããããæãããããšããããšãèµ·ããããã©å®è³ªåããããšã¯çºçããªãããšããããšã¯ééãã§ããããšããããšã¯æãç«ã€ fact6: æãããããšããããšã¯æœããšããããšãšãŽããŽãLv.9äºä»¶ãèµ·ããã«é»æ¢ããã ; $hypothesis$ = ãœããœã¡ãLv.13äºä»¶ã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{C} & {A}) -> {D} fact2: ({EB} & {JG}) fact3: ¬{B} -> (¬{C} & {A}) fact4: ¬{B} -> ¬{C} fact5: ¬{C} -> ¬({B} & ¬{A}) fact6: ({AA} & {AB}) -> ¬{B} ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | éãæããšããããšã¯çºçããªã | ¬{A} | fact1: ãå³æ°ç¡ããšããããšãèµ·ããããŽã¡ã
ãŽãLv.95äºä»¶ã¯çããªãããšããããšã¯çå®ã§ãªã fact2: ãããããã®Lv.48äºä»¶ã¯èµ·ãããªããªãå¯ããšããããšã¯èµ·ããªã fact3: ãŽã¡ã
ãŽãLv.95äºä»¶ãèµ·ãã fact4: ãå¯ããšããããšã§ã¯ãªããŠéãæããšããããšãèµ·ããããšããããšã¯ããããã®Lv.48äºä»¶ã¯çºçããªãããšããããšã«ãããããã fact5: ããããå³æ°ç¡ããšããããšãèµ·ããããŽã¡ã
ãŽãLv.95äºä»¶ã¯èµ·ããªããäž¡æ¹ãšãã ããšããããšã¯æãç«ããªããšããã°ãããã®Lv.48äºä»¶ã¯èµ·ããªã fact6: å¯ããšããããšã¯çããªã fact7: ä»®ã«ãå³æ°ç¡ããšããããšããããã¯ãŽã¡ã
ãŽãLv.95äºä»¶ãçããããšããããšã¯æãç«ããªããªãããããã®Lv.48äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã | fact1: ¬({AA} v ¬{AB}) fact2: ¬{B} -> ¬{C} fact3: {AB} fact4: ¬{B} -> (¬{C} & {A}) fact5: ¬({AA} v ¬{AB}) -> ¬{B} fact6: ¬{C} fact7: ¬({AA} v {AB}) -> ¬{B} | [
"fact5 & fact1 -> int1: ãããã®Lv.48äºä»¶ã¯çºçããªã; int1 & fact4 -> int2: å¯ããšããããšã¯èµ·ããªããéãæããšããããšãçãã; int2 -> hypothesis;"
] | [
"fact5 & fact1 -> int1: ¬{B}; int1 & fact4 -> int2: (¬{C} & {A}); int2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãå³æ°ç¡ããšããããšãèµ·ããããŽã¡ã
ãŽãLv.95äºä»¶ã¯çããªãããšããããšã¯çå®ã§ãªã fact2: ãããããã®Lv.48äºä»¶ã¯èµ·ãããªããªãå¯ããšããããšã¯èµ·ããªã fact3: ãŽã¡ã
ãŽãLv.95äºä»¶ãèµ·ãã fact4: ãå¯ããšããããšã§ã¯ãªããŠéãæããšããããšãèµ·ããããšããããšã¯ããããã®Lv.48äºä»¶ã¯çºçããªãããšããããšã«ãããããã fact5: ããããå³æ°ç¡ããšããããšãèµ·ããããŽã¡ã
ãŽãLv.95äºä»¶ã¯èµ·ããªããäž¡æ¹ãšãã ããšããããšã¯æãç«ããªããšããã°ãããã®Lv.48äºä»¶ã¯èµ·ããªã fact6: å¯ããšããããšã¯çããªã fact7: ä»®ã«ãå³æ°ç¡ããšããããšããããã¯ãŽã¡ã
ãŽãLv.95äºä»¶ãçããããšããããšã¯æãç«ããªããªãããããã®Lv.48äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã ; $hypothesis$ = éãæããšããããšã¯çºçããªã ; $proof$ = | fact5 & fact1 -> int1: ãããã®Lv.48äºä»¶ã¯çºçããªã; int1 & fact4 -> int2: å¯ããšããããšã¯èµ·ããªããéãæããšããããšãçãã; int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA} v ¬{AB}) fact2: ¬{B} -> ¬{C} fact3: {AB} fact4: ¬{B} -> (¬{C} & {A}) fact5: ¬({AA} v ¬{AB}) -> ¬{B} fact6: ¬{C} fact7: ¬({AA} v {AB}) -> ¬{B} ; $hypothesis$ = ¬{A} ; $proof$ = | fact5 & fact1 -> int1: ¬{B}; int1 & fact4 -> int2: (¬{C} & {A}); int2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.61ã¯æããæããªã | ¬{D}{b} | fact1: ä»®ã«ãã®ãã®ããLv.94ãçç£ãç¶ããããŸãã¯ããã倧人ãããŸãã¯äž¡æ¹ãšãã§ãããªãã°ãã®ãŸããŸãLv.61ã¯æããæããªã fact2: ãããã®ãã®ããLv.94ã軜ãŒããªãããã€ããã倧人ããªããªãã°ãã®ãŸããŸãLv.61ã¯è»œãŒã fact3: ãã®ãã®ããLv.94ã軜ãŒããšããã°ããã¯å€§äººã | fact1: ({C}{a} v {B}{a}) -> ¬{D}{b} fact2: (¬{A}{a} & ¬{B}{a}) -> {A}{b} fact3: {A}{a} -> {B}{a} | [] | [] | ãã®ãŸããŸãLv.61ã¯è»œãŒã | {A}{b} | [] | 4 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãã®ããLv.94ãçç£ãç¶ããããŸãã¯ããã倧人ãããŸãã¯äž¡æ¹ãšãã§ãããªãã°ãã®ãŸããŸãLv.61ã¯æããæããªã fact2: ãããã®ãã®ããLv.94ã軜ãŒããªãããã€ããã倧人ããªããªãã°ãã®ãŸããŸãLv.61ã¯è»œãŒã fact3: ãã®ãã®ããLv.94ã軜ãŒããšããã°ããã¯å€§äººã ; $hypothesis$ = ãã®ãŸããŸãLv.61ã¯æããæããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({C}{a} v {B}{a}) -> ¬{D}{b} fact2: (¬{A}{a} & ¬{B}{a}) -> {A}{b} fact3: {A}{a} -> {B}{a} ; $hypothesis$ = ¬{D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ãã¿ã¡ãLv.3ã¯çé
žã£ã±ããèŠèŸŒãã | ({D}{c} v {C}{c}) | fact1: ãããã®ã¿ãã¿ã«ãLv.10ãå¯æããã°ãã®ã·ãã·ã«Lv.53ã¯èçž®ããªã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å¯æããªããªãã°ãããã¯çé
žã£ã±ãããããã¯ããã¯èŠèŸŒããããšããããšã¯ééãã§ãã fact3: ãã®ã¿ãã¿ã¡ãLv.3ã¯è¥ã
ãã fact4: ããä»®ã«ãã®ã¿ãã¿ã«ãLv.10ãèŠèŸŒããªããšããã°ãã®ã¿ãã¿ã¡ãLv.3ã¯å¯æãã fact5: ããããã®ã·ãã·ã«Lv.53ã¯èçž®ããªããšãããããã®ã¿ãã¿ã¡ãLv.3ã¯èŠèŸŒããããšããããšã¯æ¬åœã§ãã fact6: ãã®ã¿ãã¿ã«ãLv.10ã¯å¯æãã | fact1: {A}{a} -> ¬{B}{b} fact2: (x): ¬{A}x -> ¬({D}x v {C}x) fact3: {GD}{c} fact4: ¬{C}{a} -> {A}{c} fact5: ¬{B}{b} -> {C}{c} fact6: {A}{a} | [
"fact1 & fact6 -> int1: ãã®ã·ãã·ã«Lv.53ã¯èçž®ããªã; int1 & fact5 -> int2: ãã®ã¿ãã¿ã¡ãLv.3ã¯èŠèŸŒãã; int2 -> hypothesis;"
] | [
"fact1 & fact6 -> int1: ¬{B}{b}; int1 & fact5 -> int2: {C}{c}; int2 -> hypothesis;"
] | ããã®ã¿ãã¿ã¡ãLv.3ã¯çé
žã£ã±ããèŠèŸŒããããŸãã¯äž¡æ¹ãšãã ããšããããšã¯åã§ãã | ¬({D}{c} v {C}{c}) | [
"fact7 -> int3: ããããã®ã¿ãã¿ã¡ãLv.3ã¯å¯æããªããšãããããã®ã¿ãã¿ã¡ãLv.3ã¯çé
žã£ã±ãããããã¯èŠèŸŒããããããã¯äž¡æ¹ã§ããããšããããšã¯æãç«ããªã;"
] | 4 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®ã¿ãã¿ã«ãLv.10ãå¯æããã°ãã®ã·ãã·ã«Lv.53ã¯èçž®ããªã fact2: ä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯å¯æããªããªãã°ãããã¯çé
žã£ã±ãããããã¯ããã¯èŠèŸŒããããšããããšã¯ééãã§ãã fact3: ãã®ã¿ãã¿ã¡ãLv.3ã¯è¥ã
ãã fact4: ããä»®ã«ãã®ã¿ãã¿ã«ãLv.10ãèŠèŸŒããªããšããã°ãã®ã¿ãã¿ã¡ãLv.3ã¯å¯æãã fact5: ããããã®ã·ãã·ã«Lv.53ã¯èçž®ããªããšãããããã®ã¿ãã¿ã¡ãLv.3ã¯èŠèŸŒããããšããããšã¯æ¬åœã§ãã fact6: ãã®ã¿ãã¿ã«ãLv.10ã¯å¯æãã ; $hypothesis$ = ãã®ã¿ãã¿ã¡ãLv.3ã¯çé
žã£ã±ããèŠèŸŒãã ; $proof$ = | fact1 & fact6 -> int1: ãã®ã·ãã·ã«Lv.53ã¯èçž®ããªã; int1 & fact5 -> int2: ãã®ã¿ãã¿ã¡ãLv.3ã¯èŠèŸŒãã; int2 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} -> ¬{B}{b} fact2: (x): ¬{A}x -> ¬({D}x v {C}x) fact3: {GD}{c} fact4: ¬{C}{a} -> {A}{c} fact5: ¬{B}{b} -> {C}{c} fact6: {A}{a} ; $hypothesis$ = ({D}{c} v {C}{c}) ; $proof$ = | fact1 & fact6 -> int1: ¬{B}{b}; int1 & fact5 -> int2: {C}{c}; int2 -> hypothesis; __PROVED__ |
0.3 | ãããŽããŽã¡ã
Lv.7äºä»¶ãçºçããªãããã®äžãŸããŸã«ãLv.56äºä»¶ã¯çããªãããšããããšã¯æ¬åœã§ããããšããããšã¯åœã | ¬(¬{D} & ¬{C}) | fact1: ãç°èèããšããããšãçãããäŒããé£ããšããããšã¯èµ·ããªãããšããããšã¯æ¢¯åããããšãçºçããã fact2: å
±é³Žãæããšããããšãèµ·ãã fact3: ããå
±é³Žãæããšããããšãçãããšãããç°èèããšããããšãèµ·ãããã©äŒããé£ããšããããšã¯çããªã fact4: ããä»®ã«æ¢¯åããããšãçºçãããšããã°ããŽããŽã¡ã
Lv.7äºä»¶ãçããªãããŸããŸããŸã«ãLv.56äºä»¶ã¯èµ·ãããªãããšããããšã¯ééã£ãŠãã fact5: å
±é³Žãæããšããããšã¯ç°èèããšããããšãæã fact6: ããŽããŽã¡ã
Lv.7äºä»¶ã¯çºçããããã©ãŸããŸã«ãLv.56äºä»¶ã¯èµ·ãããªãããšããããšã¯ééã£ãŠãã | fact1: ({AA} & ¬{AB}) -> {B} fact2: {A} fact3: {A} -> ({AA} & ¬{AB}) fact4: {B} -> ¬(¬{D} & ¬{C}) fact5: {A} -> {AA} fact6: ¬({D} & ¬{C}) | [
"fact3 & fact2 -> int1: ç°èèããšããããšãèµ·ãããã©äŒããé£ããšããããšã¯èµ·ããªã; int1 & fact1 -> int2: 梯åããããšãèµ·ãã; int2 & fact4 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: ({AA} & ¬{AB}); int1 & fact1 -> int2: {B}; int2 & fact4 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãç°èèããšããããšãçãããäŒããé£ããšããããšã¯èµ·ããªãããšããããšã¯æ¢¯åããããšãçºçããã fact2: å
±é³Žãæããšããããšãèµ·ãã fact3: ããå
±é³Žãæããšããããšãçãããšãããç°èèããšããããšãèµ·ãããã©äŒããé£ããšããããšã¯çããªã fact4: ããä»®ã«æ¢¯åããããšãçºçãããšããã°ããŽããŽã¡ã
Lv.7äºä»¶ãçããªãããŸããŸããŸã«ãLv.56äºä»¶ã¯èµ·ãããªãããšããããšã¯ééã£ãŠãã fact5: å
±é³Žãæããšããããšã¯ç°èèããšããããšãæã fact6: ããŽããŽã¡ã
Lv.7äºä»¶ã¯çºçããããã©ãŸããŸã«ãLv.56äºä»¶ã¯èµ·ãããªãããšããããšã¯ééã£ãŠãã ; $hypothesis$ = ãããŽããŽã¡ã
Lv.7äºä»¶ãçºçããªãããã®äžãŸããŸã«ãLv.56äºä»¶ã¯çããªãããšããããšã¯æ¬åœã§ããããšããããšã¯åœã ; $proof$ = | fact3 & fact2 -> int1: ç°èèããšããããšãèµ·ãããã©äŒããé£ããšããããšã¯èµ·ããªã; int1 & fact1 -> int2: 梯åããããšãèµ·ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA} & ¬{AB}) -> {B} fact2: {A} fact3: {A} -> ({AA} & ¬{AB}) fact4: {B} -> ¬(¬{D} & ¬{C}) fact5: {A} -> {AA} fact6: ¬({D} & ¬{C}) ; $hypothesis$ = ¬(¬{D} & ¬{C}) ; $proof$ = | fact3 & fact2 -> int1: ({AA} & ¬{AB}); int1 & fact1 -> int2: {B}; int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ã移æ€åºæ¥ãããšã¯èµ·ããªãããšããããšã¯äºå®ã§ãã | ¬{D} | fact1: 移æ€åºæ¥ãããšã誀ãç¡ããšããããšã¯ãã£ããã§ãã fact2: èæãããšããããšãçºçãã fact3: ãããæã
ãããšããããšãèµ·ããããšããããšã¯äºå®ã ãšããã誀ãç¡ããšããããšãçãã | fact1: {C} -> {D} fact2: {B} fact3: {A} -> {C} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: 移æ€åºæ¥ãããšã誀ãç¡ããšããããšã¯ãã£ããã§ãã fact2: èæãããšããããšãçºçãã fact3: ãããæã
ãããšããããšãèµ·ããããšããããšã¯äºå®ã ãšããã誀ãç¡ããšããããšãçãã ; $hypothesis$ = ã移æ€åºæ¥ãããšã¯èµ·ããªãããšããããšã¯äºå®ã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C} -> {D} fact2: {B} fact3: {A} -> {C} ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ãŸã¡ããŸã¡ãLv.83äºä»¶ã¯èµ·ããªã | ¬{B} | fact1: ããããããšããããšã¯çããªããšããããšã¯ããŽã¡ããŽã«Lv.62äºä»¶ã¯èµ·ãããªãããšããããšãå¥æ©ã§ãã fact2: ãŸã¡ããŸã¡ãLv.83äºä»¶ã¯ãããããããšããããšã¯çããªããŠããã«ã¿ãã¿ãLv.65äºä»¶ã¯èµ·ãããªãããšããããšã«é»ãŸãã fact3: ããããããšããããšã¯èµ·ããªã fact4: ãŽã¡ããŽã«Lv.62äºä»¶ã¯çºçããªã | fact1: ¬{A} -> ¬{AA} fact2: (¬{AA} & ¬{AB}) -> ¬{B} fact3: ¬{AA} fact4: ¬{A} | [] | [] | null | null | [] | null | 2 | 2 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããããããšããããšã¯çããªããšããããšã¯ããŽã¡ããŽã«Lv.62äºä»¶ã¯èµ·ãããªãããšããããšãå¥æ©ã§ãã fact2: ãŸã¡ããŸã¡ãLv.83äºä»¶ã¯ãããããããšããããšã¯çããªããŠããã«ã¿ãã¿ãLv.65äºä»¶ã¯èµ·ãããªãããšããããšã«é»ãŸãã fact3: ããããããšããããšã¯èµ·ããªã fact4: ãŽã¡ããŽã«Lv.62äºä»¶ã¯çºçããªã ; $hypothesis$ = ãŸã¡ããŸã¡ãLv.83äºä»¶ã¯èµ·ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A} -> ¬{AA} fact2: (¬{AA} & ¬{AB}) -> ¬{B} fact3: ¬{AA} fact4: ¬{A} ; $hypothesis$ = ¬{B} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ã«ãã·ãLv.79ã¯èŠãé£ããªãããšããããšã¯çå®ã | ¬{D}{a} | fact1: ããä»®ã«ãã®ã·ã«ãã·ãLv.79ã¯çã£çœããªãããã®ã·ã«ãã·ãLv.79ã¯å¿ãã£ãœããšããããšã¯ãªãäžæ¹ã§ã©ãããŠè¯ãããšããããšã¯ééãã fact2: ãã®ã·ã«ãã·ãLv.79ã¯çžè«ãæã fact3: ããã®ã·ã«ãã·ãLv.79ã¯ããã£ã±ãããããæšããªãããšããããšã¯ç¢ºãã fact4: ãããã®ã·ã«ãã·ãLv.79ã¯æšããªãäžæ¹ã§çžè«ãæããšãããšèŠãé£ããªã fact5: ãããã¢ã³ã¹ã¿ãŒã¯å¿ãã£ãœããªããã©ã©ãããŠè¯ãããšããããšã¯ééãã ãšãããã©ãããŠè¯ããšããããšã¯ãªã fact6: ãã®ã·ã«ãã·ãLv.79ãã©ãããŠè¯ããªããšãããšãã®ãŸã¡ããŸãLv.95ã¯çžè«ãæããŠãŸãèŠãé£ã | fact1: {G}{a} -> ¬(¬{F}{a} & {E}{a}) fact2: {C}{a} fact3: ({A}{a} & ¬{B}{a}) fact4: (¬{B}{a} & {C}{a}) -> ¬{D}{a} fact5: (x): ¬(¬{F}x & {E}x) -> ¬{E}x fact6: ¬{E}{a} -> ({C}{gl} & {D}{gl}) | [
"fact3 -> int1: ãã®ã·ã«ãã·ãLv.79ã¯æšããªã; int1 & fact2 -> int2: ãã®ã·ã«ãã·ãLv.79ã¯æšããªãããã©ããã¯çžè«ãæã; int2 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: ¬{B}{a}; int1 & fact2 -> int2: (¬{B}{a} & {C}{a}); int2 & fact4 -> hypothesis;"
] | ãã®ãŸã¡ããŸãLv.95ã¯ããã£ã±ããªã | ¬{A}{gl} | [
"fact8 -> int3: ä»®ã«ããã®ã·ã«ãã·ãLv.79ã¯å¿ãã£ãœããªãäžæ¹ã§ããã¯ã©ãããŠè¯ãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšããã°ãã©ãããŠè¯ããªãããšããããšã¯æãç«ã€;"
] | 6 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ã·ã«ãã·ãLv.79ã¯çã£çœããªãããã®ã·ã«ãã·ãLv.79ã¯å¿ãã£ãœããšããããšã¯ãªãäžæ¹ã§ã©ãããŠè¯ãããšããããšã¯ééãã fact2: ãã®ã·ã«ãã·ãLv.79ã¯çžè«ãæã fact3: ããã®ã·ã«ãã·ãLv.79ã¯ããã£ã±ãããããæšããªãããšããããšã¯ç¢ºãã fact4: ãããã®ã·ã«ãã·ãLv.79ã¯æšããªãäžæ¹ã§çžè«ãæããšãããšèŠãé£ããªã fact5: ãããã¢ã³ã¹ã¿ãŒã¯å¿ãã£ãœããªããã©ã©ãããŠè¯ãããšããããšã¯ééãã ãšãããã©ãããŠè¯ããšããããšã¯ãªã fact6: ãã®ã·ã«ãã·ãLv.79ãã©ãããŠè¯ããªããšãããšãã®ãŸã¡ããŸãLv.95ã¯çžè«ãæããŠãŸãèŠãé£ã ; $hypothesis$ = ããã®ã·ã«ãã·ãLv.79ã¯èŠãé£ããªãããšããããšã¯çå®ã ; $proof$ = | fact3 -> int1: ãã®ã·ã«ãã·ãLv.79ã¯æšããªã; int1 & fact2 -> int2: ãã®ã·ã«ãã·ãLv.79ã¯æšããªãããã©ããã¯çžè«ãæã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {G}{a} -> ¬(¬{F}{a} & {E}{a}) fact2: {C}{a} fact3: ({A}{a} & ¬{B}{a}) fact4: (¬{B}{a} & {C}{a}) -> ¬{D}{a} fact5: (x): ¬(¬{F}x & {E}x) -> ¬{E}x fact6: ¬{E}{a} -> ({C}{gl} & {D}{gl}) ; $hypothesis$ = ¬{D}{a} ; $proof$ = | fact3 -> int1: ¬{B}{a}; int1 & fact2 -> int2: (¬{B}{a} & {C}{a}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŸã¡ã
ãŸã«Lv.20ã¯äžžãããšããããšã¯äºå®ã | {D}{b} | fact1: ãã®ã¿ã«ãã¿ã«Lv.92ã¯æããã fact2: ãã®ã¿ã«ãã¿ã«Lv.92ã¯å¹Œããªããå ããŠãŠãã | fact1: {C}{a} fact2: ({A}{a} & {B}{a}) | [
"fact2 -> int1: ãã®ã¿ã«ãã¿ã«Lv.92ã¯å¹Œããªã; int1 & fact1 -> int2: ãã®ã¿ã«ãã¿ã«Lv.92ã¯æãããããã€å¹Œããªã;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact1 -> int2: ({C}{a} & {A}{a});"
] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ã¿ã«ãã¿ã«Lv.92ã¯æããã fact2: ãã®ã¿ã«ãã¿ã«Lv.92ã¯å¹Œããªããå ããŠãŠãã ; $hypothesis$ = ããã®ãŸã¡ã
ãŸã«Lv.20ã¯äžžãããšããããšã¯äºå®ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{a} fact2: ({A}{a} & {B}{a}) ; $hypothesis$ = {D}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | é¢åèããšããããšã¯çããªã | ¬{A} | fact1: ããä»®ã«ã説æãæããšããããšãèµ·ããããããã¯åãæ¢ããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãããšãããæ©ããšããããšã¯èµ·ãããªã fact2: ã説æãæããšããããšãèµ·ããããããã¯åãæ¢ããããšãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact3: ãã¿ã«ãã¿ã«ãLv.42äºä»¶ã¯çºçããããŸããŸã¡ãLv.35äºä»¶ã¯çããªãããšããããšã¯èª€ãã§ãããªããé¢åèããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã fact4: ããæ©ããšããããšã¯èµ·ããªããããŸãã«ãŸããŸã¡ãLv.35äºä»¶ã¯èµ·ãããªããªãé¢åèããšããããšãçãã fact5: ããä»®ã«ãã¿ãã¿ã«Lv.13äºä»¶ãèµ·ããããããæ©ããšããããšã¯çããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ã¿ãã¿ã«Lv.13äºä»¶ã¯èµ·ããªã fact6: ãããæ©ããšããããšã¯çºçããªããªãã°æ©ããšããããšã¯çããªãããŸããŸã¡ãLv.35äºä»¶ã¯çããªã fact7: ã¿ã«ãã¿ã«ãLv.42äºä»¶ãèµ·ãããšãããšãæ©ããšããããšãèµ·ããããŸããŸã¡ãLv.35äºä»¶ã¯çºçããªãããšããããšã¯ééã£ãŠãã fact8: ä»®ã«é¢åèããšããããšã¯çºçããªããšããã°ãã¿ãã¿ã«Lv.13äºä»¶ãçºçããäžæ¹ã§æ©ããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªã | fact1: ¬({AA} v {AB}) -> ¬{B} fact2: ¬({AA} v {AB}) fact3: ¬({D} v ¬{C}) -> ¬{A} fact4: (¬{B} & ¬{C}) -> {A} fact5: ¬({IS} & ¬{B}) -> ¬{IS} fact6: ¬{B} -> (¬{B} & ¬{C}) fact7: {D} -> ¬({B} & ¬{C}) fact8: ¬{A} -> ¬({IS} & ¬{B}) | [
"fact1 & fact2 -> int1: æ©ããšããããšã¯çºçããªã; int1 & fact6 -> int2: æ©ããšããããšã¯çããªããŠãŸããŸã¡ãLv.35äºä»¶ã¯çããªã; int2 & fact4 -> hypothesis;"
] | [
"fact1 & fact2 -> int1: ¬{B}; int1 & fact6 -> int2: (¬{B} & ¬{C}); int2 & fact4 -> hypothesis;"
] | ã¿ãã¿ã«Lv.13äºä»¶ã¯èµ·ãããªã | ¬{IS} | [] | 8 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ã説æãæããšããããšãèµ·ããããããã¯åãæ¢ããããšãèµ·ããããããã¯äž¡æ¹ã ããšããããšã¯ééã£ãŠãããšãããæ©ããšããããšã¯èµ·ãããªã fact2: ã説æãæããšããããšãèµ·ããããããã¯åãæ¢ããããšãèµ·ããããšããããšã¯äºå®ãšç°ãªã fact3: ãã¿ã«ãã¿ã«ãLv.42äºä»¶ã¯çºçããããŸããŸã¡ãLv.35äºä»¶ã¯çããªãããšããããšã¯èª€ãã§ãããªããé¢åèããšããããšã¯èµ·ãããªãããšããããšã¯çå®ã fact4: ããæ©ããšããããšã¯èµ·ããªããããŸãã«ãŸããŸã¡ãLv.35äºä»¶ã¯èµ·ãããªããªãé¢åèããšããããšãçãã fact5: ããä»®ã«ãã¿ãã¿ã«Lv.13äºä»¶ãèµ·ããããããæ©ããšããããšã¯çããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããªãã°ã¿ãã¿ã«Lv.13äºä»¶ã¯èµ·ããªã fact6: ãããæ©ããšããããšã¯çºçããªããªãã°æ©ããšããããšã¯çããªãããŸããŸã¡ãLv.35äºä»¶ã¯çããªã fact7: ã¿ã«ãã¿ã«ãLv.42äºä»¶ãèµ·ãããšãããšãæ©ããšããããšãèµ·ããããŸããŸã¡ãLv.35äºä»¶ã¯çºçããªãããšããããšã¯ééã£ãŠãã fact8: ä»®ã«é¢åèããšããããšã¯çºçããªããšããã°ãã¿ãã¿ã«Lv.13äºä»¶ãçºçããäžæ¹ã§æ©ããšããããšã¯èµ·ãããªãããšããããšã¯æãç«ããªã ; $hypothesis$ = é¢åèããšããããšã¯çããªã ; $proof$ = | fact1 & fact2 -> int1: æ©ããšããããšã¯çºçããªã; int1 & fact6 -> int2: æ©ããšããããšã¯çããªããŠãŸããŸã¡ãLv.35äºä»¶ã¯çããªã; int2 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬({AA} v {AB}) -> ¬{B} fact2: ¬({AA} v {AB}) fact3: ¬({D} v ¬{C}) -> ¬{A} fact4: (¬{B} & ¬{C}) -> {A} fact5: ¬({IS} & ¬{B}) -> ¬{IS} fact6: ¬{B} -> (¬{B} & ¬{C}) fact7: {D} -> ¬({B} & ¬{C}) fact8: ¬{A} -> ¬({IS} & ¬{B}) ; $hypothesis$ = ¬{A} ; $proof$ = | fact1 & fact2 -> int1: ¬{B}; int1 & fact6 -> int2: (¬{B} & ¬{C}); int2 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | åºé£ããšããããšã¯èµ·ããªã | ¬{D} | fact1: ãŽã«ããŽãLv.14äºä»¶ãèµ·ãããšããããšã¯åºé£ããšããããšãåé¿ãã fact2: ãã€ãã£ãããããšããããšãèµ·ãã fact3: æ ¹åŒ·ããšããããšãçããããã€ãŸããŸãLv.4äºä»¶ãèµ·ãã fact4: ãŽã«ããŽãLv.14äºä»¶ããæ ¹åŒ·ããšããããšãèµ·ããããšããããšã¯åå ã fact5: ãŸããŸãLv.4äºä»¶ãèµ·ãã | fact1: {C} -> ¬{D} fact2: {HC} fact3: ({A} & {B}) fact4: {A} -> {C} fact5: {B} | [
"fact3 -> int1: æ ¹åŒ·ããšããããšãèµ·ãã; int1 & fact4 -> int2: ããŽã«ããŽãLv.14äºä»¶ãçããããšããããšã¯ç¢ºãã ; int2 & fact1 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãŽã«ããŽãLv.14äºä»¶ãèµ·ãããšããããšã¯åºé£ããšããããšãåé¿ãã fact2: ãã€ãã£ãããããšããããšãèµ·ãã fact3: æ ¹åŒ·ããšããããšãçããããã€ãŸããŸãLv.4äºä»¶ãèµ·ãã fact4: ãŽã«ããŽãLv.14äºä»¶ããæ ¹åŒ·ããšããããšãèµ·ããããšããããšã¯åå ã fact5: ãŸããŸãLv.4äºä»¶ãèµ·ãã ; $hypothesis$ = åºé£ããšããããšã¯èµ·ããªã ; $proof$ = | fact3 -> int1: æ ¹åŒ·ããšããããšãèµ·ãã; int1 & fact4 -> int2: ããŽã«ããŽãLv.14äºä»¶ãçããããšããããšã¯ç¢ºãã ; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} -> ¬{D} fact2: {HC} fact3: ({A} & {B}) fact4: {A} -> {C} fact5: {B} ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 -> int1: {A}; int1 & fact4 -> int2: {C}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãèš³ç¡ããšããããšãèµ·ãããå ãæ²ãããšã¯èµ·ããªãããšããããšã¯èª€ãã§ãã | ¬({E} & ¬{D}) | fact1: é¥ãæããšããããšã¯ãèš³ç¡ããšããããšãçãããå ãæ²ãããšã¯çºçããªãããšããããšãçãããã fact2: åºã
ãããšããããšã¯ãé¥ãæããšããããšãèµ·ããããšããããšã«åž°çµãã fact3: åºã
ãããšããããšãšãŽã«ã
ãŽãLv.94äºä»¶ã©ã¡ãããçãã fact4: ããŽã«ã
ãŽãLv.94äºä»¶ãèµ·ããããšããããšã¯çå®ã fact5: ããä»®ã«åºã
ãããšããããšã¯èµ·ãããªããªããèš³ç¡ããšããããšã¯çºçãããå ãæ²ãããšã¯èµ·ãããªãããšããããšã¯èª€ãã§ãã fact6: éŠãããšããããšã¯çºçããªããšããããšã¯ã¿ã«ã¿ã®Lv.86äºä»¶ã«åŒãèµ·ãããã fact7: ãŸããŸãLv.0äºä»¶ãšéãæããšããããšã©ã¡ãããçãã | fact1: {C} -> ({E} & ¬{D}) fact2: {A} -> {C} fact3: ({A} & {B}) fact4: {B} fact5: ¬{A} -> ¬({E} & ¬{D}) fact6: {FQ} -> ¬{EQ} fact7: ({J} & {GN}) | [
"fact3 -> int1: åºã
ãããšããããšãèµ·ãã; int1 & fact2 -> int2: é¥ãæããšããããšãçºçãã; int2 & fact1 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 & fact2 -> int2: {C}; int2 & fact1 -> hypothesis;"
] | ãèš³ç¡ããšããããšãèµ·ãããå ãæ²ãããšã¯èµ·ããªãããšããããšã¯èª€ãã§ãã | ¬({E} & ¬{D}) | [] | 6 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: é¥ãæããšããããšã¯ãèš³ç¡ããšããããšãçãããå ãæ²ãããšã¯çºçããªãããšããããšãçãããã fact2: åºã
ãããšããããšã¯ãé¥ãæããšããããšãèµ·ããããšããããšã«åž°çµãã fact3: åºã
ãããšããããšãšãŽã«ã
ãŽãLv.94äºä»¶ã©ã¡ãããçãã fact4: ããŽã«ã
ãŽãLv.94äºä»¶ãèµ·ããããšããããšã¯çå®ã fact5: ããä»®ã«åºã
ãããšããããšã¯èµ·ãããªããªããèš³ç¡ããšããããšã¯çºçãããå ãæ²ãããšã¯èµ·ãããªãããšããããšã¯èª€ãã§ãã fact6: éŠãããšããããšã¯çºçããªããšããããšã¯ã¿ã«ã¿ã®Lv.86äºä»¶ã«åŒãèµ·ãããã fact7: ãŸããŸãLv.0äºä»¶ãšéãæããšããããšã©ã¡ãããçãã ; $hypothesis$ = ãèš³ç¡ããšããããšãèµ·ãããå ãæ²ãããšã¯èµ·ããªãããšããããšã¯èª€ãã§ãã ; $proof$ = | fact3 -> int1: åºã
ãããšããããšãèµ·ãã; int1 & fact2 -> int2: é¥ãæããšããããšãçºçãã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {C} -> ({E} & ¬{D}) fact2: {A} -> {C} fact3: ({A} & {B}) fact4: {B} fact5: ¬{A} -> ¬({E} & ¬{D}) fact6: {FQ} -> ¬{EQ} fact7: ({J} & {GN}) ; $hypothesis$ = ¬({E} & ¬{D}) ; $proof$ = | fact3 -> int1: {A}; int1 & fact2 -> int2: {C}; int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ã«ã·ãLv.17ã¯æž©ããªã | ¬{C}{aa} | fact1: ããããã®ãã«ã
ããLv.37ã圫ãäžãããšããããšã¯ãªããšããã°ãã®ã·ã«ã·ãLv.17ã¯æž©ãããããã«ã匱ã fact2: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã圫ãäžããªããªãã°ããã¯æž©ããªã fact3: ãã®ã·ã«ã·ãLv.17ã¯åœ«ãäžããªã fact4: ä»®ã«ããã®ãœããœãLv.76ã¯ä»æ¹ç¡ããªãããã©ããã¯æåãããšããããšã¯èª€ããªããã®ãã«ã
ããLv.37ã¯åœ«ãäžããªã | fact1: ¬{B}{a} -> ({C}{aa} & {A}{aa}) fact2: (x): ¬{B}x -> ¬{C}x fact3: ¬{B}{aa} fact4: ¬(¬{E}{b} & {D}{b}) -> ¬{B}{a} | [
"fact2 -> int1: ä»®ã«ãã®ã·ã«ã·ãLv.17ã圫ãäžããªããªãã°æž©ããªã; int1 & fact3 -> hypothesis;"
] | [
"fact2 -> int1: ¬{B}{aa} -> ¬{C}{aa}; int1 & fact3 -> hypothesis;"
] | ãã®ã·ã«ã·ãLv.17ã¯æž©ãã | {C}{aa} | [] | 6 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã®ãã«ã
ããLv.37ã圫ãäžãããšããããšã¯ãªããšããã°ãã®ã·ã«ã·ãLv.17ã¯æž©ãããããã«ã匱ã fact2: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã圫ãäžããªããªãã°ããã¯æž©ããªã fact3: ãã®ã·ã«ã·ãLv.17ã¯åœ«ãäžããªã fact4: ä»®ã«ããã®ãœããœãLv.76ã¯ä»æ¹ç¡ããªãããã©ããã¯æåãããšããããšã¯èª€ããªããã®ãã«ã
ããLv.37ã¯åœ«ãäžããªã ; $hypothesis$ = ãã®ã·ã«ã·ãLv.17ã¯æž©ããªã ; $proof$ = | fact2 -> int1: ä»®ã«ãã®ã·ã«ã·ãLv.17ã圫ãäžããªããªãã°æž©ããªã; int1 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{B}{a} -> ({C}{aa} & {A}{aa}) fact2: (x): ¬{B}x -> ¬{C}x fact3: ¬{B}{aa} fact4: ¬(¬{E}{b} & {D}{b}) -> ¬{B}{a} ; $hypothesis$ = ¬{C}{aa} ; $proof$ = | fact2 -> int1: ¬{B}{aa} -> ¬{C}{aa}; int1 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ãã·ã«ã
Lv.86ã¯æã
ãããªã | ¬{D}{b} | fact1: ããã®ããããLv.97ã¯ãã¡ã£ãããªãããšããããšã¯çå®ã§ãã fact2: ãããæ
ç¡ããªãã¢ã³ã¹ã¿ãŒãå
ãé£ããªããšããããã¡ã£ãããªã fact3: ãã®ããããLv.97ã¯åŠå®ãé£ããšããããšã¯ãªãäžæ¹ã§ããã¯ç§»ãé£ã fact4: ãã®ããããLv.97ã¯ç§»ãé£ã fact5: ãã®ããããLv.97ã¯åŠå®ãé£ããªãã移ãé£ããšãããå
ãé£ã fact6: ãã®ããããLv.97ãå
ãé£ããšãããšãã®ããããLv.97ã¯ãã¡ã£ãããªãäžæ¹ã§æ
ç¡ã fact7: ããã¡ã£ãããªãã¢ã³ã¹ã¿ãŒã¯çã
ãããªãããã©éŠŽæã¿æ·±ãããšããããšã¯æ£ãã fact8: ããããã®ããããLv.97ããã¡ã£ãããªãäžæ¹ã§ãããæ
ç¡ããšãããšãã®ã·ãã·ã«ã
Lv.86ã¯æã
ãããšããããšã¯ãªã | fact1: ¬{A}{a} fact2: (x): (¬{C}x & ¬{B}x) -> ¬{A}x fact3: (¬{AA}{a} & {AB}{a}) fact4: {AB}{a} fact5: (¬{AA}{a} & {AB}{a}) -> {B}{a} fact6: {B}{a} -> (¬{A}{a} & {C}{a}) fact7: (x): ¬{A}x -> (¬{IH}x & {IT}x) fact8: (¬{A}{a} & {C}{a}) -> ¬{D}{b} | [
"fact5 & fact3 -> int1: ãã®ããããLv.97ã¯å
ãé£ã; int1 & fact6 -> int2: ãã®ããããLv.97ã¯ãã¡ã£ãããªãããããæ
ç¡ã; int2 & fact8 -> hypothesis;"
] | [
"fact5 & fact3 -> int1: {B}{a}; int1 & fact6 -> int2: (¬{A}{a} & {C}{a}); int2 & fact8 -> hypothesis;"
] | ãã®ããªãã¡ãLv.88ã¯çã
ãããšããããšã¯ãªãã銎æã¿æ·±ã | (¬{IH}{m} & {IT}{m}) | [
"fact9 -> int3: ãããã®ããªãã¡ãLv.88ããã¡ã£ãããªããªãã°ãã®ããªãã¡ãLv.88ã¯çã
ãããªããããã銎æã¿æ·±ã; fact10 -> int4: ããã®ããªãã¡ãLv.88ã¯æ
ç¡ããªããŠãŸãå
ãé£ããªãããšããããšã¯æ¬åœã ãšããã°ããã¯ãã¡ã£ãããªã;"
] | 4 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããã®ããããLv.97ã¯ãã¡ã£ãããªãããšããããšã¯çå®ã§ãã fact2: ãããæ
ç¡ããªãã¢ã³ã¹ã¿ãŒãå
ãé£ããªããšããããã¡ã£ãããªã fact3: ãã®ããããLv.97ã¯åŠå®ãé£ããšããããšã¯ãªãäžæ¹ã§ããã¯ç§»ãé£ã fact4: ãã®ããããLv.97ã¯ç§»ãé£ã fact5: ãã®ããããLv.97ã¯åŠå®ãé£ããªãã移ãé£ããšãããå
ãé£ã fact6: ãã®ããããLv.97ãå
ãé£ããšãããšãã®ããããLv.97ã¯ãã¡ã£ãããªãäžæ¹ã§æ
ç¡ã fact7: ããã¡ã£ãããªãã¢ã³ã¹ã¿ãŒã¯çã
ãããªãããã©éŠŽæã¿æ·±ãããšããããšã¯æ£ãã fact8: ããããã®ããããLv.97ããã¡ã£ãããªãäžæ¹ã§ãããæ
ç¡ããšãããšãã®ã·ãã·ã«ã
Lv.86ã¯æã
ãããšããããšã¯ãªã ; $hypothesis$ = ãã®ã·ãã·ã«ã
Lv.86ã¯æã
ãããªã ; $proof$ = | fact5 & fact3 -> int1: ãã®ããããLv.97ã¯å
ãé£ã; int1 & fact6 -> int2: ãã®ããããLv.97ã¯ãã¡ã£ãããªãããããæ
ç¡ã; int2 & fact8 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{a} fact2: (x): (¬{C}x & ¬{B}x) -> ¬{A}x fact3: (¬{AA}{a} & {AB}{a}) fact4: {AB}{a} fact5: (¬{AA}{a} & {AB}{a}) -> {B}{a} fact6: {B}{a} -> (¬{A}{a} & {C}{a}) fact7: (x): ¬{A}x -> (¬{IH}x & {IT}x) fact8: (¬{A}{a} & {C}{a}) -> ¬{D}{b} ; $hypothesis$ = ¬{D}{b} ; $proof$ = | fact5 & fact3 -> int1: {B}{a}; int1 & fact6 -> int2: (¬{A}{a} & {C}{a}); int2 & fact8 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ãã¿ã«Lv.33ã¯æ§è¯ã | {B}{b} | fact1: ãã®ãŽã«ããŽãLv.15ã¯éãæããªã fact2: ãã®ãŽã«ããŽãLv.15ã¯éãæããªããªãã°ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ãããã€ãã§ããããšããããšã¯äºå®ãšç°ãªã fact3: ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ããŠãã§ããããšããããšã¯èª€ãã ãšããã°ãã®ã¿ãã¿ã«Lv.33ã¯æ§è¯ããªã | fact1: ¬{A}{a} fact2: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact3: ¬({AA}{b} & {AB}{b}) -> ¬{B}{b} | [
"fact2 & fact1 -> int1: ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ãããã®äžãã§ããããšããããšã¯åã ; int1 & fact3 -> hypothesis;"
] | [
"fact2 & fact1 -> int1: ¬({AA}{b} & {AB}{b}); int1 & fact3 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãŽã«ããŽãLv.15ã¯éãæããªã fact2: ãã®ãŽã«ããŽãLv.15ã¯éãæããªããªãã°ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ãããã€ãã§ããããšããããšã¯äºå®ãšç°ãªã fact3: ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ããŠãã§ããããšããããšã¯èª€ãã ãšããã°ãã®ã¿ãã¿ã«Lv.33ã¯æ§è¯ããªã ; $hypothesis$ = ãã®ã¿ãã¿ã«Lv.33ã¯æ§è¯ã ; $proof$ = | fact2 & fact1 -> int1: ããã®ã¿ãã¿ã«Lv.33ã¯å©çšãé£ãããã®äžãã§ããããšããããšã¯åã ; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{a} fact2: ¬{A}{a} -> ¬({AA}{b} & {AB}{b}) fact3: ¬({AA}{b} & {AB}{b}) -> ¬{B}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | fact2 & fact1 -> int1: ¬({AA}{b} & {AB}{b}); int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | èŸæ°èããšããããšã¯èµ·ãããªãããŸãåŒã³æããšããããšã¯çºçããªã | (¬{B} & ¬{C}) | fact1: ããããèŸæ°èããšããããšã¯çããªããåžžé£ããããšãçºçããããšããããšã¯ééãã§ããããšããããšã¯äºå®ã ãšããã°åžžé£ããããšã¯èµ·ããªã fact2: çºæããããšãçãããšãããšãèŸæ°èããšããããšã¯èµ·ããªãããã©åžžé£ããããšãçããããšããããšã¯ééãã fact3: åŒã³æããšããããšã¯çºçããªã fact4: ä»®ã«çºæããããšã¯èµ·ãããªããªãã°èŠæç¡ããšããããšã¯èµ·ããªãããã©å
±é³Žãæããšããããšãçãã fact5: ãèŸæ°èããšããããšã¯çºçããªãããšããããšã¯ãèŠæç¡ããšããããšã§ã¯ãªãå
±é³Žãæããšããããšãçããããšããããšã«èµ·å ãã fact6: ãæ¢ãæããšããããšã¯èµ·ãããªãããšããããšã¯ãçºæããããšãèµ·ãããæŽã«åŒã³æããšããããšãçºçããããšããããšãèªçºãã | fact1: ¬(¬{B} & {AC}) -> ¬{AC} fact2: {A} -> ¬(¬{B} & {AC}) fact3: ¬{C} fact4: ¬{A} -> (¬{AA} & {AB}) fact5: (¬{AA} & {AB}) -> ¬{B} fact6: ¬{D} -> ({A} & {C}) | [] | [] | åžžé£ããããšã¯çããªã | ¬{AC} | [] | 8 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããèŸæ°èããšããããšã¯çããªããåžžé£ããããšãçºçããããšããããšã¯ééãã§ããããšããããšã¯äºå®ã ãšããã°åžžé£ããããšã¯èµ·ããªã fact2: çºæããããšãçãããšãããšãèŸæ°èããšããããšã¯èµ·ããªãããã©åžžé£ããããšãçããããšããããšã¯ééãã fact3: åŒã³æããšããããšã¯çºçããªã fact4: ä»®ã«çºæããããšã¯èµ·ãããªããªãã°èŠæç¡ããšããããšã¯èµ·ããªãããã©å
±é³Žãæããšããããšãçãã fact5: ãèŸæ°èããšããããšã¯çºçããªãããšããããšã¯ãèŠæç¡ããšããããšã§ã¯ãªãå
±é³Žãæããšããããšãçããããšããããšã«èµ·å ãã fact6: ãæ¢ãæããšããããšã¯èµ·ãããªãããšããããšã¯ãçºæããããšãèµ·ãããæŽã«åŒã³æããšããããšãçºçããããšããããšãèªçºãã ; $hypothesis$ = èŸæ°èããšããããšã¯èµ·ãããªãããŸãåŒã³æããšããããšã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{B} & {AC}) -> ¬{AC} fact2: {A} -> ¬(¬{B} & {AC}) fact3: ¬{C} fact4: ¬{A} -> (¬{AA} & {AB}) fact5: (¬{AA} & {AB}) -> ¬{B} fact6: ¬{D} -> ({A} & {C}) ; $hypothesis$ = (¬{B} & ¬{C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããå©çšãé£ãã¢ã³ã¹ã¿ãŒã§ããé§ããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æ¬åœã ããšããããšã¯èª€ãã | ¬((Ex): ({AA}x & ¬{AB}x)) | fact1: ãããã®ããããLv.11ãé²ã¿æããªããšããã°ããã¯å©çšãé£ã fact2: ãã®ããããLv.11ã¯é²ã¿æããªã fact3: ããä»®ã«ãã®ããããLv.11ã¯é²ã¿æãããšããããšã¯ãªããšãããšããã®ããããLv.11ã¯å©çšãé£ãããããé§ããªãããšããããšã¯æãç«ã€ fact4: ãã®ããããLv.11ã¯å©çšãé£ã fact5: ãããäœããã®ã¢ã³ã¹ã¿ãŒãé²ã¿æãããšãããšä¹ãéããããã©å°é£ãããªã fact6: å©çšãé£ãã¢ã³ã¹ã¿ãŒã§ããŸãã«é§ãã¢ã³ã¹ã¿ãŒã¯ãã | fact1: ¬{A}{a} -> {AA}{a} fact2: ¬{A}{a} fact3: ¬{A}{a} -> ({AA}{a} & ¬{AB}{a}) fact4: {AA}{a} fact5: (x): {A}x -> ({HB}x & ¬{BD}x) fact6: (Ex): ({AA}x & {AB}x) | [
"fact3 & fact2 -> int1: ãã®ããããLv.11ã¯å©çšãé£ãããã©é§ããªã; int1 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: ({AA}{a} & ¬{AB}{a}); int1 -> hypothesis;"
] | äœããã®ã¢ã³ã¹ã¿ãŒã¯ä¹ãéããããããããã¯å°é£ãããšããããšã¯ãªã | (Ex): ({HB}x & ¬{BD}x) | [
"fact7 -> int2: ãã®ããããLv.11ãé²ã¿æãããšãããä¹ãéããäžæ¹ã§å°é£ãããªã;"
] | 5 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãããã®ããããLv.11ãé²ã¿æããªããšããã°ããã¯å©çšãé£ã fact2: ãã®ããããLv.11ã¯é²ã¿æããªã fact3: ããä»®ã«ãã®ããããLv.11ã¯é²ã¿æãããšããããšã¯ãªããšãããšããã®ããããLv.11ã¯å©çšãé£ãããããé§ããªãããšããããšã¯æãç«ã€ fact4: ãã®ããããLv.11ã¯å©çšãé£ã fact5: ãããäœããã®ã¢ã³ã¹ã¿ãŒãé²ã¿æãããšãããšä¹ãéããããã©å°é£ãããªã fact6: å©çšãé£ãã¢ã³ã¹ã¿ãŒã§ããŸãã«é§ãã¢ã³ã¹ã¿ãŒã¯ãã ; $hypothesis$ = ããå©çšãé£ãã¢ã³ã¹ã¿ãŒã§ããé§ããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯æ¬åœã ããšããããšã¯èª€ãã ; $proof$ = | fact3 & fact2 -> int1: ãã®ããããLv.11ã¯å©çšãé£ãããã©é§ããªã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{a} -> {AA}{a} fact2: ¬{A}{a} fact3: ¬{A}{a} -> ({AA}{a} & ¬{AB}{a}) fact4: {AA}{a} fact5: (x): {A}x -> ({HB}x & ¬{BD}x) fact6: (Ex): ({AA}x & {AB}x) ; $hypothesis$ = ¬((Ex): ({AA}x & ¬{AB}x)) ; $proof$ = | fact3 & fact2 -> int1: ({AA}{a} & ¬{AB}{a}); int1 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæããŠãã€å宿ããããšããããšã¯äºå®ãšç°ãªããªã | ({AA}{a} & {B}{a}) | fact1: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯å宿ãã fact2: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯èç©ããæããªã fact3: ãããã®ã¿ã¡ã
ã¿ãLv.3ãèç©ããæããªããšãããšããã¯ç¹ããæããŠãã€å°é£ãã | fact1: {B}{a} fact2: ¬{A}{a} fact3: ¬{A}{a} -> ({AA}{a} & {AB}{a}) | [
"fact3 & fact2 -> int1: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæããŠå°é£ãã; int1 -> int2: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæã; int2 & fact1 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: ({AA}{a} & {AB}{a}); int1 -> int2: {AA}{a}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯å宿ãã fact2: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯èç©ããæããªã fact3: ãããã®ã¿ã¡ã
ã¿ãLv.3ãèç©ããæããªããšãããšããã¯ç¹ããæããŠãã€å°é£ãã ; $hypothesis$ = ããã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæããŠãã€å宿ããããšããããšã¯äºå®ãšç°ãªããªã ; $proof$ = | fact3 & fact2 -> int1: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæããŠå°é£ãã; int1 -> int2: ãã®ã¿ã¡ã
ã¿ãLv.3ã¯ç¹ããæã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{a} fact2: ¬{A}{a} fact3: ¬{A}{a} -> ({AA}{a} & {AB}{a}) ; $hypothesis$ = ({AA}{a} & {B}{a}) ; $proof$ = | fact3 & fact2 -> int1: ({AA}{a} & {AB}{a}); int1 -> int2: {AA}{a}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ãã·ã¡ã
ã·ãªLv.37äºä»¶ã§ã¯ãªãèŠã
ãããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãã | ¬(¬{C} & {A}) | fact1: ã湧ãåºã§ãããšã§ã¯ãªãæ¶åãé£ããšããããšãèµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact2: ããæ·¡ããšããããšã¯çããªããšããã°ãã·ã¡ã
ã·ãªLv.37äºä»¶ã¯çºçããªããŠèŠã
ãããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãã fact3: ãèŠæç¡ããšããããšã§ã¯ãªããã¡ã
ãã«ãLv.45äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã fact4: 山深ããšããããšã¯èµ·ãããªã fact5: ãåæžåºæ¥ãããšã¯èµ·ãããªããã©ã¿ã¡ãã¿ã«ãLv.54äºä»¶ãçããããšããããšã¯æãç«ããªã fact6: ãã·ã¡ã
ã·ãªLv.37äºä»¶ãèµ·ããããããèŠã
ãããšããããšãçºçããããšããããšã¯åœã§ãã | fact1: ¬(¬{DE} & {DH}) fact2: ¬{B} -> ¬(¬{C} & {A}) fact3: ¬(¬{AA} & {AB}) fact4: ¬{DO} fact5: ¬(¬{CJ} & {HO}) fact6: ¬({C} & {A}) | [] | [] | null | null | [] | null | 2 | 2 | null | null | 4 | 0 | 4 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ã湧ãåºã§ãããšã§ã¯ãªãæ¶åãé£ããšããããšãèµ·ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact2: ããæ·¡ããšããããšã¯çããªããšããã°ãã·ã¡ã
ã·ãªLv.37äºä»¶ã¯çºçããªããŠèŠã
ãããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãã fact3: ãèŠæç¡ããšããããšã§ã¯ãªããã¡ã
ãã«ãLv.45äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã fact4: 山深ããšããããšã¯èµ·ãããªã fact5: ãåæžåºæ¥ãããšã¯èµ·ãããªããã©ã¿ã¡ãã¿ã«ãLv.54äºä»¶ãçããããšããããšã¯æãç«ããªã fact6: ãã·ã¡ã
ã·ãªLv.37äºä»¶ãèµ·ããããããèŠã
ãããšããããšãçºçããããšããããšã¯åœã§ãã ; $hypothesis$ = ãã·ã¡ã
ã·ãªLv.37äºä»¶ã§ã¯ãªãèŠã
ãããšããããšãèµ·ããããšããããšã¯èª€ã£ãŠãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{DE} & {DH}) fact2: ¬{B} -> ¬(¬{C} & {A}) fact3: ¬(¬{AA} & {AB}) fact4: ¬{DO} fact5: ¬(¬{CJ} & {HO}) fact6: ¬({C} & {A}) ; $hypothesis$ = ¬(¬{C} & {A}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã¿ã«ãã¿ãLv.33ã¯ã¡ã£ãããªãããšããããšã¯æãç«ã€ | ¬{B}{aa} | fact1: ããšããã¢ã³ã¹ã¿ãŒã¯èããé£ããªããæŒãæããªãããšããããšã¯èª€ãã§ãããšããã°ã¡ã£ãããªã fact2: æŒãæãã¢ã³ã¹ã¿ãŒã¯ã¡ã£ãããšããããšã¯ãªã | fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact2: (x): {AB}x -> ¬{B}x | [
"fact1 -> int1: ããããã®ã¿ã«ãã¿ãLv.33ã¯èããé£ããªããŠæŒãæããªãããšããããšã¯æãç«ããªããªãã°ãã®ã¿ã«ãã¿ãLv.33ã¯ã¡ã£ãããªã;"
] | [
"fact1 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa};"
] | null | null | [] | null | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããšããã¢ã³ã¹ã¿ãŒã¯èããé£ããªããæŒãæããªãããšããããšã¯èª€ãã§ãããšããã°ã¡ã£ãããªã fact2: æŒãæãã¢ã³ã¹ã¿ãŒã¯ã¡ã£ãããšããããšã¯ãªã ; $hypothesis$ = ããã®ã¿ã«ãã¿ãLv.33ã¯ã¡ã£ãããªãããšããããšã¯æãç«ã€ ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact2: (x): {AB}x -> ¬{B}x ; $hypothesis$ = ¬{B}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŸã¡ããŸã«Lv.64ã¯çŽ³å£«ããã | {D}{c} | fact1: ãã®ã¿ã¡ã
ã¿ã«ãLv.32ãæããšããããšã¯ãªããªããã®ãŸã¡ããŸã«Lv.64ã¯æããšããããšã¯ãªãããããã¯çµ±ã¹ããšããããšã¯ãªããã©ã¡ããã§ãã fact2: ããä»®ã«ãã®ãŸã¡ããŸã«Lv.64ãæããªãããããçµ±ã¹ããšããããšã¯ãªãããããã¯äž¡æ¹ãªããã®ãŸã¡ããŸã«Lv.64ã¯çŽ³å£«ããããªã fact3: ãã®ã¿ã¡ã
ã¿ã«ãLv.32ã¯æããªããããã¯ç·åŒããããšããããšã¯ãªã fact4: ãã®ã¿ãã¿ãLv.69ã¯ç·åŒããã fact5: ããã®ãŸã¡ããŸã«Lv.64ã¯äºæž¬ãé£ãããããã¯çµ±ã¹ããšããããšã¯ãªããäž¡æ¹ãšãã ããšããããšã¯æãç«ããªããšãããšæããšããããšã¯ãªã fact6: ä»®ã«ãã®ã¿ã¡ã
ã¿ã«ãLv.32ãæããªããšãããšãã®ãŸã¡ããŸã«Lv.64ã¯æããªãããŸãã¯çµ±ã¹ãããŸãã¯äž¡æ¹ã | fact1: ¬{B}{b} -> (¬{B}{c} v ¬{C}{c}) fact2: (¬{B}{c} v ¬{C}{c}) -> ¬{D}{c} fact3: (¬{B}{b} v ¬{A}{b}) fact4: {A}{a} fact5: ¬({E}{c} v ¬{C}{c}) -> ¬{B}{c} fact6: ¬{B}{b} -> (¬{B}{c} v {C}{c}) | [] | [] | ãã®ãŸã¡ããŸã«Lv.64ã¯çŽ³å£«ããã | {D}{c} | [] | 5 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ã¿ã¡ã
ã¿ã«ãLv.32ãæããšããããšã¯ãªããªããã®ãŸã¡ããŸã«Lv.64ã¯æããšããããšã¯ãªãããããã¯çµ±ã¹ããšããããšã¯ãªããã©ã¡ããã§ãã fact2: ããä»®ã«ãã®ãŸã¡ããŸã«Lv.64ãæããªãããããçµ±ã¹ããšããããšã¯ãªãããããã¯äž¡æ¹ãªããã®ãŸã¡ããŸã«Lv.64ã¯çŽ³å£«ããããªã fact3: ãã®ã¿ã¡ã
ã¿ã«ãLv.32ã¯æããªããããã¯ç·åŒããããšããããšã¯ãªã fact4: ãã®ã¿ãã¿ãLv.69ã¯ç·åŒããã fact5: ããã®ãŸã¡ããŸã«Lv.64ã¯äºæž¬ãé£ãããããã¯çµ±ã¹ããšããããšã¯ãªããäž¡æ¹ãšãã ããšããããšã¯æãç«ããªããšãããšæããšããããšã¯ãªã fact6: ä»®ã«ãã®ã¿ã¡ã
ã¿ã«ãLv.32ãæããªããšãããšãã®ãŸã¡ããŸã«Lv.64ã¯æããªãããŸãã¯çµ±ã¹ãããŸãã¯äž¡æ¹ã ; $hypothesis$ = ãã®ãŸã¡ããŸã«Lv.64ã¯çŽ³å£«ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{B}{b} -> (¬{B}{c} v ¬{C}{c}) fact2: (¬{B}{c} v ¬{C}{c}) -> ¬{D}{c} fact3: (¬{B}{b} v ¬{A}{b}) fact4: {A}{a} fact5: ¬({E}{c} v ¬{C}{c}) -> ¬{B}{c} fact6: ¬{B}{b} -> (¬{B}{c} v {C}{c}) ; $hypothesis$ = {D}{c} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãããã«Lv.48ã¯é ããªããæŽã«æµãæããšããããšã¯ãªã | (¬{D}{c} & ¬{C}{c}) | fact1: ãããããã®ãããã«Lv.48ã¯äœãããšããããšã¯äºå®ã§ããã°ãã®ããããLv.28ã¯é ããªããæŽã«æšããªã fact2: ããããã®ããããLv.28ãäœããšããã°ãã®ãã¡ãããLv.33ã¯æšã fact3: ãã®ãã¡ãããLv.33ãæšããšããã°ãã®ãããã«Lv.48ã¯é ããªãããŸãæµãæããªã | fact1: {A}{c} -> (¬{D}{a} & ¬{B}{a}) fact2: {A}{a} -> {B}{b} fact3: {B}{b} -> (¬{D}{c} & ¬{C}{c}) | [] | [] | null | null | [] | null | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããããã®ãããã«Lv.48ã¯äœãããšããããšã¯äºå®ã§ããã°ãã®ããããLv.28ã¯é ããªããæŽã«æšããªã fact2: ããããã®ããããLv.28ãäœããšããã°ãã®ãã¡ãããLv.33ã¯æšã fact3: ãã®ãã¡ãããLv.33ãæšããšããã°ãã®ãããã«Lv.48ã¯é ããªãããŸãæµãæããªã ; $hypothesis$ = ãã®ãããã«Lv.48ã¯é ããªããæŽã«æµãæããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{c} -> (¬{D}{a} & ¬{B}{a}) fact2: {A}{a} -> {B}{b} fact3: {B}{b} -> (¬{D}{c} & ¬{C}{c}) ; $hypothesis$ = (¬{D}{c} & ¬{C}{c}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã¡ãã·ã«Lv.9ã¯è¥ã | {C}{a} | fact1: ããä»®ã«ãã®ãœããœãLv.47ãåªãããšããã°ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªãããŸãã¯ããã¯åªãããªãããŸãã¯äž¡æ¹ã§ãã fact2: è©°ãŸãæããªãã¢ã³ã¹ã¿ãŒã¯ééç¡ããªãäžæ¹ã§è¥ã fact3: ãã®ã·ã¡ãã·ã«Lv.9ã¯äœãé£ã fact4: ããä»®ã«ãã®ã¿ãã¿ãLv.62ãè©°ãŸãæããŠããã«æšã¿ããŸãããªããã®ã¿ãã¿ãLv.75ã¯åªãããªã fact5: ããã®ã¿ãã¿ãLv.62ã¯è©°ãŸãæãããšããããšã¯æãç«ã€ fact6: ãã®ãŽããŽã«ãLv.50ã¯åªãã fact7: ä»®ã«ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªãããããã¯åªãããªãããŸãã¯äž¡æ¹ãšãã§ãããªãã°ããã¯è¥ã fact8: ããã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åªããããšããããšã¯æãç«ã€ | fact1: {A}{aa} -> (¬{B}{a} v ¬{A}{a}) fact2: (x): ¬{D}x -> (¬{B}x & {C}x) fact3: {I}{a} fact4: ({D}{d} & {E}{d}) -> ¬{A}{c} fact5: {D}{d} fact6: {A}{ca} fact7: (¬{B}{a} v ¬{A}{a}) -> {C}{a} fact8: (x): {A}x | [
"fact8 -> int1: ãã®ãœããœãLv.47ã¯åªãã; int1 & fact1 -> int2: ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªããåªãããªãããããã¯ã©ã¡ããã ; int2 & fact7 -> hypothesis;"
] | [
"fact8 -> int1: {A}{aa}; int1 & fact1 -> int2: (¬{B}{a} v ¬{A}{a}); int2 & fact7 -> hypothesis;"
] | å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯æµ
ã | (x): {CI}x | [
"fact9 -> int3: ãã®ã·ã¡ãã·ã«Lv.9ãè©°ãŸãæããªããšãããšããã¯ééç¡ããªããã©è¥ã;"
] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãœããœãLv.47ãåªãããšããã°ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªãããŸãã¯ããã¯åªãããªãããŸãã¯äž¡æ¹ã§ãã fact2: è©°ãŸãæããªãã¢ã³ã¹ã¿ãŒã¯ééç¡ããªãäžæ¹ã§è¥ã fact3: ãã®ã·ã¡ãã·ã«Lv.9ã¯äœãé£ã fact4: ããä»®ã«ãã®ã¿ãã¿ãLv.62ãè©°ãŸãæããŠããã«æšã¿ããŸãããªããã®ã¿ãã¿ãLv.75ã¯åªãããªã fact5: ããã®ã¿ãã¿ãLv.62ã¯è©°ãŸãæãããšããããšã¯æãç«ã€ fact6: ãã®ãŽããŽã«ãLv.50ã¯åªãã fact7: ä»®ã«ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªãããããã¯åªãããªãããŸãã¯äž¡æ¹ãšãã§ãããªãã°ããã¯è¥ã fact8: ããã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åªããããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ã·ã¡ãã·ã«Lv.9ã¯è¥ã ; $proof$ = | fact8 -> int1: ãã®ãœããœãLv.47ã¯åªãã; int1 & fact1 -> int2: ãã®ã·ã¡ãã·ã«Lv.9ã¯ééç¡ããªããåªãããªãããããã¯ã©ã¡ããã ; int2 & fact7 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{aa} -> (¬{B}{a} v ¬{A}{a}) fact2: (x): ¬{D}x -> (¬{B}x & {C}x) fact3: {I}{a} fact4: ({D}{d} & {E}{d}) -> ¬{A}{c} fact5: {D}{d} fact6: {A}{ca} fact7: (¬{B}{a} v ¬{A}{a}) -> {C}{a} fact8: (x): {A}x ; $hypothesis$ = {C}{a} ; $proof$ = | fact8 -> int1: {A}{aa}; int1 & fact1 -> int2: (¬{B}{a} v ¬{A}{a}); int2 & fact7 -> hypothesis; __PROVED__ |
0.3 | ããã®ãŽã®ãŽãªLv.69ã¯èãé£ãããšããããšã¯èª€ãã§ãªã | {B}{aa} | fact1: ããã®ãŽã®ãŽãªLv.69ã¯èŸæ°èããšããããšã¯ãªããå³ããæ·±ãããšããããšã¯ç¢ºãã§ãªã fact2: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èŸæ°èããªãäžæ¹ã§å³ããæ·±ãããšããããšã¯ééãã§ãããªãã°ããã¯èãé£ããšããããšã¯ãªã | fact1: ¬(¬{AA}{aa} & {AB}{aa}) fact2: (x): ¬(¬{AA}x & {AB}x) -> ¬{B}x | [
"fact2 -> int1: ä»®ã«ããã®ãŽã®ãŽãªLv.69ã¯èŸæ°èããªãäžæ¹ã§å³ããæ·±ãããšããããšã¯èª€ã£ãŠãããšãããšãã®ãŽã®ãŽãªLv.69ã¯èãé£ããªã; int1 & fact1 -> hypothesis;"
] | [
"fact2 -> int1: ¬(¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa}; int1 & fact1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããã®ãŽã®ãŽãªLv.69ã¯èŸæ°èããšããããšã¯ãªããå³ããæ·±ãããšããããšã¯ç¢ºãã§ãªã fact2: ããä»®ã«ããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èŸæ°èããªãäžæ¹ã§å³ããæ·±ãããšããããšã¯ééãã§ãããªãã°ããã¯èãé£ããšããããšã¯ãªã ; $hypothesis$ = ããã®ãŽã®ãŽãªLv.69ã¯èãé£ãããšããããšã¯èª€ãã§ãªã ; $proof$ = | fact2 -> int1: ä»®ã«ããã®ãŽã®ãŽãªLv.69ã¯èŸæ°èããªãäžæ¹ã§å³ããæ·±ãããšããããšã¯èª€ã£ãŠãããšãããšãã®ãŽã®ãŽãªLv.69ã¯èãé£ããªã; int1 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬(¬{AA}{aa} & {AB}{aa}) fact2: (x): ¬(¬{AA}x & {AB}x) -> ¬{B}x ; $hypothesis$ = {B}{aa} ; $proof$ = | fact2 -> int1: ¬(¬{AA}{aa} & {AB}{aa}) -> ¬{B}{aa}; int1 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãããã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ããŠå ããŠæž©ååºæ¥ãããšããããšã¯æãç«ããªãããšããããšã¯åã§ãªã | ¬({C}{a} & {D}{a}) | fact1: ããããã®ãŸã«ããŸã¡ãLv.9ãæããæããšãããšãã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ã fact2: ãã®ãŸã«ããŸã¡ãLv.9ã¯æããæãããã€ããã¯ä»²éããã fact3: ãã®ãŸã«ããŸã¡ãLv.9ã¯æž©ååºæ¥ã | fact1: {A}{a} -> {C}{a} fact2: ({A}{a} & {B}{a}) fact3: {D}{a} | [
"fact2 -> int1: ãã®ãŸã«ããŸã¡ãLv.9ã¯æããæã; int1 & fact1 -> int2: ãã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ã; int2 & fact3 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããã®ãŸã«ããŸã¡ãLv.9ãæããæããšãããšãã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ã fact2: ãã®ãŸã«ããŸã¡ãLv.9ã¯æããæãããã€ããã¯ä»²éããã fact3: ãã®ãŸã«ããŸã¡ãLv.9ã¯æž©ååºæ¥ã ; $hypothesis$ = ãããã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ããŠå ããŠæž©ååºæ¥ãããšããããšã¯æãç«ããªãããšããããšã¯åã§ãªã ; $proof$ = | fact2 -> int1: ãã®ãŸã«ããŸã¡ãLv.9ã¯æããæã; int1 & fact1 -> int2: ãã®ãŸã«ããŸã¡ãLv.9ã¯ãã€ç¡ã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> {C}{a} fact2: ({A}{a} & {B}{a}) fact3: {D}{a} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact1 -> int2: {C}{a}; int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ããããŸãã¯ãã¡ã£ãããªãããããã¯äž¡æ¹ãšãã | ({C}{b} v ¬{A}{b}) | fact1: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ãããªã fact2: ããä»®ã«ãã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããšããããšã¯ãªããªãã°ããã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ããããããã¯ãã¡ã£ãããªããäž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã fact3: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä»°ã
ãããªããšããã°ãããã¯åŽåŽãããããã¯ããã¯ããããªãããŸãã¯ã©ã¡ããã ããšããããšã¯èª€ãã§ãã fact4: ãã®ãã«ããã«ãLv.32ã¯å€èã fact5: ããã®ããããLv.50ã¯åãèŸããŠå ããŠå€èãããšããããšã¯åœã§ãã fact6: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯åãèŸããªã fact7: ããããã®ããããLv.50ã¯åãèŸããå€èãããšããããšã¯æãç«ããªããªãããã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããªãããšããããšã¯æãç«ã€ | fact1: ¬{C}{b} fact2: ¬{B}{b} -> ¬({C}{b} v ¬{A}{b}) fact3: (x): ¬{DO}x -> ¬({AE}x v ¬{GS}x) fact4: {AB}{fn} fact5: ¬({AA}{a} & {AB}{a}) fact6: ¬{AA}{b} fact7: ¬({AA}{a} & {AB}{a}) -> ¬{B}{b} | [
"fact7 & fact5 -> int1: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããªã; int1 & fact2 -> hypothesis;"
] | [
"fact7 & fact5 -> int1: ¬{B}{b}; int1 & fact2 -> hypothesis;"
] | ãã®ã¿ãªã¿ã«ã
Lv.96ã¯ä»°ã
ãããªããšããã°ããã®ã¿ãªã¿ã«ã
Lv.96ã¯åŽåŽãããããã¯ãããããšããããšã¯ãªãããããã¯ã©ã¡ããã§ããããšããããšã¯æ£ãããšããããšã¯ãªã | ¬{DO}{b} -> ¬({AE}{b} v ¬{GS}{b}) | [
"fact8 -> hypothesis;"
] | 1 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ãããªã fact2: ããä»®ã«ãã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããšããããšã¯ãªããªãã°ããã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ããããããã¯ãã¡ã£ãããªããäž¡æ¹ãšãã§ããããšããããšã¯æãç«ããªã fact3: ããä»®ã«ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯ä»°ã
ãããªããšããã°ãããã¯åŽåŽãããããã¯ããã¯ããããªãããŸãã¯ã©ã¡ããã ããšããããšã¯èª€ãã§ãã fact4: ãã®ãã«ããã«ãLv.32ã¯å€èã fact5: ããã®ããããLv.50ã¯åãèŸããŠå ããŠå€èãããšããããšã¯åœã§ãã fact6: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯åãèŸããªã fact7: ããããã®ããããLv.50ã¯åãèŸããå€èãããšããããšã¯æãç«ããªããªãããã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããªãããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ã¿ãªã¿ã«ã
Lv.96ã¯çŸã
ããããŸãã¯ãã¡ã£ãããªãããããã¯äž¡æ¹ãšãã ; $proof$ = | fact7 & fact5 -> int1: ãã®ã¿ãªã¿ã«ã
Lv.96ã¯æããããªã; int1 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{C}{b} fact2: ¬{B}{b} -> ¬({C}{b} v ¬{A}{b}) fact3: (x): ¬{DO}x -> ¬({AE}x v ¬{GS}x) fact4: {AB}{fn} fact5: ¬({AA}{a} & {AB}{a}) fact6: ¬{AA}{b} fact7: ¬({AA}{a} & {AB}{a}) -> ¬{B}{b} ; $hypothesis$ = ({C}{b} v ¬{A}{b}) ; $proof$ = | fact7 & fact5 -> int1: ¬{B}{b}; int1 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã¿ãã¿ãLv.49ã¯çºãŸãæããªã | ¬{A}{a} | fact1: ããä»®ã«ããã®ãŽããŽãLv.34ã¯å°ãåŸãªãäžæ¹ã§æ¥æ¬äººãããããšããããšã¯åã§ãããªããã®ã¿ãã¿ãLv.49ã¯æ¥æ¬äººããããªã fact2: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çºãŸãæã fact3: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯åžåããé£ãããšããããšã¯æãç«ã€ fact4: ããã¢ã³ã¹ã¿ãŒãæ¥æ¬äººããããªããšãããšããã¯çºãŸãæããªãããããèšãè¡šããã fact5: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åããæéãã | fact1: ¬(¬{E}{b} & {C}{b}) -> ¬{C}{a} fact2: (x): {A}x fact3: (x): {FG}x fact4: (x): ¬{C}x -> (¬{A}x & {B}x) fact5: (x): {HC}x | [
"fact2 -> int1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çºãŸãæã; int1 -> hypothesis;"
] | [
"fact2 -> int1: (x): {A}x; int1 -> hypothesis;"
] | ãã®ã¿ãã¿ãLv.49ã¯çºãŸãæããªã | ¬{A}{a} | [
"fact7 -> int2: ãã®ã¿ãã¿ãLv.49ãæ¥æ¬äººããããªããšããããã®ã¿ãã¿ãLv.49ã¯çºãŸãæããªãäžæ¹ã§èšãè¡šããã;"
] | 6 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ããã®ãŽããŽãLv.34ã¯å°ãåŸãªãäžæ¹ã§æ¥æ¬äººãããããšããããšã¯åã§ãããªããã®ã¿ãã¿ãLv.49ã¯æ¥æ¬äººããããªã fact2: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çºãŸãæã fact3: ãå
šãŠã®ã¢ã³ã¹ã¿ãŒã¯åžåããé£ãããšããããšã¯æãç«ã€ fact4: ããã¢ã³ã¹ã¿ãŒãæ¥æ¬äººããããªããšãããšããã¯çºãŸãæããªãããããèšãè¡šããã fact5: ãã¹ãŠã®ã¢ã³ã¹ã¿ãŒã¯åããæéãã ; $hypothesis$ = ãã®ã¿ãã¿ãLv.49ã¯çºãŸãæããªã ; $proof$ = | fact2 -> int1: å
šãŠã®ã¢ã³ã¹ã¿ãŒã¯çºãŸãæã; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬(¬{E}{b} & {C}{b}) -> ¬{C}{a} fact2: (x): {A}x fact3: (x): {FG}x fact4: (x): ¬{C}x -> (¬{A}x & {B}x) fact5: (x): {HC}x ; $hypothesis$ = ¬{A}{a} ; $proof$ = | fact2 -> int1: (x): {A}x; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ãã·ãªLv.0ã¯æšãããããªã | ¬{E}{b} | fact1: ããã®ãŽããŽãLv.94ã¯æšããããããšããããšã¯æãç«ã€ fact2: ãã®ããªãã«ãLv.62ã¯ééç¡ããªã fact3: ãã®ãŽããŽãLv.94ã¯ééç¡ãããã©æãããæããªã fact4: ããã®ãŽããŽãLv.94ã¯å¢ãé£ããªãããŸãã¯ããã¯åŸ¡æäŒãåºæ¥ãããŸãã¯ã©ã¡ããã ããšããããšã¯çå®ã§ãªããšããã°ãã®ã·ãã·ãªLv.0ã¯æšãããããªã | fact1: {E}{a} fact2: ¬{A}{bd} fact3: ({A}{a} & ¬{B}{a}) fact4: ¬(¬{D}{a} v {C}{a}) -> ¬{E}{b} | [
"fact3 -> int1: ããã®ãŽããŽãLv.94ã¯ééç¡ãããšããããšã¯ç¢ºãã ;"
] | [
"fact3 -> int1: {A}{a};"
] | null | null | [] | null | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ããã®ãŽããŽãLv.94ã¯æšããããããšããããšã¯æãç«ã€ fact2: ãã®ããªãã«ãLv.62ã¯ééç¡ããªã fact3: ãã®ãŽããŽãLv.94ã¯ééç¡ãããã©æãããæããªã fact4: ããã®ãŽããŽãLv.94ã¯å¢ãé£ããªãããŸãã¯ããã¯åŸ¡æäŒãåºæ¥ãããŸãã¯ã©ã¡ããã ããšããããšã¯çå®ã§ãªããšããã°ãã®ã·ãã·ãªLv.0ã¯æšãããããªã ; $hypothesis$ = ãã®ã·ãã·ãªLv.0ã¯æšãããããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {E}{a} fact2: ¬{A}{bd} fact3: ({A}{a} & ¬{B}{a}) fact4: ¬(¬{D}{a} v {C}{a}) -> ¬{E}{b} ; $hypothesis$ = ¬{E}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãœã®ãœãLv.33äºä»¶ã¯èµ·ããªã | ¬{D} | fact1: èµ·ãé£ããšããããšã¯ãã«ããLv.74äºä»¶ã«ããçãã fact2: ãããèµ·ãé£ããšããããšãèµ·ããããšããããšã¯æãç«ãŠã°ãœã®ãœãLv.33äºä»¶ãèµ·ãã fact3: æ¢ãã©ç¡ããšããããšãçããããã«ããLv.74äºä»¶ãçºçãã | fact1: {B} -> {C} fact2: {C} -> {D} fact3: ({A} & {B}) | [
"fact3 -> int1: ããã«ããLv.74äºä»¶ãèµ·ããããšããããšã¯æ£ãã; int1 & fact1 -> int2: èµ·ãé£ããšããããšãçãã; int2 & fact2 -> hypothesis;"
] | [
"fact3 -> int1: {B}; int1 & fact1 -> int2: {C}; int2 & fact2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: èµ·ãé£ããšããããšã¯ãã«ããLv.74äºä»¶ã«ããçãã fact2: ãããèµ·ãé£ããšããããšãèµ·ããããšããããšã¯æãç«ãŠã°ãœã®ãœãLv.33äºä»¶ãèµ·ãã fact3: æ¢ãã©ç¡ããšããããšãçããããã«ããLv.74äºä»¶ãçºçãã ; $hypothesis$ = ãœã®ãœãLv.33äºä»¶ã¯èµ·ããªã ; $proof$ = | fact3 -> int1: ããã«ããLv.74äºä»¶ãèµ·ããããšããããšã¯æ£ãã; int1 & fact1 -> int2: èµ·ãé£ããšããããšãçãã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} -> {C} fact2: {C} -> {D} fact3: ({A} & {B}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 -> int1: {B}; int1 & fact1 -> int2: {C}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.6ã¯èªããã | {D}{b} | fact1: ãã®ãã«ããã¡ãLv.9ã¯ãã©ããã©ããããŠãã£ããªã fact2: ãã®ãã«ããã¡ãLv.9ã¯ãã©ããã©ããã fact3: ããããã®ãã«ããã¡ãLv.9ããã£ããªãããããæ§ãæããªãã°ãã®ãŽããŽãLv.6ã¯èªããããªã fact4: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èªããããªããŠãã©ããã©ããããªãããšããããšã¯åã ãšãããšããã¯èªããã fact5: ãã®ãã«ããã¡ãLv.9ã¯æ§ãæã | fact1: ({A}{a} & {B}{a}) fact2: {A}{a} fact3: ({B}{a} & {C}{a}) -> ¬{D}{b} fact4: (x): ¬(¬{D}x & ¬{A}x) -> {D}x fact5: {C}{a} | [
"fact1 -> int1: ãã®ãã«ããã¡ãLv.9ã¯ãã£ããªã; int1 & fact5 -> int2: ãã®ãã«ããã¡ãLv.9ã¯ãã£ããªããå ããŠããã¯æ§ãæã; int2 & fact3 -> hypothesis;"
] | [
"fact1 -> int1: {B}{a}; int1 & fact5 -> int2: ({B}{a} & {C}{a}); int2 & fact3 -> hypothesis;"
] | ãã®ãŽããŽãLv.6ã¯èªããã | {D}{b} | [
"fact6 -> int3: ããä»®ã«ããã®ãŽããŽãLv.6ã¯èªããããªããŠãã©ããã©ããããšããããšã¯ãªãããšããããšã¯æãç«ããªããªãã°ãã®ãŽããŽãLv.6ã¯èªããã;"
] | 5 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãã«ããã¡ãLv.9ã¯ãã©ããã©ããããŠãã£ããªã fact2: ãã®ãã«ããã¡ãLv.9ã¯ãã©ããã©ããã fact3: ããããã®ãã«ããã¡ãLv.9ããã£ããªãããããæ§ãæããªãã°ãã®ãŽããŽãLv.6ã¯èªããããªã fact4: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯èªããããªããŠãã©ããã©ããããªãããšããããšã¯åã ãšãããšããã¯èªããã fact5: ãã®ãã«ããã¡ãLv.9ã¯æ§ãæã ; $hypothesis$ = ãã®ãŽããŽãLv.6ã¯èªããã ; $proof$ = | fact1 -> int1: ãã®ãã«ããã¡ãLv.9ã¯ãã£ããªã; int1 & fact5 -> int2: ãã®ãã«ããã¡ãLv.9ã¯ãã£ããªããå ããŠããã¯æ§ãæã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: {A}{a} fact3: ({B}{a} & {C}{a}) -> ¬{D}{b} fact4: (x): ¬(¬{D}x & ¬{A}x) -> {D}x fact5: {C}{a} ; $hypothesis$ = {D}{b} ; $proof$ = | fact1 -> int1: {B}{a}; int1 & fact5 -> int2: ({B}{a} & {C}{a}); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯ã¡ã£ãã | {C}{b} | fact1: ãã®ã·ã«ã
ã·ã¡ãLv.82ã矜ã°ãããšããããã®ã·ã«ã
ã·ã¡ãLv.82ã¯ã¡ã£ãã fact2: ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæã fact3: ãã®ãœã«ããœã®Lv.22ã¯è²žãæžã fact4: ããä»®ã«ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæãããããã¯ããã¯åãé£ããªãããããã¯ã©ã¡ããã ããšããããšã¯äºå®ã§ãªããšãããšã矜ã°ããããšããããšã¯èª€ãã§ãªã fact5: ããããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªãããããã¯ããã¯åãé£ããªãããšããããšã¯åœã§ãããšãããšãã®ã·ã«ã
ã·ã¡ãLv.82ã¯çŸœã°ãã fact6: ãããã®ãœã«ããœã®Lv.22ã¯è²žãæžãã°ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªããããã¯åãé£ããªãããšããããšã¯äºå®ãšç°ãªã | fact1: {B}{b} -> {C}{b} fact2: {AA}{b} fact3: {A}{a} fact4: ¬({AA}{b} v ¬{AB}{b}) -> {B}{b} fact5: ¬(¬{AA}{b} v ¬{AB}{b}) -> {B}{b} fact6: {A}{a} -> ¬(¬{AA}{b} v ¬{AB}{b}) | [
"fact6 & fact3 -> int1: ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªãããŸãã¯åãé£ããªãããããã¯äž¡æ¹ã§ããããšããããšã¯æãç«ããªã; int1 & fact5 -> int2: ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯çŸœã°ãã; int2 & fact1 -> hypothesis;"
] | [
"fact6 & fact3 -> int1: ¬(¬{AA}{b} v ¬{AB}{b}); int1 & fact5 -> int2: {B}{b}; int2 & fact1 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: ãã®ã·ã«ã
ã·ã¡ãLv.82ã矜ã°ãããšããããã®ã·ã«ã
ã·ã¡ãLv.82ã¯ã¡ã£ãã fact2: ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæã fact3: ãã®ãœã«ããœã®Lv.22ã¯è²žãæžã fact4: ããä»®ã«ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæãããããã¯ããã¯åãé£ããªãããããã¯ã©ã¡ããã ããšããããšã¯äºå®ã§ãªããšãããšã矜ã°ããããšããããšã¯èª€ãã§ãªã fact5: ããããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªãããããã¯ããã¯åãé£ããªãããšããããšã¯åœã§ãããšãããšãã®ã·ã«ã
ã·ã¡ãLv.82ã¯çŸœã°ãã fact6: ãããã®ãœã«ããœã®Lv.22ã¯è²žãæžãã°ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªããããã¯åãé£ããªãããšããããšã¯äºå®ãšç°ãªã ; $hypothesis$ = ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯ã¡ã£ãã ; $proof$ = | fact6 & fact3 -> int1: ããã®ã·ã«ã
ã·ã¡ãLv.82ã¯æã¡äžããæããªãããŸãã¯åãé£ããªãããããã¯äž¡æ¹ã§ããããšããããšã¯æãç«ããªã; int1 & fact5 -> int2: ãã®ã·ã«ã
ã·ã¡ãLv.82ã¯çŸœã°ãã; int2 & fact1 -> hypothesis; __PROVED__ | $facts$ = fact1: {B}{b} -> {C}{b} fact2: {AA}{b} fact3: {A}{a} fact4: ¬({AA}{b} v ¬{AB}{b}) -> {B}{b} fact5: ¬(¬{AA}{b} v ¬{AB}{b}) -> {B}{b} fact6: {A}{a} -> ¬(¬{AA}{b} v ¬{AB}{b}) ; $hypothesis$ = {C}{b} ; $proof$ = | fact6 & fact3 -> int1: ¬(¬{AA}{b} v ¬{AB}{b}); int1 & fact5 -> int2: {B}{b}; int2 & fact1 -> hypothesis; __PROVED__ |
0.3 | ããã®ãããã¡ãLv.75ã¯è¡åè¯ããªãäžæ¹ã§æ²¹ã£ãœãããšããããšã¯åœã§ãã | ¬(¬{D}{a} & {E}{a}) | fact1: ããä»®ã«ãã®ãããã¡ãLv.75ã¯ç°èã£ãœãããŸãã¯å¯ç¬ãããªãã°ããã¯åäžåããªã fact2: ããä»®ã«ãã®ãããã¡ãLv.75ã¯åäžåããªããªããè¡åè¯ããªããã©æ²¹ã£ãœãããšããããšã¯äºå®ãšç°ãªã fact3: ãããããã®ãŸããŸã¡ã
Lv.9ã¯ç°èã£ãœããªãããšããããšã¯æãç«ã€ãšããããã®ãããã¡ãLv.75ã¯è¡åè¯ããšããããšã¯ãªãããããæ²¹ã£ãœã fact4: ãã®ãããã¡ãLv.75ã¯å¯ç¬ãã fact5: ãããã®ãããã¡ãLv.75ã¯å¥é¢ããªããã©ç°èã£ãœãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããšããããšã¯ç¢ºãã fact6: ãã®ãããã¡ãLv.75ãè¡åè¯ããšããããã®ãããã¡ãLv.75ã¯æ¢ãæããšããããšã¯ãªã fact7: ãã®ãããã¡ãLv.75ã¯åäžåãããšããããšã¯ãªããšããã°ãè¡åè¯ãã¢ã³ã¹ã¿ãŒã§ãã£ãŠãããæ²¹ã£ãœãããšããããšã¯èª€ã£ãŠãã fact8: ããã®ãããã¡ãLv.75ã¯è¡åè¯ããŠæ²¹ã£ãœãããšããããšã¯æãç«ã€ãšããããšã¯ãªã | fact1: ({A}{a} v {B}{a}) -> ¬{C}{a} fact2: ¬{C}{a} -> ¬(¬{D}{a} & {E}{a}) fact3: ¬{A}{b} -> (¬{D}{a} & {E}{a}) fact4: {B}{a} fact5: ¬(¬{DS}{a} & {A}{a}) fact6: {D}{a} -> ¬{BN}{a} fact7: ¬{C}{a} -> ¬({D}{a} & {E}{a}) fact8: ¬({D}{a} & {E}{a}) | [
"fact4 -> int1: ãã®ãããã¡ãLv.75ã¯ç°èã£ãœãããããã¯å¯ç¬ãã; int1 & fact1 -> int2: ãã®ãããã¡ãLv.75ã¯åäžåããªã; int2 & fact2 -> hypothesis;"
] | [
"fact4 -> int1: ({A}{a} v {B}{a}); int1 & fact1 -> int2: ¬{C}{a}; int2 & fact2 -> hypothesis;"
] | ãã®ãããã¡ãLv.75ã¯è¡åè¯ããšããããšã¯ãªããããã¯æ²¹ã£ãœã | (¬{D}{a} & {E}{a}) | [] | 5 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãããã¡ãLv.75ã¯ç°èã£ãœãããŸãã¯å¯ç¬ãããªãã°ããã¯åäžåããªã fact2: ããä»®ã«ãã®ãããã¡ãLv.75ã¯åäžåããªããªããè¡åè¯ããªããã©æ²¹ã£ãœãããšããããšã¯äºå®ãšç°ãªã fact3: ãããããã®ãŸããŸã¡ã
Lv.9ã¯ç°èã£ãœããªãããšããããšã¯æãç«ã€ãšããããã®ãããã¡ãLv.75ã¯è¡åè¯ããšããããšã¯ãªãããããæ²¹ã£ãœã fact4: ãã®ãããã¡ãLv.75ã¯å¯ç¬ãã fact5: ãããã®ãããã¡ãLv.75ã¯å¥é¢ããªããã©ç°èã£ãœãããšããããšã¯æãç«ã€ãšããããšã¯ãªãããšããããšã¯ç¢ºãã fact6: ãã®ãããã¡ãLv.75ãè¡åè¯ããšããããã®ãããã¡ãLv.75ã¯æ¢ãæããšããããšã¯ãªã fact7: ãã®ãããã¡ãLv.75ã¯åäžåãããšããããšã¯ãªããšããã°ãè¡åè¯ãã¢ã³ã¹ã¿ãŒã§ãã£ãŠãããæ²¹ã£ãœãããšããããšã¯èª€ã£ãŠãã fact8: ããã®ãããã¡ãLv.75ã¯è¡åè¯ããŠæ²¹ã£ãœãããšããããšã¯æãç«ã€ãšããããšã¯ãªã ; $hypothesis$ = ããã®ãããã¡ãLv.75ã¯è¡åè¯ããªãäžæ¹ã§æ²¹ã£ãœãããšããããšã¯åœã§ãã ; $proof$ = | fact4 -> int1: ãã®ãããã¡ãLv.75ã¯ç°èã£ãœãããããã¯å¯ç¬ãã; int1 & fact1 -> int2: ãã®ãããã¡ãLv.75ã¯åäžåããªã; int2 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: ({A}{a} v {B}{a}) -> ¬{C}{a} fact2: ¬{C}{a} -> ¬(¬{D}{a} & {E}{a}) fact3: ¬{A}{b} -> (¬{D}{a} & {E}{a}) fact4: {B}{a} fact5: ¬(¬{DS}{a} & {A}{a}) fact6: {D}{a} -> ¬{BN}{a} fact7: ¬{C}{a} -> ¬({D}{a} & {E}{a}) fact8: ¬({D}{a} & {E}{a}) ; $hypothesis$ = ¬(¬{D}{a} & {E}{a}) ; $proof$ = | fact4 -> int1: ({A}{a} v {B}{a}); int1 & fact1 -> int2: ¬{C}{a}; int2 & fact2 -> hypothesis; __PROVED__ |
0.3 | å®ããšããããšã¯çºçããªã | ¬{C} | fact1: ãœã¡ã
ãœãLv.94äºä»¶ãèµ·ãããã¿ãã¿ãLv.21äºä»¶ãçºçãã fact2: ãã¿ã«ã¿ãLv.73äºä»¶ããã³ã¿ãã¿ãLv.12äºä»¶ãçºçããããšããããšã¯ããŸããŸãLv.59äºä»¶ã¯çºçããªãããšããããšã«èªçºããã fact3: ãããŸããŸãLv.59äºä»¶ãèµ·ãããªãããŸãã¯ã¿ã«ã¿ãLv.73äºä»¶ã¯èµ·ãããªããã©ã¡ããã§ãããšãããšå®ããšããããšã¯çºçããªã fact4: ã¿ã«ã¿ãLv.73äºä»¶ãèµ·ãããããã«ãŸããŸãLv.59äºä»¶ãçºçãã | fact1: ({AF} & {CN}) fact2: ¬{B} -> ({A} & {HI}) fact3: (¬{B} v ¬{A}) -> ¬{C} fact4: ({A} & {B}) | [
"fact4 -> int1: ã¿ã«ã¿ãLv.73äºä»¶ãçãã;"
] | [
"fact4 -> int1: {A};"
] | å®ããšããããšã¯çºçããªã | ¬{C} | [] | 6 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãœã¡ã
ãœãLv.94äºä»¶ãèµ·ãããã¿ãã¿ãLv.21äºä»¶ãçºçãã fact2: ãã¿ã«ã¿ãLv.73äºä»¶ããã³ã¿ãã¿ãLv.12äºä»¶ãçºçããããšããããšã¯ããŸããŸãLv.59äºä»¶ã¯çºçããªãããšããããšã«èªçºããã fact3: ãããŸããŸãLv.59äºä»¶ãèµ·ãããªãããŸãã¯ã¿ã«ã¿ãLv.73äºä»¶ã¯èµ·ãããªããã©ã¡ããã§ãããšãããšå®ããšããããšã¯çºçããªã fact4: ã¿ã«ã¿ãLv.73äºä»¶ãèµ·ãããããã«ãŸããŸãLv.59äºä»¶ãçºçãã ; $hypothesis$ = å®ããšããããšã¯çºçããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({AF} & {CN}) fact2: ¬{B} -> ({A} & {HI}) fact3: (¬{B} v ¬{A}) -> ¬{C} fact4: ({A} & {B}) ; $hypothesis$ = ¬{C} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ãã·ã®Lv.73ã¯èŠ³å¯ããªã | ¬{C}{b} | fact1: ä»®ã«ãã®ãœã«ãœãLv.7ã¯å®çŸãæããšãããšããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªããããã¯å¡©èŸãããšããããšã¯æãç«ããªã fact2: ããã®ãŽã¡ã
ãŽãLv.62ã¯æãããªããã©åã£ä»ãæãããšããããšã¯èª€ã£ãŠãã fact3: ããä»®ã«ãã®ã·ãã·ã®Lv.73ãæ°å¿ãããšããã°ãã®ã·ãã·ã®Lv.73ã¯èŠ³å¯ãã fact4: ããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªãããã©ããã¯å¡©èŸãããšããããšã¯ééãã§ãããšãããšããã¯æ°å¿ãã fact5: ãã®ãœã«ãœãLv.7ã¯å®çŸãæã fact6: ãããšããã¢ã³ã¹ã¿ãŒãå®çŸãæããªãã°ããã¯èŠ³å¯ããªã | fact1: {A}{a} -> ¬(¬{AA}{b} & {AB}{b}) fact2: ¬(¬{FD}{ba} & {FM}{ba}) fact3: {B}{b} -> {C}{b} fact4: ¬(¬{AA}{b} & {AB}{b}) -> {B}{b} fact5: {A}{a} fact6: (x): {A}x -> ¬{C}x | [
"fact1 & fact5 -> int1: ããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªããã©å¡©èŸãããšããããšã¯ééã£ãŠãã; int1 & fact4 -> int2: ãã®ã·ãã·ã®Lv.73ã¯æ°å¿ãã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact5 -> int1: ¬(¬{AA}{b} & {AB}{b}); int1 & fact4 -> int2: {B}{b}; int2 & fact3 -> hypothesis;"
] | ãã®ã·ãã·ã®Lv.73ã¯èŠ³å¯ããªã | ¬{C}{b} | [
"fact7 -> int3: ããä»®ã«ãã®ã·ãã·ã®Lv.73ãå®çŸãæããªã芳å¯ããªã;"
] | 5 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãã®ãœã«ãœãLv.7ã¯å®çŸãæããšãããšããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªããããã¯å¡©èŸãããšããããšã¯æãç«ããªã fact2: ããã®ãŽã¡ã
ãŽãLv.62ã¯æãããªããã©åã£ä»ãæãããšããããšã¯èª€ã£ãŠãã fact3: ããä»®ã«ãã®ã·ãã·ã®Lv.73ãæ°å¿ãããšããã°ãã®ã·ãã·ã®Lv.73ã¯èŠ³å¯ãã fact4: ããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªãããã©ããã¯å¡©èŸãããšããããšã¯ééãã§ãããšãããšããã¯æ°å¿ãã fact5: ãã®ãœã«ãœãLv.7ã¯å®çŸãæã fact6: ãããšããã¢ã³ã¹ã¿ãŒãå®çŸãæããªãã°ããã¯èŠ³å¯ããªã ; $hypothesis$ = ãã®ã·ãã·ã®Lv.73ã¯èŠ³å¯ããªã ; $proof$ = | fact1 & fact5 -> int1: ããã®ã·ãã·ã®Lv.73ã¯é£²ã¿é£ããªããã©å¡©èŸãããšããããšã¯ééã£ãŠãã; int1 & fact4 -> int2: ãã®ã·ãã·ã®Lv.73ã¯æ°å¿ãã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} -> ¬(¬{AA}{b} & {AB}{b}) fact2: ¬(¬{FD}{ba} & {FM}{ba}) fact3: {B}{b} -> {C}{b} fact4: ¬(¬{AA}{b} & {AB}{b}) -> {B}{b} fact5: {A}{a} fact6: (x): {A}x -> ¬{C}x ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact1 & fact5 -> int1: ¬(¬{AA}{b} & {AB}{b}); int1 & fact4 -> int2: {B}{b}; int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããä¿¡å¿æ·±ããšããããšããã³ãŸã«ã
ãŸã®Lv.57äºä»¶äž¡æ¹ãšããçºçããããšããããšã¯çå®ã§ããããšããããšã¯äºå®ã§ãªã | ¬({D} & {C}) | fact1: ä¿¡å¿æ·±ããšããããšãçãã fact2: ãæµãå§ããããšãçºçããããã©ã¡ããããšããããšã¯çºçããªãããšããããšã¯æ¬åœã§ãªããšãããšæ»
亡ããããšã¯èµ·ãããªã fact3: ããŽããŽãLv.11äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœã«ã
ãœãLv.36äºä»¶ã«é»æ¢ããã fact4: ããããæ»
亡ããããšã¯èµ·ããªãããšããããšã¯ç¢ºããªããä¿¡å¿æ·±ããšããããšããã³ãŸã«ã
ãŸã®Lv.57äºä»¶ã©ã¡ãããçºçããããšããããšã¯åœã fact5: æ»
亡ããããšããã³æµãå§ããããšäž¡æ¹ãçãã fact6: æµãå§ããããšãçºçãã | fact1: {D} fact2: ¬({B} & ¬{E}) -> ¬{A} fact3: {CF} -> {AQ} fact4: ¬{A} -> ¬({D} & {C}) fact5: ({A} & {B}) fact6: {B} | [
"fact5 -> int1: æ»
亡ããããšãèµ·ãã;"
] | [
"fact5 -> int1: {A};"
] | ããä¿¡å¿æ·±ããšããããšããã³ãŸã«ã
ãŸã®Lv.57äºä»¶äž¡æ¹ãšããçºçããããšããããšã¯çå®ã§ããããšããããšã¯äºå®ã§ãªã | ¬({D} & {C}) | [] | 7 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ä¿¡å¿æ·±ããšããããšãçãã fact2: ãæµãå§ããããšãçºçããããã©ã¡ããããšããããšã¯çºçããªãããšããããšã¯æ¬åœã§ãªããšãããšæ»
亡ããããšã¯èµ·ãããªã fact3: ããŽããŽãLv.11äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœã«ã
ãœãLv.36äºä»¶ã«é»æ¢ããã fact4: ããããæ»
亡ããããšã¯èµ·ããªãããšããããšã¯ç¢ºããªããä¿¡å¿æ·±ããšããããšããã³ãŸã«ã
ãŸã®Lv.57äºä»¶ã©ã¡ãããçºçããããšããããšã¯åœã fact5: æ»
亡ããããšããã³æµãå§ããããšäž¡æ¹ãçãã fact6: æµãå§ããããšãçºçãã ; $hypothesis$ = ããä¿¡å¿æ·±ããšããããšããã³ãŸã«ã
ãŸã®Lv.57äºä»¶äž¡æ¹ãšããçºçããããšããããšã¯çå®ã§ããããšããããšã¯äºå®ã§ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {D} fact2: ¬({B} & ¬{E}) -> ¬{A} fact3: {CF} -> {AQ} fact4: ¬{A} -> ¬({D} & {C}) fact5: ({A} & {B}) fact6: {B} ; $hypothesis$ = ¬({D} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœãLv.68äºä»¶ã¯çºçããªã | ¬{D} | fact1: ä»®ã«äžããæããšããããšãšãŸã®ãŸãLv.53äºä»¶ãèµ·ãããšããã°ãŸããŸãLv.65äºä»¶ã¯èµ·ãããªã fact2: 移ããæããšããããšãèµ·ãã fact3: 埡確èªäžããããšãçãããå ããŠæº¶ãé£ããšããããšãçãã fact4: ã埡確èªäžããããšããã³ç§»ããæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯ãœããœãLv.68äºä»¶ãåé¿ãã | fact1: ({IA} & {GP}) -> ¬{IJ} fact2: {C} fact3: ({A} & {B}) fact4: ({A} & {C}) -> ¬{D} | [
"fact3 -> int1: ã埡確èªäžããããšãèµ·ããããšããããšã¯æ£ãã; int1 & fact2 -> int2: 埡確èªäžããããšãçããã移ããæããšããããšãèµ·ãã; int2 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 & fact2 -> int2: ({A} & {C}); int2 & fact4 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | null | PROVED | null | $facts$ = fact1: ä»®ã«äžããæããšããããšãšãŸã®ãŸãLv.53äºä»¶ãèµ·ãããšããã°ãŸããŸãLv.65äºä»¶ã¯èµ·ãããªã fact2: 移ããæããšããããšãèµ·ãã fact3: 埡確èªäžããããšãçãããå ããŠæº¶ãé£ããšããããšãçãã fact4: ã埡確èªäžããããšããã³ç§»ããæããšããããšäž¡æ¹ãšããèµ·ããããšããããšã¯ãœããœãLv.68äºä»¶ãåé¿ãã ; $hypothesis$ = ãœããœãLv.68äºä»¶ã¯çºçããªã ; $proof$ = | fact3 -> int1: ã埡確èªäžããããšãèµ·ããããšããããšã¯æ£ãã; int1 & fact2 -> int2: 埡確èªäžããããšãçããã移ããæããšããããšãèµ·ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ({IA} & {GP}) -> ¬{IJ} fact2: {C} fact3: ({A} & {B}) fact4: ({A} & {C}) -> ¬{D} ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 -> int1: {A}; int1 & fact2 -> int2: ({A} & {C}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãœãªãœãLv.52ã¯è¡æ£èãããããã¯ããã¯ä»æ¹ç¡ããªãããŸãã¯äž¡æ¹ãšãã§ãã | ({A}{b} v ¬{B}{b}) | fact1: ãã®ãŽã«ãŽãLv.69ã¯è¡æ£èã fact2: ããã®ãŽã«ãŽãLv.69ã¯é£ã³èŸŒãŸãªãããŸãã¯å³ããããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã§ãã fact3: ããä»®ã«ããã®ãŽã«ãŽãLv.69ã¯é£ã³èŸŒãŸãªãããããã¯ããã¯å³ããããªãããšããããšã¯ééãã ãšãããšãã®ãŽã«ãŽãLv.69ã¯ä»æ¹ç¡ããªã fact4: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯èéããšããããšã¯ãªããªãã°ãããã¯è¡æ£èãããŸãã¯ããã¯ä»æ¹ç¡ããªãããšããããšã¯ééãã§ãã fact5: ä»®ã«ãã®ãŽã«ãŽãLv.69ãä»æ¹ç¡ããªããšããããã®ãœãªãœãLv.52ã¯è¡æ£èããããã¯ä»æ¹ç¡ããªãããããã¯ã©ã¡ããã | fact1: {A}{a} fact2: ¬(¬{AA}{a} v ¬{AB}{a}) fact3: ¬(¬{AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact4: (x): ¬{C}x -> ¬({A}x v ¬{B}x) fact5: ¬{B}{a} -> ({A}{b} v ¬{B}{b}) | [
"fact3 & fact2 -> int1: ãã®ãŽã«ãŽãLv.69ã¯ä»æ¹ç¡ããªã; int1 & fact5 -> hypothesis;"
] | [
"fact3 & fact2 -> int1: ¬{B}{a}; int1 & fact5 -> hypothesis;"
] | ããã®ãœãªãœãLv.52ã¯è¡æ£èãããããã¯ããã¯ä»æ¹ç¡ããªãããããã¯äž¡æ¹ãšãã ããšããããšã¯èª€ãã | ¬({A}{b} v ¬{B}{b}) | [
"fact6 -> int2: ãã®ãœãªãœãLv.52ã¯èéããªããšãããšãããã¯è¡æ£èãããŸãã¯ä»æ¹ç¡ããªãããšããããšã¯æãç«ããªã;"
] | 5 | 2 | 2 | 2 | 2 | 2 | 0 | 2 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãã®ãŽã«ãŽãLv.69ã¯è¡æ£èã fact2: ããã®ãŽã«ãŽãLv.69ã¯é£ã³èŸŒãŸãªãããŸãã¯å³ããããªãããããã¯äž¡æ¹ã§ããããšããããšã¯ééãã§ãã fact3: ããä»®ã«ããã®ãŽã«ãŽãLv.69ã¯é£ã³èŸŒãŸãªãããããã¯ããã¯å³ããããªãããšããããšã¯ééãã ãšãããšãã®ãŽã«ãŽãLv.69ã¯ä»æ¹ç¡ããªã fact4: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯èéããšããããšã¯ãªããªãã°ãããã¯è¡æ£èãããŸãã¯ããã¯ä»æ¹ç¡ããªãããšããããšã¯ééãã§ãã fact5: ä»®ã«ãã®ãŽã«ãŽãLv.69ãä»æ¹ç¡ããªããšããããã®ãœãªãœãLv.52ã¯è¡æ£èããããã¯ä»æ¹ç¡ããªãããããã¯ã©ã¡ããã ; $hypothesis$ = ãã®ãœãªãœãLv.52ã¯è¡æ£èãããããã¯ããã¯ä»æ¹ç¡ããªãããŸãã¯äž¡æ¹ãšãã§ãã ; $proof$ = | fact3 & fact2 -> int1: ãã®ãŽã«ãŽãLv.69ã¯ä»æ¹ç¡ããªã; int1 & fact5 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: ¬(¬{AA}{a} v ¬{AB}{a}) fact3: ¬(¬{AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact4: (x): ¬{C}x -> ¬({A}x v ¬{B}x) fact5: ¬{B}{a} -> ({A}{b} v ¬{B}{b}) ; $hypothesis$ = ({A}{b} v ¬{B}{b}) ; $proof$ = | fact3 & fact2 -> int1: ¬{B}{a}; int1 & fact5 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸã«ãLv.17ã¯æ¯ãç¶ãã | {B}{b} | fact1: ã芪ãããæé€ãæããšããããšã¯ãªããã¢ã³ã¹ã¿ãŒããããšããããã®ãŸã«ããŸã¡ãLv.78ã¯æ¯ãç¶ããªã fact2: ããããã®ãŸã«ããŸã¡ãLv.78ãéãŸãæããªããªãæé€ãæãããã€èŠªãããªã fact3: ããæé€ãæãã¢ã³ã¹ã¿ãŒã芪ãããªããšããããã®ãŸããŸã«ãLv.17ã¯æ¯ãç¶ããªã fact4: ãã®ãŸã«ããŸã¡ãLv.78ã¯éãŸãæããªã fact5: ãã®ãŸã¡ã
ãŸãLv.61ã¯æ¯ãç¶ãããšããããšã¯ãªã | fact1: (x): ({AB}x & ¬{AA}x) -> ¬{B}{a} fact2: ¬{A}{a} -> ({AA}{a} & ¬{AB}{a}) fact3: (x): ({AA}x & ¬{AB}x) -> ¬{B}{b} fact4: ¬{A}{a} fact5: ¬{B}{bc} | [
"fact2 & fact4 -> int1: ããã®ãŸã«ããŸã¡ãLv.78ã¯æé€ãæããããã芪ãããªãããšããããšã¯æ¬åœã ; int1 -> int2: æé€ãæãããã€èŠªãããªãã¢ã³ã¹ã¿ãŒã¯ãã; int2 & fact3 -> hypothesis;"
] | [
"fact2 & fact4 -> int1: ({AA}{a} & ¬{AB}{a}); int1 -> int2: (Ex): ({AA}x & ¬{AB}x); int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ã芪ãããæé€ãæããšããããšã¯ãªããã¢ã³ã¹ã¿ãŒããããšããããã®ãŸã«ããŸã¡ãLv.78ã¯æ¯ãç¶ããªã fact2: ããããã®ãŸã«ããŸã¡ãLv.78ãéãŸãæããªããªãæé€ãæãããã€èŠªãããªã fact3: ããæé€ãæãã¢ã³ã¹ã¿ãŒã芪ãããªããšããããã®ãŸããŸã«ãLv.17ã¯æ¯ãç¶ããªã fact4: ãã®ãŸã«ããŸã¡ãLv.78ã¯éãŸãæããªã fact5: ãã®ãŸã¡ã
ãŸãLv.61ã¯æ¯ãç¶ãããšããããšã¯ãªã ; $hypothesis$ = ãã®ãŸããŸã«ãLv.17ã¯æ¯ãç¶ãã ; $proof$ = | fact2 & fact4 -> int1: ããã®ãŸã«ããŸã¡ãLv.78ã¯æé€ãæããããã芪ãããªãããšããããšã¯æ¬åœã ; int1 -> int2: æé€ãæãããã€èŠªãããªãã¢ã³ã¹ã¿ãŒã¯ãã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ({AB}x & ¬{AA}x) -> ¬{B}{a} fact2: ¬{A}{a} -> ({AA}{a} & ¬{AB}{a}) fact3: (x): ({AA}x & ¬{AB}x) -> ¬{B}{b} fact4: ¬{A}{a} fact5: ¬{B}{bc} ; $hypothesis$ = {B}{b} ; $proof$ = | fact2 & fact4 -> int1: ({AA}{a} & ¬{AB}{a}); int1 -> int2: (Ex): ({AA}x & ¬{AB}x); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãŸã¡ããŸã¡ãLv.54äºä»¶ã¯çããªã | ¬{D} | fact1: ãœã®ãœã¡ãLv.87äºä»¶ãçºçãã fact2: ããŸã¡ããŸã¡ãLv.54äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœããœã«Lv.52äºä»¶ã¯çºçããªããšããããšã«é²ããã fact3: ãœããœã«Lv.52äºä»¶ãæãé£ãããšããã³ãœã®ãœã¡ãLv.87äºä»¶ã¯çºçããã«é²ããã fact4: ããæãé£ãããšã¯çºçããªããšãããšããŸã¡ããŸã¡ãLv.54äºä»¶ã¯çºçãããããããœã®ãœã¡ãLv.87äºä»¶ã¯çºçããªãããšããããšã¯äºå®ãšç°ãªã | fact1: {B} fact2: ¬{C} -> {D} fact3: ({A} & {B}) -> ¬{C} fact4: ¬{A} -> ¬({D} & ¬{B}) | [] | [] | ãŸã¡ããŸã¡ãLv.54äºä»¶ã¯çããªã | ¬{D} | [] | 6 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãœã®ãœã¡ãLv.87äºä»¶ãçºçãã fact2: ããŸã¡ããŸã¡ãLv.54äºä»¶ã¯èµ·ãããªãããšããããšã¯ãœããœã«Lv.52äºä»¶ã¯çºçããªããšããããšã«é²ããã fact3: ãœããœã«Lv.52äºä»¶ãæãé£ãããšããã³ãœã®ãœã¡ãLv.87äºä»¶ã¯çºçããã«é²ããã fact4: ããæãé£ãããšã¯çºçããªããšãããšããŸã¡ããŸã¡ãLv.54äºä»¶ã¯çºçãããããããœã®ãœã¡ãLv.87äºä»¶ã¯çºçããªãããšããããšã¯äºå®ãšç°ãªã ; $hypothesis$ = ãŸã¡ããŸã¡ãLv.54äºä»¶ã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B} fact2: ¬{C} -> {D} fact3: ({A} & {B}) -> ¬{C} fact4: ¬{A} -> ¬({D} & ¬{B}) ; $hypothesis$ = ¬{D} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãœã«ããœã«Lv.84ã¯æ¯ç»åããããšããããšã¯çå®ã | {D}{a} | fact1: ããããã®ãœã«ããœã«Lv.84ã¯æ¥ãããããã€çãæããšããã°æ¯ç»åããªã fact2: ããããã®ã·ã«ã·ãLv.57ãèŠä»ãæããšããããã®ãœã«ããœã«Lv.84ã¯æ¯ç»åãã fact3: ãã®ãœã«ããœã«Lv.84ã¯çãæã fact4: ãã®ãœã«ããœã«Lv.84ã¯èŠä»ãæã fact5: ãã®ãœããœãªLv.37ã¯çãæã fact6: æ¥ãããã¢ã³ã¹ã¿ãŒã§ãã®äžéŠããã¢ã³ã¹ã¿ãŒã¯éè³ãæããšããããšã¯ãªã fact7: ããä»®ã«ãã®ãœã«ããœã«Lv.84ãèŠä»ãæããšããã°ããã¯æ¥ããã | fact1: ({B}{a} & {C}{a}) -> ¬{D}{a} fact2: {A}{b} -> {D}{a} fact3: {C}{a} fact4: {A}{a} fact5: {C}{bo} fact6: (x): ({B}x & {FL}x) -> ¬{O}x fact7: {A}{a} -> {B}{a} | [
"fact7 & fact4 -> int1: ãã®ãœã«ããœã«Lv.84ã¯æ¥ããã; int1 & fact3 -> int2: ãã®ãœã«ããœã«Lv.84ã¯æ¥ããããããã«ããã¯çãæã; int2 & fact1 -> hypothesis;"
] | [
"fact7 & fact4 -> int1: {B}{a}; int1 & fact3 -> int2: ({B}{a} & {C}{a}); int2 & fact1 -> hypothesis;"
] | ããä»®ã«ãã®ãœã«ããœã«Lv.84ãæ¥ããããããŸãã«éŠãããªãã°éè³ãæããªã | ({B}{a} & {FL}{a}) -> ¬{O}{a} | [
"fact8 -> hypothesis;"
] | 1 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ããããã®ãœã«ããœã«Lv.84ã¯æ¥ãããããã€çãæããšããã°æ¯ç»åããªã fact2: ããããã®ã·ã«ã·ãLv.57ãèŠä»ãæããšããããã®ãœã«ããœã«Lv.84ã¯æ¯ç»åãã fact3: ãã®ãœã«ããœã«Lv.84ã¯çãæã fact4: ãã®ãœã«ããœã«Lv.84ã¯èŠä»ãæã fact5: ãã®ãœããœãªLv.37ã¯çãæã fact6: æ¥ãããã¢ã³ã¹ã¿ãŒã§ãã®äžéŠããã¢ã³ã¹ã¿ãŒã¯éè³ãæããšããããšã¯ãªã fact7: ããä»®ã«ãã®ãœã«ããœã«Lv.84ãèŠä»ãæããšããã°ããã¯æ¥ããã ; $hypothesis$ = ããã®ãœã«ããœã«Lv.84ã¯æ¯ç»åããããšããããšã¯çå®ã ; $proof$ = | fact7 & fact4 -> int1: ãã®ãœã«ããœã«Lv.84ã¯æ¥ããã; int1 & fact3 -> int2: ãã®ãœã«ããœã«Lv.84ã¯æ¥ããããããã«ããã¯çãæã; int2 & fact1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({B}{a} & {C}{a}) -> ¬{D}{a} fact2: {A}{b} -> {D}{a} fact3: {C}{a} fact4: {A}{a} fact5: {C}{bo} fact6: (x): ({B}x & {FL}x) -> ¬{O}x fact7: {A}{a} -> {B}{a} ; $hypothesis$ = {D}{a} ; $proof$ = | fact7 & fact4 -> int1: {B}{a}; int1 & fact3 -> int2: ({B}{a} & {C}{a}); int2 & fact1 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãã¡ãããLv.64ã¯å¯Ÿå¿ãæã | {C}{b} | fact1: ãããã®ãã¡ãããLv.64ãå¿ã³é£ããšããã°ããã¯å¯Ÿå¿ãæã fact2: ããã®ã·ã«ã·ã®Lv.98ã¯ä»ãé£ããããã«æ³åãæãããšããããšã¯æ£ãããªã fact3: ããã®ã·ã«ã·ã®Lv.98ã¯ä»ãé£ããªãäžæ¹ã§æ³åãæãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: ä»®ã«ãã®ã·ã«ã·ã®Lv.98ãä»ãé£ããªããã®ãã¡ãããLv.64ã¯å°ãã fact5: ããããã®ãã¡ãããLv.64ãå°ãããšãããå¿ã³é£ã | fact1: {A}{b} -> {C}{b} fact2: ¬({AA}{a} & {AB}{a}) fact3: ¬(¬{AA}{a} & {AB}{a}) fact4: {AA}{a} -> {B}{b} fact5: {B}{b} -> {A}{b} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããã®ãã¡ãããLv.64ãå¿ã³é£ããšããã°ããã¯å¯Ÿå¿ãæã fact2: ããã®ã·ã«ã·ã®Lv.98ã¯ä»ãé£ããããã«æ³åãæãããšããããšã¯æ£ãããªã fact3: ããã®ã·ã«ã·ã®Lv.98ã¯ä»ãé£ããªãäžæ¹ã§æ³åãæãããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact4: ä»®ã«ãã®ã·ã«ã·ã®Lv.98ãä»ãé£ããªããã®ãã¡ãããLv.64ã¯å°ãã fact5: ããããã®ãã¡ãããLv.64ãå°ãããšãããå¿ã³é£ã ; $hypothesis$ = ãã®ãã¡ãããLv.64ã¯å¯Ÿå¿ãæã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {A}{b} -> {C}{b} fact2: ¬({AA}{a} & {AB}{a}) fact3: ¬(¬{AA}{a} & {AB}{a}) fact4: {AA}{a} -> {B}{b} fact5: {B}{b} -> {A}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãã«ããã¡ã
Lv.65ã¯çããªã | ¬{C}{b} | fact1: ãã®ãœããœã¡ãLv.82ã¯åéããªããšãããããã®ãœããœã¡ãLv.82ã¯å€«å©Šããããªãããããã¯è¿·ãé£ããªãããšããããšã¯åã fact2: ãããããã®ãœããœã¡ãLv.82ã¯å€«å©Šããããªããè¿·ãé£ããªãããããã¯ã©ã¡ããã ããšããããšã¯åœã ãšãããšãã®ãœããœã¡ãLv.82ã¯ããã³ã°ãã fact3: ä»®ã«ãã®ãœããœã¡ãLv.82ãããã³ã°ããã°ãã®ãã«ããã¡ã
Lv.65ã¯çã | fact1: ¬{A}{a} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact2: ¬(¬{AA}{a} v ¬{AB}{a}) -> {B}{a} fact3: {B}{a} -> {C}{b} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãã®ãœããœã¡ãLv.82ã¯åéããªããšãããããã®ãœããœã¡ãLv.82ã¯å€«å©Šããããªãããããã¯è¿·ãé£ããªãããšããããšã¯åã fact2: ãããããã®ãœããœã¡ãLv.82ã¯å€«å©Šããããªããè¿·ãé£ããªãããããã¯ã©ã¡ããã ããšããããšã¯åœã ãšãããšãã®ãœããœã¡ãLv.82ã¯ããã³ã°ãã fact3: ä»®ã«ãã®ãœããœã¡ãLv.82ãããã³ã°ããã°ãã®ãã«ããã¡ã
Lv.65ã¯çã ; $hypothesis$ = ãã®ãã«ããã¡ã
Lv.65ã¯çããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{a} -> ¬(¬{AA}{a} v ¬{AB}{a}) fact2: ¬(¬{AA}{a} v ¬{AB}{a}) -> {B}{a} fact3: {B}{a} -> {C}{b} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãããã®ã¿ãªã¿ãLv.49ã¯åãã管çãæãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æ¬åœã | ¬({A}{a} & {B}{a}) | fact1: åããªãã¢ã³ã¹ã¿ãŒã¯çµ fact2: ããã®ã¿ãªã¿ãLv.49ã¯ç®¡çãæãããšããããšã¯æ¬åœã | fact1: (x): ¬{A}x -> {FE}x fact2: {B}{a} | [] | [] | ãã®ã¿ã«ã
ã¿ãLv.86ã¯çµãããŸãã«è²å¥œã | ({FE}{jk} & {S}{jk}) | [
"fact3 -> int1: ããä»®ã«ãã®ã¿ã«ã
ã¿ãLv.86ã¯åããªããšããããçµããšããããšã¯äºå®ã§ãã;"
] | 3 | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: åããªãã¢ã³ã¹ã¿ãŒã¯çµ fact2: ããã®ã¿ãªã¿ãLv.49ã¯ç®¡çãæãããšããããšã¯æ¬åœã ; $hypothesis$ = ãããã®ã¿ãªã¿ãLv.49ã¯åãã管çãæãããšããããšã¯äºå®ãšç°ãªãããšããããšã¯æ¬åœã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{A}x -> {FE}x fact2: {B}{a} ; $hypothesis$ = ¬({A}{a} & {B}{a}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ã·ãã·ãLv.26ã¯è²ã£ãœããªãããã©å±éºéããããšããããšã¯æãç«ããªã | ¬(¬{F}{b} & {E}{b}) | fact1: ãããã®ãŸããŸãLv.24ã移ãè¡ããªããšãããšãã®ã¿ãã¿ã«ãLv.81ã¯å±éºéããªããŠããã也ãæããªã fact2: ããä»®ã«ãã®ãŸããŸã¡ãLv.95ããã©ã€ããããšããããã®ã·ãã·ãLv.26ã¯å¡ãåããªã fact3: ãã®ãŸããŸãLv.24ã¯ä¹Ÿãæãããããã¯ããã¯ç§»ãè¡ã fact4: ããããã®ãŸããŸãLv.24ã也ãæããªãã°ãã®ãŸããŸã¡ãLv.95ã¯ãã©ã€ããã fact5: ä»®ã«ããã®ãŸããŸãLv.24ã¯ç§»ãè¡ãããšããããšã¯æ£ãããšãããšãã®ãŸããŸã¡ãLv.95ã¯ãã©ã€ããã | fact1: ¬{B}{a} -> (¬{E}{hs} & ¬{A}{hs}) fact2: {C}{c} -> ¬{D}{b} fact3: ({A}{a} v {B}{a}) fact4: {A}{a} -> {C}{c} fact5: {B}{a} -> {C}{c} | [
"fact3 & fact4 & fact5 -> int1: ãã®ãŸããŸã¡ãLv.95ã¯ãã©ã€ããã; int1 & fact2 -> int2: ãã®ã·ãã·ãLv.26ã¯å¡ãåããªã;"
] | [
"fact3 & fact4 & fact5 -> int1: {C}{c}; int1 & fact2 -> int2: ¬{D}{b};"
] | ãã®ã¿ãã¿ã«ãLv.81ã¯å±éºéãããšããããšã¯ãªã | ¬{E}{hs} | [] | 5 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ãŸããŸãLv.24ã移ãè¡ããªããšãããšãã®ã¿ãã¿ã«ãLv.81ã¯å±éºéããªããŠããã也ãæããªã fact2: ããä»®ã«ãã®ãŸããŸã¡ãLv.95ããã©ã€ããããšããããã®ã·ãã·ãLv.26ã¯å¡ãåããªã fact3: ãã®ãŸããŸãLv.24ã¯ä¹Ÿãæãããããã¯ããã¯ç§»ãè¡ã fact4: ããããã®ãŸããŸãLv.24ã也ãæããªãã°ãã®ãŸããŸã¡ãLv.95ã¯ãã©ã€ããã fact5: ä»®ã«ããã®ãŸããŸãLv.24ã¯ç§»ãè¡ãããšããããšã¯æ£ãããšãããšãã®ãŸããŸã¡ãLv.95ã¯ãã©ã€ããã ; $hypothesis$ = ããã®ã·ãã·ãLv.26ã¯è²ã£ãœããªãããã©å±éºéããããšããããšã¯æãç«ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{B}{a} -> (¬{E}{hs} & ¬{A}{hs}) fact2: {C}{c} -> ¬{D}{b} fact3: ({A}{a} v {B}{a}) fact4: {A}{a} -> {C}{c} fact5: {B}{a} -> {C}{c} ; $hypothesis$ = ¬(¬{F}{b} & {E}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ããªã¹ãããããšãæ§åããããšããããšããŸãã¯äž¡æ¹ãèµ·ããããšããããšã¯èª€ã£ãŠãã | ¬({B} v {AA}) | fact1: ä»®ã«ããªã¹ãããããšã¯çºçããªããŠæŽã«æ±ºãé£ããšããããšã¯çºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããšæ±ºãé£ããšããããšãçãã fact2: ããä»®ã«éããšããããšã¯çããªããšãããšæ§åããããšããããšãçºçãããã©èŸããšããããšã¯èµ·ãããªã fact3: éããšããããšã¯èµ·ããªã | fact1: ¬(¬{B} & ¬{BM}) -> {BM} fact2: ¬{A} -> ({AA} & ¬{AB}) fact3: ¬{A} | [
"fact2 & fact3 -> int1: æ§åããããšããããšãèµ·ãããèŸããšããããšã¯èµ·ãããªã; int1 -> int2: æ§åããããšããããšãçºçãã; int2 -> hypothesis;"
] | [
"fact2 & fact3 -> int1: ({AA} & ¬{AB}); int1 -> int2: {AA}; int2 -> hypothesis;"
] | ãœããœãªLv.51äºä»¶ããŸãã¯æ±ºãé£ããšããããšããããã¯äž¡æ¹ãšããèµ·ãã | ({CU} v {BM}) | [] | 6 | 3 | 3 | 3 | 3 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ããªã¹ãããããšã¯çºçããªããŠæŽã«æ±ºãé£ããšããããšã¯çºçããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªããšãããšæ±ºãé£ããšããããšãçãã fact2: ããä»®ã«éããšããããšã¯çããªããšãããšæ§åããããšããããšãçºçãããã©èŸããšããããšã¯èµ·ãããªã fact3: éããšããããšã¯èµ·ããªã ; $hypothesis$ = ããªã¹ãããããšãæ§åããããšããããšããŸãã¯äž¡æ¹ãèµ·ããããšããããšã¯èª€ã£ãŠãã ; $proof$ = | fact2 & fact3 -> int1: æ§åããããšããããšãèµ·ãããèŸããšããããšã¯èµ·ãããªã; int1 -> int2: æ§åããããšããããšãçºçãã; int2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬(¬{B} & ¬{BM}) -> {BM} fact2: ¬{A} -> ({AA} & ¬{AB}) fact3: ¬{A} ; $hypothesis$ = ¬({B} v {AA}) ; $proof$ = | fact2 & fact3 -> int1: ({AA} & ¬{AB}); int1 -> int2: {AA}; int2 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.20ã¯æ¥é£ã | {C}{b} | fact1: ããããã®ãããã¡ãLv.86ãç絡çéãããšããããšã¯ãªãããã©ãããæ§åããããªããã®ãããã¡ãLv.86ã¯å
¥ãèŸã fact2: ããä»®ã«ããã®ãããã¡ãLv.86ã¯å
¥ãèŸããªããããã«ããã¯å¥é¢ãé£ããªãããšããããšã¯äºå®ãšç°ãªããšããããã®ãŽããŽãLv.20ã¯å
¥ãèŸããªã fact3: ããããã®ãããã¡ãLv.86ãå
¥ãèŸãããŸãã¯ãããäžããæãããããã¯äž¡æ¹ãšããªããã®ãŽããŽãLv.20ã¯æ¥é£ããªã fact4: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯ããã£ãšãããšããããšã¯ãªãããã©ç絡çéãããšãããããã¯åŸ¡æªã fact5: ãã®ãããã¡ãLv.86ã¯ç絡çéããªããã©æ§åããã | fact1: (¬{AA}{a} & {AB}{a}) -> {B}{a} fact2: ¬(¬{B}{a} & ¬{E}{a}) -> ¬{B}{b} fact3: ({B}{a} v {A}{a}) -> ¬{C}{b} fact4: (x): (¬{EM}x & {AA}x) -> {IK}x fact5: (¬{AA}{a} & {AB}{a}) | [
"fact1 & fact5 -> int1: ããã®ãããã¡ãLv.86ã¯å
¥ãèŸãããšããããšã¯æãç«ã€; int1 -> int2: ãã®ãããã¡ãLv.86ã¯å
¥ãèŸããäžããæãããŸãã¯ã©ã¡ããã§ãã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact5 -> int1: {B}{a}; int1 -> int2: ({B}{a} v {A}{a}); int2 & fact3 -> hypothesis;"
] | ãããã®ãŽããŽãLv.20ãããã£ãšããªããã©ç絡çéããã°ãã®ãŽããŽãLv.20ã¯åŸ¡æªã | (¬{EM}{b} & {AA}{b}) -> {IK}{b} | [
"fact6 -> hypothesis;"
] | 1 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | PROVED | DISPROVED | PROVED | $facts$ = fact1: ããããã®ãããã¡ãLv.86ãç絡çéãããšããããšã¯ãªãããã©ãããæ§åããããªããã®ãããã¡ãLv.86ã¯å
¥ãèŸã fact2: ããä»®ã«ããã®ãããã¡ãLv.86ã¯å
¥ãèŸããªããããã«ããã¯å¥é¢ãé£ããªãããšããããšã¯äºå®ãšç°ãªããšããããã®ãŽããŽãLv.20ã¯å
¥ãèŸããªã fact3: ããããã®ãããã¡ãLv.86ãå
¥ãèŸãããŸãã¯ãããäžããæãããããã¯äž¡æ¹ãšããªããã®ãŽããŽãLv.20ã¯æ¥é£ããªã fact4: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯ããã£ãšãããšããããšã¯ãªãããã©ç絡çéãããšãããããã¯åŸ¡æªã fact5: ãã®ãããã¡ãLv.86ã¯ç絡çéããªããã©æ§åããã ; $hypothesis$ = ãã®ãŽããŽãLv.20ã¯æ¥é£ã ; $proof$ = | fact1 & fact5 -> int1: ããã®ãããã¡ãLv.86ã¯å
¥ãèŸãããšããããšã¯æãç«ã€; int1 -> int2: ãã®ãããã¡ãLv.86ã¯å
¥ãèŸããäžããæãããŸãã¯ã©ã¡ããã§ãã; int2 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{AA}{a} & {AB}{a}) -> {B}{a} fact2: ¬(¬{B}{a} & ¬{E}{a}) -> ¬{B}{b} fact3: ({B}{a} v {A}{a}) -> ¬{C}{b} fact4: (x): (¬{EM}x & {AA}x) -> {IK}x fact5: (¬{AA}{a} & {AB}{a}) ; $hypothesis$ = {C}{b} ; $proof$ = | fact1 & fact5 -> int1: {B}{a}; int1 -> int2: ({B}{a} v {A}{a}); int2 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ãœããœãLv.15ã¯çŽ°ãããŠäºæž¬ãæãããšããããšã¯æãç«ããªã | ¬({D}{b} & {E}{b}) | fact1: ãã®ã·ãã·ãLv.52ã¯é¿ãé£ã fact2: ä»®ã«ãã®ã·ãã·ãLv.52ãäŒãããé¿ãé£ããªãé£ãæããªã fact3: ãã®ãœããœãLv.15ã¯äºæž¬ãæã fact4: ããããã®ã·ãã·ãLv.52ãé£ãæããªããšãããšãã®ãœããœãLv.15ã¯äºæž¬ãæã fact5: ãã®ã·ãã·ãLv.52ã¯äŒãã fact6: ä»®ã«ãã®ã·ãã·ãLv.52ãé£ãæããªããšããããã®ãœããœãLv.15ã¯çŽ°ãããŠããã¯äºæž¬ãæã | fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{a} fact3: {E}{b} fact4: ¬{C}{a} -> {E}{b} fact5: {A}{a} fact6: ¬{C}{a} -> ({D}{b} & {E}{b}) | [
"fact5 & fact1 -> int1: ãã®ã·ãã·ãLv.52ã¯äŒãããæŽã«é¿ãé£ã; int1 & fact2 -> int2: ãã®ã·ãã·ãLv.52ã¯é£ãæããªã; int2 & fact6 -> hypothesis;"
] | [
"fact5 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{a}; int2 & fact6 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ã·ãã·ãLv.52ã¯é¿ãé£ã fact2: ä»®ã«ãã®ã·ãã·ãLv.52ãäŒãããé¿ãé£ããªãé£ãæããªã fact3: ãã®ãœããœãLv.15ã¯äºæž¬ãæã fact4: ããããã®ã·ãã·ãLv.52ãé£ãæããªããšãããšãã®ãœããœãLv.15ã¯äºæž¬ãæã fact5: ãã®ã·ãã·ãLv.52ã¯äŒãã fact6: ä»®ã«ãã®ã·ãã·ãLv.52ãé£ãæããªããšããããã®ãœããœãLv.15ã¯çŽ°ãããŠããã¯äºæž¬ãæã ; $hypothesis$ = ããã®ãœããœãLv.15ã¯çŽ°ãããŠäºæž¬ãæãããšããããšã¯æãç«ããªã ; $proof$ = | fact5 & fact1 -> int1: ãã®ã·ãã·ãLv.52ã¯äŒãããæŽã«é¿ãé£ã; int1 & fact2 -> int2: ãã®ã·ãã·ãLv.52ã¯é£ãæããªã; int2 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{a} fact2: ({A}{a} & {B}{a}) -> ¬{C}{a} fact3: {E}{b} fact4: ¬{C}{a} -> {E}{b} fact5: {A}{a} fact6: ¬{C}{a} -> ({D}{b} & {E}{b}) ; $hypothesis$ = ¬({D}{b} & {E}{b}) ; $proof$ = | fact5 & fact1 -> int1: ({A}{a} & {B}{a}); int1 & fact2 -> int2: ¬{C}{a}; int2 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽããŽãLv.91ã¯æ»ã鳎ãããªã | ¬{D}{b} | fact1: ããããšããã¢ã³ã¹ã¿ãŒãå¿å€ããããªããšãããšæ»ã鳎ããããã®äžããã¯èªäºãã fact2: ãã®ãœããœã«ã
Lv.4ã¯å¿å€ãããã fact3: ãã®ãœããœã«ã
Lv.4ã¯è»œã fact4: ãã®ãœããœã«ã
Lv.4ãèªäºããããã®äžå¿å€ãããã fact5: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æ»ã鳎ãããªããšãããã軜ãããã©èªäºããªãããšããããšã¯èª€ãã§ãã fact6: ãããã®ãœããœã«ã
Lv.4ãèªäºãããããã«è»œããšããã°ãã®ãŽããŽãLv.91ã¯æ»ã鳎ãããªã fact7: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯é£ã³åãå§ããªããšãããšãããã¯æããããªããå ããŠè»œããªãããšããããšã¯åã§ãã | fact1: (x): ¬{B}x -> ({D}x & {A}x) fact2: {B}{a} fact3: {C}{a} fact4: ({A}{a} & {B}{a}) fact5: (x): ¬{D}x -> ¬({C}x & ¬{A}x) fact6: ({A}{a} & {C}{a}) -> ¬{D}{b} fact7: (x): ¬{F}x -> ¬(¬{E}x & ¬{C}x) | [
"fact4 -> int1: ãã®ãœããœã«ã
Lv.4ã¯èªäºãã; int1 & fact3 -> int2: ãã®ãœããœã«ã
Lv.4ã¯èªäºãããããã«è»œã; int2 & fact6 -> hypothesis;"
] | [
"fact4 -> int1: {A}{a}; int1 & fact3 -> int2: ({A}{a} & {C}{a}); int2 & fact6 -> hypothesis;"
] | ãã®ãŽããŽãLv.91ã¯æ»ã鳎ãã | {D}{b} | [
"fact8 -> int3: ãããã®ãŽããŽãLv.91ã¯å¿å€ããããªããªãããã®ãŽããŽãLv.91ã¯æ»ã鳎ãããèªäºããããšããããšã¯çå®ã§ãã; fact9 -> int4: ãã®ãœããœã«ã
Lv.4ã¯é£ã³åãå§ããªããšããã°ããã®ãœããœã«ã
Lv.4ã¯æããããªããæŽã«è»œããªãããšããããšã¯æãç«ã€ãšããããšã¯ãªã;"
] | 7 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããšããã¢ã³ã¹ã¿ãŒãå¿å€ããããªããšãããšæ»ã鳎ããããã®äžããã¯èªäºãã fact2: ãã®ãœããœã«ã
Lv.4ã¯å¿å€ãããã fact3: ãã®ãœããœã«ã
Lv.4ã¯è»œã fact4: ãã®ãœããœã«ã
Lv.4ãèªäºããããã®äžå¿å€ãããã fact5: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯æ»ã鳎ãããªããšãããã軜ãããã©èªäºããªãããšããããšã¯èª€ãã§ãã fact6: ãããã®ãœããœã«ã
Lv.4ãèªäºãããããã«è»œããšããã°ãã®ãŽããŽãLv.91ã¯æ»ã鳎ãããªã fact7: ããä»®ã«ãšããã¢ã³ã¹ã¿ãŒã¯é£ã³åãå§ããªããšãããšãããã¯æããããªããå ããŠè»œããªãããšããããšã¯åã§ãã ; $hypothesis$ = ãã®ãŽããŽãLv.91ã¯æ»ã鳎ãããªã ; $proof$ = | fact4 -> int1: ãã®ãœããœã«ã
Lv.4ã¯èªäºãã; int1 & fact3 -> int2: ãã®ãœããœã«ã
Lv.4ã¯èªäºãããããã«è»œã; int2 & fact6 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬{B}x -> ({D}x & {A}x) fact2: {B}{a} fact3: {C}{a} fact4: ({A}{a} & {B}{a}) fact5: (x): ¬{D}x -> ¬({C}x & ¬{A}x) fact6: ({A}{a} & {C}{a}) -> ¬{D}{b} fact7: (x): ¬{F}x -> ¬(¬{E}x & ¬{C}x) ; $hypothesis$ = ¬{D}{b} ; $proof$ = | fact4 -> int1: {A}{a}; int1 & fact3 -> int2: ({A}{a} & {C}{a}); int2 & fact6 -> hypothesis; __PROVED__ |
0.3 | ãã®ããããLv.52ã¯ã¿ã€ãã«ããã | {C}{b} | fact1: ããä»®ã«ãã®ãã«ããã¡ãLv.73ã¯ã¿ã€ãã«ããããªãããŸãç©ããããªããšãããšåžèåãã fact2: ããä»®ã«ããã®ãã«ããã¡ãLv.73ã¯åžèåãããç©ããããªãããšããããšã¯æãç«ããªããšãããšãã®ããããLv.52ã¯çã¿æããªã fact3: ä»®ã«ããã®ããããLv.52ã¯çã¿æããªãããããåãé£ããªãããšããããšã¯æãç«ã€ãªãã¿ã€ãã«ããã fact4: é£ãç¬ç¡ããªãã¢ã³ã¹ã¿ãŒã¯çã¿æããªããŠåãé£ããªã fact5: ããããã®ãã«ããã¡ãLv.73ãã¿ã€ãã«ããããªããã®ããããLv.52ã¯ã¿ã€ãã«ããããªã fact6: ããã®ãã«ããã¡ãLv.73ã¯åžèåããäžæ¹ã§ç©ããããªãããšããããšã¯èª€ãã fact7: ãã®ããããLv.52ã¯åããªã | fact1: (¬{C}{a} & ¬{AB}{a}) -> {AA}{a} fact2: ¬({AA}{a} & ¬{AB}{a}) -> ¬{B}{b} fact3: (¬{B}{b} & ¬{A}{b}) -> {C}{b} fact4: (x): ¬{D}x -> (¬{B}x & ¬{A}x) fact5: {C}{a} -> ¬{C}{b} fact6: ¬({AA}{a} & ¬{AB}{a}) fact7: ¬{HB}{b} | [
"fact2 & fact6 -> int1: ãã®ããããLv.52ã¯çã¿æããªã;"
] | [
"fact2 & fact6 -> int1: ¬{B}{b};"
] | ãã®ããããLv.52ã¯ã¿ã€ãã«ããããªã | ¬{C}{b} | [
"fact8 -> int2: ä»®ã«ãã®ãã«ããã¡ãLv.73ãé£ãç¬ç¡ããªããšããããã®ãã«ããã¡ãLv.73ã¯çã¿æããªããŠåãé£ããªã;"
] | 5 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãã®ãã«ããã¡ãLv.73ã¯ã¿ã€ãã«ããããªãããŸãç©ããããªããšãããšåžèåãã fact2: ããä»®ã«ããã®ãã«ããã¡ãLv.73ã¯åžèåãããç©ããããªãããšããããšã¯æãç«ããªããšãããšãã®ããããLv.52ã¯çã¿æããªã fact3: ä»®ã«ããã®ããããLv.52ã¯çã¿æããªãããããåãé£ããªãããšããããšã¯æãç«ã€ãªãã¿ã€ãã«ããã fact4: é£ãç¬ç¡ããªãã¢ã³ã¹ã¿ãŒã¯çã¿æããªããŠåãé£ããªã fact5: ããããã®ãã«ããã¡ãLv.73ãã¿ã€ãã«ããããªããã®ããããLv.52ã¯ã¿ã€ãã«ããããªã fact6: ããã®ãã«ããã¡ãLv.73ã¯åžèåããäžæ¹ã§ç©ããããªãããšããããšã¯èª€ãã fact7: ãã®ããããLv.52ã¯åããªã ; $hypothesis$ = ãã®ããããLv.52ã¯ã¿ã€ãã«ããã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (¬{C}{a} & ¬{AB}{a}) -> {AA}{a} fact2: ¬({AA}{a} & ¬{AB}{a}) -> ¬{B}{b} fact3: (¬{B}{b} & ¬{A}{b}) -> {C}{b} fact4: (x): ¬{D}x -> (¬{B}x & ¬{A}x) fact5: {C}{a} -> ¬{C}{b} fact6: ¬({AA}{a} & ¬{AB}{a}) fact7: ¬{HB}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ããã®ãŽã«ãŽãLv.94ã¯éãç¡ããªããç§ããªãããšããããšã¯åœã§ãã | ¬(¬{E}{b} & ¬{F}{b}) | fact1: ä»®ã«ãåã
ãããªããçž«åãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãœããœã®Lv.26ã¯éŠŽã銎ããã fact2: ããä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯éŠŽã銎ããããšããããšã¯ãªãäžæ¹ã§åã
ããããšããããšã¯æãç«ããªããšãããšãããã¯éŠŽã銎ãããããšããããšã¯æãç«ã€ fact3: åã
ãããªãã¢ã³ã¹ã¿ãŒã§çž«åããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããã®ãœããœã®Lv.26ã銎ã銎ããããšããã°ãã®ãŽã«ãŽãLv.94ã¯ç³ã蟌ãã fact5: ãããããã®ãœããœã®Lv.26ã¯éŠŽã銎ããããªãããŸãã¯åã
ãããªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ééãã§ãããšããããã®ãŽã«ãŽãLv.94ã¯åã
ãããšããããšã¯ãªã fact6: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯åã
ãããªããªãã°ãéãç¡ããªãããã€ç§ãããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact7: ãããã®ãœããœã®Lv.26ãç§ããããŸãã¯æ©ãé£ããªãããããã¯ã©ã¡ããã§ãããªãã°ãã®ãœã¡ããœãLv.14ã¯éãç¡ããªã fact8: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çž«åãããšãããšãããã¯éŠŽã銎ããããªãããã©åã
ããããšããããšã¯ééãã fact9: ãããã®ãŽã«ãŽãLv.94ãç³ã蟌ãããšãããããã¯éãç¡ããªããããã«ç§ããªã | fact1: (x): (¬{A}x & {B}x) -> {C}{a} fact2: (x): ¬(¬{C}x & {A}x) -> {C}x fact3: (Ex): (¬{A}x & {B}x) fact4: {C}{a} -> {D}{b} fact5: ¬(¬{C}{a} v ¬{A}{a}) -> ¬{A}{b} fact6: (x): ¬{A}x -> ¬(¬{E}x & ¬{F}x) fact7: ({F}{a} v ¬{G}{a}) -> ¬{E}{hc} fact8: (x): {B}x -> ¬(¬{C}x & {A}x) fact9: {D}{b} -> (¬{E}{b} & ¬{F}{b}) | [
"fact3 & fact1 -> int1: ãã®ãœããœã®Lv.26ã¯éŠŽã銎ããã; int1 & fact4 -> int2: ãã®ãŽã«ãŽãLv.94ã¯ç³ã蟌ãã; int2 & fact9 -> hypothesis;"
] | [
"fact3 & fact1 -> int1: {C}{a}; int1 & fact4 -> int2: {D}{b}; int2 & fact9 -> hypothesis;"
] | ããã®ãŽã«ãŽãLv.94ã¯éãç¡ããªããç§ããªãããšããããšã¯åœã§ãã | ¬(¬{E}{b} & ¬{F}{b}) | [
"fact10 -> int3: ããä»®ã«ãã®ãŽã«ãŽãLv.94ã¯åã
ãããªããšããããéãç¡ããšããããšã¯ãªããããã«ç§ããªãããšããããšã¯æãç«ããªã;"
] | 5 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ä»®ã«ãåã
ãããªããçž«åãããã¢ã³ã¹ã¿ãŒããããšããã°ãã®ãœããœã®Lv.26ã¯éŠŽã銎ããã fact2: ããä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯éŠŽã銎ããããšããããšã¯ãªãäžæ¹ã§åã
ããããšããããšã¯æãç«ããªããšãããšãããã¯éŠŽã銎ãããããšããããšã¯æãç«ã€ fact3: åã
ãããªãã¢ã³ã¹ã¿ãŒã§çž«åããã¢ã³ã¹ã¿ãŒã¯ãã fact4: ãããã®ãœããœã®Lv.26ã銎ã銎ããããšããã°ãã®ãŽã«ãŽãLv.94ã¯ç³ã蟌ãã fact5: ãããããã®ãœããœã®Lv.26ã¯éŠŽã銎ããããªãããŸãã¯åã
ãããªãããããã¯äž¡æ¹ãšãã§ããããšããããšã¯ééãã§ãããšããããã®ãŽã«ãŽãLv.94ã¯åã
ãããšããããšã¯ãªã fact6: ãããäœããã®ã¢ã³ã¹ã¿ãŒã¯åã
ãããªããªãã°ãéãç¡ããªãããã€ç§ãããšããããšã¯ãªãããšããããšã¯æãç«ããªã fact7: ãããã®ãœããœã®Lv.26ãç§ããããŸãã¯æ©ãé£ããªãããããã¯ã©ã¡ããã§ãããªãã°ãã®ãœã¡ããœãLv.14ã¯éãç¡ããªã fact8: ãªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çž«åãããšãããšãããã¯éŠŽã銎ããããªãããã©åã
ããããšããããšã¯ééãã fact9: ãããã®ãŽã«ãŽãLv.94ãç³ã蟌ãããšãããããã¯éãç¡ããªããããã«ç§ããªã ; $hypothesis$ = ããã®ãŽã«ãŽãLv.94ã¯éãç¡ããªããç§ããªãããšããããšã¯åœã§ãã ; $proof$ = | fact3 & fact1 -> int1: ãã®ãœããœã®Lv.26ã¯éŠŽã銎ããã; int1 & fact4 -> int2: ãã®ãŽã«ãŽãLv.94ã¯ç³ã蟌ãã; int2 & fact9 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): (¬{A}x & {B}x) -> {C}{a} fact2: (x): ¬(¬{C}x & {A}x) -> {C}x fact3: (Ex): (¬{A}x & {B}x) fact4: {C}{a} -> {D}{b} fact5: ¬(¬{C}{a} v ¬{A}{a}) -> ¬{A}{b} fact6: (x): ¬{A}x -> ¬(¬{E}x & ¬{F}x) fact7: ({F}{a} v ¬{G}{a}) -> ¬{E}{hc} fact8: (x): {B}x -> ¬(¬{C}x & {A}x) fact9: {D}{b} -> (¬{E}{b} & ¬{F}{b}) ; $hypothesis$ = ¬(¬{E}{b} & ¬{F}{b}) ; $proof$ = | fact3 & fact1 -> int1: {C}{a}; int1 & fact4 -> int2: {D}{b}; int2 & fact9 -> hypothesis; __DISPROVED__ |
0.3 | ãå®ããšããããšã§ã¯ãªããã«ãããLv.79äºä»¶ãçºçããããšããããšã¯ééãã§ãã | ¬(¬{D} & {C}) | fact1: ãããæ±ãããããšããããšã¯çºçãããã©äŸå¥ããããšã¯çããªãããšããããšã¯åãªããèšãåãããšãçºçããããšããããšã¯æ¬åœã fact2: ããä»®ã«èšãåãããšãçããã°ãå®ããšããããšã¯çããªãããã«ãããLv.79äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã fact3: ããä»®ã«åŒã£ç¹°ãè¿ãããšãèµ·ãããšãããšãæ±ãããããšããããšãèµ·ããäžæ¹ã§äŸå¥ããããšã¯èµ·ããªãããšããããšã¯èª€ã£ãŠãã | fact1: ¬({AA} & ¬{AB}) -> {B} fact2: {B} -> ¬(¬{D} & {C}) fact3: {A} -> ¬({AA} & ¬{AB}) | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ãããæ±ãããããšããããšã¯çºçãããã©äŸå¥ããããšã¯çããªãããšããããšã¯åãªããèšãåãããšãçºçããããšããããšã¯æ¬åœã fact2: ããä»®ã«èšãåãããšãçããã°ãå®ããšããããšã¯çããªãããã«ãããLv.79äºä»¶ãèµ·ããããšããããšã¯æãç«ããªã fact3: ããä»®ã«åŒã£ç¹°ãè¿ãããšãèµ·ãããšãããšãæ±ãããããšããããšãèµ·ããäžæ¹ã§äŸå¥ããããšã¯èµ·ããªãããšããããšã¯èª€ã£ãŠãã ; $hypothesis$ = ãå®ããšããããšã§ã¯ãªããã«ãããLv.79äºä»¶ãçºçããããšããããšã¯ééãã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬({AA} & ¬{AB}) -> {B} fact2: {B} -> ¬(¬{D} & {C}) fact3: {A} -> ¬({AA} & ¬{AB}) ; $hypothesis$ = ¬(¬{D} & {C}) ; $proof$ = | __UNKNOWN__ |
0.3 | çæž©ããšããããšã¯çºçããªãããããã¯ã·ãªã·ãLv.64äºä»¶ã¯èµ·ããªã | (¬{E} v ¬{D}) | fact1: äžæ¢ãããšãèµ·ããªããšããããšã¯ãé£éããããšããããã¯åŽåŽããšããããšãçããããšããããšã¯ãã£ããã§ãã fact2: ããä»®ã«äžæ¢ãããšã¯çºçããªããªãã°ãçæž©ããšããããšã¯èµ·ããªãããããã¯ã·ãªã·ãLv.64äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ããªã fact3: é£éããããšãèµ·ãã fact4: ããåãé£ããšããããšãçãããšãããäžæ¢ãããšã¯èµ·ããªãããããã¯åŽåŽããšããããšãèµ·ãããã©ã¡ããã§ãã fact5: åãé¢ãé£ããšããããšãèµ·ãã fact6: ããã«ãããLv.94äºä»¶ã¯çºçããªãããšããããšã¯æ³šææ·±ããšããããšãèµ·ãããšããããšã«ç¹ãã fact7: ãããã·ãªã·ãLv.64äºä»¶ãèµ·ãããšãããåŽåŽããšããããšã¯èµ·ãããªããæŽã«äžæ¢ãããšã¯èµ·ãããªã fact8: ã·ãªã·ãLv.64äºä»¶ã¯ãé£éããããšã¯èµ·ãããªãããšããããšã«é²ããã | fact1: ({A} v {B}) -> ¬{C} fact2: ¬{C} -> ¬(¬{E} v ¬{D}) fact3: {A} fact4: {F} -> (¬{C} v {B}) fact5: {HM} fact6: ¬{DO} -> {IN} fact7: {D} -> (¬{B} & ¬{C}) fact8: ¬{A} -> ¬{D} | [
"fact3 -> int1: é£éããããšãçããããããã¯åŽåŽããšããããšãçºçãã; int1 & fact1 -> int2: äžæ¢ãããšã¯çããªã; int2 & fact2 -> hypothesis;"
] | [
"fact3 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> hypothesis;"
] | ãœããœãLv.9äºä»¶ã¯èµ·ããªã | ¬{EQ} | [] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: äžæ¢ãããšãèµ·ããªããšããããšã¯ãé£éããããšããããã¯åŽåŽããšããããšãçããããšããããšã¯ãã£ããã§ãã fact2: ããä»®ã«äžæ¢ãããšã¯çºçããªããªãã°ãçæž©ããšããããšã¯èµ·ããªãããããã¯ã·ãªã·ãLv.64äºä»¶ã¯èµ·ããªãããšããããšã¯æãç«ããªã fact3: é£éããããšãèµ·ãã fact4: ããåãé£ããšããããšãçãããšãããäžæ¢ãããšã¯èµ·ããªãããããã¯åŽåŽããšããããšãèµ·ãããã©ã¡ããã§ãã fact5: åãé¢ãé£ããšããããšãèµ·ãã fact6: ããã«ãããLv.94äºä»¶ã¯çºçããªãããšããããšã¯æ³šææ·±ããšããããšãèµ·ãããšããããšã«ç¹ãã fact7: ãããã·ãªã·ãLv.64äºä»¶ãèµ·ãããšãããåŽåŽããšããããšã¯èµ·ãããªããæŽã«äžæ¢ãããšã¯èµ·ãããªã fact8: ã·ãªã·ãLv.64äºä»¶ã¯ãé£éããããšã¯èµ·ãããªãããšããããšã«é²ããã ; $hypothesis$ = çæž©ããšããããšã¯çºçããªãããããã¯ã·ãªã·ãLv.64äºä»¶ã¯èµ·ããªã ; $proof$ = | fact3 -> int1: é£éããããšãçããããããã¯åŽåŽããšããããšãçºçãã; int1 & fact1 -> int2: äžæ¢ãããšã¯çããªã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} fact2: ¬{C} -> ¬(¬{E} v ¬{D}) fact3: {A} fact4: {F} -> (¬{C} v {B}) fact5: {HM} fact6: ¬{DO} -> {IN} fact7: {D} -> (¬{B} & ¬{C}) fact8: ¬{A} -> ¬{D} ; $hypothesis$ = (¬{E} v ¬{D}) ; $proof$ = | fact3 -> int1: ({A} v {B}); int1 & fact1 -> int2: ¬{C}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã¿ãã¿ãLv.69ã¯çœå¶ãããå ããŠä¿¡ãæãããšããããšã¯ééã£ãŠãã | ¬({C}{a} & {D}{a}) | fact1: ãã®ã¿ã«ãã¿ã«ãLv.83ã¯ä¿¡ãæã fact2: ãã®ã¿ãã¿ãLv.69ã¯æµããæããããã«æãç¡ã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯æµããæããªããšãããšãããã¯çœå¶ããããããä¿¡ãæãããšããããšã¯åœã fact4: ä»®ã«ãã®ã¿ãã¿ãLv.69ãæãç¡ããšããã°ãã®ã¿ãã¿ãLv.69ã¯çœå¶ãã fact5: ä»®ã«ãã®ã·ã«ãã·ãLv.68ãçŠãŸãããšããã°ãã®ã¿ãã¿ãLv.69ã¯æµããæããªããŠãããããã¯æãç¡ããšããããšã¯ãªã fact6: ãã®ã¿ãã¿ãLv.69ã¯æµããæã fact7: ããã®ã¿ãã¿ãLv.69ã¯ããããããããšããããšã¯æ¬åœã fact8: ãã®ã¿ãã¿ãLv.69ã¯ä¿¡ãæã | fact1: {D}{dq} fact2: ({A}{a} & {B}{a}) fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: {B}{a} -> {C}{a} fact5: {E}{b} -> (¬{A}{a} & ¬{B}{a}) fact6: {A}{a} fact7: {EU}{a} fact8: {D}{a} | [
"fact2 -> int1: ãã®ã¿ãã¿ãLv.69ã¯æãç¡ã; int1 & fact4 -> int2: ãã®ã¿ãã¿ãLv.69ã¯çœå¶ãã; int2 & fact8 -> hypothesis;"
] | [
"fact2 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact8 -> hypothesis;"
] | ããã®ã¿ãã¿ãLv.69ã¯çœå¶ãããå ããŠä¿¡ãæãããšããããšã¯ééã£ãŠãã | ¬({C}{a} & {D}{a}) | [
"fact9 -> int3: ãããã®ã¿ãã¿ãLv.69ã¯æµããæããªããšãããšãçœå¶ãããä¿¡ãæãããšããããšã¯æãç«ããªã;"
] | 6 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ã¿ã«ãã¿ã«ãLv.83ã¯ä¿¡ãæã fact2: ãã®ã¿ãã¿ãLv.69ã¯æµããæããããã«æãç¡ã fact3: ãããšããã¢ã³ã¹ã¿ãŒã¯æµããæããªããšãããšãããã¯çœå¶ããããããä¿¡ãæãããšããããšã¯åœã fact4: ä»®ã«ãã®ã¿ãã¿ãLv.69ãæãç¡ããšããã°ãã®ã¿ãã¿ãLv.69ã¯çœå¶ãã fact5: ä»®ã«ãã®ã·ã«ãã·ãLv.68ãçŠãŸãããšããã°ãã®ã¿ãã¿ãLv.69ã¯æµããæããªããŠãããããã¯æãç¡ããšããããšã¯ãªã fact6: ãã®ã¿ãã¿ãLv.69ã¯æµããæã fact7: ããã®ã¿ãã¿ãLv.69ã¯ããããããããšããããšã¯æ¬åœã fact8: ãã®ã¿ãã¿ãLv.69ã¯ä¿¡ãæã ; $hypothesis$ = ããã®ã¿ãã¿ãLv.69ã¯çœå¶ãããå ããŠä¿¡ãæãããšããããšã¯ééã£ãŠãã ; $proof$ = | fact2 -> int1: ãã®ã¿ãã¿ãLv.69ã¯æãç¡ã; int1 & fact4 -> int2: ãã®ã¿ãã¿ãLv.69ã¯çœå¶ãã; int2 & fact8 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {D}{dq} fact2: ({A}{a} & {B}{a}) fact3: (x): ¬{A}x -> ¬({C}x & {D}x) fact4: {B}{a} -> {C}{a} fact5: {E}{b} -> (¬{A}{a} & ¬{B}{a}) fact6: {A}{a} fact7: {EU}{a} fact8: {D}{a} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact2 -> int1: {B}{a}; int1 & fact4 -> int2: {C}{a}; int2 & fact8 -> hypothesis; __DISPROVED__ |
0.3 | ãã«ãã¡ãLv.30äºä»¶ãèµ·ãã | {B} | fact1: èãé£ããšããããšããããã¯ç 究éçºããããšããŸãã¯äž¡æ¹ãšãã¯ãææ¡ãé£ããšããããšã¯çããªãããšããããšã«ãããããã fact2: èãé£ããšããããšã¯ãã«ãã¡ãLv.30äºä»¶ã®ãã£ãããšãªã | fact1: ¬{D} -> ({A} v {C}) fact2: {A} -> {B} | [] | [] | ãã«ãã¡ãLv.30äºä»¶ã¯èµ·ãããªã | ¬{B} | [] | 6 | 2 | 2 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: èãé£ããšããããšããããã¯ç 究éçºããããšããŸãã¯äž¡æ¹ãšãã¯ãææ¡ãé£ããšããããšã¯çããªãããšããããšã«ãããããã fact2: èãé£ããšããããšã¯ãã«ãã¡ãLv.30äºä»¶ã®ãã£ãããšãªã ; $hypothesis$ = ãã«ãã¡ãLv.30äºä»¶ãèµ·ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{D} -> ({A} v {C}) fact2: {A} -> {B} ; $hypothesis$ = {B} ; $proof$ = | __UNKNOWN__ |
0.3 | ããããä»®ã«ãçŒãé£ããšããããšã¯ãªããå¿å°è¯ããªãããšããããšã¯äºå®ãšç°ãªããªãåæããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ç¢ºãã§ãªã | ¬((Ex): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x) | fact1: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯çŒãé£ããªããŠããã¯å¿å°è¯ããªãããšããããšã¯ééãã§ãããšããã°ãããã¯åæããªãããšããããšã¯ç¢ºãã fact2: ä»®ã«ãã®ãŸã®ãŸã«ã
Lv.45ãçŒãé£ããšãããšããã¯åæããªã | fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact2: {AA}{aa} -> ¬{B}{aa} | [
"fact1 -> int1: ããä»®ã«ããã®ãŸã®ãŸã«ã
Lv.45ã¯çŒãé£ããªãããããããã¯å¿å°è¯ããšããããšã¯ãªãããšããããšã¯åã§ãããªããåæããªãããšããããšã¯æãç«ã€; int1 -> hypothesis;"
] | [
"fact1 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}; int1 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ããšããã¢ã³ã¹ã¿ãŒã¯çŒãé£ããªããŠããã¯å¿å°è¯ããªãããšããããšã¯ééãã§ãããšããã°ãããã¯åæããªãããšããããšã¯ç¢ºãã fact2: ä»®ã«ãã®ãŸã®ãŸã«ã
Lv.45ãçŒãé£ããšãããšããã¯åæããªã ; $hypothesis$ = ããããä»®ã«ãçŒãé£ããšããããšã¯ãªããå¿å°è¯ããªãããšããããšã¯äºå®ãšç°ãªããªãåæããªããã¢ã³ã¹ã¿ãŒã¯ããããšããããšã¯ç¢ºãã§ãªã ; $proof$ = | fact1 -> int1: ããä»®ã«ããã®ãŸã®ãŸã«ã
Lv.45ã¯çŒãé£ããªãããããããã¯å¿å°è¯ããšããããšã¯ãªãããšããããšã¯åã§ãããªããåæããªãããšããããšã¯æãç«ã€; int1 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (x): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x fact2: {AA}{aa} -> ¬{B}{aa} ; $hypothesis$ = ¬((Ex): ¬(¬{AA}x & ¬{AB}x) -> ¬{B}x) ; $proof$ = | fact1 -> int1: ¬(¬{AA}{aa} & ¬{AB}{aa}) -> ¬{B}{aa}; int1 -> hypothesis; __DISPROVED__ |
0.3 | ãœã«ããœãLv.23äºä»¶ãçºçãã | {AB} | fact1: ããããŸã®ãŸã«Lv.26äºä»¶ãçºçãããé ããšããããšã¯çºçããããšããããšã¯èª€ãã ãšããããé ããšããããšã¯èµ·ããªãããšããããšã¯ééã£ãŠããªã fact2: ç«ãŠæããšããããšã§ã¯ãªããŠãœã«ããœãLv.23äºä»¶ãçãã | fact1: ¬({B} & {GO}) -> ¬{GO} fact2: (¬{AA} & {AB}) | [
"fact2 -> int1: ç«ãŠæããšããããšã§ã¯ãªããŠãœã«ããœãLv.23äºä»¶ãçãã; int1 -> hypothesis;"
] | [
"fact2 -> int1: (¬{AA} & {AB}); int1 -> hypothesis;"
] | é ããšããããšã§ã¯ãªããŠå±€å¥ããããšãèµ·ãã | (¬{GO} & {DE}) | [] | 4 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããŸã®ãŸã«Lv.26äºä»¶ãçºçãããé ããšããããšã¯çºçããããšããããšã¯èª€ãã ãšããããé ããšããããšã¯èµ·ããªãããšããããšã¯ééã£ãŠããªã fact2: ç«ãŠæããšããããšã§ã¯ãªããŠãœã«ããœãLv.23äºä»¶ãçãã ; $hypothesis$ = ãœã«ããœãLv.23äºä»¶ãçºçãã ; $proof$ = | fact2 -> int1: ç«ãŠæããšããããšã§ã¯ãªããŠãœã«ããœãLv.23äºä»¶ãçãã; int1 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({B} & {GO}) -> ¬{GO} fact2: (¬{AA} & {AB}) ; $hypothesis$ = {AB} ; $proof$ = | fact2 -> int1: (¬{AA} & {AB}); int1 -> hypothesis; __PROVED__ |
0.3 | ãã®ã¿ã¡ãã¿ã«ãLv.88ã¯æãŠãç¡ã | {C}{b} | fact1: ããæ¥ããããããã«å€«å©Šãããããšããããšã¯åœãªãã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããä»®ã«ããæ¥ãããã倫婊ãããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒããããšãããšãã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ã fact3: ãã®ã¿ã¡ãã¿ã«ãLv.88ãæ»ãå
¥ãããšããã°ããã¯æãŠãç¡ã fact4: ããä»®ã«ããã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ãããšããããšã¯æãç«ã€ãšããã°ããã®ã¿ã¡ãã¿ã«ãLv.88ã¯æ»ãå
¥ããªãããšããããšã¯æãç«ããªã | fact1: (Ex): ¬({AA}x & {AB}x) fact2: (x): ¬({AA}x & {AB}x) -> {A}{a} fact3: {B}{b} -> {C}{b} fact4: {A}{a} -> {B}{b} | [
"fact1 & fact2 -> int1: ãã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ã; int1 & fact4 -> int2: ãã®ã¿ã¡ãã¿ã«ãLv.88ã¯æ»ãå
¥ãã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact2 -> int1: {A}{a}; int1 & fact4 -> int2: {B}{b}; int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ããæ¥ããããããã«å€«å©Šãããããšããããšã¯åœãªãã¢ã³ã¹ã¿ãŒã¯ãã fact2: ããä»®ã«ããæ¥ãããã倫婊ãããããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒããããšãããšãã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ã fact3: ãã®ã¿ã¡ãã¿ã«ãLv.88ãæ»ãå
¥ãããšããã°ããã¯æãŠãç¡ã fact4: ããä»®ã«ããã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ãããšããããšã¯æãç«ã€ãšããã°ããã®ã¿ã¡ãã¿ã«ãLv.88ã¯æ»ãå
¥ããªãããšããããšã¯æãç«ããªã ; $hypothesis$ = ãã®ã¿ã¡ãã¿ã«ãLv.88ã¯æãŠãç¡ã ; $proof$ = | fact1 & fact2 -> int1: ãã®ãœããœã«ãLv.94ã¯æ
æ²æ·±ã; int1 & fact4 -> int2: ãã®ã¿ã¡ãã¿ã«ãLv.88ã¯æ»ãå
¥ãã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: (Ex): ¬({AA}x & {AB}x) fact2: (x): ¬({AA}x & {AB}x) -> {A}{a} fact3: {B}{b} -> {C}{b} fact4: {A}{a} -> {B}{b} ; $hypothesis$ = {C}{b} ; $proof$ = | fact1 & fact2 -> int1: {A}{a}; int1 & fact4 -> int2: {B}{b}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | äžžã£ãããšããããšãšæº¶ã蟌ããããšäž¡æ¹ãçãã | ({E} & {D}) | fact1: ãœããœã¡ãLv.19äºä»¶ãçºçãã fact2: æ¥ç¶ããããšã¯çºçããªããšããã°ãäžžã£ãããšããããšãèµ·ãããããã溶ã蟌ããããšãèµ·ããããšããããšã¯ééãã fact3: ããããœããœã¡ãLv.19äºä»¶ã¯çºçããªããªãäžžã£ãããšããããšãèµ·ããããã®äžã·ãã·ã«Lv.51äºä»¶ãçãã fact4: ãã·ãã·ã«Lv.51äºä»¶ããã³ãœããœã¡ãLv.19äºä»¶ãèµ·ããããšããããšã¯ãæ¥ç¶ããããšã¯èµ·ããªãããšããããšãçºçããã fact5: ã·ãã·ã«Lv.51äºä»¶ãèµ·ãã fact6: ä»®ã«ãœããœã¡ãLv.19äºä»¶ãèµ·ããªããŠã·ãã·ã«Lv.51äºä»¶ãçããªããªãã°ãŸã¡ããŸã¡ãLv.37äºä»¶ã¯èµ·ããªã | fact1: {B} fact2: ¬{C} -> ¬({E} & {D}) fact3: ¬{B} -> ({E} & {A}) fact4: ({A} & {B}) -> ¬{C} fact5: {A} fact6: (¬{B} & ¬{A}) -> ¬{HL} | [
"fact5 & fact1 -> int1: ã·ãã·ã«Lv.51äºä»¶ãšãœããœã¡ãLv.19äºä»¶äž¡æ¹ãšããèµ·ãã; int1 & fact4 -> int2: æ¥ç¶ããããšã¯èµ·ãããªã; int2 & fact2 -> hypothesis;"
] | [
"fact5 & fact1 -> int1: ({A} & {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact2 -> hypothesis;"
] | ãŸã¡ããŸã¡ãLv.37äºä»¶ã¯çããªã | ¬{HL} | [] | 6 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãœããœã¡ãLv.19äºä»¶ãçºçãã fact2: æ¥ç¶ããããšã¯çºçããªããšããã°ãäžžã£ãããšããããšãèµ·ãããããã溶ã蟌ããããšãèµ·ããããšããããšã¯ééãã fact3: ããããœããœã¡ãLv.19äºä»¶ã¯çºçããªããªãäžžã£ãããšããããšãèµ·ããããã®äžã·ãã·ã«Lv.51äºä»¶ãçãã fact4: ãã·ãã·ã«Lv.51äºä»¶ããã³ãœããœã¡ãLv.19äºä»¶ãèµ·ããããšããããšã¯ãæ¥ç¶ããããšã¯èµ·ããªãããšããããšãçºçããã fact5: ã·ãã·ã«Lv.51äºä»¶ãèµ·ãã fact6: ä»®ã«ãœããœã¡ãLv.19äºä»¶ãèµ·ããªããŠã·ãã·ã«Lv.51äºä»¶ãçããªããªãã°ãŸã¡ããŸã¡ãLv.37äºä»¶ã¯èµ·ããªã ; $hypothesis$ = äžžã£ãããšããããšãšæº¶ã蟌ããããšäž¡æ¹ãçãã ; $proof$ = | fact5 & fact1 -> int1: ã·ãã·ã«Lv.51äºä»¶ãšãœããœã¡ãLv.19äºä»¶äž¡æ¹ãšããèµ·ãã; int1 & fact4 -> int2: æ¥ç¶ããããšã¯èµ·ãããªã; int2 & fact2 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B} fact2: ¬{C} -> ¬({E} & {D}) fact3: ¬{B} -> ({E} & {A}) fact4: ({A} & {B}) -> ¬{C} fact5: {A} fact6: (¬{B} & ¬{A}) -> ¬{HL} ; $hypothesis$ = ({E} & {D}) ; $proof$ = | fact5 & fact1 -> int1: ({A} & {B}); int1 & fact4 -> int2: ¬{C}; int2 & fact2 -> hypothesis; __DISPROVED__ |
0.3 | ãããã«ãLv.53äºä»¶ã¯èµ·ãããªã | ¬{D} | fact1: ãŸããŸã¡ãLv.21äºä»¶ãèµ·ãã fact2: ãããã«ãLv.53äºä»¶ã¯èµ·ãããªããšããããšã¯æŽæ°åºæ¥ãããšããã³ãŸããŸã¡ãLv.21äºä»¶ãèµ·ããã«èµ·å ãã fact3: æŽæ°åºæ¥ãããšãçããããããããªãã«ãLv.27äºä»¶ã¯èµ·ããªã | fact1: {C} fact2: ({A} & {C}) -> ¬{D} fact3: ({A} & ¬{B}) | [
"fact3 -> int1: ãæŽæ°åºæ¥ãããšãèµ·ããããšããããšã¯æ£ãã; int1 & fact1 -> int2: æŽæ°åºæ¥ãããšãçºçãããæŽã«ãŸããŸã¡ãLv.21äºä»¶ãçãã; int2 & fact2 -> hypothesis;"
] | [
"fact3 -> int1: {A}; int1 & fact1 -> int2: ({A} & {C}); int2 & fact2 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ãŸããŸã¡ãLv.21äºä»¶ãèµ·ãã fact2: ãããã«ãLv.53äºä»¶ã¯èµ·ãããªããšããããšã¯æŽæ°åºæ¥ãããšããã³ãŸããŸã¡ãLv.21äºä»¶ãèµ·ããã«èµ·å ãã fact3: æŽæ°åºæ¥ãããšãçããããããããªãã«ãLv.27äºä»¶ã¯èµ·ããªã ; $hypothesis$ = ãããã«ãLv.53äºä»¶ã¯èµ·ãããªã ; $proof$ = | fact3 -> int1: ãæŽæ°åºæ¥ãããšãèµ·ããããšããããšã¯æ£ãã; int1 & fact1 -> int2: æŽæ°åºæ¥ãããšãçºçãããæŽã«ãŸããŸã¡ãLv.21äºä»¶ãçãã; int2 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: {C} fact2: ({A} & {C}) -> ¬{D} fact3: ({A} & ¬{B}) ; $hypothesis$ = ¬{D} ; $proof$ = | fact3 -> int1: {A}; int1 & fact1 -> int2: ({A} & {C}); int2 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽãªãŽãLv.65ã¯æ©ãèŸããªããå§ãããªãããŸãã¯äž¡æ¹ãšãã | (¬{A}{c} v ¬{D}{c}) | fact1: ããä»®ã«ãããã®ãŸããŸãLv.76ã¯ãããã£ãœãããŸãã¯ããã¯çããããªããã©ã¡ããã ããšããããšã¯çå®ã§ããããšããããšã¯åãªãã°ãã®ãŸããŸãLv.76ã¯æ°Žã£ãœããªã fact2: ä»®ã«ãã®ãŸããŸãLv.76ãæ°Žã£ãœããªããªããã®ãŸã«ããŸãLv.91ã¯æ©ãèŸããªã fact3: ããä»®ã«ãã®ãŸã«ããŸãLv.91ãæ©ãèŸããªããªãã°ãã®ãŽãªãŽãLv.65ã¯æ©ãèŸããªãããŸãã¯å§ãããªããäž¡æ¹ã§ãã fact4: ããã®ãŸããŸãLv.76ã¯ãããã£ãœããçããããªãããŸãã¯äž¡æ¹ãšãã ããšããããšã¯ééã£ãŠãã | fact1: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact2: ¬{B}{a} -> ¬{A}{b} fact3: ¬{A}{b} -> (¬{A}{c} v ¬{D}{c}) fact4: ¬({AA}{a} v ¬{AB}{a}) | [
"fact1 & fact4 -> int1: ãã®ãŸããŸãLv.76ã¯æ°Žã£ãœããªã; int1 & fact2 -> int2: ãã®ãŸã«ããŸãLv.91ã¯æ©ãèŸããªã; int2 & fact3 -> hypothesis;"
] | [
"fact1 & fact4 -> int1: ¬{B}{a}; int1 & fact2 -> int2: ¬{A}{b}; int2 & fact3 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 0 | 0 | 0 | PROVED | null | PROVED | null | $facts$ = fact1: ããä»®ã«ãããã®ãŸããŸãLv.76ã¯ãããã£ãœãããŸãã¯ããã¯çããããªããã©ã¡ããã ããšããããšã¯çå®ã§ããããšããããšã¯åãªãã°ãã®ãŸããŸãLv.76ã¯æ°Žã£ãœããªã fact2: ä»®ã«ãã®ãŸããŸãLv.76ãæ°Žã£ãœããªããªããã®ãŸã«ããŸãLv.91ã¯æ©ãèŸããªã fact3: ããä»®ã«ãã®ãŸã«ããŸãLv.91ãæ©ãèŸããªããªãã°ãã®ãŽãªãŽãLv.65ã¯æ©ãèŸããªãããŸãã¯å§ãããªããäž¡æ¹ã§ãã fact4: ããã®ãŸããŸãLv.76ã¯ãããã£ãœããçããããªãããŸãã¯äž¡æ¹ãšãã ããšããããšã¯ééã£ãŠãã ; $hypothesis$ = ãã®ãŽãªãŽãLv.65ã¯æ©ãèŸããªããå§ãããªãããŸãã¯äž¡æ¹ãšãã ; $proof$ = | fact1 & fact4 -> int1: ãã®ãŸããŸãLv.76ã¯æ°Žã£ãœããªã; int1 & fact2 -> int2: ãã®ãŸã«ããŸãLv.91ã¯æ©ãèŸããªã; int2 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬({AA}{a} v ¬{AB}{a}) -> ¬{B}{a} fact2: ¬{B}{a} -> ¬{A}{b} fact3: ¬{A}{b} -> (¬{A}{c} v ¬{D}{c}) fact4: ¬({AA}{a} v ¬{AB}{a}) ; $hypothesis$ = (¬{A}{c} v ¬{D}{c}) ; $proof$ = | fact1 & fact4 -> int1: ¬{B}{a}; int1 & fact2 -> int2: ¬{A}{b}; int2 & fact3 -> hypothesis; __PROVED__ |
0.3 | ããããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããªããŠãã®äžå¥³ã®åããããªãããšããããšã¯æãç«ã€ããšããããšã¯ééãã ããšããããšã¯æãç«ã€ | ¬(¬{B}{b} & ¬{C}{b}) | fact1: ãã®ãŸã¡ã
ãŸãLv.55ã¯éã£ãœã fact2: ããããªãããã®ã¢ã³ã¹ã¿ãŒã¯éã£ãœããªããªãã°ãå£æ±ããªãããã€ããã¯å¥³ã®åããããªãããšããããšã¯æãç«ããªã fact3: ãã®ã·ã«ãã·ãLv.93ã¯å¥³ã®åããããªã fact4: ãããããã®ãŸã¡ã
ãŸãLv.55ã¯éã£ãœãããšããããšã¯æãç«ã€ãªããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããªã | fact1: {A}{a} fact2: (x): ¬{A}x -> ¬(¬{B}x & ¬{C}x) fact3: ¬{C}{b} fact4: {A}{a} -> ¬{B}{b} | [
"fact4 & fact1 -> int1: ãã®ã·ã«ãã·ãLv.93ã¯å£æ±ããšããããšã¯ãªã; int1 & fact3 -> hypothesis;"
] | [
"fact4 & fact1 -> int1: ¬{B}{b}; int1 & fact3 -> hypothesis;"
] | ããããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããªããŠãã®äžå¥³ã®åããããªãããšããããšã¯æãç«ã€ããšããããšã¯ééãã ããšããããšã¯æãç«ã€ | ¬(¬{B}{b} & ¬{C}{b}) | [
"fact5 -> int2: ããããã®ã·ã«ãã·ãLv.93ã¯éã£ãœããªããªãããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããšããããšã¯ãªããããŸãã«ããã¯å¥³ã®åããããªãããšããããšã¯æãç«ããªã;"
] | 6 | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãŸã¡ã
ãŸãLv.55ã¯éã£ãœã fact2: ããããªãããã®ã¢ã³ã¹ã¿ãŒã¯éã£ãœããªããªãã°ãå£æ±ããªãããã€ããã¯å¥³ã®åããããªãããšããããšã¯æãç«ããªã fact3: ãã®ã·ã«ãã·ãLv.93ã¯å¥³ã®åããããªã fact4: ãããããã®ãŸã¡ã
ãŸãLv.55ã¯éã£ãœãããšããããšã¯æãç«ã€ãªããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããªã ; $hypothesis$ = ããããã®ã·ã«ãã·ãLv.93ã¯å£æ±ããªããŠãã®äžå¥³ã®åããããªãããšããããšã¯æãç«ã€ããšããããšã¯ééãã ããšããããšã¯æãç«ã€ ; $proof$ = | fact4 & fact1 -> int1: ãã®ã·ã«ãã·ãLv.93ã¯å£æ±ããšããããšã¯ãªã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {A}{a} fact2: (x): ¬{A}x -> ¬(¬{B}x & ¬{C}x) fact3: ¬{C}{b} fact4: {A}{a} -> ¬{B}{b} ; $hypothesis$ = ¬(¬{B}{b} & ¬{C}{b}) ; $proof$ = | fact4 & fact1 -> int1: ¬{B}{b}; int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãã | {A}{b} | fact1: ããã®ãŽããŽã®Lv.5ã¯å
èŠãããªãäžæ¹ã§ã¡ã£ããããšããããšã¯åã§ãããšããããã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãããªã fact2: ããã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãããªãããã©ã¡ã£ããããšããããšã¯æãç«ããªã fact3: ããããã®ãŽããŽã®Lv.5ãç
ãããšãããšãã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãã fact4: ããã®ãŽã¡ã
ãŽãLv.16ã¯éŠŽæã¿é£ããªããå
èŠããããšããããšã¯èª€ã£ãŠãã fact5: ããã®ãŽã¡ã
ãŽãLv.16ã¯æ±ºã蟌ãŸãªãäžæ¹ã§ããã¯æ匷ãããšããããšã¯åœã§ãã fact6: ããã®ãŽããŽã®Lv.5ã¯ç
ãããªãäžæ¹ã§ã¡ã£ããããšããããšã¯ééãã§ãã | fact1: ¬(¬{AA}{a} & {AB}{a}) -> ¬{A}{b} fact2: ¬(¬{A}{b} & {AB}{b}) fact3: {A}{a} -> {A}{b} fact4: ¬(¬{BA}{b} & {AA}{b}) fact5: ¬(¬{IR}{b} & {FQ}{b}) fact6: ¬(¬{A}{a} & {AB}{a}) | [] | [] | ãã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãã | {A}{b} | [] | 4 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããã®ãŽããŽã®Lv.5ã¯å
èŠãããªãäžæ¹ã§ã¡ã£ããããšããããšã¯åã§ãããšããããã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãããªã fact2: ããã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãããªãããã©ã¡ã£ããããšããããšã¯æãç«ããªã fact3: ããããã®ãŽããŽã®Lv.5ãç
ãããšãããšãã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãã fact4: ããã®ãŽã¡ã
ãŽãLv.16ã¯éŠŽæã¿é£ããªããå
èŠããããšããããšã¯èª€ã£ãŠãã fact5: ããã®ãŽã¡ã
ãŽãLv.16ã¯æ±ºã蟌ãŸãªãäžæ¹ã§ããã¯æ匷ãããšããããšã¯åœã§ãã fact6: ããã®ãŽããŽã®Lv.5ã¯ç
ãããªãäžæ¹ã§ã¡ã£ããããšããããšã¯ééãã§ãã ; $hypothesis$ = ãã®ãŽã¡ã
ãŽãLv.16ã¯ç
ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬(¬{AA}{a} & {AB}{a}) -> ¬{A}{b} fact2: ¬(¬{A}{b} & {AB}{b}) fact3: {A}{a} -> {A}{b} fact4: ¬(¬{BA}{b} & {AA}{b}) fact5: ¬(¬{IR}{b} & {FQ}{b}) fact6: ¬(¬{A}{a} & {AB}{a}) ; $hypothesis$ = {A}{b} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã®ã¿ãLv.11ã¯ãã¡ã£ãããªã | ¬{C}{c} | fact1: ããããã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããããšããããšã¯ãªããªããåããã©ãããšããããšã¯çå®ã§ãã fact2: ãã®ã·ãã·ã«ãLv.70ã¯ãŸã ãã£ããã fact3: ãã®ã·ãã·ã«ãLv.70ãåããã©ããšãããšãã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããã fact4: ããããã®ã¿ã¡ãã¿ã«Lv.59ããŸã ãã£ããããšãããšãã®ã¿ã®ã¿ãLv.11ã¯ãã¡ã£ãããªã fact5: ä»®ã«ããã®ã·ãã·ã«ãLv.70ã¯ãã¡ã£ããããšããããšã¯æãç«ã€ãšããããã®ã¿ã®ã¿ãLv.11ã¯æãç¡ã fact6: ããã®ã·ãã·ã«ãLv.70ã¯æãç¡ããªããã©å¿ããããšããããšã¯åœã§ãã fact7: ãŸã ãã£ãããã¢ã³ã¹ã¿ãŒã¯ãã¡ã£ãã fact8: ãããããã®ã·ãã·ã«ãLv.70ã¯æãç¡ããšããããšã¯ãªãããããããã¯å¿ããããšããããšã¯ééã£ãŠãããšããã°åããã©ã | fact1: ¬{A}{b} -> {B}{b} fact2: {A}{a} fact3: {B}{a} -> {A}{b} fact4: {A}{b} -> ¬{C}{c} fact5: {C}{a} -> {AA}{c} fact6: ¬(¬{AA}{a} & {AB}{a}) fact7: (x): {A}x -> {C}x fact8: ¬(¬{AA}{a} & {AB}{a}) -> {B}{a} | [
"fact8 & fact6 -> int1: ãã®ã·ãã·ã«ãLv.70ã¯åããã©ã; int1 & fact3 -> int2: ãã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããã; int2 & fact4 -> hypothesis;"
] | [
"fact8 & fact6 -> int1: {B}{a}; int1 & fact3 -> int2: {A}{b}; int2 & fact4 -> hypothesis;"
] | ãã®ã¿ã®ã¿ãLv.11ã¯ãã¡ã£ãã | {C}{c} | [
"fact9 -> int3: ããä»®ã«ãã®ã¿ã®ã¿ãLv.11ããŸã ãã£ããããšããã°ããã¯ãã¡ã£ãã;"
] | 4 | 3 | 3 | 3 | 3 | 4 | 0 | 4 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ããããã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããããšããããšã¯ãªããªããåããã©ãããšããããšã¯çå®ã§ãã fact2: ãã®ã·ãã·ã«ãLv.70ã¯ãŸã ãã£ããã fact3: ãã®ã·ãã·ã«ãLv.70ãåããã©ããšãããšãã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããã fact4: ããããã®ã¿ã¡ãã¿ã«Lv.59ããŸã ãã£ããããšãããšãã®ã¿ã®ã¿ãLv.11ã¯ãã¡ã£ãããªã fact5: ä»®ã«ããã®ã·ãã·ã«ãLv.70ã¯ãã¡ã£ããããšããããšã¯æãç«ã€ãšããããã®ã¿ã®ã¿ãLv.11ã¯æãç¡ã fact6: ããã®ã·ãã·ã«ãLv.70ã¯æãç¡ããªããã©å¿ããããšããããšã¯åœã§ãã fact7: ãŸã ãã£ãããã¢ã³ã¹ã¿ãŒã¯ãã¡ã£ãã fact8: ãããããã®ã·ãã·ã«ãLv.70ã¯æãç¡ããšããããšã¯ãªãããããããã¯å¿ããããšããããšã¯ééã£ãŠãããšããã°åããã©ã ; $hypothesis$ = ãã®ã¿ã®ã¿ãLv.11ã¯ãã¡ã£ãããªã ; $proof$ = | fact8 & fact6 -> int1: ãã®ã·ãã·ã«ãLv.70ã¯åããã©ã; int1 & fact3 -> int2: ãã®ã¿ã¡ãã¿ã«Lv.59ã¯ãŸã ãã£ããã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ¬{A}{b} -> {B}{b} fact2: {A}{a} fact3: {B}{a} -> {A}{b} fact4: {A}{b} -> ¬{C}{c} fact5: {C}{a} -> {AA}{c} fact6: ¬(¬{AA}{a} & {AB}{a}) fact7: (x): {A}x -> {C}x fact8: ¬(¬{AA}{a} & {AB}{a}) -> {B}{a} ; $hypothesis$ = ¬{C}{c} ; $proof$ = | fact8 & fact6 -> int1: {B}{a}; int1 & fact3 -> int2: {A}{b}; int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ã¿ãã¿ã«ãLv.75äºä»¶ãèµ·ããªãããããã¯ãŸããŸã¡ãLv.70äºä»¶ã¯çºçããããŸãã¯ã©ã¡ããã§ãã | (¬{C} v {D}) | fact1: ã¿ãã¿ã«ãLv.75äºä»¶ã¯ãéãããšãèµ·ããããŸãã¯èŠåãããšãèµ·ããããšããããšã«é²ããã | fact1: ({A} v {B}) -> ¬{C} | [] | [] | null | null | [] | null | 3 | 3 | null | null | 0 | 0 | 0 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ã¿ãã¿ã«ãLv.75äºä»¶ã¯ãéãããšãèµ·ããããŸãã¯èŠåãããšãèµ·ããããšããããšã«é²ããã ; $hypothesis$ = ã¿ãã¿ã«ãLv.75äºä»¶ãèµ·ããªãããããã¯ãŸããŸã¡ãLv.70äºä»¶ã¯çºçããããŸãã¯ã©ã¡ããã§ãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ({A} v {B}) -> ¬{C} ; $hypothesis$ = (¬{C} v {D}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã«ã¿ãLv.19ã¯è³¢ã | {B}{aa} | fact1: ããããã¢ã³ã¹ã¿ãŒã¯å¡©ã£èŸããªã fact2: ãã®ã¿ã«ã¿ãLv.19ã¯æ Œå¥œè¯ããšããããšã¯ãªã fact3: ãã®ã¿ã«ã¿ãLv.19ãæ Œå¥œè¯ããŠããã«é¢åèããšããã°ãã®ã¿ã«ã¿ãLv.19ã¯è³¢ã fact4: ããããã¢ã³ã¹ã¿ãŒã¯æ Œå¥œè¯ããªããã©é¢åèããšãããšè³¢ã fact5: ããããã®ã¿ã«ã¿ãLv.19ãæµæµªããªããã©ããã¯äºæž¬ãé£ããšããã°ããã®ã¿ã«ã¿ãLv.19ã¯æ Œå¥œè¯ãããšããããšã¯æãç«ã€ fact6: ãã®ã¿ã«ã¿ãLv.19ã¯èãèŸããªããæ
ãæ·±ã | fact1: (x): ¬{D}x fact2: ¬{AA}{aa} fact3: ({AA}{aa} & {AB}{aa}) -> {B}{aa} fact4: (x): (¬{AA}x & {AB}x) -> {B}x fact5: (¬{DO}{aa} & {DF}{aa}) -> {AA}{aa} fact6: (¬{CK}{aa} & {S}{aa}) | [
"fact4 -> int1: ããããã®ã¿ã«ã¿ãLv.19ãæ Œå¥œè¯ããªãäžæ¹ã§é¢åèããªããã®ã¿ã«ã¿ãLv.19ã¯è³¢ã;"
] | [
"fact4 -> int1: (¬{AA}{aa} & {AB}{aa}) -> {B}{aa};"
] | ãã®ã¿ã«ã¿ãLv.19ã¯è³¢ããªã | ¬{B}{aa} | [
"fact7 -> int2: ãã®ãã®ããªLv.67ã¯å¡©ã£èŸããªã;"
] | 5 | 2 | 2 | null | null | 5 | 0 | 5 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããã¢ã³ã¹ã¿ãŒã¯å¡©ã£èŸããªã fact2: ãã®ã¿ã«ã¿ãLv.19ã¯æ Œå¥œè¯ããšããããšã¯ãªã fact3: ãã®ã¿ã«ã¿ãLv.19ãæ Œå¥œè¯ããŠããã«é¢åèããšããã°ãã®ã¿ã«ã¿ãLv.19ã¯è³¢ã fact4: ããããã¢ã³ã¹ã¿ãŒã¯æ Œå¥œè¯ããªããã©é¢åèããšãããšè³¢ã fact5: ããããã®ã¿ã«ã¿ãLv.19ãæµæµªããªããã©ããã¯äºæž¬ãé£ããšããã°ããã®ã¿ã«ã¿ãLv.19ã¯æ Œå¥œè¯ãããšããããšã¯æãç«ã€ fact6: ãã®ã¿ã«ã¿ãLv.19ã¯èãèŸããªããæ
ãæ·±ã ; $hypothesis$ = ãã®ã¿ã«ã¿ãLv.19ã¯è³¢ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{D}x fact2: ¬{AA}{aa} fact3: ({AA}{aa} & {AB}{aa}) -> {B}{aa} fact4: (x): (¬{AA}x & {AB}x) -> {B}x fact5: (¬{DO}{aa} & {DF}{aa}) -> {AA}{aa} fact6: (¬{CK}{aa} & {S}{aa}) ; $hypothesis$ = {B}{aa} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãããã¡ãLv.89ã¯ç¥è¡ãã | {B}{a} | fact1: éãã¢ã³ã¹ã¿ãŒã¯ä¹ãæããšããããšã¯ãªããã©çœã fact2: ããããã®ã·ãã·ã«ãLv.17ãä¹ãæããªãããã©çœããšããããã®ãããã¡ãLv.89ã¯ç¥è¡ãã fact3: ãã®ã·ãã·ã«ãLv.17ã¯éã fact4: ãä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯éããç²æç²æããããšããããšã¯ééã£ãŠããã°ãç¥è¡ããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ | fact1: (x): {A}x -> (¬{AA}x & {AB}x) fact2: (¬{AA}{aa} & {AB}{aa}) -> {B}{a} fact3: {A}{aa} fact4: (x): ¬({A}x & {C}x) -> ¬{B}x | [
"fact1 -> int1: ä»®ã«ãã®ã·ãã·ã«ãLv.17ãéããšãããšä¹ãæããªããŠçœã; int1 & fact3 -> int2: ãã®ã·ãã·ã«ãLv.17ã¯ä¹ãæããªããçœã; int2 & fact2 -> hypothesis;"
] | [
"fact1 -> int1: {A}{aa} -> (¬{AA}{aa} & {AB}{aa}); int1 & fact3 -> int2: (¬{AA}{aa} & {AB}{aa}); int2 & fact2 -> hypothesis;"
] | ãã®ãããã¡ãLv.89ã¯ç¥è¡ããªã | ¬{B}{a} | [
"fact5 -> int3: ããã®ãããã¡ãLv.89ã¯éããããŸãã«ããã¯ç²æç²æããããšããããšã¯ééãã§ãããšãããšç¥è¡ãããšããããšã¯ãªã;"
] | 4 | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: éãã¢ã³ã¹ã¿ãŒã¯ä¹ãæããšããããšã¯ãªããã©çœã fact2: ããããã®ã·ãã·ã«ãLv.17ãä¹ãæããªãããã©çœããšããããã®ãããã¡ãLv.89ã¯ç¥è¡ãã fact3: ãã®ã·ãã·ã«ãLv.17ã¯éã fact4: ãä»®ã«ããªãããã®ã¢ã³ã¹ã¿ãŒã¯éããç²æç²æããããšããããšã¯ééã£ãŠããã°ãç¥è¡ããªãããšããããšã¯æãç«ã€ããšããããšã¯æãç«ã€ ; $hypothesis$ = ãã®ãããã¡ãLv.89ã¯ç¥è¡ãã ; $proof$ = | fact1 -> int1: ä»®ã«ãã®ã·ãã·ã«ãLv.17ãéããšãããšä¹ãæããªããŠçœã; int1 & fact3 -> int2: ãã®ã·ãã·ã«ãLv.17ã¯ä¹ãæããªããçœã; int2 & fact2 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): {A}x -> (¬{AA}x & {AB}x) fact2: (¬{AA}{aa} & {AB}{aa}) -> {B}{a} fact3: {A}{aa} fact4: (x): ¬({A}x & {C}x) -> ¬{B}x ; $hypothesis$ = {B}{a} ; $proof$ = | fact1 -> int1: {A}{aa} -> (¬{AA}{aa} & {AB}{aa}); int1 & fact3 -> int2: (¬{AA}{aa} & {AB}{aa}); int2 & fact2 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŽããŽã«Lv.32ã¯å
å®ããªã | ¬{D}{d} | fact1: ãããã®ãããã«ãLv.75ãå®çŽããã°ãã®ãŽããŽã«Lv.32ã¯å
å®ããªã fact2: ãã®ãŸã¡ããŸãLv.22ã¯æ°ä»ãæã fact3: ããããã®ãŽããŽã«Lv.32ãå
¥ãæããšããããšã¯ãªããªããã®ãŽããŽã«Lv.32ã¯æ°ä»ãæããŠå ããŠå
å®ãã fact4: ããä»®ã«ãã®ãŸã¡ããŸãLv.22ãæ°ä»ãæããªããã®ãã¡ã
ãã«Lv.76ã¯å
¥ãæã fact5: ããããã®ãã¡ã
ãã«Lv.76ã¯å®çŽãããšãããããã®ãããã«ãLv.75ã¯å
¥ãæãããšããããšã¯æ¬åœã§ãã fact6: ãã®ãŽããŽã«Lv.32ã¯æ°ä»ãæã | fact1: {C}{c} -> ¬{D}{d} fact2: {A}{a} fact3: ¬{B}{d} -> ({A}{d} & {D}{d}) fact4: {A}{a} -> {B}{b} fact5: {C}{b} -> {B}{c} fact6: {A}{d} | [
"fact4 & fact2 -> int1: ãã®ãã¡ã
ãã«Lv.76ã¯å
¥ãæã;"
] | [
"fact4 & fact2 -> int1: {B}{b};"
] | ãã®ãŽããŽã«Lv.32ã¯å
å®ãã | {D}{d} | [] | 6 | 3 | 3 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãããã®ãããã«ãLv.75ãå®çŽããã°ãã®ãŽããŽã«Lv.32ã¯å
å®ããªã fact2: ãã®ãŸã¡ããŸãLv.22ã¯æ°ä»ãæã fact3: ããããã®ãŽããŽã«Lv.32ãå
¥ãæããšããããšã¯ãªããªããã®ãŽããŽã«Lv.32ã¯æ°ä»ãæããŠå ããŠå
å®ãã fact4: ããä»®ã«ãã®ãŸã¡ããŸãLv.22ãæ°ä»ãæããªããã®ãã¡ã
ãã«Lv.76ã¯å
¥ãæã fact5: ããããã®ãã¡ã
ãã«Lv.76ã¯å®çŽãããšãããããã®ãããã«ãLv.75ã¯å
¥ãæãããšããããšã¯æ¬åœã§ãã fact6: ãã®ãŽããŽã«Lv.32ã¯æ°ä»ãæã ; $hypothesis$ = ãã®ãŽããŽã«Lv.32ã¯å
å®ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {C}{c} -> ¬{D}{d} fact2: {A}{a} fact3: ¬{B}{d} -> ({A}{d} & {D}{d}) fact4: {A}{a} -> {B}{b} fact5: {C}{b} -> {B}{c} fact6: {A}{d} ; $hypothesis$ = ¬{D}{d} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãŽããŽãLv.41ã¯èç©ããæããªã | ¬{C}{a} | fact1: ããããã®ãŽããŽãLv.41ãçã延ã³ããšããã°ãã®ã·ã«ã·ã«Lv.80ã¯çã延ã³ã fact2: ãã®ãŽããŽãLv.41ã¯è¿·ãé£ãããŸãæåŸãã fact3: ãã®ã·ãã·ã¡ãLv.97ã¯æåŸãã fact4: ãã®ãŽããŽãLv.41ã¯ç
ãã fact5: ãã®ã·ãã·ãLv.83ã¯æåŸãã fact6: ããããã®ãŽããŽãLv.41ãæåŸãããšããã°èç©ããæã | fact1: {JD}{a} -> {JD}{ai} fact2: ({A}{a} & {B}{a}) fact3: {B}{ds} fact4: {CF}{a} fact5: {B}{hn} fact6: {B}{a} -> {C}{a} | [
"fact2 -> int1: ãã®ãŽããŽãLv.41ã¯æåŸãã; int1 & fact6 -> hypothesis;"
] | [
"fact2 -> int1: {B}{a}; int1 & fact6 -> hypothesis;"
] | ãã®ã·ã«ã·ã«Lv.80ã¯çã延ã³ããå ããŠä¿è²ãã | ({JD}{ai} & {HN}{ai}) | [] | 4 | 2 | 2 | 2 | 2 | 4 | 0 | 4 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ããããã®ãŽããŽãLv.41ãçã延ã³ããšããã°ãã®ã·ã«ã·ã«Lv.80ã¯çã延ã³ã fact2: ãã®ãŽããŽãLv.41ã¯è¿·ãé£ãããŸãæåŸãã fact3: ãã®ã·ãã·ã¡ãLv.97ã¯æåŸãã fact4: ãã®ãŽããŽãLv.41ã¯ç
ãã fact5: ãã®ã·ãã·ãLv.83ã¯æåŸãã fact6: ããããã®ãŽããŽãLv.41ãæåŸãããšããã°èç©ããæã ; $hypothesis$ = ãã®ãŽããŽãLv.41ã¯èç©ããæããªã ; $proof$ = | fact2 -> int1: ãã®ãŽããŽãLv.41ã¯æåŸãã; int1 & fact6 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {JD}{a} -> {JD}{ai} fact2: ({A}{a} & {B}{a}) fact3: {B}{ds} fact4: {CF}{a} fact5: {B}{hn} fact6: {B}{a} -> {C}{a} ; $hypothesis$ = ¬{C}{a} ; $proof$ = | fact2 -> int1: {B}{a}; int1 & fact6 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.39ã¯å¿ãŸå¿ãŸãããªã | ¬{C}{a} | fact1: ãã®ãŸããŸãLv.39ã¯æããã fact2: ãã®ãŸããŸãLv.39ã¯èžãäžããããã€æããã fact3: ããããã®ãŸããŸãLv.39ã¯èžãäžããªãããšããããšã¯èª€ã£ãŠãããšããããã®ãŸããŸãLv.39ã¯å¿ãŸå¿ãŸãã | fact1: {B}{a} fact2: ({A}{a} & {B}{a}) fact3: {A}{a} -> {C}{a} | [
"fact2 -> int1: ãã®ãŸããŸãLv.39ã¯èžãäžãã; int1 & fact3 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact3 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 1 | 0 | 1 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ãã®ãŸããŸãLv.39ã¯æããã fact2: ãã®ãŸããŸãLv.39ã¯èžãäžããããã€æããã fact3: ããããã®ãŸããŸãLv.39ã¯èžãäžããªãããšããããšã¯èª€ã£ãŠãããšããããã®ãŸããŸãLv.39ã¯å¿ãŸå¿ãŸãã ; $hypothesis$ = ãã®ãŸããŸãLv.39ã¯å¿ãŸå¿ãŸãããªã ; $proof$ = | fact2 -> int1: ãã®ãŸããŸãLv.39ã¯èžãäžãã; int1 & fact3 -> hypothesis; __DISPROVED__ | $facts$ = fact1: {B}{a} fact2: ({A}{a} & {B}{a}) fact3: {A}{a} -> {C}{a} ; $hypothesis$ = ¬{C}{a} ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact3 -> hypothesis; __DISPROVED__ |
0.3 | ããã®ã·ã«ãã·ãLv.47ã¯ãã©ããªããŠããã«èŠããããšããããšã¯äºå®ãšç°ãªã | ¬({C}{b} & {D}{b}) | fact1: ãã®ã·ã¡ãã·ã«ãLv.66ã¯æå
¥ã fact2: ãã©ããªããªãã¢ã³ã¹ã¿ãŒã¯åŒãç¶ãããæå
¥ã fact3: ããã®ã·ã«ãã·ãLv.47ã¯èŠããããšããããšã¯çå®ã§ãã | fact1: {B}{a} fact2: (x): ¬{C}x -> ({A}x & {B}x) fact3: {D}{b} | [
"fact1 -> int1: ãã®ã·ã¡ãã·ã«ãLv.66ã¯åŒãç¶ãããšããããšã¯ãªãããŸãã¯ããã¯æå
¥ãããããã¯äž¡æ¹ãšãã ;"
] | [
"fact1 -> int1: (¬{A}{a} v {B}{a});"
] | ãã®ãœããœãLv.6ã¯æå
¥ã | {B}{cg} | [
"fact4 -> int2: ããããã®ãœããœãLv.6ã¯ãã©ããªããšããããšã¯ãªããªãããã®ãœããœãLv.6ãåŒãç¶ããããã®äžæå
¥ãããšããããšã¯æãç«ã€;"
] | 5 | 3 | 3 | null | null | 1 | 0 | 1 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãã®ã·ã¡ãã·ã«ãLv.66ã¯æå
¥ã fact2: ãã©ããªããªãã¢ã³ã¹ã¿ãŒã¯åŒãç¶ãããæå
¥ã fact3: ããã®ã·ã«ãã·ãLv.47ã¯èŠããããšããããšã¯çå®ã§ãã ; $hypothesis$ = ããã®ã·ã«ãã·ãLv.47ã¯ãã©ããªããŠããã«èŠããããšããããšã¯äºå®ãšç°ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: {B}{a} fact2: (x): ¬{C}x -> ({A}x & {B}x) fact3: {D}{b} ; $hypothesis$ = ¬({C}{b} & {D}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãœããœã¡ã
Lv.37äºä»¶ã¯ãç²æç²æãããšããããšã¯çºçããªãããœããœã¡ã
Lv.37äºä»¶ãçºçããããšããããšãæã | {B} -> (¬{A} & {B}) | fact1: æžå
ããããšãšæ¡åããããšãèµ·ããã¯æ¡åããããšã«ç±æ¥ãã fact2: ããœãªãœã¡ãLv.71äºä»¶ã¯èµ·ããªãããšããããšã¯ç¢ºãã fact3: ç²æç²æãããšããããšã¯èµ·ããªã | fact1: {GB} -> ({IB} & {GB}) fact2: ¬{P} fact3: ¬{A} | [
"void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã¡ã
Lv.37äºä»¶ãèµ·ãã; fact3 & assump1 -> int1: ç²æç²æãããšããããšã§ã¯ãªããœããœã¡ã
Lv.37äºä»¶ãçºçãã; [assump1] & int1 -> hypothesis;"
] | [
"void -> assump1: {B}; fact3 & assump1 -> int1: (¬{A} & {B}); [assump1] & int1 -> hypothesis;"
] | null | null | [] | null | 3 | 2 | 3 | 2 | 2 | 0 | 2 | PROVED | null | PROVED | null | $facts$ = fact1: æžå
ããããšãšæ¡åããããšãèµ·ããã¯æ¡åããããšã«ç±æ¥ãã fact2: ããœãªãœã¡ãLv.71äºä»¶ã¯èµ·ããªãããšããããšã¯ç¢ºãã fact3: ç²æç²æãããšããããšã¯èµ·ããªã ; $hypothesis$ = ãœããœã¡ã
Lv.37äºä»¶ã¯ãç²æç²æãããšããããšã¯çºçããªãããœããœã¡ã
Lv.37äºä»¶ãçºçããããšããããšãæã ; $proof$ = | void -> assump1: 以äžã®ããã«ä»®å®ããããœããœã¡ã
Lv.37äºä»¶ãèµ·ãã; fact3 & assump1 -> int1: ç²æç²æãããšããããšã§ã¯ãªããœããœã¡ã
Lv.37äºä»¶ãçºçãã; [assump1] & int1 -> hypothesis; __PROVED__ | $facts$ = fact1: {GB} -> ({IB} & {GB}) fact2: ¬{P} fact3: ¬{A} ; $hypothesis$ = {B} -> (¬{A} & {B}) ; $proof$ = | void -> assump1: {B}; fact3 & assump1 -> int1: (¬{A} & {B}); [assump1] & int1 -> hypothesis; __PROVED__ |
0.3 | ããã®ãããã«Lv.13ã¯æºãåãããå¢è³ããããšããããšã¯åœã§ãã | ¬({C}{a} & {D}{a}) | fact1: ãã®ãããã«Lv.13ã¯åããããã«ããã¯å€ãããã fact2: å€ãããããªãã¢ã³ã¹ã¿ãŒã¯åç¯ãããå ããŠåã fact3: ããã®ãããã«Lv.13ã¯å€ããããããšããããšã¯æãç«ãŠã°ããã¯æºãåãã fact4: ãã®ãããã«Lv.13ã¯å¢è³ãã fact5: ãã®ã¿ãã¿ãLv.91ã¯æºãåãã | fact1: ({A}{a} & {B}{a}) fact2: (x): ¬{B}x -> ({HD}x & {A}x) fact3: {B}{a} -> {C}{a} fact4: {D}{a} fact5: {C}{jj} | [
"fact1 -> int1: ããã®ãããã«Lv.13ã¯å€ãããããªãããšããããšã¯èª€ã£ãŠãã; int1 & fact3 -> int2: ãã®ãããã«Lv.13ã¯æºãåãã; int2 & fact4 -> hypothesis;"
] | [
"fact1 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact4 -> hypothesis;"
] | ãã®ã¿ãã¿ãLv.91ã¯å¢è³ããããã®äžåç¯ãã | ({D}{jj} & {HD}{jj}) | [
"fact6 -> int3: ããããã®ã¿ãã¿ãLv.91ã¯å€ãããããªãããšããããšã¯äºå®ã ãšããã°ãã®ã¿ãã¿ãLv.91ã¯åç¯ããããã®äžåã;"
] | 4 | 3 | 3 | 3 | 3 | 2 | 0 | 2 | DISPROVED | UNKNOWN | DISPROVED | UNKNOWN | $facts$ = fact1: ãã®ãããã«Lv.13ã¯åããããã«ããã¯å€ãããã fact2: å€ãããããªãã¢ã³ã¹ã¿ãŒã¯åç¯ãããå ããŠåã fact3: ããã®ãããã«Lv.13ã¯å€ããããããšããããšã¯æãç«ãŠã°ããã¯æºãåãã fact4: ãã®ãããã«Lv.13ã¯å¢è³ãã fact5: ãã®ã¿ãã¿ãLv.91ã¯æºãåãã ; $hypothesis$ = ããã®ãããã«Lv.13ã¯æºãåãããå¢è³ããããšããããšã¯åœã§ãã ; $proof$ = | fact1 -> int1: ããã®ãããã«Lv.13ã¯å€ãããããªãããšããããšã¯èª€ã£ãŠãã; int1 & fact3 -> int2: ãã®ãããã«Lv.13ã¯æºãåãã; int2 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ({A}{a} & {B}{a}) fact2: (x): ¬{B}x -> ({HD}x & {A}x) fact3: {B}{a} -> {C}{a} fact4: {D}{a} fact5: {C}{jj} ; $hypothesis$ = ¬({C}{a} & {D}{a}) ; $proof$ = | fact1 -> int1: {B}{a}; int1 & fact3 -> int2: {C}{a}; int2 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŸããŸãLv.44ã¯ãã©ã³ã¹äººããã | {C}{b} | fact1: ãã®ãœã«ããœã¡ãLv.42ã¯ç Žå£ãå§ãã fact2: ããããã®ãœã«ããœã¡ãLv.42ã¯éã
ãããšããããšã¯ãªããšãããããã®ãŸããŸãLv.44ã¯ã§ã£ããããšããããšã¯æãç«ã€ fact3: ããã®ãœããœã«ãLv.14ã¯éŠŽã銎ããããã©æŽå°ãããšããããšã¯ãªãããšããããšã¯æãç«ããªããšããããã®ãœã«ããœã¡ãLv.42ã¯ã¯ãªã¢åºæ¥ãªã fact4: ä»®ã«ãã®ãŸããŸãLv.44ãã§ã£ãããšããããã©ã³ã¹äººããã fact5: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯ç Žå£ãå§ãããªãããããã¯æè¬ããªãããŸãããã¯éºããããšããããšã¯çå®ã§ããããšããããšã¯æ¬åœã§ãªã fact6: ãããããã®ãœã«ããœã¡ãLv.42ã¯ç Žå£ãå§ããããšããããšã¯æ¬åœã ãšãããšããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããªãããããããã¯éã
ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact7: ãããããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããªããéã
ããããšããããšã¯åã§ãããªãã°ãã®ãŸããŸãLv.44ã¯ã§ã£ãã fact8: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯ç Žå£ãå§ãããã§ã£ããããšããããšã¯äºå®ã§ãªããšããã°ããã¯ãã©ã³ã¹äººããããªã fact9: ãã®ãœã«ããœã¡ãLv.42ã¯ã§ã£ãã | fact1: {A}{a} fact2: ¬{AB}{a} -> {B}{b} fact3: ¬({E}{c} & ¬{F}{c}) -> ¬{D}{a} fact4: {B}{b} -> {C}{b} fact5: (x): {A}x -> ¬(¬{IQ}x & {JJ}x) fact6: {A}{a} -> ¬(¬{AA}{a} & {AB}{a}) fact7: ¬(¬{AA}{a} & {AB}{a}) -> {B}{b} fact8: (x): ¬({A}x & {B}x) -> ¬{C}x fact9: {B}{a} | [
"fact6 & fact1 -> int1: ããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããšããããšã¯ãªããéã
ããããšããããšã¯äºå®ãšç°ãªã; int1 & fact7 -> int2: ãã®ãŸããŸãLv.44ã¯ã§ã£ãã; int2 & fact4 -> hypothesis;"
] | [
"fact6 & fact1 -> int1: ¬(¬{AA}{a} & {AB}{a}); int1 & fact7 -> int2: {B}{b}; int2 & fact4 -> hypothesis;"
] | ä»®ã«ãã®ãœã«ããœã¡ãLv.42ã¯ç Žå£ãå§ãããšããã°ããã®ãœã«ããœã¡ãLv.42ã¯æè¬ããªããã©éºããããšããããšã¯æ¬åœã§ãªã | {A}{a} -> ¬(¬{IQ}{a} & {JJ}{a}) | [
"fact10 -> hypothesis;"
] | 1 | 3 | 3 | 3 | 3 | 5 | 0 | 5 | PROVED | PROVED | PROVED | PROVED | $facts$ = fact1: ãã®ãœã«ããœã¡ãLv.42ã¯ç Žå£ãå§ãã fact2: ããããã®ãœã«ããœã¡ãLv.42ã¯éã
ãããšããããšã¯ãªããšãããããã®ãŸããŸãLv.44ã¯ã§ã£ããããšããããšã¯æãç«ã€ fact3: ããã®ãœããœã«ãLv.14ã¯éŠŽã銎ããããã©æŽå°ãããšããããšã¯ãªãããšããããšã¯æãç«ããªããšããããã®ãœã«ããœã¡ãLv.42ã¯ã¯ãªã¢åºæ¥ãªã fact4: ä»®ã«ãã®ãŸããŸãLv.44ãã§ã£ãããšããããã©ã³ã¹äººããã fact5: ããä»®ã«äœããã®ã¢ã³ã¹ã¿ãŒã¯ç Žå£ãå§ãããªãããããã¯æè¬ããªãããŸãããã¯éºããããšããããšã¯çå®ã§ããããšããããšã¯æ¬åœã§ãªã fact6: ãããããã®ãœã«ããœã¡ãLv.42ã¯ç Žå£ãå§ããããšããããšã¯æ¬åœã ãšãããšããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããªãããããããã¯éã
ããããšããããšã¯æãç«ã€ãšããããšã¯ãªã fact7: ãããããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããªããéã
ããããšããããšã¯åã§ãããªãã°ãã®ãŸããŸãLv.44ã¯ã§ã£ãã fact8: ä»®ã«ãããã¢ã³ã¹ã¿ãŒã¯ç Žå£ãå§ãããã§ã£ããããšããããšã¯äºå®ã§ãªããšããã°ããã¯ãã©ã³ã¹äººããããªã fact9: ãã®ãœã«ããœã¡ãLv.42ã¯ã§ã£ãã ; $hypothesis$ = ãã®ãŸããŸãLv.44ã¯ãã©ã³ã¹äººããã ; $proof$ = | fact6 & fact1 -> int1: ããã®ãœã«ããœã¡ãLv.42ã¯æãé£ããšããããšã¯ãªããéã
ããããšããããšã¯äºå®ãšç°ãªã; int1 & fact7 -> int2: ãã®ãŸããŸãLv.44ã¯ã§ã£ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: {A}{a} fact2: ¬{AB}{a} -> {B}{b} fact3: ¬({E}{c} & ¬{F}{c}) -> ¬{D}{a} fact4: {B}{b} -> {C}{b} fact5: (x): {A}x -> ¬(¬{IQ}x & {JJ}x) fact6: {A}{a} -> ¬(¬{AA}{a} & {AB}{a}) fact7: ¬(¬{AA}{a} & {AB}{a}) -> {B}{b} fact8: (x): ¬({A}x & {B}x) -> ¬{C}x fact9: {B}{a} ; $hypothesis$ = {C}{b} ; $proof$ = | fact6 & fact1 -> int1: ¬(¬{AA}{a} & {AB}{a}); int1 & fact7 -> int2: {B}{b}; int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãã«ãã¡ãLv.58ã¯éä¿¡ããªã | ¬{C}{a} | fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯è©å®ããªããªããå ªãéããªãããã®äžçéãé£ããªãããšããããšã¯åã§ãã fact2: ãã®ã·ãã·ãLv.1ããã§ãããªãããããã¯æªæ¯ã£ãœãããããã¯äž¡æ¹ãšãã§ãããªãã°ãã®ãã«ãã¡ãLv.58ã¯éä¿¡ãã fact3: çéãé£ããªãã¢ã³ã¹ã¿ãŒã¯éä¿¡ãããšããããšã¯ãªãããŸãã¯æªæ¯ã£ãœããªãããããã¯äž¡æ¹ã§ãã fact4: ããã®ãŽããŽãLv.35ã¯å ªãéããªããçéãé£ããªãããšããããšã¯æãç«ããªããªãã°ãã®ãã«ãã¡ãLv.58ã¯çéãé£ããªã | fact1: (x): ¬{F}x -> ¬(¬{E}x & ¬{D}x) fact2: (¬{A}{aa} v {B}{aa}) -> {C}{a} fact3: (x): ¬{D}x -> (¬{C}x v ¬{B}x) fact4: ¬(¬{E}{b} & ¬{D}{b}) -> ¬{D}{a} | [] | [] | ãã®ã¿ãã¿ãªLv.48ã¯ãã§ãã | {A}{fq} | [
"fact5 -> int1: ããããã®ãã«ãã¡ãLv.58ãçéãé£ããšããããšã¯ãªããªãããã¯éä¿¡ããªãããããã¯æªæ¯ã£ãœããªã; fact6 -> int2: ä»®ã«ãã®ãŽããŽãLv.35ã¯è©å®ããªããšããã°ããããã¯å ªãéãããšããããšã¯ãªããŠçéãé£ããšããããšã¯ãªãããšããããšã¯æ¬åœã§ããããšããããšã¯æãç«ããªã;"
] | 6 | 2 | 2 | null | null | 3 | 0 | 3 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ãªãããã®ã¢ã³ã¹ã¿ãŒã¯è©å®ããªããªããå ªãéããªãããã®äžçéãé£ããªãããšããããšã¯åã§ãã fact2: ãã®ã·ãã·ãLv.1ããã§ãããªãããããã¯æªæ¯ã£ãœãããããã¯äž¡æ¹ãšãã§ãããªãã°ãã®ãã«ãã¡ãLv.58ã¯éä¿¡ãã fact3: çéãé£ããªãã¢ã³ã¹ã¿ãŒã¯éä¿¡ãããšããããšã¯ãªãããŸãã¯æªæ¯ã£ãœããªãããããã¯äž¡æ¹ã§ãã fact4: ããã®ãŽããŽãLv.35ã¯å ªãéããªããçéãé£ããªãããšããããšã¯æãç«ããªããªãã°ãã®ãã«ãã¡ãLv.58ã¯çéãé£ããªã ; $hypothesis$ = ãã®ãã«ãã¡ãLv.58ã¯éä¿¡ããªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬{F}x -> ¬(¬{E}x & ¬{D}x) fact2: (¬{A}{aa} v {B}{aa}) -> {C}{a} fact3: (x): ¬{D}x -> (¬{C}x v ¬{B}x) fact4: ¬(¬{E}{b} & ¬{D}{b}) -> ¬{D}{a} ; $hypothesis$ = ¬{C}{a} ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã·ã®ã·ã¡ãLv.52ã¯æ¥è¿ãæããªãããŸãã¯ããã¯æŒãä»ãããŸããããŸãã¯äž¡æ¹ãšãã§ãã | (¬{C}{b} v {E}{b}) | fact1: ä»®ã«ãã®ãŸã«ããŸã®Lv.83ãããŠãè¯ããªããªããã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªã fact2: ä»®ã«ãã®ãŸã«ããŸã®Lv.83ãåãæããªããªããã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªã fact3: ãã®ãŸã«ããŸã®Lv.83ã¯ããŠãè¯ããªããåãæããšããããšã¯ãªãããããã¯ã©ã¡ããã§ãã fact4: ããä»®ã«ãã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªããªãããã®ã·ã®ã·ã¡ãLv.52ã¯æ¥è¿ãæããªãããŸãã¯æŒãä»ãããŸããããšããããšã¯çå®ã§ãªã | fact1: ¬{A}{a} -> ¬{C}{c} fact2: ¬{B}{a} -> ¬{C}{c} fact3: (¬{A}{a} v ¬{B}{a}) fact4: ¬{C}{c} -> ¬(¬{C}{b} v {E}{b}) | [
"fact3 & fact1 & fact2 -> int1: ãã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããšããããšã¯ãªã; int1 & fact4 -> hypothesis;"
] | [
"fact3 & fact1 & fact2 -> int1: ¬{C}{c}; int1 & fact4 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 0 | 0 | 0 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ä»®ã«ãã®ãŸã«ããŸã®Lv.83ãããŠãè¯ããªããªããã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªã fact2: ä»®ã«ãã®ãŸã«ããŸã®Lv.83ãåãæããªããªããã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªã fact3: ãã®ãŸã«ããŸã®Lv.83ã¯ããŠãè¯ããªããåãæããšããããšã¯ãªãããããã¯ã©ã¡ããã§ãã fact4: ããä»®ã«ãã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããªããªãããã®ã·ã®ã·ã¡ãLv.52ã¯æ¥è¿ãæããªãããŸãã¯æŒãä»ãããŸããããšããããšã¯çå®ã§ãªã ; $hypothesis$ = ãã®ã·ã®ã·ã¡ãLv.52ã¯æ¥è¿ãæããªãããŸãã¯ããã¯æŒãä»ãããŸããããŸãã¯äž¡æ¹ãšãã§ãã ; $proof$ = | fact3 & fact1 & fact2 -> int1: ãã®ãœããœã«ãLv.76ã¯æ¥è¿ãæããšããããšã¯ãªã; int1 & fact4 -> hypothesis; __DISPROVED__ | $facts$ = fact1: ¬{A}{a} -> ¬{C}{c} fact2: ¬{B}{a} -> ¬{C}{c} fact3: (¬{A}{a} v ¬{B}{a}) fact4: ¬{C}{c} -> ¬(¬{C}{b} v {E}{b}) ; $hypothesis$ = (¬{C}{b} v {E}{b}) ; $proof$ = | fact3 & fact1 & fact2 -> int1: ¬{C}{c}; int1 & fact4 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ã·ãã·ãLv.11ã¯å¥³ã
ãããšããããšã¯ãªããããã欲深ã | (¬{E}{b} & {F}{b}) | fact1: ä»®ã«ãã®ããããLv.75ãæ±æžããªããªããã®ãã«ã
ããLv.57ã¯æ¥µãŸãæªã fact2: ãã®ã·ãã·ãLv.11ã¯å¡åžãããªãããã®ã·ãã·ãLv.11ã¯å¥³ã
ãããªãããã©æ¬²æ·±ãããšããããšã¯åã fact3: ãããã®ãã«ã
ããLv.57ã極ãŸãæªããšãããšãã®ã·ãã·ãLv.11ã¯å¡åžãã fact4: ãã®ããããLv.75ã¯æ±æžãããšããããšã¯ãªããããã¯èšãããªããäž¡æ¹ã fact5: ããã®ã·ãã·ãLv.11ã¯å¥³ã
ããããã€æ¬²æ·±ãããšããããšã¯æãç«ããªã fact6: ãã®ã·ãã·ãLv.11ã¯å¡åžãããšãããšãããã¯å¥³ã
ãããããã«æ¬²æ·±ãããšããããšã¯åœã§ãã | fact1: ¬{A}{a} -> {C}{c} fact2: {D}{b} -> ¬(¬{E}{b} & {F}{b}) fact3: {C}{c} -> {D}{b} fact4: (¬{A}{a} v ¬{B}{a}) fact5: ¬({E}{b} & {F}{b}) fact6: {D}{b} -> ¬({E}{b} & {F}{b}) | [] | [] | null | null | [] | null | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | null | UNKNOWN | null | $facts$ = fact1: ä»®ã«ãã®ããããLv.75ãæ±æžããªããªããã®ãã«ã
ããLv.57ã¯æ¥µãŸãæªã fact2: ãã®ã·ãã·ãLv.11ã¯å¡åžãããªãããã®ã·ãã·ãLv.11ã¯å¥³ã
ãããªãããã©æ¬²æ·±ãããšããããšã¯åã fact3: ãããã®ãã«ã
ããLv.57ã極ãŸãæªããšãããšãã®ã·ãã·ãLv.11ã¯å¡åžãã fact4: ãã®ããããLv.75ã¯æ±æžãããšããããšã¯ãªããããã¯èšãããªããäž¡æ¹ã fact5: ããã®ã·ãã·ãLv.11ã¯å¥³ã
ããããã€æ¬²æ·±ãããšããããšã¯æãç«ããªã fact6: ãã®ã·ãã·ãLv.11ã¯å¡åžãããšãããšãããã¯å¥³ã
ãããããã«æ¬²æ·±ãããšããããšã¯åœã§ãã ; $hypothesis$ = ãã®ã·ãã·ãLv.11ã¯å¥³ã
ãããšããããšã¯ãªããããã欲深ã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: ¬{A}{a} -> {C}{c} fact2: {D}{b} -> ¬(¬{E}{b} & {F}{b}) fact3: {C}{c} -> {D}{b} fact4: (¬{A}{a} v ¬{B}{a}) fact5: ¬({E}{b} & {F}{b}) fact6: {D}{b} -> ¬({E}{b} & {F}{b}) ; $hypothesis$ = (¬{E}{b} & {F}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ã¿ã«ã¿ãªLv.70ã¯æãæããªãããã€ããã¯åŸ¹ãããšããããšã¯ãªã | (¬{C}{b} & ¬{D}{b}) | fact1: ããä»®ã«ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çæž©ãããªããŠå¿åŒ±ããªãããšããããšã¯çå®ã§ããããšããããšã¯åœã ãšãããšããã¯çæž©ãã fact2: ããä»®ã«ããã®ãŽã«ãŽã¡ãLv.4ã¯çœ¹ãæãããšããããšã¯æ£ãããªãã°ãã®ã¿ã«ã¿ãªLv.70ã¯æãæããªã fact3: ãã®ã¿ã«ã¿ãªLv.70ã¯åŸ¹ããªã fact4: ãã®ãŽã«ãŽã¡ãLv.4ã¯çæž©ãã | fact1: (x): ¬(¬{A}x & ¬{E}x) -> {A}x fact2: {B}{a} -> ¬{C}{b} fact3: ¬{D}{b} fact4: {A}{a} | [] | [] | ããã®ã¿ã«ã¿ãªLv.70ã¯æãæãããšããããšã¯ãªããŠããŸãã«åŸ¹ãããšããããšã¯ãªãããšããããšã¯ééã£ãŠãã | ¬(¬{C}{b} & ¬{D}{b}) | [
"fact5 -> int1: ãããããã®ãŽã«ãŽã¡ãLv.4ã¯çæž©ãããªããå¿åŒ±ããªãããšããããšã¯èª€ã£ãŠãããªãããã¯çæž©ãã;"
] | 5 | 3 | 3 | null | null | 2 | 0 | 2 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããä»®ã«ãããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯çæž©ãããªããŠå¿åŒ±ããªãããšããããšã¯çå®ã§ããããšããããšã¯åœã ãšãããšããã¯çæž©ãã fact2: ããä»®ã«ããã®ãŽã«ãŽã¡ãLv.4ã¯çœ¹ãæãããšããããšã¯æ£ãããªãã°ãã®ã¿ã«ã¿ãªLv.70ã¯æãæããªã fact3: ãã®ã¿ã«ã¿ãªLv.70ã¯åŸ¹ããªã fact4: ãã®ãŽã«ãŽã¡ãLv.4ã¯çæž©ãã ; $hypothesis$ = ãã®ã¿ã«ã¿ãªLv.70ã¯æãæããªãããã€ããã¯åŸ¹ãããšããããšã¯ãªã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬(¬{A}x & ¬{E}x) -> {A}x fact2: {B}{a} -> ¬{C}{b} fact3: ¬{D}{b} fact4: {A}{a} ; $hypothesis$ = (¬{C}{b} & ¬{D}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãã¡ããã¡ãLv.69ã¯ïŒ¯ïŒ¢èããªãããã©æãããã | (¬{B}{a} & {C}{a}) | fact1: ããããã®ã¿ãã¿ã«ãLv.11ãçãããªãå©ãé£ããªãäžæ¹ã§ç©ãã fact2: ããã®ãã¡ããã¡ãLv.69ã¯æããããšããããšã¯æãç«ã€ fact3: ãã®ãã¡ããã¡ãLv.69ãæãããšãããèããªããæãããã fact4: ããããã®ãã¡ããã¡ãLv.69ãæãããšããããã®ãã¡ããã¡ãLv.69ã¯ïŒ¯ïŒ¢èããªã fact5: ãã®ãã¡ããã¡ãLv.69ã¯èŠèãã | fact1: {EG}{fk} -> (¬{HF}{fk} & {EM}{fk}) fact2: {A}{a} fact3: {A}{a} -> (¬{B}{a} & {C}{a}) fact4: {A}{a} -> ¬{B}{a} fact5: {BH}{a} | [
"fact2 -> int1: ããã®ãã¡ããã¡ãLv.69ã¯æããããšããããšã¯æãç«ã€; int1 & fact3 -> hypothesis;"
] | [
"fact2 -> int1: {A}{a}; int1 & fact3 -> hypothesis;"
] | null | null | [] | null | 2 | 2 | 2 | 2 | 3 | 0 | 3 | PROVED | null | PROVED | null | $facts$ = fact1: ããããã®ã¿ãã¿ã«ãLv.11ãçãããªãå©ãé£ããªãäžæ¹ã§ç©ãã fact2: ããã®ãã¡ããã¡ãLv.69ã¯æããããšããããšã¯æãç«ã€ fact3: ãã®ãã¡ããã¡ãLv.69ãæãããšãããèããªããæãããã fact4: ããããã®ãã¡ããã¡ãLv.69ãæãããšããããã®ãã¡ããã¡ãLv.69ã¯ïŒ¯ïŒ¢èããªã fact5: ãã®ãã¡ããã¡ãLv.69ã¯èŠèãã ; $hypothesis$ = ãã®ãã¡ããã¡ãLv.69ã¯ïŒ¯ïŒ¢èããªãããã©æãããã ; $proof$ = | fact2 -> int1: ããã®ãã¡ããã¡ãLv.69ã¯æããããšããããšã¯æãç«ã€; int1 & fact3 -> hypothesis; __PROVED__ | $facts$ = fact1: {EG}{fk} -> (¬{HF}{fk} & {EM}{fk}) fact2: {A}{a} fact3: {A}{a} -> (¬{B}{a} & {C}{a}) fact4: {A}{a} -> ¬{B}{a} fact5: {BH}{a} ; $hypothesis$ = (¬{B}{a} & {C}{a}) ; $proof$ = | fact2 -> int1: {A}{a}; int1 & fact3 -> hypothesis; __PROVED__ |
0.3 | ãã®ã·ã«ã·ãLv.74ã¯å°è³¢ãããªã | ¬{C}{b} | fact1: ãããã®ããããLv.48ãéãç¡ãäžæ¹ã§ç£èŠãæããšããããšã¯ãªããšããããã®ã·ã«ã·ãLv.74ã¯å æžãã fact2: ããããªãããã®ã¢ã³ã¹ã¿ãŒãå æžããªããªãããã¯å°è³¢ãããããã¯ç©æ¬²ãã fact3: ããä»®ã«ãã®ããããLv.48ãéãç¡ããªããç£èŠãæããªããªããã®ã·ã«ã·ãLv.74ã¯å æžãã fact4: ãã®ã·ã«ã·ãLv.74ãå æžããããã®äžç©æ¬²ãããšãããããã¯å°è³¢ãããªã fact5: ãã®ããããLv.48ã¯éãç¡ããšããããšã¯ãªãããŸãç£èŠãæããªã fact6: ãã®ããããLv.48ã¯éãç¡ããšããããšã¯ãªã fact7: ãã®ã·ã«ã·ãLv.74ã¯ç©æ¬²ãã | fact1: ({AA}{a} & ¬{AB}{a}) -> {B}{b} fact2: (x): ¬{B}x -> ({C}x & {A}x) fact3: (¬{AA}{a} & ¬{AB}{a}) -> {B}{b} fact4: ({B}{b} & {A}{b}) -> ¬{C}{b} fact5: (¬{AA}{a} & ¬{AB}{a}) fact6: ¬{AA}{a} fact7: {A}{b} | [
"fact3 & fact5 -> int1: ããã®ã·ã«ã·ãLv.74ã¯å æžããããšããããšã¯ç¢ºãã§ãã; int1 & fact7 -> int2: ãã®ã·ã«ã·ãLv.74ã¯å æžãããç©æ¬²ãã; int2 & fact4 -> hypothesis;"
] | [
"fact3 & fact5 -> int1: {B}{b}; int1 & fact7 -> int2: ({B}{b} & {A}{b}); int2 & fact4 -> hypothesis;"
] | ããã®ããããLv.48ã¯å°è³¢ããããšããããšã¯æãç«ã€ | {C}{a} | [
"fact8 -> int3: ããã®ããããLv.48ã¯å æžããªãããšããããšã¯æ£ãããšããã°ãã®ããããLv.48ã¯å°è³¢ãããå ããŠç©æ¬²ãã;"
] | 4 | 3 | 3 | 3 | 3 | 3 | 0 | 3 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããã®ããããLv.48ãéãç¡ãäžæ¹ã§ç£èŠãæããšããããšã¯ãªããšããããã®ã·ã«ã·ãLv.74ã¯å æžãã fact2: ããããªãããã®ã¢ã³ã¹ã¿ãŒãå æžããªããªãããã¯å°è³¢ãããããã¯ç©æ¬²ãã fact3: ããä»®ã«ãã®ããããLv.48ãéãç¡ããªããç£èŠãæããªããªããã®ã·ã«ã·ãLv.74ã¯å æžãã fact4: ãã®ã·ã«ã·ãLv.74ãå æžããããã®äžç©æ¬²ãããšãããããã¯å°è³¢ãããªã fact5: ãã®ããããLv.48ã¯éãç¡ããšããããšã¯ãªãããŸãç£èŠãæããªã fact6: ãã®ããããLv.48ã¯éãç¡ããšããããšã¯ãªã fact7: ãã®ã·ã«ã·ãLv.74ã¯ç©æ¬²ãã ; $hypothesis$ = ãã®ã·ã«ã·ãLv.74ã¯å°è³¢ãããªã ; $proof$ = | fact3 & fact5 -> int1: ããã®ã·ã«ã·ãLv.74ã¯å æžããããšããããšã¯ç¢ºãã§ãã; int1 & fact7 -> int2: ãã®ã·ã«ã·ãLv.74ã¯å æžãããç©æ¬²ãã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: ({AA}{a} & ¬{AB}{a}) -> {B}{b} fact2: (x): ¬{B}x -> ({C}x & {A}x) fact3: (¬{AA}{a} & ¬{AB}{a}) -> {B}{b} fact4: ({B}{b} & {A}{b}) -> ¬{C}{b} fact5: (¬{AA}{a} & ¬{AB}{a}) fact6: ¬{AA}{a} fact7: {A}{b} ; $hypothesis$ = ¬{C}{b} ; $proof$ = | fact3 & fact5 -> int1: {B}{b}; int1 & fact7 -> int2: ({B}{b} & {A}{b}); int2 & fact4 -> hypothesis; __PROVED__ |
0.3 | ãã®ãŸããŸãLv.26ã¯ã¯ãããªããŠããã¯å£æãã | ({A}{b} & {C}{b}) | fact1: ããããããããªãããŸãã¯ç ããããããã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒãããã°ãã®ã·ãã·ã¡ãLv.99ã¯ã¯ãããªããªã fact2: ãã®ã·ã«ã
ã·ã«ãLv.16ãåãçãããªããšããããã®ã·ã«ã
ã·ã«ãLv.16ã¯å€ªãæããŠããã«ã¡ããæã fact3: ã¡ããæããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ã¯ãããªããŠããã«å€ªãæã fact4: ä»®ã«ãã®ã·ãã·ã¡ãLv.99ã¯ã¯ãããªããªããšãããããã®ãŸããŸãLv.26ã¯ã¯ãããªããŠããã«å£æããããšããããšã¯æãç«ããªã fact5: ããããããããªãããŸãã¯ã¯ãããªããã©ã¡ããã ããšããããšã¯æãç«ã€ãšããããšã¯ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ããä»®ã«ããã¢ã³ã¹ã¿ãŒã倪ãæããšããã°ããã¯å£æãããªãããããã¯ãããªã | fact1: (x): ¬(¬{AA}x v {AB}x) -> ¬{A}{a} fact2: ¬{E}{hf} -> ({B}{hf} & {D}{hf}) fact3: (x): ¬{D}x -> ({A}x & {B}x) fact4: ¬{A}{a} -> ¬({A}{b} & {C}{b}) fact5: (Ex): ¬(¬{AA}x v {A}x) fact6: (x): {B}x -> (¬{C}x & {A}x) | [] | [] | ãã®ãŸããŸãLv.26ã¯ã¯ãããªããŠããã¯å£æãã | ({A}{b} & {C}{b}) | [
"fact7 -> int1: ããããã®ãŸããŸãLv.26ãã¡ããæããªããªãã¯ãããªããããã«ããã¯å€ªãæã;"
] | 4 | 3 | 3 | null | null | 4 | 0 | 4 | UNKNOWN | UNKNOWN | UNKNOWN | UNKNOWN | $facts$ = fact1: ããããããããªãããŸãã¯ç ããããããã¯ã©ã¡ããã ããšããããšã¯æãç«ããªããã¢ã³ã¹ã¿ãŒãããã°ãã®ã·ãã·ã¡ãLv.99ã¯ã¯ãããªããªã fact2: ãã®ã·ã«ã
ã·ã«ãLv.16ãåãçãããªããšããããã®ã·ã«ã
ã·ã«ãLv.16ã¯å€ªãæããŠããã«ã¡ããæã fact3: ã¡ããæããšããããšã¯ãªãã¢ã³ã¹ã¿ãŒã¯ã¯ãããªããŠããã«å€ªãæã fact4: ä»®ã«ãã®ã·ãã·ã¡ãLv.99ã¯ã¯ãããªããªããšãããããã®ãŸããŸãLv.26ã¯ã¯ãããªããŠããã«å£æããããšããããšã¯æãç«ããªã fact5: ããããããããªãããŸãã¯ã¯ãããªããã©ã¡ããã ããšããããšã¯æãç«ã€ãšããããšã¯ãªããã¢ã³ã¹ã¿ãŒã¯ãã fact6: ããä»®ã«ããã¢ã³ã¹ã¿ãŒã倪ãæããšããã°ããã¯å£æãããªãããããã¯ãããªã ; $hypothesis$ = ãã®ãŸããŸãLv.26ã¯ã¯ãããªããŠããã¯å£æãã ; $proof$ = | __UNKNOWN__ | $facts$ = fact1: (x): ¬(¬{AA}x v {AB}x) -> ¬{A}{a} fact2: ¬{E}{hf} -> ({B}{hf} & {D}{hf}) fact3: (x): ¬{D}x -> ({A}x & {B}x) fact4: ¬{A}{a} -> ¬({A}{b} & {C}{b}) fact5: (Ex): ¬(¬{AA}x v {A}x) fact6: (x): {B}x -> (¬{C}x & {A}x) ; $hypothesis$ = ({A}{b} & {C}{b}) ; $proof$ = | __UNKNOWN__ |
0.3 | ãã®ãœããœã¡ã
Lv.32ã¯çã£é»ã | {C}{b} | fact1: ããããã®ã·ã¡ã
ã·ã«ãLv.48ã詳ãããªããããã埡ç¥ãç³ãäžãããšããããšã¯ãªããªããã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããšããããšã¯ãªã fact2: ä»®ã«ãã®ãœããœã¡ã
Lv.32ã¯ç®èŠãŸãããããããã£ãããªããªã埡ç¥ãç³ãäžããªã fact3: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯åç¶ãé£ã fact4: ä»®ã«ãã®ã·ã¡ã
ã·ã«ãLv.48ãçã£é»ããªããæŽã«è©³ãããªããšããããã®ã·ã¡ã
ã·ã«ãLv.48ã¯åŸ¡ç¥ãç³ãäžãããšããããšã¯ãªã fact5: ãããã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããªããªãããã®ãœããœã¡ã
Lv.32ã¯çã£é»ããªãããšããããšã¯æ£ãã fact6: ãã®ãœããœã¡ã
Lv.32ã¯åç¶ãé£ããªã fact7: ããããã®ã·ã¡ã
ã·ã«ãLv.48ãåç¶ãé£ããšããããã®ã·ã¡ã
ã·ã«ãLv.48ã¯è©³ãããªããŠãã€ããã¯åŸ¡ç¥ãç³ãäžãããšããããšã¯ãªã fact8: ä»®ã«ãã®ã·ã¡ã
ã·ã«ãLv.48ãçã£é»ããä¿¡ãæããªããªãã°ããã¯è©³ãããšããããšã¯ãªã | fact1: (¬{AA}{a} & ¬{AB}{a}) -> ¬{B}{a} fact2: ({II}{b} & ¬{IF}{b}) -> ¬{AB}{b} fact3: {A}{a} fact4: (¬{C}{a} & ¬{AA}{a}) -> ¬{AB}{a} fact5: ¬{B}{a} -> ¬{C}{b} fact6: ¬{A}{b} fact7: {A}{a} -> (¬{AA}{a} & ¬{AB}{a}) fact8: ({C}{a} & ¬{B}{a}) -> ¬{AA}{a} | [
"fact7 & fact3 -> int1: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯è©³ãããªããŠåŸ¡ç¥ãç³ãäžããªã; int1 & fact1 -> int2: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããšããããšã¯ãªã; int2 & fact5 -> hypothesis;"
] | [
"fact7 & fact3 -> int1: (¬{AA}{a} & ¬{AB}{a}); int1 & fact1 -> int2: ¬{B}{a}; int2 & fact5 -> hypothesis;"
] | null | null | [] | null | 3 | 3 | 3 | 3 | 4 | 0 | 4 | DISPROVED | null | DISPROVED | null | $facts$ = fact1: ããããã®ã·ã¡ã
ã·ã«ãLv.48ã詳ãããªããããã埡ç¥ãç³ãäžãããšããããšã¯ãªããªããã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããšããããšã¯ãªã fact2: ä»®ã«ãã®ãœããœã¡ã
Lv.32ã¯ç®èŠãŸãããããããã£ãããªããªã埡ç¥ãç³ãäžããªã fact3: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯åç¶ãé£ã fact4: ä»®ã«ãã®ã·ã¡ã
ã·ã«ãLv.48ãçã£é»ããªããæŽã«è©³ãããªããšããããã®ã·ã¡ã
ã·ã«ãLv.48ã¯åŸ¡ç¥ãç³ãäžãããšããããšã¯ãªã fact5: ãããã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããªããªãããã®ãœããœã¡ã
Lv.32ã¯çã£é»ããªãããšããããšã¯æ£ãã fact6: ãã®ãœããœã¡ã
Lv.32ã¯åç¶ãé£ããªã fact7: ããããã®ã·ã¡ã
ã·ã«ãLv.48ãåç¶ãé£ããšããããã®ã·ã¡ã
ã·ã«ãLv.48ã¯è©³ãããªããŠãã€ããã¯åŸ¡ç¥ãç³ãäžãããšããããšã¯ãªã fact8: ä»®ã«ãã®ã·ã¡ã
ã·ã«ãLv.48ãçã£é»ããä¿¡ãæããªããªãã°ããã¯è©³ãããšããããšã¯ãªã ; $hypothesis$ = ãã®ãœããœã¡ã
Lv.32ã¯çã£é»ã ; $proof$ = | fact7 & fact3 -> int1: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯è©³ãããªããŠåŸ¡ç¥ãç³ãäžããªã; int1 & fact1 -> int2: ãã®ã·ã¡ã
ã·ã«ãLv.48ã¯ä¿¡ãæããšããããšã¯ãªã; int2 & fact5 -> hypothesis; __DISPROVED__ | $facts$ = fact1: (¬{AA}{a} & ¬{AB}{a}) -> ¬{B}{a} fact2: ({II}{b} & ¬{IF}{b}) -> ¬{AB}{b} fact3: {A}{a} fact4: (¬{C}{a} & ¬{AA}{a}) -> ¬{AB}{a} fact5: ¬{B}{a} -> ¬{C}{b} fact6: ¬{A}{b} fact7: {A}{a} -> (¬{AA}{a} & ¬{AB}{a}) fact8: ({C}{a} & ¬{B}{a}) -> ¬{AA}{a} ; $hypothesis$ = {C}{b} ; $proof$ = | fact7 & fact3 -> int1: (¬{AA}{a} & ¬{AB}{a}); int1 & fact1 -> int2: ¬{B}{a}; int2 & fact5 -> hypothesis; __DISPROVED__ |
0.3 | ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åã | {B}{b} | fact1: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åããã©ããã¯å蚺ããªãããšããããšã¯èª€ãã§ãããšãããåããªã fact2: ããè¥ãããã®äžç£èŠãæããªãããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒããããªããã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã¯åŸ¡è¥ã fact3: ããã®ã¿ãã¿ãLv.37ã¯è¥ããã©ç£èŠãæããªãããšããããšã¯æãç«ããªã fact4: ããä»®ã«ãã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã埡è¥ããªãã°ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åã | fact1: (x): ¬({B}x & ¬{C}x) -> ¬{B}x fact2: (x): ¬({AA}x & ¬{AB}x) -> {A}{a} fact3: ¬({AA}{aa} & ¬{AB}{aa}) fact4: {A}{a} -> {B}{b} | [
"fact3 -> int1: ããè¥ããç£èŠãæããªãããšããããšã¯åœã§ãããã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact2 -> int2: ãã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã¯åŸ¡è¥ã; int2 & fact4 -> hypothesis;"
] | [
"fact3 -> int1: (Ex): ¬({AA}x & ¬{AB}x); int1 & fact2 -> int2: {A}{a}; int2 & fact4 -> hypothesis;"
] | ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åããšããããšã¯ãªã | ¬{B}{b} | [
"fact5 -> int3: ããããã®ãŽã«ããŽã¡ã
Lv.45ã¯åããå蚺ããªãããšããããšã¯æãç«ããªããšããã°ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åããªã;"
] | 4 | 3 | 3 | 3 | 3 | 1 | 0 | 1 | PROVED | UNKNOWN | PROVED | UNKNOWN | $facts$ = fact1: ãããããªã«ãããã®ã¢ã³ã¹ã¿ãŒã¯åããã©ããã¯å蚺ããªãããšããããšã¯èª€ãã§ãããšãããåããªã fact2: ããè¥ãããã®äžç£èŠãæããªãããšããããšã¯èª€ã£ãŠãããã¢ã³ã¹ã¿ãŒããããªããã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã¯åŸ¡è¥ã fact3: ããã®ã¿ãã¿ãLv.37ã¯è¥ããã©ç£èŠãæããªãããšããããšã¯æãç«ããªã fact4: ããä»®ã«ãã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã埡è¥ããªãã°ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åã ; $hypothesis$ = ãã®ãŽã«ããŽã¡ã
Lv.45ã¯åã ; $proof$ = | fact3 -> int1: ããè¥ããç£èŠãæããªãããšããããšã¯åœã§ãããã¢ã³ã¹ã¿ãŒã¯ãã; int1 & fact2 -> int2: ãã®ã¿ã¡ã
ã¿ã¡ã
Lv.93ã¯åŸ¡è¥ã; int2 & fact4 -> hypothesis; __PROVED__ | $facts$ = fact1: (x): ¬({B}x & ¬{C}x) -> ¬{B}x fact2: (x): ¬({AA}x & ¬{AB}x) -> {A}{a} fact3: ¬({AA}{aa} & ¬{AB}{aa}) fact4: {A}{a} -> {B}{b} ; $hypothesis$ = {B}{b} ; $proof$ = | fact3 -> int1: (Ex): ¬({AA}x & ¬{AB}x); int1 & fact2 -> int2: {A}{a}; int2 & fact4 -> hypothesis; __PROVED__ |