TSTP Solution File: LCL097-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL097-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:28 EDT 2022
% Result : Unsatisfiable 0.73s 0.90s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of clauses : 30 ( 19 unt; 0 nHn; 14 RR)
% Number of literals : 44 ( 0 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(lg_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) ).
cnf(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)) ).
cnf(prove_lg_4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30),equivalent(equivalent(X_32,X_29),X_30)))
| is_a_theorem(equivalent(equivalent(X_32,X_29),X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30))),bind(Y,$fot(equivalent(equivalent(X_32,X_29),X_30)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7))
| is_a_theorem(X_7) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7)),
inference(subst,[],[lg_3:[bind(U,$fot(X_6)),bind(V,$fot(X_7)),bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7))
| is_a_theorem(X_7) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),X_7),X_7)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6))) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_18,X_19),equivalent(X_18,X_15)),equivalent(X_19,X_15)),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15)))),
inference(subst,[],[lg_2:[bind(U,$fot(equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15)))),bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_18,X_19),equivalent(X_18,X_15)),equivalent(X_19,X_15)),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))))
| is_a_theorem(equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))) ),
inference(subst,[],[refute_0_3:[bind(X_10,$fot(X_15)),bind(X_6,$fot(equivalent(X_19,X_15))),bind(X_7,$fot(equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15)))),bind(X_8,$fot(X_18)),bind(X_9,$fot(X_19))]]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_18,X_19),equivalent(X_18,X_15)),equivalent(X_19,X_15)),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15))),equivalent(equivalent(X_19,X_15),equivalent(X_19,X_15)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)))),
inference(subst,[],[refute_0_7:[bind(X_15,$fot(equivalent(equivalent(X_9,X_10),X_6))),bind(X_19,$fot(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)))) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30),equivalent(equivalent(X_32,X_29),X_30))),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_29)),bind(X_6,$fot(X_30)),bind(X_8,$fot(X_31)),bind(X_9,$fot(X_32))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30))
| is_a_theorem(equivalent(equivalent(X_32,X_29),X_30)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_31,X_32),equivalent(X_31,X_29)),X_30),equivalent(equivalent(X_32,X_29),X_30))) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),equivalent(equivalent(X_1070,X_1071),X_1066)),equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),X_1069)),equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1070,X_1071),X_1066),X_1069),equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069)))) ),
inference(subst,[],[refute_0_11:[bind(X_29,$fot(X_1069)),bind(X_30,$fot(equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069)))),bind(X_31,$fot(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)))),bind(X_32,$fot(equivalent(equivalent(X_1070,X_1071),X_1066)))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6)))) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6)))))]]) ).
cnf(refute_0_14,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_24),equivalent(equivalent(X_9,X_10),X_24)),equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24)))))
| is_a_theorem(equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24)))) ),
inference(subst,[],[refute_0_3:[bind(X_6,$fot(X_24)),bind(X_7,$fot(equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24)))))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(equivalent(X,Y),X_15)),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))))),
inference(subst,[],[lg_3:[bind(U,$fot(equivalent(equivalent(X,Y),X_15))),bind(V,$fot(equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))))]]) ).
cnf(refute_0_16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(equivalent(X,Y),X_15)),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))))
| is_a_theorem(equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))) ),
inference(subst,[],[refute_0_3:[bind(X_10,$fot(X_15)),bind(X_6,$fot(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))),bind(X_7,$fot(equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))))),bind(X_8,$fot(equivalent(X,Y))),bind(X_9,$fot(equivalent(X,Z)))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(equivalent(X,Y),X_15)),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15)))),equivalent(equivalent(equivalent(X,Z),X_15),equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),X_15))))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_24),equivalent(equivalent(X_9,X_10),X_24)),equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24))))),
inference(subst,[],[refute_0_17:[bind(X,$fot(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)))),bind(Y,$fot(X_23)),bind(Z,$fot(X_24)),bind(X_15,$fot(equivalent(equivalent(X_9,X_10),X_24)))]]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_24),equivalent(equivalent(X_9,X_10),X_24)),equivalent(equivalent(X_23,X_24),equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_23),equivalent(equivalent(X_9,X_10),X_24))))) )],[refute_0_18,refute_0_14]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6))))),
inference(subst,[],[refute_0_19:[bind(X_10,$fot(X_43)),bind(X_23,$fot(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6))),bind(X_24,$fot(equivalent(equivalent(X_9,X_10),X_6))),bind(X_8,$fot(X_46)),bind(X_9,$fot(X_47))]]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6),equivalent(equivalent(X_9,X_10),X_6)),equivalent(equivalent(equivalent(equivalent(X_46,X_47),equivalent(X_46,X_43)),equivalent(equivalent(equivalent(X_8,X_9),equivalent(X_8,X_10)),X_6)),equivalent(equivalent(X_47,X_43),equivalent(equivalent(X_9,X_10),X_6))))) )],[refute_0_20,refute_0_13]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),equivalent(equivalent(X_1070,X_1071),X_1066)),equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),X_1069)),equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069)))),
inference(subst,[],[refute_0_21:[bind(X_10,$fot(X_1065)),bind(X_43,$fot(X_1066)),bind(X_46,$fot(equivalent(X_1070,X_1071))),bind(X_47,$fot(equivalent(X_1070,X_1065))),bind(X_6,$fot(X_1069)),bind(X_8,$fot(X_1070)),bind(X_9,$fot(X_1071))]]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_1070,X_1071),X_1066),X_1069),equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),equivalent(equivalent(X_1070,X_1071),X_1066)),equivalent(equivalent(equivalent(X_1070,X_1071),equivalent(X_1070,X_1065)),X_1069)),equivalent(equivalent(equivalent(X_1070,X_1065),X_1066),equivalent(equivalent(X_1071,X_1065),X_1069)))) )],[refute_0_22,refute_0_12]) ).
cnf(refute_0_24,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(subst,[],[refute_0_23:[bind(X_1065,$fot(falsehood)),bind(X_1066,$fot(c)),bind(X_1069,$fot(e)),bind(X_1070,$fot(a)),bind(X_1071,$fot(b))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))) )],[refute_0_24,prove_lg_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL097-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 06:33:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.73/0.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.73/0.90
% 0.73/0.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.73/0.91
%------------------------------------------------------------------------------