TSTP Solution File: LCL008-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL008-1 : 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 12:48:45 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 35 ( 20 unt; 0 nHn; 11 RR)
% Number of literals : 54 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(yql,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) ).
cnf(prove_ec_4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z))))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X,Y))
| is_a_theorem(equivalent(equivalent(Z,Y),equivalent(X,Z))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(X_39,X_39))
| is_a_theorem(equivalent(equivalent(Z,X_39),equivalent(X_39,Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_39)),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(X_29,X_29),equivalent(X_30,X_30)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_30,X_30)),equivalent(equivalent(X_29,X_29),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_29,X_29))),bind(Y,$fot(equivalent(X_30,X_30)))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11)))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))),bind(Y,$fot(equivalent(equivalent(X_8,X_9),X_11)))]]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z))))
| is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X,Y))),bind(Y,$fot(equivalent(equivalent(Z,Y),equivalent(X,Z)))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(X_7,equivalent(equivalent(Z,Y),equivalent(X,Z))),equivalent(equivalent(X,Y),X_7))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))) )],[yql,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))))
| is_a_theorem(equivalent(equivalent(X_8,X_9),X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_10,X_9),equivalent(X_8,X_10))),equivalent(equivalent(X_8,X_9),X_11))) )],[refute_0_7,refute_0_4]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(X_27,X_27),equivalent(equivalent(X_27,X_26),equivalent(X_26,X_27))))
| is_a_theorem(equivalent(equivalent(X_26,X_26),equivalent(X_27,X_27))) ),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_27)),bind(X_11,$fot(equivalent(X_27,X_27))),bind(X_8,$fot(X_26)),bind(X_9,$fot(X_26))]]) ).
cnf(refute_0_10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24))))
| is_a_theorem(equivalent(equivalent(X_8,X_25),equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))) ),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_24)),bind(X_11,$fot(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))),bind(X_9,$fot(X_25))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22)))
| is_a_theorem(equivalent(equivalent(Z,equivalent(X_21,X_22)),equivalent(equivalent(X_21,X_22),Z))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_21,X_22))),bind(Y,$fot(equivalent(X_21,X_22)))]]) ).
cnf(refute_0_12,plain,
is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))),
inference(subst,[],[yql:[bind(X,$fot(X_19)),bind(Y,$fot(X_20)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_13,plain,
( ~ is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17))))
| is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_20))) ),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_17)),bind(X_11,$fot(equivalent(X_19,X_20))),bind(X_8,$fot(X_19)),bind(X_9,$fot(X_20))]]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(X_19,X_20))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_19,X_20),equivalent(equivalent(X_17,X_20),equivalent(X_19,X_17)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22))),
inference(subst,[],[refute_0_14:[bind(X_19,$fot(X_21)),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_21,X_22)),equivalent(equivalent(X_21,X_22),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_21,X_22),equivalent(X_21,X_22))) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24)))),
inference(subst,[],[refute_0_16:[bind(Z,$fot(equivalent(X_8,X_24))),bind(X_21,$fot(X_24)),bind(X_22,$fot(X_25))]]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(X_8,X_25),equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_8,X_24),equivalent(X_24,X_25)),equivalent(equivalent(X_24,X_25),equivalent(X_8,X_24)))) )],[refute_0_17,refute_0_10]) ).
cnf(refute_0_19,plain,
is_a_theorem(equivalent(equivalent(X_27,X_27),equivalent(equivalent(X_27,X_26),equivalent(X_26,X_27)))),
inference(subst,[],[refute_0_18:[bind(X_24,$fot(X_26)),bind(X_25,$fot(X_27)),bind(X_8,$fot(X_27))]]) ).
cnf(refute_0_20,plain,
is_a_theorem(equivalent(equivalent(X_26,X_26),equivalent(X_27,X_27))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_27,X_27),equivalent(equivalent(X_27,X_26),equivalent(X_26,X_27)))) )],[refute_0_19,refute_0_9]) ).
cnf(refute_0_21,plain,
is_a_theorem(equivalent(equivalent(X_29,X_29),equivalent(X_30,X_30))),
inference(subst,[],[refute_0_20:[bind(X_26,$fot(X_29)),bind(X_27,$fot(X_30))]]) ).
cnf(refute_0_22,plain,
is_a_theorem(equivalent(equivalent(Z,equivalent(X_30,X_30)),equivalent(equivalent(X_29,X_29),Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_29,X_29),equivalent(X_30,X_30))) )],[refute_0_21,refute_0_3]) ).
cnf(refute_0_23,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)),equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)))),
inference(subst,[],[refute_0_22:[bind(Z,$fot(equivalent(X_30,X_30))),bind(X_29,$fot(X_30))]]) ).
cnf(refute_0_24,plain,
( ~ is_a_theorem(equivalent(X_29,X_29))
| ~ is_a_theorem(equivalent(equivalent(X_29,X_29),equivalent(X_30,X_30)))
| is_a_theorem(equivalent(X_30,X_30)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_29,X_29))),bind(Y,$fot(equivalent(X_30,X_30)))]]) ).
cnf(refute_0_25,plain,
( ~ is_a_theorem(equivalent(X_29,X_29))
| is_a_theorem(equivalent(X_30,X_30)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_29,X_29),equivalent(X_30,X_30))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)),equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30))))
| is_a_theorem(equivalent(X_38,X_38)) ),
inference(subst,[],[refute_0_25:[bind(X_29,$fot(equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)))),bind(X_30,$fot(X_38))]]) ).
cnf(refute_0_27,plain,
is_a_theorem(equivalent(X_38,X_38)),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)),equivalent(equivalent(X_30,X_30),equivalent(X_30,X_30)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(equivalent(X_39,X_39)),
inference(subst,[],[refute_0_27:[bind(X_38,$fot(X_39))]]) ).
cnf(refute_0_29,plain,
is_a_theorem(equivalent(equivalent(Z,X_39),equivalent(X_39,Z))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_39,X_39)) )],[refute_0_28,refute_0_2]) ).
cnf(refute_0_30,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))),
inference(subst,[],[refute_0_29:[bind(Z,$fot(a)),bind(X_39,$fot(b))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(a,b),equivalent(b,a))) )],[refute_0_30,prove_ec_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 10:30:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------