TSTP Solution File: LCL106-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL106-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 12:49:31 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 13 unt; 0 nHn; 10 RR)
% Number of literals : 39 ( 0 equ; 16 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(q_1,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))) ).
cnf(q_4,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))) ).
cnf(prove_q_2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)))
| is_a_theorem(equivalent(Y,Z)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(Y,$fot(equivalent(Y,Z)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z)))
| is_a_theorem(equivalent(Y,Z)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))) )],[q_4,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_73,X_74),equivalent(X_73,X_72)),equivalent(equivalent(X_73,X_74),equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72)))))
| is_a_theorem(equivalent(equivalent(X_73,X_72),equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72)))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_73,X_74))),bind(Y,$fot(equivalent(X_73,X_72))),bind(Z,$fot(equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72))))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66))),equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66))))))
| is_a_theorem(equivalent(equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66)),equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66))))) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(equivalent(X_65,X_66))),bind(Y,$fot(equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66)))),bind(Z,$fot(equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66)))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(equivalent(X_22,X_23))
| ~ is_a_theorem(equivalent(equivalent(X_22,X_23),equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19))))))
| is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19))))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_22,X_23))),bind(Y,$fot(equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19))))))]]) ).
cnf(refute_0_5,plain,
is_a_theorem(equivalent(X_6,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6)))),
inference(subst,[],[q_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
( ~ is_a_theorem(X_6)
| ~ is_a_theorem(equivalent(X_6,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6))))
| is_a_theorem(equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_6)),bind(Y,$fot(equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6))))]]) ).
cnf(refute_0_7,plain,
( ~ is_a_theorem(X_6)
| is_a_theorem(equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_6,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X_6)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X))))
| is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_9,X_8),equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))))) ),
inference(subst,[],[refute_0_7:[bind(Y,$fot(X_8)),bind(Z,$fot(X_9)),bind(X_6,$fot(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))))]]) ).
cnf(refute_0_9,plain,
is_a_theorem(equivalent(equivalent(X_8,X_9),equivalent(equivalent(X_9,X_8),equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))) )],[q_1,refute_0_8]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(equivalent(X_22,X_23),equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19)))))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_19)),bind(Y,$fot(X_20)),bind(Z,$fot(X_21)),bind(X_8,$fot(X_22)),bind(X_9,$fot(X_23))]]) ).
cnf(refute_0_11,plain,
( ~ is_a_theorem(equivalent(X_22,X_23))
| is_a_theorem(equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19))))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_22,X_23),equivalent(equivalent(X_23,X_22),equivalent(X_19,equivalent(equivalent(X_20,X_21),equivalent(equivalent(X_21,X_20),X_19)))))) )],[refute_0_10,refute_0_4]) ).
cnf(refute_0_12,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)))
| is_a_theorem(equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),equivalent(X_59,equivalent(equivalent(X_60,X_61),equivalent(equivalent(X_61,X_60),X_59))))) ),
inference(subst,[],[refute_0_11:[bind(X_19,$fot(X_59)),bind(X_20,$fot(X_60)),bind(X_21,$fot(X_61)),bind(X_22,$fot(equivalent(equivalent(X,Y),equivalent(X,Z)))),bind(X_23,$fot(equivalent(Y,Z)))]]) ).
cnf(refute_0_13,plain,
is_a_theorem(equivalent(equivalent(equivalent(Y,Z),equivalent(equivalent(X,Y),equivalent(X,Z))),equivalent(X_59,equivalent(equivalent(X_60,X_61),equivalent(equivalent(X_61,X_60),X_59))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))) )],[q_4,refute_0_12]) ).
cnf(refute_0_14,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66))),equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66)))))),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_64)),bind(Y,$fot(X_65)),bind(Z,$fot(X_66)),bind(X_59,$fot(equivalent(X_65,X_66))),bind(X_60,$fot(X_68)),bind(X_61,$fot(X_69))]]) ).
cnf(refute_0_15,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66)),equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66))))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_64,X_65),equivalent(X_64,X_66))),equivalent(equivalent(X_65,X_66),equivalent(equivalent(X_68,X_69),equivalent(equivalent(X_69,X_68),equivalent(X_65,X_66)))))) )],[refute_0_14,refute_0_3]) ).
cnf(refute_0_16,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_73,X_74),equivalent(X_73,X_72)),equivalent(equivalent(X_73,X_74),equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72))))),
inference(subst,[],[refute_0_15:[bind(X_64,$fot(X_73)),bind(X_65,$fot(X_74)),bind(X_66,$fot(X_72)),bind(X_68,$fot(X_73)),bind(X_69,$fot(X_74))]]) ).
cnf(refute_0_17,plain,
is_a_theorem(equivalent(equivalent(X_73,X_72),equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(X_73,X_74),equivalent(X_73,X_72)),equivalent(equivalent(X_73,X_74),equivalent(equivalent(X_74,X_73),equivalent(X_74,X_72))))) )],[refute_0_16,refute_0_2]) ).
cnf(refute_0_18,plain,
is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
inference(subst,[],[refute_0_17:[bind(X_72,$fot(b)),bind(X_73,$fot(a)),bind(X_74,$fot(c))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))) )],[refute_0_18,prove_q_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL106-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 06:48:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------