TSTP Solution File: LCL013-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:48:47 EDT 2022
% Result : Unsatisfiable 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 26 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).
cnf(xgf,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y)))) ).
cnf(prove_um,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))) ).
cnf(refute_0_0,plain,
is_a_theorem(equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(equivalent(X_23,equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(X_20,X_24))),equivalent(equivalent(X_20,X_24),X_23)))),
inference(subst,[],[xgf:[bind(X,$fot(equivalent(X_24,equivalent(X_23,X_20)))),bind(Y,$fot(X_23)),bind(Z,$fot(equivalent(X_20,X_24)))]]) ).
cnf(refute_0_1,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)))
| ~ is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)),equivalent(X_12,X_11)))
| is_a_theorem(equivalent(X_12,X_11)) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)))),bind(Y,$fot(equivalent(X_12,X_11)))]]) ).
cnf(refute_0_2,plain,
is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y)))),
inference(subst,[],[xgf:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_3,plain,
( ~ is_a_theorem(X_3)
| ~ is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y))) ),
inference(subst,[],[condensed_detachment:[bind(X,$fot(X_3)),bind(Y,$fot(equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y))))]]) ).
cnf(refute_0_4,plain,
( ~ is_a_theorem(X_3)
| is_a_theorem(equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y))) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(X_3,equivalent(equivalent(Y,equivalent(X_3,Z)),equivalent(Z,Y)))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y))))
| is_a_theorem(equivalent(equivalent(X_5,equivalent(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y))),X_6)),equivalent(X_6,X_5))) ),
inference(subst,[],[refute_0_4:[bind(Y,$fot(X_5)),bind(Z,$fot(X_6)),bind(X_3,$fot(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y)))))]]) ).
cnf(refute_0_6,plain,
is_a_theorem(equivalent(equivalent(X_5,equivalent(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y))),X_6)),equivalent(X_6,X_5))),
inference(resolve,[$cnf( is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(X,Z)),equivalent(Z,Y)))) )],[xgf,refute_0_5]) ).
cnf(refute_0_7,plain,
is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)),equivalent(X_12,X_11))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(X_10)),bind(X_5,$fot(X_11)),bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_8,plain,
( ~ is_a_theorem(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)))
| is_a_theorem(equivalent(X_12,X_11)) ),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_11,equivalent(equivalent(X_8,equivalent(equivalent(X_9,equivalent(X_8,X_10)),equivalent(X_10,X_9))),X_12)),equivalent(X_12,X_11))) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
( ~ is_a_theorem(equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(equivalent(X_23,equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(X_20,X_24))),equivalent(equivalent(X_20,X_24),X_23))))
| is_a_theorem(equivalent(equivalent(equivalent(X_20,X_24),X_23),equivalent(X_24,equivalent(X_23,X_20)))) ),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_20)),bind(X_11,$fot(equivalent(X_24,equivalent(X_23,X_20)))),bind(X_12,$fot(equivalent(equivalent(X_20,X_24),X_23))),bind(X_8,$fot(X_23)),bind(X_9,$fot(X_24))]]) ).
cnf(refute_0_10,plain,
is_a_theorem(equivalent(equivalent(equivalent(X_20,X_24),X_23),equivalent(X_24,equivalent(X_23,X_20)))),
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(equivalent(X_23,equivalent(equivalent(X_24,equivalent(X_23,X_20)),equivalent(X_20,X_24))),equivalent(equivalent(X_20,X_24),X_23)))) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(subst,[],[refute_0_10:[bind(X_20,$fot(a)),bind(X_23,$fot(c)),bind(X_24,$fot(b))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))) )],[refute_0_11,prove_um]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 21:20:30 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------