TSTP Solution File: SET047-5 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET047-5 : 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 : Tue Jul 19 03:31:49 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of clauses : 36 ( 4 unt; 16 nHn; 29 RR)
% Number of literals : 90 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(element_substitution1,axiom,
( ~ set_equal(X,Y)
| ~ element(Z,X)
| element(Z,Y) ) ).
cnf(element_substitution2,axiom,
( ~ set_equal(X,Y)
| ~ element(Z,Y)
| element(Z,X) ) ).
cnf(clause_3,axiom,
( element(f(X,Y),X)
| element(f(X,Y),Y)
| set_equal(X,Y) ) ).
cnf(clause_4,axiom,
( ~ element(f(X,Y),Y)
| ~ element(f(X,Y),X)
| set_equal(X,Y) ) ).
cnf(prove_symmetry1,negated_conjecture,
( set_equal(a,b)
| set_equal(b,a) ) ).
cnf(prove_symmetry2,negated_conjecture,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ) ).
cnf(refute_0_0,plain,
( element(f(b,Y),Y)
| element(f(b,Y),b)
| set_equal(b,Y) ),
inference(subst,[],[clause_3:[bind(X,$fot(b))]]) ).
cnf(refute_0_1,plain,
( ~ element(Z,b)
| ~ set_equal(a,b)
| element(Z,a) ),
inference(subst,[],[element_substitution2:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_2,plain,
( ~ element(X_7,b)
| ~ set_equal(b,a)
| element(X_7,a) ),
inference(subst,[],[element_substitution1:[bind(X,$fot(b)),bind(Y,$fot(a)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( ~ element(X_7,b)
| element(X_7,a)
| set_equal(a,b) ),
inference(resolve,[$cnf( set_equal(b,a) )],[prove_symmetry1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ element(f(X_13,b),b)
| element(f(X_13,b),a)
| set_equal(a,b) ),
inference(subst,[],[refute_0_3:[bind(X_7,$fot(f(X_13,b)))]]) ).
cnf(refute_0_5,plain,
( element(f(X_13,b),X_13)
| element(f(X_13,b),b)
| set_equal(X_13,b) ),
inference(subst,[],[clause_3:[bind(X,$fot(X_13)),bind(Y,$fot(b))]]) ).
cnf(refute_0_6,plain,
( element(f(X_13,b),X_13)
| element(f(X_13,b),a)
| set_equal(X_13,b)
| set_equal(a,b) ),
inference(resolve,[$cnf( element(f(X_13,b),b) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( element(f(a,b),a)
| set_equal(a,b) ),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(a))]]) ).
cnf(refute_0_8,plain,
( ~ element(f(a,b),a)
| ~ element(f(a,b),b)
| set_equal(a,b) ),
inference(subst,[],[clause_4:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_9,plain,
( ~ element(X_11,a)
| ~ set_equal(b,a)
| element(X_11,b) ),
inference(subst,[],[element_substitution2:[bind(X,$fot(b)),bind(Y,$fot(a)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_10,plain,
( ~ element(X_11,a)
| element(X_11,b)
| set_equal(a,b) ),
inference(resolve,[$cnf( set_equal(b,a) )],[prove_symmetry1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ element(f(a,X_14),a)
| element(f(a,X_14),b)
| set_equal(a,b) ),
inference(subst,[],[refute_0_10:[bind(X_11,$fot(f(a,X_14)))]]) ).
cnf(refute_0_12,plain,
( element(f(a,X_14),X_14)
| element(f(a,X_14),a)
| set_equal(a,X_14) ),
inference(subst,[],[clause_3:[bind(X,$fot(a)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_13,plain,
( element(f(a,X_14),X_14)
| element(f(a,X_14),b)
| set_equal(a,X_14)
| set_equal(a,b) ),
inference(resolve,[$cnf( element(f(a,X_14),a) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( element(f(a,b),b)
| set_equal(a,b) ),
inference(subst,[],[refute_0_13:[bind(X_14,$fot(b))]]) ).
cnf(refute_0_15,plain,
( ~ element(f(a,b),a)
| set_equal(a,b) ),
inference(resolve,[$cnf( element(f(a,b),b) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
set_equal(a,b),
inference(resolve,[$cnf( element(f(a,b),a) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ element(Z,b)
| element(Z,a) ),
inference(resolve,[$cnf( set_equal(a,b) )],[refute_0_16,refute_0_1]) ).
cnf(refute_0_18,plain,
( ~ element(f(b,Y),b)
| element(f(b,Y),a) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(f(b,Y)))]]) ).
cnf(refute_0_19,plain,
( element(f(b,Y),Y)
| element(f(b,Y),a)
| set_equal(b,Y) ),
inference(resolve,[$cnf( element(f(b,Y),b) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( element(f(b,a),a)
| set_equal(b,a) ),
inference(subst,[],[refute_0_19:[bind(Y,$fot(a))]]) ).
cnf(refute_0_21,plain,
( ~ element(f(b,a),a)
| ~ element(f(b,a),b)
| set_equal(b,a) ),
inference(subst,[],[clause_4:[bind(X,$fot(b)),bind(Y,$fot(a))]]) ).
cnf(refute_0_22,plain,
( ~ element(Z,a)
| ~ set_equal(a,b)
| element(Z,b) ),
inference(subst,[],[element_substitution1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_23,plain,
( ~ element(Z,a)
| element(Z,b) ),
inference(resolve,[$cnf( set_equal(a,b) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ element(f(b,a),a)
| element(f(b,a),b) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(f(b,a)))]]) ).
cnf(refute_0_25,plain,
( element(f(b,a),b)
| set_equal(b,a) ),
inference(resolve,[$cnf( element(f(b,a),a) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ element(f(b,a),a)
| set_equal(b,a) ),
inference(resolve,[$cnf( element(f(b,a),b) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
set_equal(b,a),
inference(resolve,[$cnf( element(f(b,a),a) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
~ set_equal(a,b),
inference(resolve,[$cnf( set_equal(b,a) )],[refute_0_27,prove_symmetry2]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( set_equal(a,b) )],[refute_0_16,refute_0_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 00:53:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------