%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET622+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n031.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 : 300s
% DateTime : Fri Jul 25 03:32:24 PM UTC 2025
% Result : Theorem 1.81s 0.59s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th98,plain,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th98) ).
fof(prove_th98_negated,plain,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(negate_conjecture,[status(cth)],[prove_th98]) ).
cnf(29,plain,
difference(sK3,symmetric_difference(sK4,sK5)) != union(difference(sK3,union(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),
inference(cnf,[status(esa)],[prove_th98_negated]) ).
cnf(l0,plain,
difference(sK3,symmetric_difference(sK4,sK5)) != union(difference(sK3,union(sK4,sK5)),intersection(intersection(sK3,sK4),sK5)),
inference(instantiation,[status(thm)],[29]) ).
fof(associativity_of_intersection,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_intersection) ).
cnf(0,plain,
intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf,[status(esa)],[associativity_of_intersection]) ).
cnf(l19,plain,
intersection(intersection(sK3,sK4),sK5) = intersection(sK3,intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[0]) ).
fof(difference_difference_union2,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union2) ).
cnf(1,plain,
difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(cnf,[status(esa)],[difference_difference_union2]) ).
cnf(l21,plain,
difference(sK3,difference(union(sK4,sK5),intersection(sK4,sK5))) = union(difference(sK3,union(sK4,sK5)),intersection(sK3,intersection(sK4,sK5))),
inference(instantiation,[status(thm)],[1]) ).
fof(symmetric_difference_and_difference,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_and_difference) ).
cnf(2,plain,
symmetric_difference(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(cnf,[status(esa)],[symmetric_difference_and_difference]) ).
cnf(l27,plain,
symmetric_difference(sK4,sK5) = difference(union(sK4,sK5),intersection(sK4,sK5)),
inference(instantiation,[status(thm)],[2]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l19,l21,l27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET622+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n031.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 : 300
% 0.14/0.34 % DateTime : Mon Jul 21 22:08:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.14/0.36 % launching worker at depth: 11
% 1.81/0.59 % SZS status Theorem for theBenchmark
% 1.81/0.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------