%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET621+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 : n025.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 03:32:23 PM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th97,plain,
! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th97) ).
fof(prove_th97_negated,plain,
~ ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))),
inference(negate_conjecture,[status(cth)],[prove_th97]) ).
cnf(24,plain,
difference(symmetric_difference(sK3,sK4),sK5) != union(difference(sK3,union(sK4,sK5)),difference(sK4,union(sK3,sK5))),
inference(cnf,[status(esa)],[prove_th97_negated]) ).
cnf(l0,plain,
difference(symmetric_difference(sK3,sK4),sK5) != union(difference(sK3,union(sK4,sK5)),difference(sK4,union(sK3,sK5))),
inference(instantiation,[status(thm)],[24]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(12,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l27,plain,
union(difference(sK3,union(sK4,sK5)),difference(sK4,union(sK3,sK5))) = union(difference(sK4,union(sK3,sK5)),difference(sK3,union(sK4,sK5))),
inference(instantiation,[status(thm)],[12]) ).
fof(symmetric_difference_defn,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
cnf(0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf,[status(esa)],[symmetric_difference_defn]) ).
cnf(l7,plain,
symmetric_difference(sK3,sK4) = union(difference(sK3,sK4),difference(sK4,sK3)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l16,plain,
union(difference(difference(sK3,sK4),sK5),difference(difference(sK4,sK3),sK5)) = union(difference(difference(sK4,sK3),sK5),difference(difference(sK3,sK4),sK5)),
inference(instantiation,[status(thm)],[12]) ).
fof(difference_distributes_over_union,plain,
! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_distributes_over_union) ).
cnf(2,plain,
difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(cnf,[status(esa)],[difference_distributes_over_union]) ).
cnf(l17,plain,
difference(union(difference(sK3,sK4),difference(sK4,sK3)),sK5) = union(difference(difference(sK3,sK4),sK5),difference(difference(sK4,sK3),sK5)),
inference(instantiation,[status(thm)],[2]) ).
fof(difference_difference_union,plain,
! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_difference_union) ).
cnf(1,plain,
difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(cnf,[status(esa)],[difference_difference_union]) ).
cnf(l30,plain,
difference(difference(sK3,sK4),sK5) = difference(sK3,union(sK4,sK5)),
inference(instantiation,[status(thm)],[1]) ).
cnf(l28,plain,
difference(difference(sK4,sK3),sK5) = difference(sK4,union(sK3,sK5)),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l27,l7,l16,l17,l30,l28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET621+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.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 : 300
% 0.12/0.33 % DateTime : Mon Jul 21 22:08:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.35 % launching worker at depth: 11
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------