%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET968+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n021.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 03:33:04 PM UTC 2025
% Result : Theorem 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 17 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t121_zfmisc_1,plain,
! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(t121_zfmisc_1_negated,plain,
~ ! [A,B,C,D] : cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)),
inference(negate_conjecture,[status(cth)],[t121_zfmisc_1]) ).
cnf(8,plain,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(cnf,[status(esa)],[t121_zfmisc_1_negated]) ).
cnf(l0,plain,
cartesian_product2(set_union2(sK3,sK4),set_union2(sK5,sK6)) != set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)),
inference(instantiation,[status(thm)],[8]) ).
fof(t4_xboole_1,plain,
! [A,B,C] : set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
cnf(9,plain,
set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf,[status(esa)],[t4_xboole_1]) ).
cnf(l11,plain,
set_union2(set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),cartesian_product2(sK4,sK5)),cartesian_product2(sK4,sK6)) = set_union2(set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6))),
inference(instantiation,[status(thm)],[9]) ).
fof(commutativity_k2_xboole_0,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
cnf(0,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(l8,plain,
set_union2(sK3,sK4) = set_union2(sK4,sK3),
inference(instantiation,[status(thm)],[0]) ).
fof(t120_zfmisc_1,plain,
! [A,B,C] :
( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C))
& cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
cnf(6,plain,
cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf,[status(esa)],[t120_zfmisc_1]) ).
cnf(l14,plain,
cartesian_product2(set_union2(sK4,sK3),set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK4,set_union2(sK5,sK6)),cartesian_product2(sK3,set_union2(sK5,sK6))),
inference(instantiation,[status(thm)],[6]) ).
cnf(l15,plain,
set_union2(cartesian_product2(sK4,set_union2(sK5,sK6)),cartesian_product2(sK3,set_union2(sK5,sK6))) = set_union2(cartesian_product2(sK3,set_union2(sK5,sK6)),cartesian_product2(sK4,set_union2(sK5,sK6))),
inference(instantiation,[status(thm)],[0]) ).
cnf(7,plain,
cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
inference(cnf,[status(esa)],[t120_zfmisc_1]) ).
cnf(l7,plain,
cartesian_product2(sK4,set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK4,sK5),cartesian_product2(sK4,sK6)),
inference(instantiation,[status(thm)],[7]) ).
cnf(l9,plain,
cartesian_product2(sK3,set_union2(sK5,sK6)) = set_union2(cartesian_product2(sK3,sK5),cartesian_product2(sK3,sK6)),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l11,l8,l14,l15,l7,l9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SET968+1 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n021.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 23:07:04 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.31 % launching worker at depth: 10
% 0.13/0.31 % launching worker at depth: 11
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------