%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET979+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 : n023.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 03:33:05 PM UTC 2025
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 2 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 19 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,plain,
! [A,B,C] :
( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
& cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(t132_zfmisc_1_negated,plain,
~ ! [A,B,C] :
( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
& cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ),
inference(negate_conjecture,[status(cth)],[t132_zfmisc_1]) ).
cnf(9,plain,
( cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5))
| cartesian_product2(sK5,unordered_pair(sK3,sK4)) != set_union2(cartesian_product2(sK5,singleton(sK3)),cartesian_product2(sK5,singleton(sK4))) ),
inference(cnf,[status(esa)],[t132_zfmisc_1_negated]) ).
cnf(l0,plain,
( cartesian_product2(unordered_pair(sK3,sK4),sK5) != set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5))
| cartesian_product2(sK5,unordered_pair(sK3,sK4)) != set_union2(cartesian_product2(sK5,singleton(sK3)),cartesian_product2(sK5,singleton(sK4))) ),
inference(instantiation,[status(thm)],[9]) ).
fof(t41_enumset1,plain,
! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).
cnf(10,plain,
unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf,[status(esa)],[t41_enumset1]) ).
cnf(l14,plain,
unordered_pair(sK3,sK4) = set_union2(singleton(sK3),singleton(sK4)),
inference(instantiation,[status(thm)],[10]) ).
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(8,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(l6,plain,
cartesian_product2(sK5,set_union2(singleton(sK3),singleton(sK4))) = set_union2(cartesian_product2(sK5,singleton(sK3)),cartesian_product2(sK5,singleton(sK4))),
inference(instantiation,[status(thm)],[8]) ).
cnf(7,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(l2,plain,
cartesian_product2(set_union2(singleton(sK3),singleton(sK4)),sK5) = set_union2(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK5)),
inference(instantiation,[status(thm)],[7]) ).
cnf(l7,plain,
unordered_pair(sK3,sK4) = set_union2(singleton(sK3),singleton(sK4)),
inference(instantiation,[status(thm)],[10]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l14,l6,l2,l7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET979+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 23:09:04 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.34 % SZS status Theorem for theBenchmark
% 0.13/0.34 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------