%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET971+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 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 27 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t124_zfmisc_1,plain,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_zfmisc_1) ).
fof(t124_zfmisc_1_negated,plain,
~ ! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negate_conjecture,[status(cth)],[t124_zfmisc_1]) ).
cnf(8,plain,
set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5),
inference(cnf,[status(esa)],[t124_zfmisc_1_negated]) ).
cnf(l0,plain,
set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5),
inference(instantiation,[status(thm)],[8]) ).
fof(t28_xboole_1,plain,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
cnf(9,plain,
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf,[status(esa)],[t28_xboole_1]) ).
cnf(l7,plain,
( ~ subset(sK3,sK4)
| set_intersection2(sK3,sK4) = sK3 ),
inference(instantiation,[status(thm)],[9]) ).
cnf(6,plain,
subset(sK3,sK4),
inference(cnf,[status(esa)],[t124_zfmisc_1_negated]) ).
cnf(l10,plain,
subset(sK3,sK4),
inference(instantiation,[status(thm)],[6]) ).
fof(t123_zfmisc_1,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
cnf(5,plain,
cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf,[status(esa)],[t123_zfmisc_1]) ).
cnf(l24,plain,
cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) = set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)),
inference(instantiation,[status(thm)],[5]) ).
fof(commutativity_k3_xboole_0,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
cnf(0,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(l26,plain,
set_intersection2(sK6,sK5) = set_intersection2(sK5,sK6),
inference(instantiation,[status(thm)],[0]) ).
cnf(l6,plain,
( ~ subset(sK5,sK6)
| set_intersection2(sK5,sK6) = sK5 ),
inference(instantiation,[status(thm)],[9]) ).
cnf(7,plain,
subset(sK5,sK6),
inference(cnf,[status(esa)],[t124_zfmisc_1_negated]) ).
cnf(l11,plain,
subset(sK5,sK6),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l7,l10,l24,l26,l6,l11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET971+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 23:07:19 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 4
% 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: 7
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.29 % launching worker at depth: 10
% 0.09/0.30 % launching worker at depth: 11
% 0.13/0.51 % SZS status Theorem for theBenchmark
% 0.13/0.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------