%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET976+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n022.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 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 1 unt; 0 def)
% Number of atoms : 60 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 28 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t129_zfmisc_1,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(t129_zfmisc_1_negated,plain,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& B = D ) ),
inference(negate_conjecture,[status(cth)],[t129_zfmisc_1]) ).
cnf(16,plain,
( sK5 = sK7
| in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(cnf,[status(esa)],[t129_zfmisc_1_negated]) ).
cnf(l0,plain,
( sK5 = sK7
| in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(17,plain,
( sK5 != sK7
| ~ in(sK4,sK6)
| ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(cnf,[status(esa)],[t129_zfmisc_1_negated]) ).
cnf(l2,plain,
( sK5 != sK7
| ~ in(sK4,sK6)
| ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(instantiation,[status(thm)],[17]) ).
fof(l55_zfmisc_1,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
cnf(10,plain,
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf,[status(esa)],[l55_zfmisc_1]) ).
cnf(l4,plain,
( ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7)))
| in(sK4,sK6) ),
inference(instantiation,[status(thm)],[10]) ).
fof(d1_tarski,plain,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
cnf(2,plain,
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l15,plain,
( singleton(sK7) != singleton(sK7)
| ~ in(sK5,singleton(sK7))
| sK5 = sK7 ),
inference(instantiation,[status(thm)],[2]) ).
cnf(11,plain,
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf,[status(esa)],[l55_zfmisc_1]) ).
cnf(l22,plain,
( ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7)))
| in(sK5,singleton(sK7)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(3,plain,
( X0 != singleton(X1)
| X2 != X1
| in(X2,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l1,plain,
( singleton(sK7) != singleton(sK7)
| sK5 != sK7
| in(sK5,singleton(sK7)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(12,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf,[status(esa)],[l55_zfmisc_1]) ).
cnf(l3,plain,
( ~ in(sK4,sK6)
| ~ in(sK5,singleton(sK7))
| in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l11,plain,
( sK5 != sK7
| ~ in(sK4,sK6)
| ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l43,plain,
( ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7)))
| in(sK4,sK6) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(15,plain,
( in(sK4,sK6)
| in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(cnf,[status(esa)],[t129_zfmisc_1_negated]) ).
cnf(l7,plain,
( in(sK4,sK6)
| in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7))) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l56,plain,
( ~ in(ordered_pair(sK4,sK5),cartesian_product2(sK6,singleton(sK7)))
| in(sK4,sK6) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l4,l15,l22,l1,l3,l11,l43,l7,l56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET976+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n022.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 23:08:49 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 2
% 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: 8
% 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: 4
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------