%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET977+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 : n018.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 10.84s 1.69s
% Output : CNFRefutation 10.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 62 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 29 ~; 20 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t130_zfmisc_1,plain,
! [A,B] :
( A != empty_set
=> ( cartesian_product2(singleton(B),A) != empty_set
& cartesian_product2(A,singleton(B)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(t130_zfmisc_1_negated,plain,
~ ! [A,B] :
( A != empty_set
=> ( cartesian_product2(singleton(B),A) != empty_set
& cartesian_product2(A,singleton(B)) != empty_set ) ),
inference(negate_conjecture,[status(cth)],[t130_zfmisc_1]) ).
cnf(16,plain,
( cartesian_product2(singleton(sK5),sK4) = empty_set
| cartesian_product2(sK4,singleton(sK5)) = empty_set ),
inference(cnf,[status(esa)],[t130_zfmisc_1_negated]) ).
cnf(l0,plain,
( cartesian_product2(singleton(sK5),sK4) = empty_set
| cartesian_product2(sK4,singleton(sK5)) = empty_set ),
inference(instantiation,[status(thm)],[16]) ).
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/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
cnf(14,plain,
( X0 != X1
| ~ in(X2,X3)
| in(ordered_pair(X2,X0),cartesian_product2(X3,singleton(X1))) ),
inference(cnf,[status(esa)],[t129_zfmisc_1]) ).
cnf(l68,plain,
( sK5 != sK5
| ~ in(sK1(sK4),sK4)
| in(ordered_pair(sK1(sK4),sK5),cartesian_product2(sK4,singleton(sK5))) ),
inference(instantiation,[status(thm)],[14]) ).
fof(t128_zfmisc_1,plain,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( A = C
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
cnf(11,plain,
( X0 != X1
| ~ in(X2,X3)
| in(ordered_pair(X0,X2),cartesian_product2(singleton(X1),X3)) ),
inference(cnf,[status(esa)],[t128_zfmisc_1]) ).
cnf(l1,plain,
( cartesian_product2(singleton(sK5),sK4) != empty_set
| ~ in(ordered_pair(sK5,sK1(sK4)),cartesian_product2(singleton(sK5),sK4))
| in(ordered_pair(cartesian_product2(singleton(sK5),sK4),ordered_pair(sK5,sK1(sK4))),cartesian_product2(singleton(empty_set),cartesian_product2(singleton(sK5),sK4))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(10,plain,
( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| in(X1,X3) ),
inference(cnf,[status(esa)],[t128_zfmisc_1]) ).
cnf(l56,plain,
( ~ in(ordered_pair(cartesian_product2(singleton(sK5),sK4),ordered_pair(sK5,sK1(sK4))),cartesian_product2(singleton(empty_set),cartesian_product2(singleton(sK5),sK4)))
| in(ordered_pair(sK5,sK1(sK4)),cartesian_product2(singleton(sK5),sK4)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l11,plain,
( sK5 != sK5
| ~ in(sK1(sK4),sK4)
| in(ordered_pair(sK5,sK1(sK4)),cartesian_product2(singleton(sK5),sK4)) ),
inference(instantiation,[status(thm)],[11]) ).
fof(d1_xboole_0,plain,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
cnf(3,plain,
( X0 = empty_set
| in(sK1(X0),X0) ),
inference(cnf,[status(esa)],[d1_xboole_0]) ).
cnf(l17,plain,
( sK4 = empty_set
| in(sK1(sK4),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l69,plain,
( sK4 = empty_set
| in(sK1(sK4),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(15,plain,
sK4 != empty_set,
inference(cnf,[status(esa)],[t130_zfmisc_1_negated]) ).
cnf(l71,plain,
sK4 != empty_set,
inference(instantiation,[status(thm)],[15]) ).
cnf(l29,plain,
sK4 != empty_set,
inference(instantiation,[status(thm)],[15]) ).
fof(d5_tarski,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
cnf(4,plain,
ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf,[status(esa)],[d5_tarski]) ).
cnf(l64,plain,
ordered_pair(sK5,sK1(sK4)) = unordered_pair(unordered_pair(sK5,sK1(sK4)),singleton(sK5)),
inference(instantiation,[status(thm)],[4]) ).
cnf(l123,plain,
ordered_pair(sK1(sK4),sK5) = unordered_pair(unordered_pair(sK1(sK4),sK5),singleton(sK1(sK4))),
inference(instantiation,[status(thm)],[4]) ).
cnf(2,plain,
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf,[status(esa)],[d1_xboole_0]) ).
cnf(l82,plain,
( cartesian_product2(singleton(sK5),sK4) != empty_set
| ~ in(unordered_pair(unordered_pair(sK5,sK1(sK4)),singleton(sK5)),cartesian_product2(singleton(sK5),sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(commutativity_k2_tarski,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
cnf(1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf,[status(esa)],[commutativity_k2_tarski]) ).
cnf(l144,plain,
unordered_pair(sK1(sK4),sK5) = unordered_pair(sK5,sK1(sK4)),
inference(instantiation,[status(thm)],[1]) ).
cnf(l124,plain,
unordered_pair(unordered_pair(sK1(sK4),sK5),singleton(sK1(sK4))) = unordered_pair(singleton(sK1(sK4)),unordered_pair(sK1(sK4),sK5)),
inference(instantiation,[status(thm)],[1]) ).
cnf(l154,plain,
unordered_pair(singleton(sK1(sK4)),unordered_pair(sK5,sK1(sK4))) = unordered_pair(unordered_pair(sK5,sK1(sK4)),singleton(sK1(sK4))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l153,plain,
( cartesian_product2(sK4,singleton(sK5)) != empty_set
| ~ in(unordered_pair(unordered_pair(sK5,sK1(sK4)),singleton(sK1(sK4))),cartesian_product2(sK4,singleton(sK5))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l68,l1,l56,l11,l17,l69,l71,l29,l64,l123,l82,l144,l124,l154,l153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET977+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.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 23:08:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.34 % launching worker at depth: 4
% 0.18/0.34 % launching worker at depth: 1
% 0.18/0.34 % launching worker at depth: 5
% 0.18/0.34 % launching worker at depth: 2
% 0.18/0.34 % launching worker at depth: 3
% 0.18/0.34 % launching worker at depth: 6
% 0.18/0.34 % launching worker at depth: 7
% 0.18/0.34 % launching worker at depth: 8
% 0.18/0.34 % launching worker at depth: 9
% 0.18/0.34 % launching worker at depth: 10
% 0.18/0.45 % launching worker at depth: 11
% 10.84/1.69 % SZS status Theorem for theBenchmark
% 10.84/1.69 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------