%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET950+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 : 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 03:33:02 PM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 63 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 69 ( 31 ~; 24 |; 10 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 38 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t103_zfmisc_1,plain,
! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(t103_zfmisc_1_negated,plain,
~ ! [A,B,C,D] :
~ ( subset(A,cartesian_product2(B,C))
& in(D,A)
& ! [E,F] :
~ ( in(E,B)
& in(F,C)
& D = ordered_pair(E,F) ) ),
inference(negate_conjecture,[status(cth)],[t103_zfmisc_1]) ).
cnf(22,plain,
( sK16 != ordered_pair(X0,X1)
| ~ in(X0,sK14)
| ~ in(X1,sK15) ),
inference(cnf,[status(esa)],[t103_zfmisc_1_negated]) ).
cnf(l0,plain,
( sK16 != ordered_pair(sK1(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK2(sK14,sK15,cartesian_product2(sK14,sK15),sK16))
| ~ in(sK1(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK14)
| ~ in(sK2(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK15) ),
inference(instantiation,[status(thm)],[22]) ).
fof(d2_zfmisc_1,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
cnf(4,plain,
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| X3 = ordered_pair(sK1(X1,X2,X0,X3),sK2(X1,X2,X0,X3)) ),
inference(cnf,[status(esa)],[d2_zfmisc_1]) ).
cnf(l1,plain,
( cartesian_product2(sK14,sK15) != cartesian_product2(sK14,sK15)
| ~ in(sK16,cartesian_product2(sK14,sK15))
| sK16 = ordered_pair(sK1(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK2(sK14,sK15,cartesian_product2(sK14,sK15),sK16)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(d3_tarski,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
cnf(12,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l3,plain,
( ~ in(sK16,sK13)
| ~ subset(sK13,cartesian_product2(sK14,sK15))
| in(sK16,cartesian_product2(sK14,sK15)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(20,plain,
subset(sK13,cartesian_product2(sK14,sK15)),
inference(cnf,[status(esa)],[t103_zfmisc_1_negated]) ).
cnf(l14,plain,
subset(sK13,cartesian_product2(sK14,sK15)),
inference(instantiation,[status(thm)],[20]) ).
cnf(21,plain,
in(sK16,sK13),
inference(cnf,[status(esa)],[t103_zfmisc_1_negated]) ).
cnf(l7,plain,
in(sK16,sK13),
inference(instantiation,[status(thm)],[21]) ).
cnf(2,plain,
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| in(sK1(X1,X2,X0,X3),X1) ),
inference(cnf,[status(esa)],[d2_zfmisc_1]) ).
cnf(l23,plain,
( cartesian_product2(sK14,sK15) != cartesian_product2(sK14,sK15)
| ~ in(sK16,cartesian_product2(sK14,sK15))
| in(sK1(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK14) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l25,plain,
( ~ in(sK16,sK13)
| ~ subset(sK13,cartesian_product2(sK14,sK15))
| in(sK16,cartesian_product2(sK14,sK15)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(3,plain,
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| in(sK2(X1,X2,X0,X3),X2) ),
inference(cnf,[status(esa)],[d2_zfmisc_1]) ).
cnf(l24,plain,
( cartesian_product2(sK14,sK15) != cartesian_product2(sK14,sK15)
| ~ in(sK16,cartesian_product2(sK14,sK15))
| in(sK2(sK14,sK15,cartesian_product2(sK14,sK15),sK16),sK15) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l29,plain,
( ~ in(sK16,sK13)
| ~ subset(sK13,cartesian_product2(sK14,sK15))
| in(sK16,cartesian_product2(sK14,sK15)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l39,plain,
in(sK16,sK13),
inference(instantiation,[status(thm)],[21]) ).
cnf(l50,plain,
subset(sK13,cartesian_product2(sK14,sK15)),
inference(instantiation,[status(thm)],[20]) ).
cnf(l38,plain,
in(sK16,sK13),
inference(instantiation,[status(thm)],[21]) ).
cnf(l44,plain,
subset(sK13,cartesian_product2(sK14,sK15)),
inference(instantiation,[status(thm)],[20]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l14,l7,l23,l25,l24,l29,l39,l50,l38,l44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET950+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n018.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 23:04:19 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % launching worker at depth: 1
% 0.13/0.33 % launching worker at depth: 6
% 0.13/0.33 % launching worker at depth: 4
% 0.13/0.33 % launching worker at depth: 3
% 0.13/0.33 % launching worker at depth: 2
% 0.13/0.33 % launching worker at depth: 5
% 0.13/0.33 % launching worker at depth: 7
% 0.13/0.33 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.19/0.40 % SZS status Theorem for theBenchmark
% 0.19/0.40 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------