%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:09 PM UTC 2026
% Result : Theorem 3.25s 1.36s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 68 ( 5 unt; 2 def)
% Number of atoms : 341 ( 129 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 419 ( 146 ~; 145 |; 116 &)
% ( 7 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-3 aty)
% Number of variables : 265 ( 172 !; 93 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,cartesian_product2(X0,X1))
& X4 = X3
& ? [X9,X10] :
( ordered_pair(X9,X10) = X3
& in(X9,X0)
& X10 = singleton(X9) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) ) ) ),
inference(flattening,[],[f19]) ).
fof(f22,definition,
! [X4,X0] :
( ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(X7,X0)
& X8 = singleton(X7) )
| ~ sP0(X4,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f23,definition,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) ) )
| sP1(X0) ),
inference(definition_folding,[],[f20,f23,f22]) ).
fof(f25,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& X5 = singleton(X4) ) )
| in(X3,X2) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( ~ in(X3,cartesian_product2(X0,X1))
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X4,X0)
| singleton(X4) != X5 )
| ~ in(X3,X2) )
& ( ( in(X3,cartesian_product2(X0,X1))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X6,X0)
& singleton(X6) = X7 ) )
| in(X3,X2) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X2] :
( ( ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK4(X2)
| ~ in(X4,sK2)
| singleton(X4) != X5 )
| ~ in(sK4(X2),X2) )
& ( ( in(sK4(X2),cartesian_product2(sK2,sK3))
& sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
& in(sK5(X2),sK2)
& sK6(X2) = singleton(sK5(X2)) )
| in(sK4(X2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X6,sK5(X2)),skolemize(X7,sK6(X2))],[f27]) ).
fof(f29,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(X5,X0)
& X6 = singleton(X5) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f30,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ? [X4,X5] :
( ordered_pair(X4,X5) = X2
& in(X4,X0)
& singleton(X4) = X5 )
& X1 = X3
& sP0(X3,X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( sK8(X0) != sK9(X0)
& sK7(X0) = sK8(X0)
& sK8(X0) = ordered_pair(sK10(X0),sK11(X0))
& in(sK10(X0),X0)
& sK11(X0) = singleton(sK10(X0))
& sK7(X0) = sK9(X0)
& sP0(sK9(X0),X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0)),skolemize(X3,sK9(X0)),skolemize(X4,sK10(X0)),skolemize(X5,sK11(X0))],[f30]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X9] :
! [X10] :
( ( in(X10,X9)
| ! [X11] :
( ~ in(X11,cartesian_product2(X0,X1))
| X10 != X11
| ! [X12,X13] :
( ordered_pair(X12,X13) != X10
| ~ in(X12,X0)
| singleton(X12) != X13 ) ) )
& ( ? [X11] :
( in(X11,cartesian_product2(X0,X1))
& X10 = X11
& ? [X12,X13] :
( ordered_pair(X12,X13) = X10
& in(X12,X0)
& singleton(X12) = X13 ) )
| ~ in(X10,X9) ) )
| sP1(X0) ),
inference(nnf_transformation,[],[f24]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ? [X7] :
( in(X7,cartesian_product2(X0,X1))
& X3 = X7
& ? [X8,X9] :
( ordered_pair(X8,X9) = X3
& in(X8,X0)
& singleton(X8) = X9 ) )
| ~ in(X3,X2) ) )
| sP1(X0) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK14(X0,X1))
| ! [X4] :
( ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ! [X5,X6] :
( ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6 ) ) )
& ( ( in(sK15(X0,X1,X3),cartesian_product2(X0,X1))
& sK15(X0,X1,X3) = X3
& ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3
& in(sK16(X0,X3),X0)
& sK17(X0,X3) = singleton(sK16(X0,X3)) )
| ~ in(X3,sK14(X0,X1)) ) )
| sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X2,sK14(X0,X1)),skolemize(X7,sK15(X0,X1,X3)),skolemize(X8,sK16(X0,X3)),skolemize(X9,sK17(X0,X3))],[f36]) ).
fof(f40,plain,
! [X2] :
( sK6(X2) = singleton(sK5(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X2] :
( in(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X2] :
( sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
! [X2] :
( in(sK4(X2),cartesian_product2(sK2,sK3))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X2,X4,X5] :
( ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ordered_pair(X4,X5) != sK4(X2)
| ~ in(X4,sK2)
| singleton(X4) != X5
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X0] :
( sK7(X0) = sK9(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
! [X0] :
( sK7(X0) = sK8(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X0] :
( sK8(X0) != sK9(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X3,X0,X1] :
( sK17(X0,X3) = singleton(sK16(X0,X3))
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X3,X0,X1] :
( in(sK16(X0,X3),X0)
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X3,X0,X1] :
( ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X3,X0,X1] :
( sK15(X0,X1,X3) = X3
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X3,X0,X1] :
( in(sK15(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK14(X0,X1))
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f60,plain,
! [X3,X0,X1,X6,X4,X5] :
( in(X3,sK14(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| X3 != X4
| ordered_pair(X5,X6) != X3
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f65,plain,
! [X2,X4] :
( sK4(X2) != ordered_pair(X4,singleton(X4))
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(X4,sK2)
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f44]) ).
fof(f66,plain,
! [X0,X1,X6,X4,X5] :
( in(X4,sK14(X0,X1))
| ~ in(X4,cartesian_product2(X0,X1))
| ordered_pair(X5,X6) != X4
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(equality_resolution,[],[f60]) ).
fof(f67,plain,
! [X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),sK14(X0,X1))
| ~ in(ordered_pair(X5,X6),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| singleton(X5) != X6
| sP1(X0) ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,singleton(X5)),sK14(X0,X1))
| ~ in(ordered_pair(X5,singleton(X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0)
| sP1(X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f83,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| ~ sP1(X0)
| ~ sP1(X0) ),
inference(superposition,[],[f51,f46]) ).
fof(f84,plain,
! [X0] :
( sK7(X0) != sK8(X0)
| ~ sP1(X0) ),
inference(duplicate_literal_removal,[],[f83]) ).
fof(f85,plain,
! [X0] : ~ sP1(X0),
inference(forward_subsumption_resolution,[],[f84,f50]) ).
fof(f92,plain,
! [X3,X0,X1] :
( in(sK16(X0,X3),X0)
| ~ in(X3,sK14(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f56,f85]) ).
fof(f102,plain,
! [X3,X0,X1] :
( sK15(X0,X1,X3) = X3
| ~ in(X3,sK14(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f58,f85]) ).
fof(f107,plain,
! [X3,X0,X1] :
( sK17(X0,X3) = singleton(sK16(X0,X3))
| ~ in(X3,sK14(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f55,f85]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( sK4(X2) != ordered_pair(sK16(X0,X1),sK17(X0,X1))
| ~ in(sK4(X2),cartesian_product2(sK2,sK3))
| ~ in(sK16(X0,X1),sK2)
| ~ in(sK4(X2),X2)
| ~ in(X1,sK14(X0,X3)) ),
inference(superposition,[],[f65,f107]) ).
fof(f110,plain,
! [X3,X0,X1] :
( in(sK15(X0,X1,X3),cartesian_product2(X0,X1))
| ~ in(X3,sK14(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f59,f85]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X2))
| ~ in(X0,sK14(X1,X2))
| ~ in(X0,sK14(X1,X2)) ),
inference(superposition,[],[f110,f102]) ).
fof(f113,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(X1,X2))
| ~ in(X0,sK14(X1,X2)) ),
inference(duplicate_literal_removal,[],[f112]) ).
fof(f118,plain,
! [X3,X0,X1] :
( ordered_pair(sK16(X0,X3),sK17(X0,X3)) = X3
| ~ in(X3,sK14(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f57,f85]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( sK4(X1) != X0
| ~ in(sK4(X1),cartesian_product2(sK2,sK3))
| ~ in(sK16(X2,X0),sK2)
| ~ in(sK4(X1),X1)
| ~ in(X0,sK14(X2,X3))
| ~ in(X0,sK14(X2,X4)) ),
inference(superposition,[],[f109,f118]) ).
fof(f127,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,singleton(X5)),sK14(X0,X1))
| ~ in(ordered_pair(X5,singleton(X5)),cartesian_product2(X0,X1))
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f68,f85]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ in(sK16(X1,sK4(X0)),sK2)
| ~ in(sK4(X0),cartesian_product2(sK2,sK3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X1,X2))
| ~ in(sK4(X0),sK14(X1,X3)) ),
inference(equality_resolution,[],[f123]) ).
fof(f130,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,X2))
| ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(sK4(X0),X0) ),
inference(superposition,[],[f127,f40]) ).
fof(f134,plain,
! [X2,X0,X1] :
( in(sK4(X0),sK14(X1,X2))
| ~ in(sK4(X0),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(sK4(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f130,f42]) ).
fof(f135,plain,
! [X2,X0,X1] :
( in(sK4(X0),sK14(X1,X2))
| ~ in(sK4(X0),cartesian_product2(X1,X2))
| ~ in(sK5(X0),X1)
| in(sK4(X0),X0) ),
inference(duplicate_literal_removal,[],[f134]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(X0),sK14(sK2,X3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(sK2,X1))
| ~ in(sK4(X0),sK14(sK2,X2))
| ~ in(sK4(X0),cartesian_product2(sK2,sK3)) ),
inference(resolution,[],[f128,f92]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(sK2,X2))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(sK2,X1))
| ~ in(sK4(X0),cartesian_product2(sK2,sK3)) ),
inference(factoring,[],[f167]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK14(sK2,X1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(sK2,sK3)) ),
inference(factoring,[],[f172]) ).
fof(f185,plain,
! [X0] :
( ~ in(sK4(sK14(sK2,X0)),sK14(sK2,X0))
| ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,sK3)) ),
inference(factoring,[],[f180]) ).
fof(f203,plain,
! [X0] :
( ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,sK3))
| ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,X0))
| ~ in(sK5(sK14(sK2,X0)),sK2)
| in(sK4(sK14(sK2,X0)),sK14(sK2,X0)) ),
inference(resolution,[],[f185,f135]) ).
fof(f206,plain,
! [X0] :
( ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,X0))
| ~ in(sK5(sK14(sK2,X0)),sK2)
| in(sK4(sK14(sK2,X0)),sK14(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f203,f43]) ).
fof(f207,plain,
! [X0] :
( in(sK4(sK14(sK2,X0)),sK14(sK2,X0))
| ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f206,f41]) ).
fof(f227,plain,
! [X0] :
( ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,sK3))
| ~ in(sK4(sK14(sK2,X0)),cartesian_product2(sK2,X0)) ),
inference(resolution,[],[f207,f185]) ).
fof(f248,plain,
~ in(sK4(sK14(sK2,sK3)),cartesian_product2(sK2,sK3)),
inference(factoring,[],[f227]) ).
fof(f249,plain,
in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3)),
inference(resolution,[],[f248,f43]) ).
fof(f256,plain,
( ~ in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3))
| ~ in(sK4(sK14(sK2,sK3)),cartesian_product2(sK2,sK3)) ),
inference(resolution,[],[f249,f180]) ).
fof(f264,plain,
~ in(sK4(sK14(sK2,sK3)),sK14(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f256,f113]) ).
fof(f267,plain,
$false,
inference(forward_subsumption_resolution,[],[f264,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:28:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/1.36 % (1872717)Detected formulas, will run a generic FOF schedule.
% 3.25/1.36 % (1872823)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2872601448:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.25/1.36 % (1872825)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1526564245:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.25/1.36 % (1872829)dis-21_1_sil=8000:lcm=predicate:random_seed=4223673203:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.25/1.36 % (1872827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1546669290:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.25/1.36 % (1872824)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2547299303:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.25/1.36 % (1872828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=373847588:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.25/1.36 % (1872827)First to succeed.
% 3.25/1.36 % (1872827)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1872717"
% 3.25/1.36 % (1872828)Also succeeded, but the first one will report.
% 3.25/1.36 % (1872826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1983364745:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.25/1.36 % (1872826)Refutation not found, incomplete strategy
% 3.25/1.36 % (1872826)------------------------------
% 3.25/1.36 % (1872826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (1872826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (1872826)CaDiCaL version: 2.1.3
% 3.25/1.36 % (1872826)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.36 % (1872826)Time elapsed: 0.004 s
% 3.25/1.36 % (1872826)Peak memory usage: 88 MB
% 3.25/1.36 % (1872826)Instructions burned: 4 (million)
% 3.25/1.36 % (1872829)Instruction limit reached!
% 3.25/1.36 % (1872829)------------------------------
% 3.25/1.36 % (1872829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.36 % (1872829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.36 % (1872829)CaDiCaL version: 2.1.3
% 3.25/1.36 % (1872829)Termination reason: Instruction limit
% 3.25/1.36 % (1872829)Termination phase: Saturation
% 3.25/1.36 % (1872829)Time elapsed: 0.068 s
% 3.25/1.36 % (1872829)Peak memory usage: 88 MB
% 3.25/1.36 % (1872829)Instructions burned: 130 (million)
% 3.25/1.36 % (1872844)lrs+10_1_sil=8000:sp=occurrence:random_seed=2714242568:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.25/1.36 % (1872827)Refutation found. Thanks to Tanya!
% 3.25/1.36 % SZS status Theorem for theBenchmark
% 3.25/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.47 % (1872827)------------------------------
% 3.92/1.47 % (1872827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.92/1.47 % (1872827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/1.47 % (1872827)CaDiCaL version: 2.1.3
% 3.92/1.47 % (1872827)Termination reason: Refutation
% 3.92/1.47 % (1872827)Time elapsed: 0.011 s
% 3.92/1.47 % (1872827)Peak memory usage: 88 MB
% 3.92/1.47 % (1872827)Instructions burned: 14 (million)
% 3.92/1.47 % (1872827)------------------------------
% 3.92/1.47 % (1872827)------------------------------
% 3.92/1.47 % (1872717)Success in time 0.485 s
% 3.92/1.47 % Vampire exiting
%------------------------------------------------------------------------------