%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU277+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:48:07 PM UTC 2026
% Result : Theorem 2.23s 1.32s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 72 ( 8 unt; 1 def)
% Number of atoms : 425 ( 89 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 573 ( 220 ~; 217 |; 119 &)
% ( 7 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 3 con; 0-4 aty)
% Number of variables : 307 ( 200 !; 107 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,cartesian_product2(X0,X0))
& X5 = X4
& ? [X10,X11] :
( X4 = ordered_pair(X10,X11)
& in(ordered_pair(apply(X2,X10),apply(X2,X11)),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( relation(X1)
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
=> X4 = X5 )
=> ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( in(X12,cartesian_product2(X0,X0))
& X11 = X12
& ? [X13,X14] :
( ordered_pair(X13,X14) = X11
& in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( in(X12,cartesian_product2(X0,X0))
& X11 = X12
& ? [X13,X14] :
( ordered_pair(X13,X14) = X11
& in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( in(X12,cartesian_product2(X0,X0))
& X11 = X12
& ? [X13,X14] :
( ordered_pair(X13,X14) = X11
& in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f25]) ).
fof(f29,definition,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
| ~ sP0(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( in(X12,cartesian_product2(X0,X0))
& X11 = X12
& ? [X13,X14] :
( ordered_pair(X13,X14) = X11
& in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) ) )
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_folding,[],[f26,f29]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
| in(X4,X3) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f24]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X5,X6] :
( X4 = ordered_pair(X5,X6)
& in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) ) )
| in(X4,X3) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,cartesian_product2(X0,X0))
| ! [X5,X6] :
( ordered_pair(X5,X6) != X4
| ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1) )
| ~ in(X4,X3) )
& ( ( in(X4,cartesian_product2(X0,X0))
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1) ) )
| in(X4,X3) ) )
& relation(X1)
& relation(X2)
& function(X2) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
( ! [X3] :
( ( ~ in(sK4(X3),cartesian_product2(sK1,sK1))
| ! [X5,X6] :
( ordered_pair(X5,X6) != sK4(X3)
| ~ in(ordered_pair(apply(sK3,X5),apply(sK3,X6)),sK2) )
| ~ in(sK4(X3),X3) )
& ( ( in(sK4(X3),cartesian_product2(sK1,sK1))
& sK4(X3) = ordered_pair(sK5(X3),sK6(X3))
& in(ordered_pair(apply(sK3,sK5(X3)),apply(sK3,sK6(X3))),sK2) )
| in(sK4(X3),X3) ) )
& relation(sK2)
& relation(sK3)
& function(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X4,sK4(X3)),skolemize(X7,sK5(X3)),skolemize(X8,sK6(X3))],[f33]) ).
fof(f35,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& ? [X6,X7] :
( X4 = ordered_pair(X6,X7)
& in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) )
& X3 = X5
& ? [X8,X9] :
( X5 = ordered_pair(X8,X9)
& in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1) ) )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5,X6] :
( ordered_pair(X5,X6) = X3
& in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0) )
& X2 = X4
& ? [X7,X8] :
( ordered_pair(X7,X8) = X4
& in(ordered_pair(apply(X1,X7),apply(X1,X8)),X0) ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( sK8(X0,X1) != sK9(X0,X1)
& sK7(X0,X1) = sK8(X0,X1)
& sK8(X0,X1) = ordered_pair(sK10(X0,X1),sK11(X0,X1))
& in(ordered_pair(apply(X1,sK10(X0,X1)),apply(X1,sK11(X0,X1))),X0)
& sK7(X0,X1) = sK9(X0,X1)
& sK9(X0,X1) = ordered_pair(sK12(X0,X1),sK13(X0,X1))
& in(ordered_pair(apply(X1,sK12(X0,X1)),apply(X1,sK13(X0,X1))),X0) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1)),skolemize(X6,sK11(X0,X1)),skolemize(X7,sK12(X0,X1)),skolemize(X8,sK13(X0,X1))],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( ( in(X11,X10)
| ! [X12] :
( ~ in(X12,cartesian_product2(X0,X0))
| X11 != X12
| ! [X13,X14] :
( ordered_pair(X13,X14) != X11
| ~ in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) ) )
& ( ? [X12] :
( in(X12,cartesian_product2(X0,X0))
& X11 = X12
& ? [X13,X14] :
( ordered_pair(X13,X14) = X11
& in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1) ) )
| ~ in(X11,X10) ) )
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f30]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(X5,cartesian_product2(X0,X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) ) ) )
& ( ? [X8] :
( in(X8,cartesian_product2(X0,X0))
& X4 = X8
& ? [X9,X10] :
( ordered_pair(X9,X10) = X4
& in(ordered_pair(apply(X2,X9),apply(X2,X10)),X1) ) )
| ~ in(X4,X3) ) )
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK14(X0,X1,X2))
| ! [X5] :
( ~ in(X5,cartesian_product2(X0,X0))
| X4 != X5
| ! [X6,X7] :
( ordered_pair(X6,X7) != X4
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1) ) ) )
& ( ( in(sK15(X0,X1,X2,X4),cartesian_product2(X0,X0))
& sK15(X0,X1,X2,X4) = X4
& ordered_pair(sK16(X1,X2,X4),sK17(X1,X2,X4)) = X4
& in(ordered_pair(apply(X2,sK16(X1,X2,X4)),apply(X2,sK17(X1,X2,X4))),X1) )
| ~ in(X4,sK14(X0,X1,X2)) ) )
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X8,sK15(X0,X1,X2,X4)),skolemize(X9,sK16(X1,X2,X4)),skolemize(X10,sK17(X1,X2,X4))],[f39]) ).
fof(f45,plain,
function(sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
relation(sK3),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
relation(sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
! [X3] :
( in(ordered_pair(apply(sK3,sK5(X3)),apply(sK3,sK6(X3))),sK2)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
! [X3] :
( sK4(X3) = ordered_pair(sK5(X3),sK6(X3))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
! [X3] :
( in(sK4(X3),cartesian_product2(sK1,sK1))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK4(X3)
| ~ in(sK4(X3),cartesian_product2(sK1,sK1))
| ~ in(ordered_pair(apply(sK3,X5),apply(sK3,X6)),sK2)
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] :
( sK7(X0,X1) = sK9(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0,X1] :
( sK7(X0,X1) = sK8(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X0,X1] :
( sK8(X0,X1) != sK9(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(apply(X2,sK16(X1,X2,X4)),apply(X2,sK17(X1,X2,X4))),X1)
| ~ in(X4,sK14(X0,X1,X2))
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f60,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK16(X1,X2,X4),sK17(X1,X2,X4)) = X4
| ~ in(X4,sK14(X0,X1,X2))
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f61,plain,
! [X2,X0,X1,X4] :
( sK15(X0,X1,X2,X4) = X4
| ~ in(X4,sK14(X0,X1,X2))
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( in(sK15(X0,X1,X2,X4),cartesian_product2(X0,X0))
| ~ in(X4,sK14(X0,X1,X2))
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK14(X0,X1,X2))
| ~ in(X5,cartesian_product2(X0,X0))
| X4 != X5
| ordered_pair(X6,X7) != X4
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(X5,sK14(X0,X1,X2))
| ~ in(X5,cartesian_product2(X0,X0))
| ordered_pair(X6,X7) != X5
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f75,plain,
! [X2,X0,X1,X6,X7] :
( in(ordered_pair(X6,X7),sK14(X0,X1,X2))
| ~ in(ordered_pair(X6,X7),cartesian_product2(X0,X0))
| ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| sP0(X1,X2)
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f74]) ).
fof(f84,plain,
! [X0,X1] :
( sK7(X0,X1) != sK8(X0,X1)
| ~ sP0(X0,X1)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f58,f54]) ).
fof(f85,plain,
! [X0,X1] :
( sK7(X0,X1) != sK8(X0,X1)
| ~ sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f86,plain,
! [X0,X1] : ~ sP0(X0,X1),
inference(forward_subsumption_resolution,[],[f85,f57]) ).
fof(f89,plain,
! [X2,X0,X1,X4] :
( sK15(X0,X1,X2,X4) = X4
| ~ in(X4,sK14(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f61,f86]) ).
fof(f90,plain,
! [X2,X0,X1,X4] :
( in(sK15(X0,X1,X2,X4),cartesian_product2(X0,X0))
| ~ in(X4,sK14(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f62,f86]) ).
fof(f92,plain,
! [X2,X3,X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sK14(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X0,sK14(X1,X2,X3))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(superposition,[],[f90,f89]) ).
fof(f93,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK14(X1,X2,X3))
| in(X0,cartesian_product2(X1,X1))
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f95,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK16(X1,X2,X4),sK17(X1,X2,X4)) = X4
| ~ in(X4,sK14(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f60,f86]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4] :
( sK4(X3) != X0
| ~ in(sK4(X3),cartesian_product2(sK1,sK1))
| ~ in(ordered_pair(apply(sK3,sK16(X1,X2,X0)),apply(sK3,sK17(X1,X2,X0))),sK2)
| ~ in(sK4(X3),X3)
| ~ in(X0,sK14(X4,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(superposition,[],[f51,f95]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(apply(sK3,sK16(X1,X2,sK4(X0))),apply(sK3,sK17(X1,X2,sK4(X0)))),sK2)
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X3,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f98]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( in(ordered_pair(apply(X2,sK16(X1,X2,X4)),apply(X2,sK17(X1,X2,X4))),X1)
| ~ in(X4,sK14(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f59,f86]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(X1,sK2,sK3))
| ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X2,sK2,sK3))
| ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3) ),
inference(resolution,[],[f100,f99]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(X1,sK2,sK3))
| ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X2,sK2,sK3)) ),
inference(duplicate_literal_removal,[],[f103]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(X1,sK2,sK3))
| ~ relation(sK3)
| ~ function(sK3)
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X2,sK2,sK3)) ),
inference(forward_subsumption_resolution,[],[f107,f47]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(X1,sK2,sK3))
| ~ function(sK3)
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X2,sK2,sK3)) ),
inference(forward_subsumption_resolution,[],[f108,f46]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0),sK14(X2,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),sK14(X1,sK2,sK3)) ),
inference(forward_subsumption_resolution,[],[f109,f45]) ).
fof(f111,plain,
! [X2,X0,X1,X6,X7] :
( ~ in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X0,X0))
| in(ordered_pair(X6,X7),sK14(X0,X1,X2))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f75,f86]) ).
fof(f114,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK14(X1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(sK1,sK1))
| ~ in(sK4(X0),X0) ),
inference(factoring,[],[f110]) ).
fof(f117,plain,
! [X0] :
( ~ in(sK4(sK14(X0,sK2,sK3)),sK14(X0,sK2,sK3))
| ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(sK1,sK1)) ),
inference(factoring,[],[f114]) ).
fof(f119,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X1))
| in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,sK2,sK3))
| ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3)
| in(sK4(X0),X0) ),
inference(resolution,[],[f111,f48]) ).
fof(f122,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X1))
| in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,sK2,sK3))
| ~ relation(sK3)
| ~ function(sK3)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f119,f47]) ).
fof(f123,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X1))
| in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,sK2,sK3))
| ~ function(sK3)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f122,f46]) ).
fof(f124,plain,
! [X0,X1] :
( in(ordered_pair(sK5(X0),sK6(X0)),sK14(X1,sK2,sK3))
| ~ in(ordered_pair(sK5(X0),sK6(X0)),cartesian_product2(X1,X1))
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f123,f45]) ).
fof(f131,plain,
! [X0,X1] :
( in(sK4(X0),sK14(X1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(X1,X1))
| in(sK4(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f124,f49]) ).
fof(f132,plain,
! [X0,X1] :
( in(sK4(X0),sK14(X1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(X1,X1))
| in(sK4(X0),X0) ),
inference(duplicate_literal_removal,[],[f131]) ).
fof(f140,plain,
! [X0] :
( ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(sK1,sK1))
| ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(X0,X0))
| in(sK4(sK14(X0,sK2,sK3)),sK14(X0,sK2,sK3)) ),
inference(resolution,[],[f117,f132]) ).
fof(f142,plain,
! [X0] :
( in(sK4(sK14(X0,sK2,sK3)),sK14(X0,sK2,sK3))
| ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(X0,X0)) ),
inference(forward_subsumption_resolution,[],[f140,f50]) ).
fof(f143,plain,
! [X0] :
( ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(sK1,sK1))
| ~ in(sK4(sK14(X0,sK2,sK3)),cartesian_product2(X0,X0)) ),
inference(resolution,[],[f142,f117]) ).
fof(f153,plain,
~ in(sK4(sK14(sK1,sK2,sK3)),cartesian_product2(sK1,sK1)),
inference(factoring,[],[f143]) ).
fof(f162,plain,
in(sK4(sK14(sK1,sK2,sK3)),sK14(sK1,sK2,sK3)),
inference(resolution,[],[f153,f50]) ).
fof(f169,plain,
( in(sK4(sK14(sK1,sK2,sK3)),cartesian_product2(sK1,sK1))
| ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3) ),
inference(resolution,[],[f162,f93]) ).
fof(f171,plain,
( ~ relation(sK2)
| ~ relation(sK3)
| ~ function(sK3) ),
inference(forward_subsumption_resolution,[],[f169,f153]) ).
fof(f174,plain,
( ~ relation(sK3)
| ~ function(sK3) ),
inference(forward_subsumption_resolution,[],[f171,f47]) ).
fof(f175,plain,
~ function(sK3),
inference(forward_subsumption_resolution,[],[f174,f46]) ).
fof(f176,plain,
$false,
inference(forward_subsumption_resolution,[],[f175,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU277+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 04:25:10 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.23/1.32 % (2023632)Detected formulas, will run a generic FOF schedule.
% 2.23/1.32 % (2023638)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=534047372:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.23/1.32 % (2023641)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=690199846:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.23/1.32 % (2023642)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=58424763:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.23/1.32 % (2023639)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=918633095:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.23/1.32 % (2023640)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4183825762:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.23/1.32 % (2023637)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=3732109298:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.23/1.32 % (2023643)dis-21_1_sil=8000:lcm=predicate:random_seed=2581111935: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)
% 2.23/1.32 % (2023640)Refutation not found, incomplete strategy
% 2.23/1.32 % (2023640)------------------------------
% 2.23/1.32 % (2023640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.32 % (2023640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.32 % (2023640)CaDiCaL version: 2.1.3
% 2.23/1.32 % (2023640)Termination reason: Refutation not found, incomplete strategy
% 2.23/1.32 % (2023640)Time elapsed: 0.004 s
% 2.23/1.32 % (2023640)Peak memory usage: 88 MB
% 2.23/1.32 % (2023640)Instructions burned: 4 (million)
% 2.23/1.32 % (2023641)First to succeed.
% 2.23/1.32 % (2023641)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2023632"
% 2.23/1.32 % (2023642)Refutation not found, incomplete strategy
% 2.23/1.32 % (2023642)------------------------------
% 2.23/1.32 % (2023642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.32 % (2023642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.32 % (2023642)CaDiCaL version: 2.1.3
% 2.23/1.32 % (2023642)Termination reason: Refutation not found, incomplete strategy
% 2.23/1.32 % (2023642)Time elapsed: 0.010 s
% 2.23/1.32 % (2023642)Peak memory usage: 88 MB
% 2.23/1.32 % (2023642)Instructions burned: 13 (million)
% 2.23/1.32 % (2023643)Refutation not found, incomplete strategy
% 2.23/1.32 % (2023643)------------------------------
% 2.23/1.32 % (2023643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/1.32 % (2023643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/1.32 % (2023643)CaDiCaL version: 2.1.3
% 2.23/1.32 % (2023643)Termination reason: Refutation not found, incomplete strategy
% 2.23/1.32 % (2023643)Time elapsed: 0.024 s
% 2.23/1.32 % (2023643)Peak memory usage: 89 MB
% 2.23/1.32 % (2023643)Instructions burned: 39 (million)
% 2.23/1.32 % (2023640)------------------------------
% 2.23/1.32 % (2023640)------------------------------
% 2.23/1.32 % (2023642)------------------------------
% 2.23/1.32 % (2023642)------------------------------
% 2.23/1.32 % (2023643)------------------------------
% 2.23/1.32 % (2023643)------------------------------
% 2.23/1.32 % (2023641)Refutation found. Thanks to Tanya!
% 2.23/1.32 % SZS status Theorem for theBenchmark
% 2.23/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.52 % (2023641)------------------------------
% 3.75/1.52 % (2023641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.52 % (2023641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.52 % (2023641)CaDiCaL version: 2.1.3
% 3.75/1.52 % (2023641)Termination reason: Refutation
% 3.75/1.52 % (2023641)Time elapsed: 0.008 s
% 3.75/1.52 % (2023641)Peak memory usage: 88 MB
% 3.75/1.52 % (2023641)Instructions burned: 11 (million)
% 3.75/1.52 % (2023641)------------------------------
% 3.75/1.52 % (2023641)------------------------------
% 3.75/1.52 % (2023632)Success in time 0.443 s
% 3.75/1.52 % Vampire exiting
%------------------------------------------------------------------------------