%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU272+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 : n016.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 12:48:06 PM UTC 2026
% Result : Theorem 2.51s 1.28s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 129 ( 11 unt; 10 def)
% Number of atoms : 559 ( 97 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 705 ( 275 ~; 285 |; 121 &)
% ( 15 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 260 ( 0 sgn 192 !; 68 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e8_6__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ordinal(X1)
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f15,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X0) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,succ(X1))
& X4 = X3
& ? [X7] :
( ordinal(X7)
& X3 = X7
& in(X7,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e8_6__wellord2__1) ).
fof(f16,plain,
! [X0,X1] :
( ordinal(X1)
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X0) ) )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,succ(X1))
& X8 = X9
& ? [X10] :
( ordinal(X10)
& X8 = X10
& in(X10,X0) ) ) ) ) ),
inference(rectify,[],[f15]) ).
fof(f18,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) ) )
& ordinal(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,succ(X1))
& X8 = X9
& ? [X10] :
( ordinal(X10)
& X8 = X10
& in(X10,X0) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X0) ) )
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,succ(X1))
& X8 = X9
& ? [X10] :
( ordinal(X10)
& X8 = X10
& in(X10,X0) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X0) ) )
| ~ ordinal(X1) ),
inference(flattening,[],[f25]) ).
fof(f27,definition,
! [X4,X0] :
( ? [X6] :
( ordinal(X6)
& X4 = X6
& in(X6,X0) )
| ~ sP0(X4,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f28,definition,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,succ(X1))
& X8 = X9
& ? [X10] :
( ordinal(X10)
& X8 = X10
& in(X10,X0) ) ) )
| sP1(X0)
| ~ ordinal(X1) ),
inference(definition_folding,[],[f26,f28,f27]) ).
fof(f30,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) )
| in(X3,X2) ) )
& ordinal(X1) ),
inference(nnf_transformation,[],[f18]) ).
fof(f31,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ( in(X3,succ(X1))
& ? [X4] :
( ordinal(X4)
& X3 = X4
& in(X4,X0) ) )
| in(X3,X2) ) )
& ordinal(X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,succ(X1))
| ! [X4] :
( ~ ordinal(X4)
| X3 != X4
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ( in(X3,succ(X1))
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) ) )
| in(X3,X2) ) )
& ordinal(X1) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
( ! [X2] :
( ( ~ in(sK4(X2),succ(sK3))
| ! [X4] :
( ~ ordinal(X4)
| sK4(X2) != X4
| ~ in(X4,sK2) )
| ~ in(sK4(X2),X2) )
& ( ( in(sK4(X2),succ(sK3))
& ordinal(sK5(X2))
& sK4(X2) = sK5(X2)
& in(sK5(X2),sK2) )
| in(sK4(X2),X2) ) )
& ordinal(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X5,sK5(X2))],[f32]) ).
fof(f38,plain,
! [X0] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( ordinal(X5)
& X3 = X5
& in(X5,X0) )
& X2 = X4
& sP0(X4,X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f28]) ).
fof(f39,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& X1 = X2
& ? [X4] :
( ordinal(X4)
& X2 = X4
& in(X4,X0) )
& X1 = X3
& sP0(X3,X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ( sK11(X0) != sK12(X0)
& sK10(X0) = sK11(X0)
& ordinal(sK13(X0))
& sK11(X0) = sK13(X0)
& in(sK13(X0),X0)
& sK10(X0) = sK12(X0)
& sP0(sK12(X0),X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0)),skolemize(X3,sK12(X0)),skolemize(X4,sK13(X0))],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ~ in(X9,succ(X1))
| X8 != X9
| ! [X10] :
( ~ ordinal(X10)
| X8 != X10
| ~ in(X10,X0) ) ) )
& ( ? [X9] :
( in(X9,succ(X1))
& X8 = X9
& ? [X10] :
( ordinal(X10)
& X8 = X10
& in(X10,X0) ) )
| ~ in(X8,X7) ) )
| sP1(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,succ(X1))
| X3 != X4
| ! [X5] :
( ~ ordinal(X5)
| X3 != X5
| ~ in(X5,X0) ) ) )
& ( ? [X6] :
( in(X6,succ(X1))
& X3 = X6
& ? [X7] :
( ordinal(X7)
& X3 = X7
& in(X7,X0) ) )
| ~ in(X3,X2) ) )
| sP1(X0)
| ~ ordinal(X1) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK15(X0,X1))
| ! [X4] :
( ~ in(X4,succ(X1))
| X3 != X4
| ! [X5] :
( ~ ordinal(X5)
| X3 != X5
| ~ in(X5,X0) ) ) )
& ( ( in(sK16(X0,X1,X3),succ(X1))
& sK16(X0,X1,X3) = X3
& ordinal(sK17(X0,X3))
& sK17(X0,X3) = X3
& in(sK17(X0,X3),X0) )
| ~ in(X3,sK15(X0,X1)) ) )
| sP1(X0)
| ~ ordinal(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X6,sK16(X0,X1,X3)),skolemize(X7,sK17(X0,X3))],[f45]) ).
fof(f47,plain,
ordinal(sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X2] :
( in(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X2] :
( in(sK4(X2),X2)
| sK4(X2) = sK5(X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X2] :
( ordinal(sK5(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X2] :
( in(sK4(X2),succ(sK3))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
! [X2,X4] :
( ~ in(sK4(X2),succ(sK3))
| ~ ordinal(X4)
| sK4(X2) != X4
| ~ in(X4,sK2)
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f75,plain,
! [X0] :
( sK10(X0) = sK12(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
! [X0] :
( sK10(X0) = sK11(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f80,plain,
! [X0] :
( sK11(X0) != sK12(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f84,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK15(X0,X1))
| in(sK17(X0,X3),X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK15(X0,X1))
| sK17(X0,X3) = X3
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f86,plain,
! [X3,X0,X1] :
( ordinal(sK17(X0,X3))
| ~ in(X3,sK15(X0,X1))
| sP1(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f87,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK15(X0,X1))
| sK16(X0,X1,X3) = X3
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK15(X0,X1))
| in(sK16(X0,X1,X3),succ(X1))
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f89,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK15(X0,X1))
| ~ in(X4,succ(X1))
| X3 != X4
| ~ ordinal(X5)
| X3 != X5
| ~ in(X5,X0)
| sP1(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f90,plain,
! [X2] :
( ~ ordinal(sK4(X2))
| ~ in(sK4(X2),succ(sK3))
| ~ in(sK4(X2),sK2)
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f52]) ).
fof(f91,plain,
! [X0,X1,X4,X5] :
( in(X4,sK15(X0,X1))
| ~ in(X4,succ(X1))
| ~ ordinal(X5)
| X4 != X5
| ~ in(X5,X0)
| sP1(X0)
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f89]) ).
fof(f92,plain,
! [X0,X1,X5] :
( sP1(X0)
| ~ in(X5,succ(X1))
| ~ ordinal(X5)
| ~ in(X5,X0)
| in(X5,sK15(X0,X1))
| ~ ordinal(X1) ),
inference(equality_resolution,[],[f91]) ).
fof(f135,plain,
! [X0] :
( sK11(X0) = sK12(X0)
| ~ sP1(X0)
| ~ sP1(X0) ),
inference(superposition,[],[f75,f79]) ).
fof(f136,plain,
! [X0] :
( sK11(X0) = sK12(X0)
| ~ sP1(X0) ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f140,plain,
! [X0] : ~ sP1(X0),
inference(forward_subsumption_resolution,[],[f136,f80]) ).
fof(f142,plain,
! [X2,X0,X1] :
( in(X0,sK15(X2,X1))
| ~ ordinal(X0)
| ~ in(X0,X2)
| ~ in(X0,succ(X1))
| ~ ordinal(X1) ),
inference(resolution,[],[f140,f92]) ).
fof(f143,plain,
! [X2,X0,X1] :
( in(sK16(X1,X2,X0),succ(X2))
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(resolution,[],[f140,f88]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sK16(X1,X2,X0) = X0
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(resolution,[],[f140,f87]) ).
fof(f145,plain,
! [X2,X0,X1] :
( sK17(X1,X0) = X0
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(resolution,[],[f140,f85]) ).
fof(f146,plain,
! [X2,X0,X1] :
( in(sK17(X1,X0),X1)
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(resolution,[],[f140,f84]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( ordinal(X0)
| ~ in(X0,sK15(X1,X2))
| sP1(X1)
| ~ ordinal(X2)
| ~ in(X0,sK15(X1,X3))
| ~ ordinal(X3) ),
inference(superposition,[],[f86,f145]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( ordinal(X0)
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2)
| ~ in(X0,sK15(X1,X3))
| ~ ordinal(X3) ),
inference(forward_subsumption_resolution,[],[f147,f140]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK15(X1,X2))
| in(X0,X1)
| ~ ordinal(X2)
| ~ in(X0,sK15(X1,X3))
| ~ ordinal(X3) ),
inference(superposition,[],[f146,f145]) ).
fof(f153,plain,
! [X2,X0,X1] :
( in(X0,succ(X2))
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2)
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(superposition,[],[f143,f144]) ).
fof(f154,plain,
! [X2,X0,X1] :
( in(X0,succ(X2))
| ~ in(X0,sK15(X1,X2))
| ~ ordinal(X2) ),
inference(duplicate_literal_removal,[],[f153]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(X0),sK2)
| ~ ordinal(X2)
| ~ in(sK4(X0),sK15(X1,X3))
| ~ ordinal(X3)
| ~ in(sK4(X0),succ(sK3))
| ~ in(sK4(X0),sK15(X1,X2))
| ~ in(sK4(X0),X0) ),
inference(resolution,[],[f148,f90]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ in(sK4(sK15(X0,X1)),sK15(X0,X2))
| ~ ordinal(X1)
| in(sK4(sK15(X0,X1)),X0)
| ~ ordinal(X2)
| sK4(sK15(X0,X1)) = sK5(sK15(X0,X1)) ),
inference(resolution,[],[f150,f49]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ in(X0,sK15(X1,X2))
| in(X0,X1)
| ~ ordinal(X2)
| ~ ordinal(X2) ),
inference(factoring,[],[f150]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ in(X0,sK15(X1,X2))
| in(X0,X1)
| ~ ordinal(X2) ),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f183,plain,
! [X0,X1] :
( ~ ordinal(X0)
| in(sK4(sK15(X1,X0)),X1)
| ~ ordinal(X0)
| sK4(sK15(X1,X0)) = sK5(sK15(X1,X0))
| sK4(sK15(X1,X0)) = sK5(sK15(X1,X0)) ),
inference(resolution,[],[f175,f49]) ).
fof(f186,plain,
! [X0,X1] :
( in(sK4(sK15(X1,X0)),X1)
| ~ ordinal(X0)
| sK4(sK15(X1,X0)) = sK5(sK15(X1,X0)) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( ~ ordinal(X0)
| ~ in(sK4(sK15(sK2,X1)),sK15(X2,X3))
| ~ ordinal(X3)
| ~ in(sK4(sK15(sK2,X1)),succ(sK3))
| ~ in(sK4(sK15(sK2,X1)),sK15(X2,X0))
| ~ in(sK4(sK15(sK2,X1)),sK15(sK2,X1))
| ~ ordinal(X1)
| sK4(sK15(sK2,X1)) = sK5(sK15(sK2,X1)) ),
inference(resolution,[],[f163,f186]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(sK15(sK2,X1)),succ(sK3))
| ~ in(sK4(sK15(sK2,X1)),sK15(X2,X3))
| ~ ordinal(X3)
| ~ ordinal(X0)
| ~ in(sK4(sK15(sK2,X1)),sK15(X2,X0))
| ~ ordinal(X1)
| sK4(sK15(sK2,X1)) = sK5(sK15(sK2,X1)) ),
inference(forward_subsumption_resolution,[],[f195,f49]) ).
fof(f269,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK4(sK15(sK2,X0)),sK15(X1,X2))
| ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(sK4(sK15(sK2,X0)),sK15(X1,X3))
| ~ ordinal(X0)
| sK4(sK15(sK2,X0)) = sK5(sK15(sK2,X0))
| ~ in(sK4(sK15(sK2,X0)),sK15(X4,sK3))
| ~ ordinal(sK3) ),
inference(resolution,[],[f197,f154]) ).
fof(f270,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK4(sK15(sK2,X0)),sK15(X4,sK3))
| ~ ordinal(X2)
| ~ ordinal(X3)
| ~ in(sK4(sK15(sK2,X0)),sK15(X1,X3))
| ~ ordinal(X0)
| sK4(sK15(sK2,X0)) = sK5(sK15(sK2,X0))
| ~ in(sK4(sK15(sK2,X0)),sK15(X1,X2)) ),
inference(forward_subsumption_resolution,[],[f269,f47]) ).
fof(f283,definition,
( spl18_6
<=> sK4(sK15(sK2,sK3)) = sK5(sK15(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f285,plain,
( sK4(sK15(sK2,sK3)) = sK5(sK15(sK2,sK3))
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f287,definition,
( spl18_7
<=> ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X0))
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f288,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X1))
| ~ ordinal(X1)
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X0))
| ~ ordinal(X0) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f293,plain,
( in(sK4(sK15(sK2,sK3)),sK2)
| in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3))
| ~ spl18_6 ),
inference(superposition,[],[f48,f285]) ).
fof(f294,plain,
( ordinal(sK4(sK15(sK2,sK3)))
| in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3))
| ~ spl18_6 ),
inference(superposition,[],[f50,f285]) ).
fof(f296,definition,
( spl18_8
<=> in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f297,plain,
( ~ in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3))
| spl18_8 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3))
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f300,definition,
( spl18_9
<=> ordinal(sK4(sK15(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
fof(f303,plain,
( spl18_8
| spl18_9
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f294,f283,f300,f296]) ).
fof(f305,definition,
( spl18_10
<=> in(sK4(sK15(sK2,sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
fof(f307,plain,
( in(sK4(sK15(sK2,sK3)),sK2)
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f308,plain,
( spl18_8
| spl18_10
| ~ spl18_6 ),
inference(avatar_split_clause,[],[f293,f283,f305,f296]) ).
fof(f322,plain,
( ! [X0,X1] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X0,X1))
| ~ ordinal(X1)
| ~ ordinal(X1) )
| ~ spl18_7 ),
inference(factoring,[],[f288]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X0,X1))
| ~ ordinal(X1) )
| ~ spl18_7 ),
inference(duplicate_literal_removal,[],[f322]) ).
fof(f328,definition,
( spl18_12
<=> ! [X2,X1] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X1,X2))
| ~ ordinal(X2) ) ),
introduced(definition,[new_symbols(definition,[spl18_12])],[avatar_definition]) ).
fof(f329,plain,
( ! [X2,X1] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X1,X2))
| ~ ordinal(X2) )
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f356,plain,
( spl18_12
| ~ spl18_7 ),
inference(avatar_split_clause,[],[f323,f287,f328]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X1))
| ~ ordinal(sK3)
| sK4(sK15(sK2,sK3)) = sK5(sK15(sK2,sK3))
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X0)) )
| ~ spl18_8 ),
inference(resolution,[],[f298,f270]) ).
fof(f375,plain,
( in(sK4(sK15(sK2,sK3)),sK2)
| ~ ordinal(sK3)
| ~ spl18_8 ),
inference(resolution,[],[f298,f181]) ).
fof(f379,plain,
( in(sK4(sK15(sK2,sK3)),sK2)
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f375,f47]) ).
fof(f381,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X1))
| sK4(sK15(sK2,sK3)) = sK5(sK15(sK2,sK3))
| ~ in(sK4(sK15(sK2,sK3)),sK15(X2,X0)) )
| ~ spl18_8 ),
inference(forward_subsumption_resolution,[],[f372,f47]) ).
fof(f382,plain,
( spl18_10
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f379,f296,f305]) ).
fof(f384,plain,
( spl18_6
| spl18_7
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f381,f296,f287,f283]) ).
fof(f387,plain,
( sK4(sK15(sK2,sK3)) = sK5(sK15(sK2,sK3))
| spl18_8 ),
inference(resolution,[],[f297,f49]) ).
fof(f388,plain,
( ~ ordinal(sK4(sK15(sK2,sK3)))
| ~ in(sK4(sK15(sK2,sK3)),sK2)
| ~ in(sK4(sK15(sK2,sK3)),succ(sK3))
| ~ ordinal(sK3)
| spl18_8 ),
inference(resolution,[],[f297,f142]) ).
fof(f389,plain,
( spl18_6
| spl18_8 ),
inference(avatar_split_clause,[],[f387,f296,f283]) ).
fof(f390,plain,
( ~ ordinal(sK4(sK15(sK2,sK3)))
| ~ in(sK4(sK15(sK2,sK3)),sK2)
| ~ in(sK4(sK15(sK2,sK3)),succ(sK3))
| spl18_8 ),
inference(forward_subsumption_resolution,[],[f388,f47]) ).
fof(f392,definition,
( spl18_17
<=> in(sK4(sK15(sK2,sK3)),succ(sK3)) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
fof(f394,plain,
( ~ in(sK4(sK15(sK2,sK3)),succ(sK3))
| spl18_17 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f395,plain,
( ~ spl18_17
| ~ spl18_10
| ~ spl18_9
| spl18_8 ),
inference(avatar_split_clause,[],[f390,f296,f300,f305,f392]) ).
fof(f402,definition,
( spl18_18
<=> ! [X0] : ~ in(sK4(sK15(sK2,sK3)),sK15(X0,sK3)) ),
introduced(definition,[new_symbols(definition,[spl18_18])],[avatar_definition]) ).
fof(f403,plain,
( ! [X0] : ~ in(sK4(sK15(sK2,sK3)),sK15(X0,sK3))
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ in(sK4(sK15(sK2,sK3)),sK15(X1,X2))
| ~ ordinal(X2)
| ~ in(sK4(sK15(sK2,sK3)),succ(sK3))
| ~ in(sK4(sK15(sK2,sK3)),sK15(X1,X0))
| ~ in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3)) )
| ~ spl18_10 ),
inference(resolution,[],[f307,f163]) ).
fof(f434,plain,
( ! [X0] :
( ~ in(sK4(sK15(sK2,sK3)),sK15(X0,sK3))
| ~ ordinal(sK3) )
| spl18_17 ),
inference(resolution,[],[f394,f154]) ).
fof(f435,plain,
( ! [X0] : ~ in(sK4(sK15(sK2,sK3)),sK15(X0,sK3))
| spl18_17 ),
inference(forward_subsumption_resolution,[],[f434,f47]) ).
fof(f438,plain,
( spl18_18
| spl18_17 ),
inference(avatar_split_clause,[],[f435,f392,f402]) ).
fof(f441,plain,
( ~ spl18_8
| ~ spl18_17
| spl18_7
| ~ spl18_10 ),
inference(avatar_split_clause,[],[f414,f305,f287,f392,f296]) ).
fof(f445,plain,
( in(sK4(sK15(sK2,sK3)),sK15(sK2,sK3))
| spl18_17 ),
inference(resolution,[],[f394,f51]) ).
fof(f448,plain,
( spl18_8
| spl18_17 ),
inference(avatar_split_clause,[],[f445,f392,f296]) ).
fof(f473,plain,
( $false
| ~ spl18_8
| ~ spl18_18 ),
inference(resolution,[],[f403,f298]) ).
fof(f476,plain,
( ~ spl18_8
| ~ spl18_18 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f531,plain,
( ~ ordinal(sK3)
| ~ spl18_8
| ~ spl18_12 ),
inference(resolution,[],[f329,f298]) ).
fof(f535,plain,
( $false
| ~ spl18_8
| ~ spl18_12 ),
inference(forward_subsumption_resolution,[],[f531,f47]) ).
fof(f536,plain,
( ~ spl18_8
| ~ spl18_12 ),
inference(avatar_contradiction_clause,[],[f535]) ).
cnf(s4,plain,
( ~ spl18_6
| spl18_8
| spl18_9 ),
inference(sat_conversion,[],[f303]) ).
cnf(s5,plain,
( ~ spl18_6
| spl18_8
| spl18_10 ),
inference(sat_conversion,[],[f308]) ).
cnf(s9,plain,
( ~ spl18_7
| spl18_12 ),
inference(sat_conversion,[],[f356]) ).
cnf(s16,plain,
( ~ spl18_8
| spl18_10 ),
inference(sat_conversion,[],[f382]) ).
cnf(s18,plain,
( spl18_6
| spl18_7
| ~ spl18_8 ),
inference(sat_conversion,[],[f384]) ).
cnf(s20,plain,
( spl18_6
| spl18_8 ),
inference(sat_conversion,[],[f389]) ).
cnf(s21,plain,
( spl18_8
| ~ spl18_9
| ~ spl18_10
| ~ spl18_17 ),
inference(sat_conversion,[],[f395]) ).
cnf(s27,plain,
( spl18_17
| spl18_18 ),
inference(sat_conversion,[],[f438]) ).
cnf(s28,plain,
( spl18_7
| ~ spl18_8
| ~ spl18_10
| ~ spl18_17 ),
inference(sat_conversion,[],[f441]) ).
cnf(s31,plain,
( spl18_8
| spl18_17 ),
inference(sat_conversion,[],[f448]) ).
cnf(s34,plain,
( ~ spl18_8
| ~ spl18_18 ),
inference(sat_conversion,[],[f476]) ).
cnf(s39,plain,
( ~ spl18_8
| ~ spl18_12 ),
inference(sat_conversion,[],[f536]) ).
cnf(s40,plain,
( spl18_6
| ~ spl18_8 ),
inference(rat,[],[s9,s39,s18]) ).
cnf(s41,plain,
spl18_6,
inference(rat,[],[s40,s20]) ).
cnf(s42,plain,
spl18_8,
inference(rat,[],[s21,s4,s5,s31,s41]) ).
cnf(s43,plain,
~ spl18_12,
inference(rat,[],[s39,s42]) ).
cnf(s44,plain,
~ spl18_18,
inference(rat,[],[s34,s42]) ).
cnf(s46,plain,
spl18_10,
inference(rat,[],[s16,s42]) ).
cnf(s47,plain,
~ spl18_7,
inference(rat,[],[s9,s43]) ).
cnf(s48,plain,
spl18_17,
inference(rat,[],[s27,s44]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s28,s48,s42,s46,s47]) ).
fof(f537,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU272+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:30:33 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.51/1.28 % (3258747)Detected formulas, will run a generic FOF schedule.
% 2.51/1.28 % (3258754)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=1791554002:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.28 % (3258757)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2133481711:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.28 % (3258756)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3437724804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.28 % (3258755)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=371159093:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.28 % (3258752)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=2208336243:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.28 % (3258753)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=4065452143:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.28 % (3258758)dis-21_1_sil=8000:lcm=predicate:random_seed=175195533: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)
% 2.51/1.28 % (3258757)First to succeed.
% 2.51/1.28 % (3258757)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3258747"
% 2.51/1.28 % (3258755)Instruction limit reached!
% 2.51/1.28 % (3258755)------------------------------
% 2.51/1.28 % (3258755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.28 % (3258755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.28 % (3258755)CaDiCaL version: 2.1.3
% 2.51/1.28 % (3258755)Termination reason: Instruction limit
% 2.51/1.28 % (3258755)Termination phase: Saturation
% 2.51/1.28 % (3258755)Time elapsed: 0.068 s
% 2.51/1.28 % (3258755)Peak memory usage: 89 MB
% 2.51/1.28 % (3258755)Instructions burned: 109 (million)
% 2.51/1.28 % (3258756)Instruction limit reached!
% 2.51/1.28 % (3258756)------------------------------
% 2.51/1.28 % (3258756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.28 % (3258756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.28 % (3258756)CaDiCaL version: 2.1.3
% 2.51/1.28 % (3258756)Termination reason: Instruction limit
% 2.51/1.28 % (3258756)Termination phase: Saturation
% 2.51/1.28 % (3258756)Time elapsed: 0.074 s
% 2.51/1.28 % (3258756)Peak memory usage: 88 MB
% 2.51/1.28 % (3258756)Instructions burned: 120 (million)
% 2.51/1.28 % (3258758)Instruction limit reached!
% 2.51/1.28 % (3258758)------------------------------
% 2.51/1.28 % (3258758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.28 % (3258758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.28 % (3258758)CaDiCaL version: 2.1.3
% 2.51/1.28 % (3258758)Termination reason: Instruction limit
% 2.51/1.28 % (3258758)Termination phase: Saturation
% 2.51/1.28 % (3258758)Time elapsed: 0.076 s
% 2.51/1.28 % (3258758)Peak memory usage: 89 MB
% 2.51/1.28 % (3258758)Instructions burned: 129 (million)
% 2.51/1.28 % (3258766)lrs+10_1_sil=8000:sp=occurrence:random_seed=4041917086:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.51/1.28 % (3258767)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1851499602:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.51/1.28 % (3258768)lrs+1011_1_sil=32000:sp=occurrence:random_seed=188081523:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.51/1.28 % (3258768)Also succeeded, but the first one will report.
% 2.51/1.28 % (3258757)Refutation found. Thanks to Tanya!
% 2.51/1.28 % SZS status Theorem for theBenchmark
% 2.51/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.49 % (3258757)------------------------------
% 3.56/1.49 % (3258757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.49 % (3258757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.49 % (3258757)CaDiCaL version: 2.1.3
% 3.56/1.49 % (3258757)Termination reason: Refutation
% 3.56/1.49 % (3258757)Time elapsed: 0.023 s
% 3.56/1.49 % (3258757)Peak memory usage: 90 MB
% 3.56/1.49 % (3258757)Instructions burned: 30 (million)
% 3.56/1.49 % (3258757)------------------------------
% 3.56/1.49 % (3258757)------------------------------
% 3.56/1.49 % (3258747)Success in time 0.422 s
% 3.56/1.49 % Vampire exiting
%------------------------------------------------------------------------------