%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU183+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:17 PM UTC 2026
% Result : Theorem 2.82s 1.00s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 86 ( 23 unt; 5 def)
% Number of atoms : 296 ( 32 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 362 ( 152 ~; 151 |; 37 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-4 aty)
% Number of variables : 189 ( 0 sgn 167 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f30,conjecture,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f42,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f42]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ~ subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
& relation(X1) )
& relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f56,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK1(X0,X1)),X0)
| ~ in(sK1(X0,X1),X1) )
& ( in(ordered_pair(sK2(X0,X1),sK1(X0,X1)),X0)
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK3(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f59]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK4(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK5(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK4(X0,X1,X2),sK6(X0,X1,X2)),X0)
& in(ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),X1) )
| in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK7(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK7(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2)),skolemize(X6,sK6(X0,X1,X2)),skolemize(X10,sK7(X0,X1,X7,X8))],[f62]) ).
fof(f71,plain,
( ~ subset(relation_rng(relation_composition(sK14,sK15)),relation_rng(sK15))
& relation(sK15)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f48]) ).
fof(f73,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f75,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f76,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f77,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK3(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f78,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f81,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f82,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK7(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f108,plain,
relation(sK14),
inference(cnf_transformation,[],[f71]) ).
fof(f109,plain,
relation(sK15),
inference(cnf_transformation,[],[f71]) ).
fof(f110,plain,
~ subset(relation_rng(relation_composition(sK14,sK15)),relation_rng(sK15)),
inference(cnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f78,f81]) ).
fof(f119,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f77,f81]) ).
fof(f125,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK7(X0,X1,X7,X8),X8),singleton(sK7(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f81,f81]) ).
fof(f127,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f118]) ).
fof(f128,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| in(unordered_pair(unordered_pair(sK3(X0,X5),X5),singleton(sK3(X0,X5))),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f131,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK7(X0,X1,X7,X8),X8),singleton(sK7(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f132,definition,
sF16 = relation_composition(sK14,sK15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f133,plain,
relation_composition(sK14,sK15) = sF16,
inference(reorient_equations,[],[f132]) ).
fof(f134,definition,
sF17 = relation_rng(sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f135,plain,
relation_rng(sF16) = sF17,
inference(reorient_equations,[],[f134]) ).
fof(f136,definition,
sF18 = relation_rng(sK15),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f137,plain,
relation_rng(sK15) = sF18,
inference(reorient_equations,[],[f136]) ).
fof(f138,plain,
~ subset(sF17,sF18),
inference(definition_folding,[],[f110,f137,f135,f133]) ).
fof(f139,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK7(X0,X1,X7,X8),X8),singleton(sK7(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f131,f88]) ).
fof(f142,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(singleton(sK7(X0,X1,X7,X8)),unordered_pair(sK7(X0,X1,X7,X8),X8)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f139,f73]) ).
fof(f145,plain,
! [X0,X1,X8,X7] :
( in(unordered_pair(singleton(sK7(X0,X1,X7,X8)),unordered_pair(X8,sK7(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f142,f73]) ).
fof(f148,plain,
! [X0,X1,X8,X7] :
( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
| in(unordered_pair(singleton(sK7(X0,X1,X7,X8)),unordered_pair(X8,sK7(X0,X1,X7,X8))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f145,f73]) ).
fof(f176,plain,
in(sK0(sF17,sF18),sF17),
inference(resolution,[],[f75,f138]) ).
fof(f181,plain,
( relation(sF16)
| ~ relation(sK14)
| ~ relation(sK15) ),
inference(superposition,[],[f88,f133]) ).
fof(f182,plain,
( relation(sF16)
| ~ relation(sK15) ),
inference(forward_subsumption_resolution,[],[f181,f108]) ).
fof(f183,plain,
relation(sF16),
inference(forward_subsumption_resolution,[],[f182,f109]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) ),
inference(superposition,[],[f127,f73]) ).
fof(f226,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(X0,relation_rng(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f223,f73]) ).
fof(f233,plain,
! [X0] :
( ~ in(X0,sF17)
| in(unordered_pair(unordered_pair(sK3(sF16,X0),X0),singleton(sK3(sF16,X0))),sF16)
| ~ relation(sF16) ),
inference(superposition,[],[f128,f135]) ).
fof(f236,plain,
! [X0] :
( ~ in(X0,sF17)
| in(unordered_pair(unordered_pair(sK3(sF16,X0),X0),singleton(sK3(sF16,X0))),sF16) ),
inference(forward_subsumption_resolution,[],[f233,f183]) ).
fof(f238,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sF16,X0)),unordered_pair(sK3(sF16,X0),X0)),sF16)
| ~ in(X0,sF17) ),
inference(forward_demodulation,[],[f236,f73]) ).
fof(f240,plain,
! [X0] :
( in(unordered_pair(singleton(sK3(sF16,X0)),unordered_pair(X0,sK3(sF16,X0))),sF16)
| ~ in(X0,sF17) ),
inference(forward_demodulation,[],[f238,f73]) ).
fof(f297,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sF16)
| in(unordered_pair(singleton(sK7(sK14,sK15,X0,X1)),unordered_pair(X1,sK7(sK14,sK15,X0,X1))),sK15)
| ~ relation(sK15)
| ~ relation(sK14) ),
inference(superposition,[],[f148,f133]) ).
fof(f298,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sF16)
| in(unordered_pair(singleton(sK7(sK14,sK15,X0,X1)),unordered_pair(X1,sK7(sK14,sK15,X0,X1))),sK15)
| ~ relation(sK14) ),
inference(forward_subsumption_resolution,[],[f297,f109]) ).
fof(f299,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK7(sK14,sK15,X0,X1)),unordered_pair(X1,sK7(sK14,sK15,X0,X1))),sK15)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sF16) ),
inference(forward_subsumption_resolution,[],[f298,f108]) ).
fof(f495,plain,
! [X0,X1] :
( in(X0,relation_rng(sK15))
| ~ relation(sK15)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sF16) ),
inference(resolution,[],[f226,f299]) ).
fof(f499,plain,
! [X0,X1] :
( in(X0,relation_rng(sK15))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sF16) ),
inference(forward_subsumption_resolution,[],[f495,f109]) ).
fof(f505,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sF16)
| in(X0,sF18) ),
inference(forward_demodulation,[],[f499,f137]) ).
fof(f615,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sF16)
| in(X0,sF18) ),
inference(superposition,[],[f505,f73]) ).
fof(f2924,plain,
! [X0] :
( in(X0,sF18)
| ~ in(X0,sF17) ),
inference(resolution,[],[f615,f240]) ).
fof(f4084,definition,
( spl19_224
<=> ! [X0] :
( in(X0,sF18)
| ~ in(X0,sF17) ) ),
introduced(definition,[new_symbols(definition,[spl19_224])],[avatar_definition]) ).
fof(f4085,plain,
( ! [X0] :
( ~ in(X0,sF17)
| in(X0,sF18) )
| ~ spl19_224 ),
inference(avatar_component_clause,[],[f4084]) ).
fof(f4087,plain,
spl19_224,
inference(avatar_split_clause,[],[f2924,f4084]) ).
fof(f5642,plain,
( in(sK0(sF17,sF18),sF18)
| ~ spl19_224 ),
inference(resolution,[],[f4085,f176]) ).
fof(f5755,definition,
( spl19_282
<=> in(sK0(sF17,sF18),sF18) ),
introduced(definition,[new_symbols(definition,[spl19_282])],[avatar_definition]) ).
fof(f5757,plain,
( in(sK0(sF17,sF18),sF18)
| ~ spl19_282 ),
inference(avatar_component_clause,[],[f5755]) ).
fof(f5763,plain,
( spl19_282
| ~ spl19_224 ),
inference(avatar_split_clause,[],[f5642,f4084,f5755]) ).
fof(f6401,plain,
( subset(sF17,sF18)
| ~ spl19_282 ),
inference(resolution,[],[f5757,f76]) ).
fof(f6408,plain,
( $false
| ~ spl19_282 ),
inference(forward_subsumption_resolution,[],[f6401,f138]) ).
fof(f6409,plain,
~ spl19_282,
inference(avatar_contradiction_clause,[],[f6408]) ).
cnf(s176,plain,
spl19_224,
inference(sat_conversion,[],[f4087]) ).
cnf(s259,plain,
( ~ spl19_224
| spl19_282 ),
inference(sat_conversion,[],[f5763]) ).
cnf(s288,plain,
~ spl19_282,
inference(sat_conversion,[],[f6409]) ).
cnf(s289,plain,
~ spl19_224,
inference(rat,[],[s259,s288]) ).
cnf(s300,plain,
$false,
inference(rat,[],[s176,s289]) ).
fof(f6410,plain,
$false,
inference(avatar_sat_refutation,[],[s300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU183+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:53:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.82/1.00 % (2010382)Will run a generic schedule for satisfiability detection.
% 2.82/1.00 % (2010387)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1066346413_2999 on theBenchmark for (2999ds/0Mi)
% 2.82/1.00 % TRYING [1]
% 2.82/1.00 % TRYING [2]
% 2.82/1.00 % TRYING [3]
% 2.82/1.00 % (2010390)dis+10_1_sil=32000:sp=arity:random_seed=3323858137:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.82/1.00 % (2010389)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1627861131:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.82/1.00 % (2010391)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3885034084:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.82/1.00 % (2010392)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2188607626:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.82/1.00 % (2010393)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3844211913:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.82/1.00 % (2010388)% WARNING: option uhcvi not known.
% 2.82/1.00 % (2010388)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3476301704:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.82/1.00 % TRYING [4]
% 2.82/1.00 % TRYING [5]
% 2.82/1.00 % (2010390)Instruction limit reached!
% 2.82/1.00 % (2010390)------------------------------
% 2.82/1.00 % (2010390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010390)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010390)Termination reason: Instruction limit
% 2.82/1.00 % (2010390)Termination phase: Saturation
% 2.82/1.00 % (2010390)Time elapsed: 0.065 s
% 2.82/1.00 % (2010390)Peak memory usage: 12 MB
% 2.82/1.00 % (2010390)Instructions burned: 104 (million)
% 2.82/1.00 % (2010391)Instruction limit reached!
% 2.82/1.00 % (2010391)------------------------------
% 2.82/1.00 % (2010391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010391)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010391)Termination reason: Instruction limit
% 2.82/1.00 % (2010391)Termination phase: Saturation
% 2.82/1.00 % (2010391)Time elapsed: 0.070 s
% 2.82/1.00 % (2010391)Peak memory usage: 13 MB
% 2.82/1.00 % (2010391)Instructions burned: 117 (million)
% 2.82/1.00 % (2010392)Instruction limit reached!
% 2.82/1.00 % (2010392)------------------------------
% 2.82/1.00 % (2010392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010392)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010392)Termination reason: Instruction limit
% 2.82/1.00 % (2010392)Termination phase: Saturation
% 2.82/1.00 % (2010392)Time elapsed: 0.072 s
% 2.82/1.00 % (2010392)Peak memory usage: 13 MB
% 2.82/1.00 % (2010392)Instructions burned: 131 (million)
% 2.82/1.00 % (2010401)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3872507613:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.82/1.00 % (2010393)Instruction limit reached!
% 2.82/1.00 % (2010393)------------------------------
% 2.82/1.00 % (2010393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010393)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010393)Termination reason: Instruction limit
% 2.82/1.00 % (2010393)Termination phase: Saturation
% 2.82/1.00 % (2010393)Time elapsed: 0.086 s
% 2.82/1.00 % (2010393)Peak memory usage: 12 MB
% 2.82/1.00 % (2010393)Instructions burned: 159 (million)
% 2.82/1.00 % (2010402)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2463518565:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.82/1.00 % TRYING [1]
% 2.82/1.00 % TRYING [2]
% 2.82/1.00 % (2010403)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3739775189:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.82/1.00 % TRYING [3]
% 2.82/1.00 % (2010405)ott-21_1_sil=16000:fs=off:random_seed=653312360:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.82/1.00 % TRYING [4]
% 2.82/1.00 % TRYING [5]
% 2.82/1.00 % (2010402)Instruction limit reached!
% 2.82/1.00 % (2010402)------------------------------
% 2.82/1.00 % (2010402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010402)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010402)Termination reason: Instruction limit
% 2.82/1.00 % (2010402)Termination phase: Saturation
% 2.82/1.00 % (2010402)Time elapsed: 0.076 s
% 2.82/1.00 % (2010402)Peak memory usage: 13 MB
% 2.82/1.00 % (2010402)Instructions burned: 132 (million)
% 2.82/1.00 % (2010409)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2250955895:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.82/1.00 % (2010405)Instruction limit reached!
% 2.82/1.00 % (2010405)------------------------------
% 2.82/1.00 % (2010405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010405)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010405)Termination reason: Instruction limit
% 2.82/1.00 % (2010405)Termination phase: Saturation
% 2.82/1.00 % (2010405)Time elapsed: 0.099 s
% 2.82/1.00 % (2010405)Peak memory usage: 12 MB
% 2.82/1.00 % (2010405)Instructions burned: 182 (million)
% 2.82/1.00 % TRYING [6]
% 2.82/1.00 % (2010411)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2954938169:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.82/1.00 % TRYING [1]
% 2.82/1.00 % TRYING [2]
% 2.82/1.00 % TRYING [3]
% 2.82/1.00 % TRYING [4]
% 2.82/1.00 % TRYING [6]
% 2.82/1.00 % (2010401)Instruction limit reached!
% 2.82/1.00 % (2010401)------------------------------
% 2.82/1.00 % (2010401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010401)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010401)Termination reason: Instruction limit
% 2.82/1.00 % (2010401)Termination phase: Finite model building constraint generation
% 2.82/1.00 % (2010401)Time elapsed: 0.264 s
% 2.82/1.00 % (2010401)Peak memory usage: 34 MB
% 2.82/1.00 % (2010401)Instructions burned: 715 (million)
% 2.82/1.00 % (2010413)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3028248267:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 2.82/1.00 % (2010403)Instruction limit reached!
% 2.82/1.00 % (2010403)------------------------------
% 2.82/1.00 % (2010403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010403)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010403)Termination reason: Instruction limit
% 2.82/1.00 % (2010403)Termination phase: Saturation
% 2.82/1.00 % (2010403)Time elapsed: 0.386 s
% 2.82/1.00 % (2010403)Peak memory usage: 18 MB
% 2.82/1.00 % (2010403)Instructions burned: 684 (million)
% 2.82/1.00 % (2010415)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=772596448:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 2.82/1.00 % (2010409)Instruction limit reached!
% 2.82/1.00 % (2010409)------------------------------
% 2.82/1.00 % (2010409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010409)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010409)Termination reason: Instruction limit
% 2.82/1.00 % (2010409)Termination phase: Saturation
% 2.82/1.00 % (2010409)Time elapsed: 0.322 s
% 2.82/1.00 % (2010409)Peak memory usage: 14 MB
% 2.82/1.00 % (2010409)Instructions burned: 477 (million)
% 2.82/1.00 % (2010417)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=901955001:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 2.82/1.00 % TRYING [5]
% 2.82/1.00 % (2010413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2010382-2010413"...
% 2.82/1.00 % (2010413)...printing done.
% 2.82/1.00 % (2010413)Refutation found. Thanks to Tanya!
% 2.82/1.00 % SZS status Theorem for theBenchmark
% 2.82/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.00 % (2010413)------------------------------
% 2.82/1.00 % (2010413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.82/1.00 % (2010413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.00 % (2010413)CaDiCaL version: 2.1.3
% 2.82/1.00 % (2010413)Termination reason: Refutation
% 2.82/1.00 % (2010413)Time elapsed: 0.172 s
% 2.82/1.00 % (2010413)Peak memory usage: 16 MB
% 2.82/1.00 % (2010413)Instructions burned: 270 (million)
% 2.82/1.00 % (2010382)Success in time 0.59 s
% 2.82/1.00 % Vampire exiting
%------------------------------------------------------------------------------