%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:52:23 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 9 unt; 4 def)
% Number of atoms : 328 ( 27 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 429 ( 182 ~; 179 |; 49 &)
% ( 14 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 170 ( 0 sgn 136 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f35,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<~> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f35]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK0(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK0(X0,X1,X2),sK1(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK2(X0,X1,X6)),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f48]) ).
fof(f50,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,[],[f36]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f51]) ).
fof(f58,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(nnf_transformation,[],[f40]) ).
fof(f59,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X4] :
( in(X4,relation_rng(X2))
& in(ordered_pair(X0,X4),X2)
& in(X4,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
( ( ! [X3] :
( ~ in(X3,relation_rng(sK13))
| ~ in(ordered_pair(sK11,X3),sK13)
| ~ in(X3,sK12) )
| ~ in(sK11,relation_inverse_image(sK13,sK12)) )
& ( ( in(sK14,relation_rng(sK13))
& in(ordered_pair(sK11,sK14),sK13)
& in(sK14,sK12) )
| in(sK11,relation_inverse_image(sK13,sK12)) )
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X4,sK14)],[f60]) ).
fof(f64,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f66,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK2(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f75,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f92,plain,
relation(sK13),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
( in(sK14,sK12)
| in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f94,plain,
( in(ordered_pair(sK11,sK14),sK13)
| in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f96,plain,
! [X3] :
( ~ in(X3,relation_rng(sK13))
| ~ in(ordered_pair(sK11,X3),sK13)
| ~ in(X3,sK12)
| ~ in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f104,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f67,f75]) ).
fof(f105,plain,
! [X2,X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f66,f75]) ).
fof(f108,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,[],[f72,f75]) ).
fof(f111,plain,
! [X3] :
( ~ in(X3,relation_rng(sK13))
| ~ in(unordered_pair(unordered_pair(sK11,X3),singleton(sK11)),sK13)
| ~ in(X3,sK12)
| ~ in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(definition_unfolding,[],[f96,f75]) ).
fof(f112,plain,
( in(unordered_pair(unordered_pair(sK11,sK14),singleton(sK11)),sK13)
| in(sK11,relation_inverse_image(sK13,sK12)) ),
inference(definition_unfolding,[],[f94,f75]) ).
fof(f113,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_inverse_image(X0,X1))
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f104]) ).
fof(f114,plain,
! [X0,X1,X6] :
( in(unordered_pair(unordered_pair(X6,sK2(X0,X1,X6)),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f115,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f65]) ).
fof(f116,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),singleton(X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f119,definition,
( spl15_1
<=> in(sK11,relation_inverse_image(sK13,sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f120,plain,
( ~ in(sK11,relation_inverse_image(sK13,sK12))
| spl15_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f121,plain,
( in(sK11,relation_inverse_image(sK13,sK12))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,definition,
( spl15_2
<=> in(sK14,sK12) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f125,plain,
( in(sK14,sK12)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f93,f123,f119]) ).
fof(f128,definition,
( spl15_3
<=> in(unordered_pair(unordered_pair(sK11,sK14),singleton(sK11)),sK13) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f130,plain,
( in(unordered_pair(unordered_pair(sK11,sK14),singleton(sK11)),sK13)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f112,f128,f119]) ).
fof(f138,definition,
( spl15_5
<=> ! [X3] :
( ~ in(X3,relation_rng(sK13))
| ~ in(X3,sK12)
| ~ in(unordered_pair(unordered_pair(sK11,X3),singleton(sK11)),sK13) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f139,plain,
( ! [X3] :
( ~ in(X3,relation_rng(sK13))
| ~ in(X3,sK12)
| ~ in(unordered_pair(unordered_pair(sK11,X3),singleton(sK11)),sK13) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f140,plain,
( ~ spl15_1
| spl15_5 ),
inference(avatar_split_clause,[],[f111,f138,f119]) ).
fof(f161,plain,
( in(unordered_pair(singleton(sK11),unordered_pair(sK11,sK14)),sK13)
| ~ spl15_3 ),
inference(superposition,[],[f130,f64]) ).
fof(f179,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X5)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f116,f64]) ).
fof(f186,plain,
! [X0,X1,X6,X7] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| in(X6,relation_inverse_image(X0,X1))
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f113,f64]) ).
fof(f187,plain,
! [X0,X1,X6] :
( in(unordered_pair(singleton(X6),unordered_pair(X6,sK2(X0,X1,X6))),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f114,f64]) ).
fof(f191,plain,
( ! [X0] :
( in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK14,X0)
| ~ relation(sK13) )
| ~ spl15_3 ),
inference(resolution,[],[f186,f161]) ).
fof(f194,plain,
( ! [X0] :
( in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK14,X0) )
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f191,f92]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_inverse_image(X1,X2))
| ~ relation(X1)
| in(sK2(X1,X2,X0),relation_rng(X1))
| ~ relation(X1) ),
inference(resolution,[],[f187,f179]) ).
fof(f200,plain,
! [X2,X0,X1] :
( in(sK2(X1,X2,X0),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_inverse_image(X1,X2)) ),
inference(duplicate_literal_removal,[],[f196]) ).
fof(f203,plain,
( ~ in(sK14,sK12)
| spl15_1
| ~ spl15_3 ),
inference(resolution,[],[f194,f120]) ).
fof(f207,plain,
( $false
| spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f203,f125]) ).
fof(f208,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f209,plain,
( ! [X3] :
( ~ in(unordered_pair(singleton(sK11),unordered_pair(sK11,X3)),sK13)
| ~ in(X3,relation_rng(sK13))
| ~ in(X3,sK12) )
| ~ spl15_5 ),
inference(forward_demodulation,[],[f139,f64]) ).
fof(f214,plain,
( ! [X0] :
( ~ in(sK2(sK13,X0,sK11),relation_rng(sK13))
| ~ in(sK2(sK13,X0,sK11),sK12)
| ~ in(sK11,relation_inverse_image(sK13,X0))
| ~ relation(sK13) )
| ~ spl15_5 ),
inference(resolution,[],[f209,f187]) ).
fof(f217,plain,
( ! [X0] :
( ~ in(sK2(sK13,X0,sK11),relation_rng(sK13))
| ~ in(sK2(sK13,X0,sK11),sK12)
| ~ in(sK11,relation_inverse_image(sK13,X0)) )
| ~ spl15_5 ),
inference(forward_subsumption_resolution,[],[f214,f92]) ).
fof(f394,plain,
( ! [X0] :
( ~ relation(sK13)
| ~ in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK2(sK13,X0,sK11),sK12)
| ~ in(sK11,relation_inverse_image(sK13,X0)) )
| ~ spl15_5 ),
inference(resolution,[],[f200,f217]) ).
fof(f401,plain,
( ! [X0] :
( ~ relation(sK13)
| ~ in(sK11,relation_inverse_image(sK13,X0))
| ~ in(sK2(sK13,X0,sK11),sK12) )
| ~ spl15_5 ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f404,plain,
( ! [X0] :
( ~ in(sK2(sK13,X0,sK11),sK12)
| ~ in(sK11,relation_inverse_image(sK13,X0)) )
| ~ spl15_5 ),
inference(forward_subsumption_resolution,[],[f401,f92]) ).
fof(f405,plain,
( ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ relation(sK13)
| ~ spl15_5 ),
inference(resolution,[],[f404,f115]) ).
fof(f406,plain,
( ~ in(sK11,relation_inverse_image(sK13,sK12))
| ~ relation(sK13)
| ~ spl15_5 ),
inference(duplicate_literal_removal,[],[f405]) ).
fof(f407,plain,
( ~ relation(sK13)
| ~ spl15_1
| ~ spl15_5 ),
inference(forward_subsumption_resolution,[],[f406,f121]) ).
fof(f408,plain,
( $false
| ~ spl15_1
| ~ spl15_5 ),
inference(forward_subsumption_resolution,[],[f407,f92]) ).
fof(f409,plain,
( ~ spl15_1
| ~ spl15_5 ),
inference(avatar_contradiction_clause,[],[f408]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f126]) ).
cnf(s2,plain,
( spl15_1
| spl15_3 ),
inference(sat_conversion,[],[f131]) ).
cnf(s4,plain,
( ~ spl15_1
| spl15_5 ),
inference(sat_conversion,[],[f140]) ).
cnf(s5,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f208]) ).
cnf(s10,plain,
( ~ spl15_1
| ~ spl15_5 ),
inference(sat_conversion,[],[f409]) ).
cnf(s11,plain,
spl15_1,
inference(rat,[],[s5,s1,s2]) ).
cnf(s12,plain,
~ spl15_5,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12,s11]) ).
fof(f410,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n002.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 04:06:07 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % (4135669)Will run a generic schedule for satisfiability detection.
% 0.15/0.44 % (4135677)dis+10_1_sil=32000:sp=arity:random_seed=3318301466:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.44 % (4135675)% WARNING: option uhcvi not known.
% 0.15/0.44 % (4135677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4135669-4135677"...
% 0.15/0.44 % (4135674)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4286849813_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.44 % (4135677)...printing done.
% 0.15/0.44 % (4135675)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1615289429:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.44 % (4135676)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=792042540:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.44 % (4135680)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3777808666:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.44 % (4135678)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=285559135:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.44 % (4135677)Refutation found. Thanks to Tanya!
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.44 % (4135677)------------------------------
% 0.15/0.44 % (4135677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.44 % (4135677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.44 % (4135677)CaDiCaL version: 2.1.3
% 0.15/0.44 % (4135677)Termination reason: Refutation
% 0.15/0.44 % (4135677)Time elapsed: 0.007 s
% 0.15/0.44 % (4135677)Peak memory usage: 12 MB
% 0.15/0.44 % (4135677)Instructions burned: 16 (million)
% 0.15/0.44 % (4135669)Success in time 0.03 s
% 0.15/0.44 % Vampire exiting
%------------------------------------------------------------------------------