%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU241+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 : n020.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 12:52:34 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 128 ( 13 unt; 8 def)
% Number of atoms : 461 ( 50 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 582 ( 249 ~; 265 |; 42 &)
% ( 15 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 138 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f8,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(f25,conjecture,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f46,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f47]) ).
fof(f52,plain,
? [X0] :
( ( antisymmetric(X0)
<~> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0] :
( ( antisymmetric(X0)
<~> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(flattening,[],[f52]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f57]) ).
fof(f62,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) )
& ( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ( sK0(X0,X1) != sK1(X0,X1)
& in(sK0(X0,X1),X1)
& in(sK1(X0,X1),X1)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f64]) ).
fof(f67,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f68,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X4,X3),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
( ( ( sK4 != sK5
& in(ordered_pair(sK4,sK5),sK3)
& in(ordered_pair(sK5,sK4),sK3) )
| ~ antisymmetric(sK3) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),sK3)
| ~ in(ordered_pair(X4,X3),sK3) )
| antisymmetric(sK3) )
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f69]) ).
fof(f80,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f82,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f85,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f86,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f89,plain,
! [X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f90,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f98,plain,
relation(sK3),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),sK3)
| ~ in(ordered_pair(X4,X3),sK3)
| antisymmetric(sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
( in(ordered_pair(sK5,sK4),sK3)
| ~ antisymmetric(sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
( in(ordered_pair(sK4,sK5),sK3)
| ~ antisymmetric(sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
( sK4 != sK5
| ~ antisymmetric(sK3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f116,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f120,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f86,f90]) ).
fof(f121,plain,
! [X0,X1] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f85,f90]) ).
fof(f122,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f84,f90,f90]) ).
fof(f124,plain,
( in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3)
| ~ antisymmetric(sK3) ),
inference(definition_unfolding,[],[f101,f90]) ).
fof(f125,plain,
( in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3)
| ~ antisymmetric(sK3) ),
inference(definition_unfolding,[],[f100,f90]) ).
fof(f126,plain,
! [X3,X4] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| antisymmetric(sK3) ),
inference(definition_unfolding,[],[f99,f90,f90]) ).
fof(f127,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f116,f90]) ).
fof(f128,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f115,f90]) ).
fof(f130,definition,
( spl11_1
<=> antisymmetric(sK3) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f131,plain,
( ~ antisymmetric(sK3)
| spl11_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f132,plain,
( antisymmetric(sK3)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl11_2
<=> ! [X4,X3] :
( X3 = X4
| ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f135,plain,
( ! [X3,X4] :
( ~ in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| X3 = X4
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f136,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f126,f134,f130]) ).
fof(f138,definition,
( spl11_3
<=> in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f140,plain,
( in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3)
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f141,plain,
( ~ spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f125,f138,f130]) ).
fof(f143,definition,
( spl11_4
<=> in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f145,plain,
( in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3)
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( ~ spl11_1
| spl11_4 ),
inference(avatar_split_clause,[],[f124,f143,f130]) ).
fof(f148,definition,
( spl11_5
<=> sK4 = sK5 ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f150,plain,
( sK4 != sK5
| spl11_5 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f102,f148,f130]) ).
fof(f170,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(X1,X0),singleton(X1)),sK3) )
| ~ spl11_2 ),
inference(superposition,[],[f135,f80]) ).
fof(f171,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| X0 = X1 )
| ~ spl11_2 ),
inference(forward_demodulation,[],[f170,f80]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f127,f80]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f128,f80]) ).
fof(f245,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f120,f80]) ).
fof(f246,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK1(X0,X1),sK0(X0,X1))),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f121,f80]) ).
fof(f247,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f246,f80]) ).
fof(f250,plain,
( ! [X0] :
( is_antisymmetric_in(sK3,X0)
| ~ relation(sK3)
| ~ in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(resolution,[],[f245,f171]) ).
fof(f258,plain,
( ! [X0] :
( is_antisymmetric_in(sK3,X0)
| ~ in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK1(sK3,X0),sK0(sK3,X0))),sK3)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f250,f98]) ).
fof(f259,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK1(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3)
| is_antisymmetric_in(sK3,X0)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(forward_demodulation,[],[f258,f80]) ).
fof(f260,plain,
( ! [X0] :
( is_antisymmetric_in(sK3,X0)
| ~ relation(sK3)
| is_antisymmetric_in(sK3,X0)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(resolution,[],[f247,f259]) ).
fof(f265,plain,
( ! [X0] :
( is_antisymmetric_in(sK3,X0)
| ~ relation(sK3)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f267,plain,
( ! [X0] :
( is_antisymmetric_in(sK3,X0)
| sK1(sK3,X0) = sK0(sK3,X0) )
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f265,f98]) ).
fof(f268,plain,
( sK1(sK3,relation_field(sK3)) = sK0(sK3,relation_field(sK3))
| antisymmetric(sK3)
| ~ relation(sK3)
| ~ spl11_2 ),
inference(resolution,[],[f267,f83]) ).
fof(f269,plain,
( sK1(sK3,relation_field(sK3)) = sK0(sK3,relation_field(sK3))
| ~ relation(sK3)
| spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f268,f131]) ).
fof(f270,plain,
( sK1(sK3,relation_field(sK3)) = sK0(sK3,relation_field(sK3))
| spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f269,f98]) ).
fof(f271,plain,
! [X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f122,f80]) ).
fof(f272,plain,
! [X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f271,f80]) ).
fof(f275,plain,
( sK0(sK3,relation_field(sK3)) != sK0(sK3,relation_field(sK3))
| is_antisymmetric_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| spl11_1
| ~ spl11_2 ),
inference(superposition,[],[f89,f270]) ).
fof(f277,plain,
( is_antisymmetric_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| spl11_1
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f275]) ).
fof(f278,plain,
( is_antisymmetric_in(sK3,relation_field(sK3))
| spl11_1
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f277,f98]) ).
fof(f282,definition,
( spl11_9
<=> is_antisymmetric_in(sK3,relation_field(sK3)) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f284,plain,
( is_antisymmetric_in(sK3,relation_field(sK3))
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f298,plain,
( spl11_9
| spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f278,f134,f130,f282]) ).
fof(f299,plain,
( antisymmetric(sK3)
| ~ relation(sK3)
| ~ spl11_9 ),
inference(resolution,[],[f284,f83]) ).
fof(f300,plain,
( ~ relation(sK3)
| spl11_1
| ~ spl11_9 ),
inference(forward_subsumption_resolution,[],[f299,f131]) ).
fof(f301,plain,
( $false
| spl11_1
| ~ spl11_9 ),
inference(forward_subsumption_resolution,[],[f300,f98]) ).
fof(f302,plain,
( spl11_1
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f303,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),sK3)
| ~ spl11_3 ),
inference(forward_demodulation,[],[f140,f80]) ).
fof(f304,plain,
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK3)
| ~ spl11_4 ),
inference(forward_demodulation,[],[f145,f80]) ).
fof(f306,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3)
| ~ spl11_3 ),
inference(forward_demodulation,[],[f303,f80]) ).
fof(f313,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),sK3)
| sK4 = sK5
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ is_antisymmetric_in(sK3,X0)
| ~ relation(sK3) )
| ~ spl11_4 ),
inference(resolution,[],[f304,f272]) ).
fof(f314,plain,
( in(sK5,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_4 ),
inference(resolution,[],[f304,f235]) ).
fof(f315,plain,
( in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_4 ),
inference(resolution,[],[f304,f234]) ).
fof(f319,plain,
( in(sK4,relation_field(sK3))
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f315,f98]) ).
fof(f320,plain,
( in(sK5,relation_field(sK3))
| ~ spl11_4 ),
inference(forward_subsumption_resolution,[],[f314,f98]) ).
fof(f321,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),sK3)
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ is_antisymmetric_in(sK3,X0)
| ~ relation(sK3) )
| ~ spl11_4
| spl11_5 ),
inference(forward_subsumption_resolution,[],[f313,f150]) ).
fof(f323,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),sK3)
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ is_antisymmetric_in(sK3,X0) )
| ~ spl11_4
| spl11_5 ),
inference(forward_subsumption_resolution,[],[f321,f98]) ).
fof(f325,plain,
( ! [X0] :
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3)
| ~ in(sK5,X0)
| ~ in(sK4,X0)
| ~ is_antisymmetric_in(sK3,X0) )
| ~ spl11_4
| spl11_5 ),
inference(forward_demodulation,[],[f323,f80]) ).
fof(f327,definition,
( spl11_12
<=> ! [X0] :
( ~ in(sK5,X0)
| ~ is_antisymmetric_in(sK3,X0)
| ~ in(sK4,X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f328,plain,
( ! [X0] :
( ~ is_antisymmetric_in(sK3,X0)
| ~ in(sK5,X0)
| ~ in(sK4,X0) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f330,definition,
( spl11_13
<=> in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
fof(f333,plain,
( spl11_12
| ~ spl11_13
| ~ spl11_4
| spl11_5 ),
inference(avatar_split_clause,[],[f325,f148,f143,f330,f327]) ).
fof(f334,plain,
( spl11_13
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f306,f138,f330]) ).
fof(f351,plain,
( ~ in(sK5,relation_field(sK3))
| ~ in(sK4,relation_field(sK3))
| ~ antisymmetric(sK3)
| ~ relation(sK3)
| ~ spl11_12 ),
inference(resolution,[],[f328,f82]) ).
fof(f353,plain,
( ~ in(sK4,relation_field(sK3))
| ~ antisymmetric(sK3)
| ~ relation(sK3)
| ~ spl11_4
| ~ spl11_12 ),
inference(forward_subsumption_resolution,[],[f351,f320]) ).
fof(f354,plain,
( ~ antisymmetric(sK3)
| ~ relation(sK3)
| ~ spl11_4
| ~ spl11_12 ),
inference(forward_subsumption_resolution,[],[f353,f319]) ).
fof(f355,plain,
( ~ relation(sK3)
| ~ spl11_1
| ~ spl11_4
| ~ spl11_12 ),
inference(forward_subsumption_resolution,[],[f354,f132]) ).
fof(f356,plain,
( $false
| ~ spl11_1
| ~ spl11_4
| ~ spl11_12 ),
inference(forward_subsumption_resolution,[],[f355,f98]) ).
fof(f357,plain,
( ~ spl11_1
| ~ spl11_4
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[],[f356]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f136]) ).
cnf(s2,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f141]) ).
cnf(s3,plain,
( ~ spl11_1
| spl11_4 ),
inference(sat_conversion,[],[f146]) ).
cnf(s4,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(sat_conversion,[],[f151]) ).
cnf(s9,plain,
( spl11_1
| ~ spl11_2
| spl11_9 ),
inference(sat_conversion,[],[f298]) ).
cnf(s10,plain,
( spl11_1
| ~ spl11_9 ),
inference(sat_conversion,[],[f302]) ).
cnf(s12,plain,
( ~ spl11_4
| spl11_5
| spl11_12
| ~ spl11_13 ),
inference(sat_conversion,[],[f333]) ).
cnf(s13,plain,
( ~ spl11_3
| spl11_13 ),
inference(sat_conversion,[],[f334]) ).
cnf(s15,plain,
( ~ spl11_1
| ~ spl11_4
| ~ spl11_12 ),
inference(sat_conversion,[],[f357]) ).
cnf(s16,plain,
( spl11_1
| spl11_9 ),
inference(rat,[],[s1,s9]) ).
cnf(s17,plain,
spl11_1,
inference(rat,[],[s16,s10]) ).
cnf(s18,plain,
~ spl11_5,
inference(rat,[],[s4,s17]) ).
cnf(s19,plain,
spl11_4,
inference(rat,[],[s3,s17]) ).
cnf(s20,plain,
spl11_3,
inference(rat,[],[s2,s17]) ).
cnf(s21,plain,
~ spl11_12,
inference(rat,[],[s15,s17,s19]) ).
cnf(s22,plain,
spl11_13,
inference(rat,[],[s13,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s12,s19,s18,s22,s21]) ).
fof(f358,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU241+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n020.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 04:16:50 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.45 % (4018174)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (4018180)% WARNING: option uhcvi not known.
% 0.14/0.45 % (4018183)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=810320913:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.45 % (4018185)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1616997159:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.45 % (4018179)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=478152083_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % (4018182)dis+10_1_sil=32000:sp=arity:random_seed=2651659550:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (4018181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=536537605:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.45 % (4018180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2207010133:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.45 % (4018184)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1400822196:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % TRYING [2]
% 0.14/0.45 % TRYING [3]
% 0.14/0.45 % (4018182) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018174-4018182"...
% 0.14/0.45 % (4018183) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018174-4018183"...
% 0.14/0.45 % (4018184) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018174-4018184"...
% 0.14/0.45 % (4018182)...printing done.
% 0.14/0.45 % (4018183)...printing done.
% 0.14/0.45 % (4018182)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (4018182)------------------------------
% 0.14/0.45 % (4018182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (4018182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (4018182)CaDiCaL version: 2.1.3
% 0.14/0.45 % (4018182)Termination reason: Refutation
% 0.14/0.45 % (4018182)Time elapsed: 0.010 s
% 0.14/0.45 % (4018182)Peak memory usage: 12 MB
% 0.14/0.45 % (4018182)Instructions burned: 13 (million)
% 0.14/0.45 % (4018174)Success in time 0.048 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------