%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU240+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 12:52:33 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 119 ( 11 unt; 6 def)
% Number of atoms : 463 ( 4 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 606 ( 262 ~; 274 |; 46 &)
% ( 13 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 198 ( 0 sgn 178 !; 20 ?)
% 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)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f7,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(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(X2,X1)
& in(X3,X1)
& in(X4,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X4),X0) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
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] :
( ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(X4,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(X4,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f48]) ).
fof(f52,plain,
? [X0] :
( ( transitive(X0)
<~> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0] :
( ( transitive(X0)
<~> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),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] :
( ( ( transitive(X0)
| ~ is_transitive_in(X0,relation_field(X0)) )
& ( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(X2,X1)
& in(X3,X1)
& in(X4,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X2,X3,X4] :
( in(ordered_pair(X2,X4),X0)
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(X4,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X4),X0) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ? [X2,X3,X4] :
( ~ in(ordered_pair(X2,X4),X0)
& in(X2,X1)
& in(X3,X1)
& in(X4,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X4),X0) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X6,X7),X0) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( is_transitive_in(X0,X1)
| ( ~ in(ordered_pair(sK0(X0,X1),sK2(X0,X1)),X0)
& in(sK0(X0,X1),X1)
& in(sK1(X0,X1),X1)
& in(sK2(X0,X1),X1)
& in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ) )
& ( ! [X5,X6,X7] :
( in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X6,X7),X0) )
| ~ is_transitive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X4,sK2(X0,X1))],[f64]) ).
fof(f67,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
| ~ transitive(X0) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) )
| transitive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f68,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
| ~ transitive(X0) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) )
| transitive(X0) )
& relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
? [X0] :
( ( ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
| ~ transitive(X0) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X6),X0) )
| transitive(X0) )
& relation(X0) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
( ( ( ~ in(ordered_pair(sK5,sK7),sK4)
& in(ordered_pair(sK5,sK6),sK4)
& in(ordered_pair(sK6,sK7),sK4) )
| ~ transitive(sK4) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),sK4)
| ~ in(ordered_pair(X4,X5),sK4)
| ~ in(ordered_pair(X5,X6),sK4) )
| transitive(sK4) )
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f69]) ).
fof(f80,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f82,plain,
! [X0] :
( is_transitive_in(X0,relation_field(X0))
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f86,plain,
! [X0,X1,X6,X7,X5] :
( in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X6,X7),X0)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f88,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ in(ordered_pair(sK0(X0,X1),sK2(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
relation(sK4),
inference(cnf_transformation,[],[f70]) ).
fof(f100,plain,
! [X6,X4,X5] :
( in(ordered_pair(X4,X6),sK4)
| ~ in(ordered_pair(X4,X5),sK4)
| ~ in(ordered_pair(X5,X6),sK4)
| transitive(sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
( in(ordered_pair(sK6,sK7),sK4)
| ~ transitive(sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f102,plain,
( in(ordered_pair(sK5,sK6),sK4)
| ~ transitive(sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f103,plain,
( ~ in(ordered_pair(sK5,sK7),sK4)
| ~ transitive(sK4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f116,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f117,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f121,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK2(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f92,f84]) ).
fof(f122,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f88,f84]) ).
fof(f123,plain,
! [X0,X1] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK1(X0,X1),sK2(X0,X1)),singleton(sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f87,f84]) ).
fof(f124,plain,
! [X0,X1,X6,X7,X5] :
( in(unordered_pair(unordered_pair(X5,X7),singleton(X5)),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f86,f84,f84,f84]) ).
fof(f126,plain,
( ~ in(unordered_pair(unordered_pair(sK5,sK7),singleton(sK5)),sK4)
| ~ transitive(sK4) ),
inference(definition_unfolding,[],[f103,f84]) ).
fof(f127,plain,
( in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK4)
| ~ transitive(sK4) ),
inference(definition_unfolding,[],[f102,f84]) ).
fof(f128,plain,
( in(unordered_pair(unordered_pair(sK6,sK7),singleton(sK6)),sK4)
| ~ transitive(sK4) ),
inference(definition_unfolding,[],[f101,f84]) ).
fof(f129,plain,
! [X6,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK4)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK4)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4)
| transitive(sK4) ),
inference(definition_unfolding,[],[f100,f84,f84,f84]) ).
fof(f130,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f117,f84]) ).
fof(f131,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f116,f84]) ).
fof(f133,definition,
( spl13_1
<=> transitive(sK4) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f135,plain,
( transitive(sK4)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl13_2
<=> ! [X6,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK4)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK4) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f138,plain,
( ! [X6,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4)
| in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),sK4)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),sK4) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f139,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f129,f137,f133]) ).
fof(f141,definition,
( spl13_3
<=> in(unordered_pair(unordered_pair(sK6,sK7),singleton(sK6)),sK4) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f143,plain,
( in(unordered_pair(unordered_pair(sK6,sK7),singleton(sK6)),sK4)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( ~ spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f128,f141,f133]) ).
fof(f146,definition,
( spl13_4
<=> in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f148,plain,
( in(unordered_pair(unordered_pair(sK5,sK6),singleton(sK5)),sK4)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( ~ spl13_1
| spl13_4 ),
inference(avatar_split_clause,[],[f127,f146,f133]) ).
fof(f151,definition,
( spl13_5
<=> in(unordered_pair(unordered_pair(sK5,sK7),singleton(sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f153,plain,
( ~ in(unordered_pair(unordered_pair(sK5,sK7),singleton(sK5)),sK4)
| spl13_5 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( ~ spl13_1
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f126,f151,f133]) ).
fof(f173,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),sK4)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),sK4) )
| ~ spl13_2 ),
inference(superposition,[],[f138,f80]) ).
fof(f174,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4)
| ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),sK4) )
| ~ spl13_2 ),
inference(forward_demodulation,[],[f173,f80]) ).
fof(f178,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),sK4)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4) )
| ~ spl13_2 ),
inference(forward_demodulation,[],[f174,f80]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f130,f80]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(forward_demodulation,[],[f131,f80]) ).
fof(f257,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK2(X0,X1))),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f121,f80]) ).
fof(f258,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f122,f80]) ).
fof(f261,plain,
! [X0,X1] :
( in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK1(X0,X1),sK2(X0,X1))),X0)
| is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f123,f80]) ).
fof(f265,plain,
( ! [X0,X1] :
( is_transitive_in(sK4,X0)
| ~ relation(sK4)
| in(unordered_pair(singleton(sK0(sK4,X0)),unordered_pair(sK0(sK4,X0),X1)),sK4)
| ~ in(unordered_pair(singleton(sK1(sK4,X0)),unordered_pair(sK1(sK4,X0),X1)),sK4) )
| ~ spl13_2 ),
inference(resolution,[],[f258,f178]) ).
fof(f273,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK1(sK4,X0)),unordered_pair(sK1(sK4,X0),X1)),sK4)
| in(unordered_pair(singleton(sK0(sK4,X0)),unordered_pair(sK0(sK4,X0),X1)),sK4)
| is_transitive_in(sK4,X0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f265,f99]) ).
fof(f277,plain,
( ! [X0] :
( is_transitive_in(sK4,X0)
| ~ relation(sK4)
| in(unordered_pair(singleton(sK0(sK4,X0)),unordered_pair(sK0(sK4,X0),sK2(sK4,X0))),sK4)
| is_transitive_in(sK4,X0) )
| ~ spl13_2 ),
inference(resolution,[],[f261,f273]) ).
fof(f287,plain,
( ! [X0] :
( is_transitive_in(sK4,X0)
| ~ relation(sK4)
| in(unordered_pair(singleton(sK0(sK4,X0)),unordered_pair(sK0(sK4,X0),sK2(sK4,X0))),sK4) )
| ~ spl13_2 ),
inference(duplicate_literal_removal,[],[f277]) ).
fof(f290,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK0(sK4,X0)),unordered_pair(sK0(sK4,X0),sK2(sK4,X0))),sK4)
| is_transitive_in(sK4,X0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f287,f99]) ).
fof(f295,plain,
( ! [X0] :
( is_transitive_in(sK4,X0)
| is_transitive_in(sK4,X0)
| ~ relation(sK4) )
| ~ spl13_2 ),
inference(resolution,[],[f290,f257]) ).
fof(f299,plain,
( ! [X0] :
( is_transitive_in(sK4,X0)
| ~ relation(sK4) )
| ~ spl13_2 ),
inference(duplicate_literal_removal,[],[f295]) ).
fof(f305,definition,
( spl13_10
<=> ! [X0] : is_transitive_in(sK4,X0) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f306,plain,
( ! [X0] : is_transitive_in(sK4,X0)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f308,plain,
( ! [X0] : is_transitive_in(sK4,X0)
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f299,f99]) ).
fof(f311,plain,
( spl13_10
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f308,f137,f305]) ).
fof(f312,plain,
! [X0,X1,X6,X7,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f124,f80]) ).
fof(f313,plain,
! [X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f312,f80]) ).
fof(f314,plain,
! [X0,X1,X6,X7,X5] :
( ~ in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),X0)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X0)
| ~ in(X5,X1)
| ~ in(X6,X1)
| ~ in(X7,X1)
| ~ is_transitive_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f313,f80]) ).
fof(f315,plain,
( transitive(sK4)
| ~ relation(sK4)
| ~ spl13_10 ),
inference(resolution,[],[f306,f83]) ).
fof(f319,plain,
( in(unordered_pair(singleton(sK6),unordered_pair(sK6,sK7)),sK4)
| ~ spl13_3 ),
inference(forward_demodulation,[],[f143,f80]) ).
fof(f320,plain,
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK6)),sK4)
| ~ spl13_4 ),
inference(forward_demodulation,[],[f148,f80]) ).
fof(f321,plain,
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK7)),sK4)
| spl13_5 ),
inference(forward_demodulation,[],[f153,f80]) ).
fof(f322,plain,
( transitive(sK4)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f315,f99]) ).
fof(f323,plain,
( spl13_1
| ~ spl13_10 ),
inference(avatar_split_clause,[],[f322,f305,f133]) ).
fof(f326,plain,
( in(sK7,relation_field(sK4))
| ~ relation(sK4)
| ~ spl13_3 ),
inference(resolution,[],[f319,f249]) ).
fof(f327,plain,
( in(sK6,relation_field(sK4))
| ~ relation(sK4)
| ~ spl13_3 ),
inference(resolution,[],[f319,f248]) ).
fof(f332,plain,
( in(sK6,relation_field(sK4))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f327,f99]) ).
fof(f333,plain,
( in(sK7,relation_field(sK4))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f326,f99]) ).
fof(f337,plain,
( in(sK5,relation_field(sK4))
| ~ relation(sK4)
| ~ spl13_4 ),
inference(resolution,[],[f320,f248]) ).
fof(f342,plain,
( in(sK5,relation_field(sK4))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f337,f99]) ).
fof(f350,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK6)),sK4)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK7)),sK4)
| ~ in(X0,X1)
| ~ in(sK6,X1)
| ~ in(sK7,X1)
| ~ is_transitive_in(sK4,X1)
| ~ relation(sK4) )
| ~ spl13_3 ),
inference(resolution,[],[f314,f319]) ).
fof(f357,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,sK6)),sK4)
| in(unordered_pair(singleton(X0),unordered_pair(X0,sK7)),sK4)
| ~ in(X0,X1)
| ~ in(sK6,X1)
| ~ in(sK7,X1)
| ~ is_transitive_in(sK4,X1) )
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f350,f99]) ).
fof(f383,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK7)),sK4)
| ~ in(sK5,X0)
| ~ in(sK6,X0)
| ~ in(sK7,X0)
| ~ is_transitive_in(sK4,X0) )
| ~ spl13_3
| ~ spl13_4 ),
inference(resolution,[],[f357,f320]) ).
fof(f386,plain,
( ! [X0] :
( ~ is_transitive_in(sK4,X0)
| ~ in(sK6,X0)
| ~ in(sK7,X0)
| ~ in(sK5,X0) )
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f383,f321]) ).
fof(f387,plain,
( ~ in(sK6,relation_field(sK4))
| ~ in(sK7,relation_field(sK4))
| ~ in(sK5,relation_field(sK4))
| ~ transitive(sK4)
| ~ relation(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(resolution,[],[f386,f82]) ).
fof(f389,plain,
( ~ in(sK7,relation_field(sK4))
| ~ in(sK5,relation_field(sK4))
| ~ transitive(sK4)
| ~ relation(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f387,f332]) ).
fof(f390,plain,
( ~ in(sK5,relation_field(sK4))
| ~ transitive(sK4)
| ~ relation(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f389,f333]) ).
fof(f391,plain,
( ~ transitive(sK4)
| ~ relation(sK4)
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f390,f342]) ).
fof(f392,plain,
( ~ relation(sK4)
| ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f391,f135]) ).
fof(f393,plain,
( $false
| ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f392,f99]) ).
fof(f394,plain,
( ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(avatar_contradiction_clause,[],[f393]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f139]) ).
cnf(s2,plain,
( ~ spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f144]) ).
cnf(s3,plain,
( ~ spl13_1
| spl13_4 ),
inference(sat_conversion,[],[f149]) ).
cnf(s4,plain,
( ~ spl13_1
| ~ spl13_5 ),
inference(sat_conversion,[],[f154]) ).
cnf(s8,plain,
( ~ spl13_2
| spl13_10 ),
inference(sat_conversion,[],[f311]) ).
cnf(s10,plain,
( spl13_1
| ~ spl13_10 ),
inference(sat_conversion,[],[f323]) ).
cnf(s14,plain,
( ~ spl13_1
| ~ spl13_3
| ~ spl13_4
| spl13_5 ),
inference(sat_conversion,[],[f394]) ).
cnf(s15,plain,
spl13_1,
inference(rat,[],[s8,s1,s10]) ).
cnf(s16,plain,
~ spl13_5,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl13_4,
inference(rat,[],[s3,s15]) ).
cnf(s18,plain,
spl13_3,
inference(rat,[],[s2,s15]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s14,s16,s15,s17,s18]) ).
fof(f395,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU240+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:17:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.46 % (4018587)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (4018596)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3877675950:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (4018592)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=120501816_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % (4018598)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3208816029:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (4018594)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3248765669:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (4018595)dis+10_1_sil=32000:sp=arity:random_seed=2322259300:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (4018597)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1774178489:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % (4018593)% WARNING: option uhcvi not known.
% 0.09/0.46 % TRYING [1]
% 0.09/0.46 % TRYING [2]
% 0.09/0.46 % (4018593)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3405316679:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % (4018595) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018587-4018595"...
% 0.09/0.46 % (4018597) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4018587-4018597"...
% 0.09/0.46 % (4018595)...printing done.
% 0.09/0.46 % (4018595)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.46 % (4018595)------------------------------
% 0.09/0.46 % (4018595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.46 % (4018595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.46 % (4018595)CaDiCaL version: 2.1.3
% 0.09/0.46 % (4018595)Termination reason: Refutation
% 0.09/0.46 % (4018595)Time elapsed: 0.012 s
% 0.09/0.46 % (4018595)Peak memory usage: 12 MB
% 0.09/0.46 % (4018595)Instructions burned: 17 (million)
% 0.09/0.46 % (4018587)Success in time 0.046 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------