%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU269+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 : Fri Sep 25 02:56:26 PM UTC 2026
% Result : Theorem 25.52s 10.19s
% Output : CNFRefutation 25.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 103 ( 24 unt; 0 def)
% Number of atoms : 403 ( 49 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 528 ( 228 ~; 231 |; 52 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 205 ( 0 sgn 192 !; 13 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
fof(f10,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ( in(X3,X0)
& in(X2,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f11,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(f13,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1) )
=> in(ordered_pair(X2,X4),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
fof(f16,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f44,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f47,conjecture,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f48,negated_conjecture,
~ ! [X0] : transitive(inclusion_relation(X0)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f70,plain,
! [X0] :
( ~ relation(X0)
| ( transitive(X0)
<=> is_transitive_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f71,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f72,plain,
! [X0,X1] :
( ~ relation(X1)
| ( X1 = inclusion_relation(X0)
<=> ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) )
& relation_field(X1) = X0 ) ) ),
inference(flattening,[],[f71]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_transitive_in(X0,X1)
<=> ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) ) ),
inference(flattening,[],[f74]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f79]) ).
fof(f83,plain,
? [X0] : ~ transitive(inclusion_relation(X0)),
inference(ennf_transformation,[],[f48]) ).
fof(f90,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ transitive(X0)
| is_transitive_in(X0,relation_field(X0)) )
& ( ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f91,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f92,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X2,X3] :
( ~ in(X3,X0)
| ~ in(X2,X0)
| ( ( ~ in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ subset(X2,X3)
| in(ordered_pair(X2,X3),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ? [X2,X3] :
( in(X3,X0)
& in(X2,X0)
& ( in(ordered_pair(X2,X3),X1)
| subset(X2,X3) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( inclusion_relation(X0) != X1
| ( ! [X4,X5] :
( ~ in(X5,X0)
| ~ in(X4,X0)
| ( ( ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ) ) )
& relation_field(X1) = X0 ) )
& ( ( in(sK1(X0,X1),X0)
& in(sK0(X0,X1),X0)
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| subset(sK0(X0,X1),sK1(X0,X1)) )
& ( ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ subset(sK0(X0,X1),sK1(X0,X1)) ) )
| relation_field(X1) != X0
| X1 = inclusion_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X4,X1)
| ~ in(X3,X1)
| ~ in(X2,X1)
| in(ordered_pair(X2,X4),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f96,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ? [X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
& in(ordered_pair(X2,X3),X0)
& in(X4,X1)
& in(X3,X1)
& in(X2,X1)
& ~ in(ordered_pair(X2,X4),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_transitive_in(X0,X1)
| ! [X5,X6,X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X7,X1)
| ~ in(X6,X1)
| ~ in(X5,X1)
| in(ordered_pair(X5,X7),X0) ) )
& ( ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
& in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
& in(sK4(X0,X1),X1)
& in(sK3(X0,X1),X1)
& in(sK2(X0,X1),X1)
& ~ in(ordered_pair(sK2(X0,X1),sK4(X0,X1)),X0) )
| is_transitive_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1)),skolemize(X4,sK4(X0,X1))],[f96]) ).
fof(f109,plain,
~ transitive(inclusion_relation(sK15)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f83]) ).
fof(f120,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f123,plain,
! [X0] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| transitive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f124,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| subset(X4,X5) ),
inference(cnf_transformation,[],[f94]) ).
fof(f125,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f126,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f94]) ).
fof(f131,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f134,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f135,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK4(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK3(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f138,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK2(X0,X1),X1)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f139,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK2(X0,X1),sK4(X0,X1)),X0)
| is_transitive_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f140,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f184,plain,
~ transitive(inclusion_relation(sK15)),
inference(cnf_transformation,[],[f109]) ).
fof(f192,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1) ),
inference(definition_unfolding,[],[f125,f131]) ).
fof(f193,plain,
! [X0,X1,X4,X5] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| subset(X4,X5) ),
inference(definition_unfolding,[],[f124,f131]) ).
fof(f194,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK4(X0,X1)),singleton(sK2(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f139,f131]) ).
fof(f195,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f135,f131]) ).
fof(f196,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK4(X0,X1)),singleton(sK3(X0,X1))),X0)
| is_transitive_in(X0,X1) ),
inference(definition_unfolding,[],[f134,f131]) ).
fof(f203,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f126]) ).
fof(f204,plain,
! [X0,X4,X5] :
( ~ relation(inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ subset(X4,X5)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_relation(X0)) ),
inference(equality_resolution,[],[f192]) ).
fof(f205,plain,
! [X0,X4,X5] :
( ~ relation(inclusion_relation(X0))
| ~ in(X5,X0)
| ~ in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_relation(X0))
| subset(X4,X5) ),
inference(equality_resolution,[],[f193]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f120]) ).
tcf(c_59,plain,
! [X0: $i] :
( transitive(X0)
| ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),inclusion_relation(X1))
| ~ relation(inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ relation(inclusion_relation(X2))
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),inclusion_relation(X2)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK4(X0,X1)),singleton(sK2(X0,X1))),X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(sK4(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK4(X0,X1)),singleton(sK3(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_76,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f140]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_120,negated_conjecture,
~ transitive(inclusion_relation(sK15)),
inference(cnf_transformation,[],[f184]) ).
tcf(c_152,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_65,c_76,c_65]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),inclusion_relation(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_67,c_76]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_66,c_76]) ).
tcf(c_604,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),sK4(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_74,c_57]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_73,c_57]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_377,c_57]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),inclusion_relation(X2)) ),
inference(demodulation,[status(thm)],[c_376,c_57]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i] :
( is_transitive_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK4(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_69,c_57]) ).
tcf(c_640,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ is_transitive_in(X0,relation_field(X0))
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_120]) ).
tcf(c_641,plain,
( ~ relation(inclusion_relation(sK15))
| ~ is_transitive_in(inclusion_relation(sK15),relation_field(inclusion_relation(sK15))) ),
inference(unflattening,[status(thm)],[c_640]) ).
tcf(c_646,plain,
~ is_transitive_in(inclusion_relation(sK15),relation_field(inclusion_relation(sK15))),
inference(forward_subsumption_resolution,[status(thm)],[c_641,c_76]) ).
tcf(c_2363,plain,
~ is_transitive_in(inclusion_relation(sK15),sK15),
inference(demodulation,[status(thm)],[c_646,c_152]) ).
tcf(c_2622,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK4(X0,X1))),X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_608,c_2363]) ).
tcf(c_2623,plain,
( ~ relation(inclusion_relation(sK15))
| ~ in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2622]) ).
tcf(c_2628,plain,
~ in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)),
inference(forward_subsumption_resolution,[status(thm)],[c_2623,c_76]) ).
tcf(c_2630,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0)
| ~ relation(X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_605,c_2363]) ).
tcf(c_2631,plain,
( in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK3(inclusion_relation(sK15),sK15))),inclusion_relation(sK15))
| ~ relation(inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2630]) ).
tcf(c_2636,plain,
in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK3(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)),
inference(forward_subsumption_resolution,[status(thm)],[c_2631,c_76]) ).
tcf(c_2638,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK3(X0,X1),sK4(X0,X1))),X0)
| ~ relation(X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_604,c_2363]) ).
tcf(c_2639,plain,
( in(unordered_pair(singleton(sK3(inclusion_relation(sK15),sK15)),unordered_pair(sK3(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15))
| ~ relation(inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2638]) ).
tcf(c_2644,plain,
in(unordered_pair(singleton(sK3(inclusion_relation(sK15),sK15)),unordered_pair(sK3(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)),
inference(forward_subsumption_resolution,[status(thm)],[c_2639,c_76]) ).
tcf(c_2646,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X1)
| ~ relation(X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_2363]) ).
tcf(c_2647,plain,
( in(sK4(inclusion_relation(sK15),sK15),sK15)
| ~ relation(inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2646]) ).
tcf(c_2652,plain,
in(sK4(inclusion_relation(sK15),sK15),sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_2647,c_76]) ).
tcf(c_2654,plain,
! [X0: $i,X1: $i] :
( in(sK3(X0,X1),X1)
| ~ relation(X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_2363]) ).
tcf(c_2655,plain,
( in(sK3(inclusion_relation(sK15),sK15),sK15)
| ~ relation(inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2654]) ).
tcf(c_2660,plain,
in(sK3(inclusion_relation(sK15),sK15),sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_2655,c_76]) ).
tcf(c_2662,plain,
! [X0: $i,X1: $i] :
( in(sK2(X0,X1),X1)
| ~ relation(X0)
| ( X1 != sK15 )
| ( inclusion_relation(sK15) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_2363]) ).
tcf(c_2663,plain,
( in(sK2(inclusion_relation(sK15),sK15),sK15)
| ~ relation(inclusion_relation(sK15)) ),
inference(unflattening,[status(thm)],[c_2662]) ).
tcf(c_2668,plain,
in(sK2(inclusion_relation(sK15),sK15),sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_2663,c_76]) ).
tcf(c_5962,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),X0)),inclusion_relation(sK15))
| ~ in(X0,sK15)
| ~ in(sK2(inclusion_relation(sK15),sK15),sK15)
| ~ subset(sK2(inclusion_relation(sK15),sK15),X0) ),
inference(instantiation,[status(thm)],[c_606]) ).
tcf(c_5977,plain,
! [X0: $i] :
( in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),X0)),inclusion_relation(sK15))
| ~ in(X0,sK15)
| ~ subset(sK2(inclusion_relation(sK15),sK15),X0) ),
inference(global_subsumption_just,[status(thm)],[c_5962,c_2668,c_5962]) ).
tcf(c_6015,plain,
( subset(sK2(inclusion_relation(sK15),sK15),sK3(inclusion_relation(sK15),sK15))
| ~ in(sK3(inclusion_relation(sK15),sK15),sK15)
| ~ in(sK2(inclusion_relation(sK15),sK15),sK15)
| ~ in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK3(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)) ),
inference(instantiation,[status(thm)],[c_607]) ).
tcf(c_6044,plain,
( subset(sK3(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))
| ~ in(sK3(inclusion_relation(sK15),sK15),sK15)
| ~ in(sK4(inclusion_relation(sK15),sK15),sK15)
| ~ in(unordered_pair(singleton(sK3(inclusion_relation(sK15),sK15)),unordered_pair(sK3(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15)) ),
inference(instantiation,[status(thm)],[c_607]) ).
tcf(c_6603,plain,
( in(unordered_pair(singleton(sK2(inclusion_relation(sK15),sK15)),unordered_pair(sK2(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))),inclusion_relation(sK15))
| ~ in(sK4(inclusion_relation(sK15),sK15),sK15)
| ~ subset(sK2(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15)) ),
inference(instantiation,[status(thm)],[c_5977]) ).
tcf(c_10286,plain,
! [X0: $i] :
( subset(sK2(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))
| ~ subset(X0,sK4(inclusion_relation(sK15),sK15))
| ~ subset(sK2(inclusion_relation(sK15),sK15),X0) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_10288,plain,
! [X0: $i] :
( ~ subset(sK2(inclusion_relation(sK15),sK15),X0)
| ~ subset(X0,sK4(inclusion_relation(sK15),sK15)) ),
inference(global_subsumption_just,[status(thm)],[c_10286,c_2628,c_2652,c_6603,c_10286]) ).
tcf(c_10289,plain,
! [X0: $i] :
( ~ subset(X0,sK4(inclusion_relation(sK15),sK15))
| ~ subset(sK2(inclusion_relation(sK15),sK15),X0) ),
inference(renaming,[status(thm)],[c_10288]) ).
tcf(c_16766,plain,
( ~ subset(sK3(inclusion_relation(sK15),sK15),sK4(inclusion_relation(sK15),sK15))
| ~ subset(sK2(inclusion_relation(sK15),sK15),sK3(inclusion_relation(sK15),sK15)) ),
inference(instantiation,[status(thm)],[c_10289]) ).
tcf(c_16767,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16766,c_6044,c_6015,c_2668,c_2660,c_2652,c_2644,c_2636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU269+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.62 % Computer : n008.cluster.edu
% 0.12/5.62 % Model : x86_64 x86_64
% 0.12/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.62 % Memory : 8046.5625MB
% 0.12/5.62 % OS : Linux 6.8.0-71-generic
% 0.12/5.62 % CPULimit : 300
% 0.12/5.62 % WCLimit : 300
% 0.12/5.62 % DateTime : Thu Sep 24 13:29:46 UTC 2026
% 0.12/5.62 % CPUTime :
% 0.12/5.62 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.68 Running first-order theorem proving
% 0.12/5.68 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.69
% 0.12/5.69 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.69
% 0.12/5.70 % Detected problem language: tptp
% 0.16/5.71 % Proving...
% 25.52/10.19 % SZS status Started for theBenchmark.p
% 25.52/10.19 % SZS status Theorem for theBenchmark.p
% 25.52/10.19
% 25.52/10.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.52/10.19
% 25.52/10.19 % ------ iProver source info
% 25.52/10.19
% 25.52/10.19 % git: date: 2026-07-19 20:42:38 +0200
% 25.52/10.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.52/10.19 % git: non_committed_changes: false
% 25.52/10.19
% 25.52/10.19 % ------ Parsing...
% 25.52/10.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.52/10.19
% 25.52/10.19 % ------ Preprocessing... sup_sim: 8 sf_s rm: 30 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 6 0s sf_e pe_s pe_e %
% 25.52/10.19
% 25.52/10.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.52/10.19
% 25.52/10.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.52/10.19 % ------ Proving...
% 25.52/10.19 % ------ Problem Properties
% 25.52/10.19
% 25.52/10.19 %
% 25.52/10.19 % clauses 49
% 25.52/10.19 % conjectures 0
% 25.52/10.19 % EPR 22
% 25.52/10.19 % Horn 40
% 25.52/10.19 % unary 22
% 25.52/10.19 % binary 9
% 25.52/10.19 % lits 103
% 25.52/10.19 % lits eq 12
% 25.52/10.19 % fd_pure 0
% 25.52/10.19 % fd_pseudo 0
% 25.52/10.19 % fd_cond 1
% 25.52/10.19 % fd_pseudo_cond 1
% 25.52/10.19 % AC symbols 0
% 25.52/10.19
% 25.52/10.19 % ------ Input Options Time Limit: Unbounded
% 25.52/10.19
% 25.52/10.19
% 25.52/10.19 % ------
% 25.52/10.19 % Current options:
% 25.52/10.19 % ------
% 25.52/10.19
% 25.52/10.19
% 25.52/10.19 %
% 25.52/10.19
% 25.52/10.19 % ------ Proving...
% 25.52/10.19 %
% 25.52/10.19
% 25.52/10.19 % SZS status Theorem for theBenchmark.p
% 25.52/10.19
% 25.52/10.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.52/10.19
% 25.52/10.19
%------------------------------------------------------------------------------