%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU271+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 : n026.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 4.81s 2.29s
% Output : CNFRefutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 22 unt; 1 def)
% Number of atoms : 350 ( 58 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 442 ( 180 ~; 193 |; 52 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 177 ( 0 sgn 166 !; 11 ?; 62 :)
% 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,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f11,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(f12,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f13,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(f17,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f49,conjecture,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f50,negated_conjecture,
~ ! [X0] : antisymmetric(inclusion_relation(X0)),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f70,plain,
! [X0] :
( ~ relation(X0)
| ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f10]) ).
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,[],[f11]) ).
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(f73,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) ) ),
inference(flattening,[],[f73]) ).
fof(f84,plain,
? [X0] : ~ antisymmetric(inclusion_relation(X0)),
inference(ennf_transformation,[],[f50]) ).
fof(f88,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f89,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ antisymmetric(X0)
| is_antisymmetric_in(X0,relation_field(X0)) )
& ( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(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_antisymmetric_in(X0,X1)
| ! [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(X3,X1)
| ~ in(X2,X1)
| X2 = X3 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f96,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ? [X2,X3] :
( in(ordered_pair(X3,X2),X0)
& in(ordered_pair(X2,X3),X0)
& in(X3,X1)
& in(X2,X1)
& X2 != X3 )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_antisymmetric_in(X0,X1)
| ! [X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| X4 = X5 ) )
& ( ( in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
& in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
& in(sK3(X0,X1),X1)
& in(sK2(X0,X1),X1)
& sK2(X0,X1) != sK3(X0,X1) )
| is_antisymmetric_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f96]) ).
fof(f109,plain,
~ antisymmetric(inclusion_relation(sK14)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f84]) ).
fof(f120,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f124,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f126,plain,
! [X0] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f127,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(f129,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f94]) ).
fof(f135,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X0)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f137,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK3(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f138,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK2(X0,X1),X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f139,plain,
! [X0,X1] :
( ~ relation(X0)
| sK2(X0,X1) != sK3(X0,X1)
| is_antisymmetric_in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f140,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f142,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f187,plain,
~ antisymmetric(inclusion_relation(sK14)),
inference(cnf_transformation,[],[f109]) ).
fof(f194,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,[],[f127,f140]) ).
fof(f195,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f136,f140]) ).
fof(f196,plain,
! [X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK2(X0,X1)),singleton(sK3(X0,X1))),X0)
| is_antisymmetric_in(X0,X1) ),
inference(definition_unfolding,[],[f135,f140]) ).
fof(f205,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f129]) ).
fof(f207,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,[],[f194]) ).
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,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_62,plain,
! [X0: $i] :
( antisymmetric(X0)
| ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_68,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_70,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,[],[f207]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| ~ relation(X0)
| ( sK2(X0,X1) != sK3(X0,X1) ) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_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_75,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(unordered_pair(sK3(X0,X1),sK2(X0,X1)),singleton(sK3(X0,X1))),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_78,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f142]) ).
tcf(c_123,negated_conjecture,
~ antisymmetric(inclusion_relation(sK14)),
inference(cnf_transformation,[],[f187]) ).
tcf(c_153,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_68,c_78,c_68]) ).
tcf(c_375,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_70,c_78]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(X0,X1)
| in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0)
| ~ relation(X0) ),
inference(demodulation,[status(thm)],[c_75,c_57]) ).
tcf(c_740,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_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_74,c_57]) ).
tcf(c_763,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_375,c_57]) ).
tcf(c_852,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0))
| ( inclusion_relation(sK14) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_123]) ).
tcf(c_853,plain,
( ~ relation(inclusion_relation(sK14))
| ~ is_antisymmetric_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))) ),
inference(unflattening,[status(thm)],[c_852]) ).
tcf(c_858,plain,
~ is_antisymmetric_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),
inference(forward_subsumption_resolution,[status(thm)],[c_853,c_78]) ).
tcf(c_1210,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_antisymmetric_in(X0,X1)
| ( inclusion_relation(X2) != X0 )
| ( sK2(X0,X1) != sK3(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_78]) ).
tcf(c_1211,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| ( sK2(inclusion_relation(X0),X1) != sK3(inclusion_relation(X0),X1) ) ),
inference(unflattening,[status(thm)],[c_1210]) ).
tcf(c_2395,plain,
~ is_antisymmetric_in(inclusion_relation(sK14),sK14),
inference(demodulation,[status(thm)],[c_858,c_153]) ).
tcf(c_3755,definition,
iPr_def_10 = inclusion_relation(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3756,plain,
~ is_antisymmetric_in(iPr_def_10,sK14),
inference(demodulation,[status(thm)],[c_2395,c_3755]) ).
tcf(c_4969,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X1)
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),inclusion_relation(X2)) ),
inference(superposition,[status(thm)],[c_57,c_763]) ).
tcf(c_5186,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_740,c_763]) ).
tcf(c_5197,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5186,c_78]) ).
tcf(c_9522,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_730,c_4969]) ).
tcf(c_9532,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9522,c_78]) ).
tcf(c_12094,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| ( sK2(inclusion_relation(X0),X1) = sK3(inclusion_relation(X0),X1) )
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1)) ),
inference(superposition,[status(thm)],[c_5197,c_59]) ).
tcf(c_29417,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_740,c_763]) ).
tcf(c_29430,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29417,c_78]) ).
tcf(c_29871,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ in(sK3(inclusion_relation(X0),X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_29430,c_1211,c_9532,c_12094]) ).
tcf(c_29872,plain,
! [X0: $i,X1: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X1)
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(renaming,[status(thm)],[c_29871]) ).
tcf(c_29880,plain,
! [X0: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0),X0),X0) ),
inference(superposition,[status(thm)],[c_72,c_29872]) ).
tcf(c_29883,plain,
! [X0: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X0)
| ~ in(sK3(inclusion_relation(X0),X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29880,c_78]) ).
tcf(c_29935,plain,
! [X0: $i] :
( is_antisymmetric_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(superposition,[status(thm)],[c_73,c_29883]) ).
tcf(c_29938,plain,
! [X0: $i] : is_antisymmetric_in(inclusion_relation(X0),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_29935,c_78]) ).
tcf(c_29940,plain,
is_antisymmetric_in(iPr_def_10,sK14),
inference(superposition,[status(thm)],[c_3755,c_29938]) ).
tcf(c_29941,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29940,c_3756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU271+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:32:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 0.15/0.45
% 0.15/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.45
% 0.15/0.45 % Detected problem language: tptp
% 0.15/0.47 % Proving...
% 4.81/2.29 % SZS status Started for theBenchmark.p
% 4.81/2.29 % SZS status Theorem for theBenchmark.p
% 4.81/2.29
% 4.81/2.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.81/2.29
% 4.81/2.29 % ------ iProver source info
% 4.81/2.29
% 4.81/2.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.81/2.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.81/2.29 % git: non_committed_changes: false
% 4.81/2.29
% 4.81/2.29 % ------ Parsing...
% 4.81/2.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.81/2.29
% 4.81/2.29 % ------ 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 %
% 4.81/2.29
% 4.81/2.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.81/2.29
% 4.81/2.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.81/2.29 % ------ Proving...
% 4.81/2.29 % ------ Problem Properties
% 4.81/2.29
% 4.81/2.29 %
% 4.81/2.29 % clauses 49
% 4.81/2.29 % conjectures 0
% 4.81/2.29 % EPR 23
% 4.81/2.29 % Horn 41
% 4.81/2.29 % unary 23
% 4.81/2.29 % binary 9
% 4.81/2.29 % lits 100
% 4.81/2.29 % lits eq 16
% 4.81/2.29 % fd_pure 0
% 4.81/2.29 % fd_pseudo 0
% 4.81/2.29 % fd_cond 1
% 4.81/2.29 % fd_pseudo_cond 3
% 4.81/2.29 % AC symbols 0
% 4.81/2.29
% 4.81/2.29 % ------ Schedule dynamic 5 is on
% 4.81/2.29
% 4.81/2.29 % ------ no conjectures: strip conj schedule
% 4.81/2.29
% 4.81/2.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.81/2.29
% 4.81/2.29
% 4.81/2.29 % ------
% 4.81/2.29 % Current options:
% 4.81/2.29 % ------
% 4.81/2.29
% 4.81/2.29
% 4.81/2.29 %
% 4.81/2.29
% 4.81/2.29 % ------ Proving...
% 4.81/2.29 %
% 4.81/2.29
% 4.81/2.29 % SZS status Theorem for theBenchmark.p
% 4.81/2.29
% 4.81/2.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.81/2.29
% 4.81/2.29
%------------------------------------------------------------------------------