%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU270+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 : n004.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 0.81s 10.92s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 102 ( 19 unt; 1 def)
% Number of atoms : 436 ( 44 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 541 ( 230 ~; 235 |; 53 &)
% ( 13 <=>; 10 =>; 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 : 10 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 188 ( 0 sgn 177 !; 11 ?; 61 :)
% 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] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_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,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f14,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f17,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f42,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f47,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f51,conjecture,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f52,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f73,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f74,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f76,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(f77,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,[],[f76]) ).
fof(f79,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f82,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(flattening,[],[f87]) ).
fof(f93,plain,
? [X0] :
( ordinal(X0)
& ~ connected(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f98,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ connected(X0)
| is_connected_in(X0,relation_field(X0)) )
& ( ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f99,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,[],[f77]) ).
fof(f100,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,[],[f99]) ).
fof(f101,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,[],[f100]) ).
fof(f102,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))],[f101]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f104,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
| is_connected_in(X0,X1) ) ) ),
inference(rectify,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( ~ is_connected_in(X0,X1)
| ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) ) )
& ( ( ~ in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
& ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
& sK2(X0,X1) != sK3(X0,X1)
& in(sK3(X0,X1),X1)
& in(sK2(X0,X1),X1) )
| is_connected_in(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f104]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f118,plain,
( ordinal(sK14)
& ~ connected(inclusion_relation(sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f93]) ).
fof(f129,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f131,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f133,plain,
! [X0] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| connected(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f135,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,[],[f102]) ).
fof(f136,plain,
! [X0,X1] :
( ~ relation(X1)
| inclusion_relation(X0) != X1
| relation_field(X1) = X0 ),
inference(cnf_transformation,[],[f102]) ).
fof(f141,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f144,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f145,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f147,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK3(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f148,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK2(X0,X1),X1)
| is_connected_in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f149,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f186,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f192,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ in(X0,X1)
| ordinal(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f197,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f118]) ).
fof(f198,plain,
~ connected(inclusion_relation(sK14)),
inference(cnf_transformation,[],[f118]) ).
fof(f205,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,[],[f135,f141]) ).
fof(f207,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f145,f141]) ).
fof(f208,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK3(X0,X1),sK2(X0,X1)),singleton(sK3(X0,X1))),X0)
| is_connected_in(X0,X1) ),
inference(definition_unfolding,[],[f144,f141]) ).
fof(f215,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| relation_field(inclusion_relation(X0)) = X0 ),
inference(equality_resolution,[],[f136]) ).
fof(f216,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,[],[f205]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_60,plain,
! [X0: $i] :
( connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( relation_field(inclusion_relation(X0)) = X0 )
| ~ relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_67,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,[],[f216]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK3(X0,X1),sK2(X0,X1)),singleton(sK3(X0,X1))),X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_76,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f149]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ordinal(X0)
| ~ ordinal(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_124,negated_conjecture,
~ connected(inclusion_relation(sK14)),
inference(cnf_transformation,[],[f198]) ).
tcf(c_125,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f197]) ).
tcf(c_157,plain,
! [X0: $i] : relation_field(inclusion_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_66,c_76,c_66]) ).
tcf(c_384,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_67,c_76]) ).
tcf(c_800,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_384,c_57]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK3(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_74,c_57]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] :
( is_connected_in(X0,X1)
| ~ relation(X0)
| ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK3(X0,X1))),X0) ),
inference(demodulation,[status(thm)],[c_73,c_57]) ).
tcf(c_922,plain,
! [X0: $i] :
( ~ relation(X0)
| ~ is_connected_in(X0,relation_field(X0))
| ( inclusion_relation(sK14) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_124]) ).
tcf(c_923,plain,
( ~ relation(inclusion_relation(sK14))
| ~ is_connected_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))) ),
inference(unflattening,[status(thm)],[c_922]) ).
tcf(c_928,plain,
~ is_connected_in(inclusion_relation(sK14),relation_field(inclusion_relation(sK14))),
inference(forward_subsumption_resolution,[status(thm)],[c_923,c_76]) ).
tcf(c_3091,plain,
~ is_connected_in(inclusion_relation(sK14),sK14),
inference(demodulation,[status(thm)],[c_928,c_157]) ).
tcf(c_5003,definition,
iPr_def_10 = inclusion_relation(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_5004,plain,
~ is_connected_in(iPr_def_10,sK14),
inference(demodulation,[status(thm)],[c_3091,c_5003]) ).
tcf(c_6029,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_5003,c_76]) ).
tcf(c_6240,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X2,X0)),inclusion_relation(X1))
| ~ subset(X0,X2)
| ~ in(X2,X1)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_800]) ).
tcf(c_6324,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_59,c_114]) ).
tcf(c_6724,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1)) ),
inference(superposition,[status(thm)],[c_800,c_836]) ).
tcf(c_6725,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6724,c_76]) ).
tcf(c_6817,plain,
( is_connected_in(iPr_def_10,sK14)
| in(sK2(iPr_def_10,sK14),sK14)
| ~ relation(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_6861,plain,
( is_connected_in(iPr_def_10,sK14)
| in(sK3(iPr_def_10,sK14),sK14)
| ~ relation(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_7093,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0))
| ~ 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_6240,c_826]) ).
tcf(c_7120,plain,
! [X0: $i,X1: $i] :
( is_connected_in(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(forward_subsumption_resolution,[status(thm)],[c_7093,c_76]) ).
tcf(c_7179,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_6324,c_114]) ).
tcf(c_15824,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
| ~ ordinal(sK3(inclusion_relation(X0),X1))
| ~ ordinal(sK2(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_7179,c_6725]) ).
tcf(c_34237,plain,
! [X0: $i] :
( ordinal(sK2(iPr_def_10,sK14))
| ~ ordinal(X0)
| ~ in(sK2(iPr_def_10,sK14),X0) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_66515,plain,
( ordinal(sK2(iPr_def_10,sK14))
| ~ ordinal(sK14)
| ~ in(sK2(iPr_def_10,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_34237]) ).
tcf(c_70166,plain,
! [X0: $i] :
( ordinal(sK3(iPr_def_10,sK14))
| ~ ordinal(X0)
| ~ in(sK3(iPr_def_10,sK14),X0) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_94520,plain,
( ordinal(sK3(iPr_def_10,sK14))
| ~ ordinal(sK14)
| ~ in(sK3(iPr_def_10,sK14),sK14) ),
inference(instantiation,[status(thm)],[c_70166]) ).
tcf(c_116013,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ ordinal(sK2(inclusion_relation(X0),X1))
| ~ ordinal(sK3(inclusion_relation(X0),X1)) ),
inference(global_subsumption_just,[status(thm)],[c_15824,c_7120,c_15824]) ).
tcf(c_116014,plain,
! [X0: $i,X1: $i] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ ordinal(sK3(inclusion_relation(X0),X1))
| ~ ordinal(sK2(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(renaming,[status(thm)],[c_116013]) ).
tcf(c_116026,plain,
! [X0: $i] :
( is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| ~ ordinal(sK3(inclusion_relation(X0),X0))
| ~ ordinal(sK2(inclusion_relation(X0),X0))
| ~ in(sK3(inclusion_relation(X0),X0),X0) ),
inference(superposition,[status(thm)],[c_70,c_116014]) ).
tcf(c_116030,plain,
! [X0: $i] :
( is_connected_in(inclusion_relation(X0),X0)
| ~ ordinal(sK3(inclusion_relation(X0),X0))
| ~ ordinal(sK2(inclusion_relation(X0),X0))
| ~ in(sK3(inclusion_relation(X0),X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116026,c_76]) ).
tcf(c_116068,plain,
! [X0: $i] :
( is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| ~ ordinal(sK3(inclusion_relation(X0),X0))
| ~ ordinal(sK2(inclusion_relation(X0),X0)) ),
inference(superposition,[status(thm)],[c_71,c_116030]) ).
tcf(c_116072,plain,
! [X0: $i] :
( is_connected_in(inclusion_relation(X0),X0)
| ~ ordinal(sK3(inclusion_relation(X0),X0))
| ~ ordinal(sK2(inclusion_relation(X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116068,c_76]) ).
tcf(c_116090,plain,
( is_connected_in(inclusion_relation(sK14),sK14)
| ~ ordinal(sK3(iPr_def_10,sK14))
| ~ ordinal(sK2(inclusion_relation(sK14),sK14)) ),
inference(superposition,[status(thm)],[c_5003,c_116072]) ).
tcf(c_116091,plain,
( is_connected_in(iPr_def_10,sK14)
| ~ ordinal(sK3(iPr_def_10,sK14))
| ~ ordinal(sK2(iPr_def_10,sK14)) ),
inference(light_normalisation,[status(thm)],[c_116090,c_5003]) ).
tcf(c_116092,plain,
( ~ ordinal(sK3(iPr_def_10,sK14))
| ~ ordinal(sK2(iPr_def_10,sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116091,c_5004]) ).
tcf(c_116111,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116092,c_94520,c_66515,c_6861,c_6817,c_6029,c_5004,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n004.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 : Thu Sep 24 13:28:38 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43
% 0.15/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.43
% 0.15/0.43 % Detected problem language: tptp
% 0.15/0.44 % Proving...
% 0.81/10.92 % SZS status Started for theBenchmark.p
% 0.81/10.92 % SZS status Theorem for theBenchmark.p
% 0.81/10.92
% 0.81/10.92 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.81/10.92
% 0.81/10.92 % ------ iProver source info
% 0.81/10.92
% 0.81/10.92 % git: date: 2026-07-19 20:42:38 +0200
% 0.81/10.92 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.81/10.92 % git: non_committed_changes: false
% 0.81/10.92
% 0.81/10.92 % ------ Parsing...
% 0.81/10.92 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.81/10.92
% 0.81/10.92 % ------ Preprocessing... sup_sim: 8 sf_s rm: 9 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 1 sf_s rm: 5 0s sf_e pe_s pe_e %
% 0.81/10.92
% 0.81/10.92 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.81/10.92
% 0.81/10.92 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.81/10.92 % ------ Proving...
% 0.81/10.92 % ------ Problem Properties
% 0.81/10.92
% 0.81/10.92 %
% 0.81/10.92 % clauses 59
% 0.81/10.92 % conjectures 1
% 0.81/10.92 % EPR 33
% 0.81/10.92 % Horn 51
% 0.81/10.92 % unary 28
% 0.81/10.92 % binary 11
% 0.81/10.92 % lits 121
% 0.81/10.92 % lits eq 15
% 0.81/10.92 % fd_pure 0
% 0.81/10.92 % fd_pseudo 0
% 0.81/10.92 % fd_cond 1
% 0.81/10.92 % fd_pseudo_cond 2
% 0.81/10.92 % AC symbols 0
% 0.81/10.92
% 0.81/10.92 % ------ Schedule dynamic 5 is on
% 0.81/10.92
% 0.81/10.92 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.81/10.92
% 0.81/10.92
% 0.81/10.92 % ------
% 0.81/10.92 % Current options:
% 0.81/10.92 % ------
% 0.81/10.92
% 0.81/10.92
% 0.81/10.92 %
% 0.81/10.92
% 0.81/10.92 % ------ Proving...
% 0.81/10.92 %
% 0.81/10.92
% 0.81/10.92 % SZS status Theorem for theBenchmark.p
% 0.81/10.92
% 0.81/10.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.81/10.92
% 0.81/10.92
%------------------------------------------------------------------------------