TSTP Solution File: SEU270+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU270+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:57:30 EDT 2023
% Result : Theorem 77.13s 11.36s
% Output : Refutation 77.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 158
% Syntax : Number of formulae : 790 ( 88 unt; 0 def)
% Number of atoms : 3179 ( 111 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 4117 (1728 ~;2059 |; 173 &)
% ( 124 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 125 ( 123 usr; 106 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-2 aty)
% Number of variables : 1035 (; 996 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f93561,plain,
$false,
inference(avatar_smt_refutation,[],[f247,f252,f257,f262,f267,f272,f273,f278,f283,f290,f295,f300,f305,f310,f315,f320,f325,f330,f335,f340,f345,f350,f355,f360,f365,f370,f375,f380,f385,f390,f395,f400,f405,f410,f413,f414,f426,f431,f436,f441,f446,f451,f461,f471,f480,f489,f494,f503,f508,f517,f522,f604,f608,f661,f674,f1762,f30755,f30820,f31111,f31115,f31119,f31123,f40437,f42090,f42185,f42190,f42191,f42196,f42201,f42206,f42837,f42838,f42842,f48646,f48650,f48654,f48658,f48662,f48666,f48670,f48674,f70022,f70026,f70030,f70035,f70043,f70049,f70098,f80259,f80347,f80348,f80349,f80350,f88013,f88014,f88018,f88022,f88026,f88027,f88074,f88081,f88082,f88083,f88084,f88085,f88086,f88551,f88552,f89740,f89748,f89752,f89753,f89757,f89761,f89762,f90265,f90461,f90481,f90482,f91035,f91832,f91833,f91834,f91835,f91841,f91855,f91860,f91865,f91870,f91874,f91900,f93560]) ).
fof(f93560,plain,
( ~ spl19_2
| spl19_1 ),
inference(avatar_split_clause,[],[f93551,f244,f249]) ).
fof(f249,plain,
( spl19_2
<=> ordinal(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f244,plain,
( spl19_1
<=> connected(inclusion_relation(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f93551,plain,
( ~ ordinal(sK4)
| spl19_1 ),
inference(resolution,[],[f92750,f246]) ).
fof(f246,plain,
( ~ connected(inclusion_relation(sK4))
| spl19_1 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f92750,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f92308,f149]) ).
fof(f149,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',dt_k1_wellord2) ).
fof(f92308,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(resolution,[],[f92284,f415]) ).
fof(f415,plain,
! [X0] : sP1(inclusion_relation(X0)),
inference(resolution,[],[f162,f149]) ).
fof(f162,plain,
! [X0] :
( ~ relation(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f68,f99,f98]) ).
fof(f98,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X0)
| X2 = X3
| ~ in(X3,X1)
| ~ in(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f68,plain,
! [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) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f14]) ).
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/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',d6_relat_2) ).
fof(f92284,plain,
! [X0] :
( ~ sP1(inclusion_relation(X0))
| ~ ordinal(X0)
| ~ relation(inclusion_relation(X0))
| connected(inclusion_relation(X0)) ),
inference(duplicate_literal_removal,[],[f92274]) ).
fof(f92274,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| ~ ordinal(X0)
| ~ sP1(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| connected(inclusion_relation(X0)) ),
inference(resolution,[],[f92246,f750]) ).
fof(f750,plain,
! [X0] :
( ~ is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| connected(inclusion_relation(X0)) ),
inference(duplicate_literal_removal,[],[f748]) ).
fof(f748,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f557,f570]) ).
fof(f570,plain,
! [X0] :
( sP2(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f238,f191]) ).
fof(f191,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f80,f102,f101]) ).
fof(f101,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f102,plain,
! [X0,X1] :
( ( inclusion_relation(X0) = X1
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f80,plain,
! [X0,X1] :
( ( inclusion_relation(X0) = X1
<=> ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 ) )
| ~ relation(X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( inclusion_relation(X0) = X1
<=> ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [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) ) )
& relation_field(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',d1_wellord2) ).
fof(f238,plain,
! [X0] :
( ~ sP3(X0,inclusion_relation(X0))
| sP2(inclusion_relation(X0),X0) ),
inference(equality_resolution,[],[f182]) ).
fof(f182,plain,
! [X0,X1] :
( sP2(X1,X0)
| inclusion_relation(X0) != X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( ( inclusion_relation(X0) = X1
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| inclusion_relation(X0) != X1 ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f102]) ).
fof(f557,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| connected(X0)
| ~ relation(X0)
| ~ is_connected_in(X0,X1) ),
inference(superposition,[],[f153,f184]) ).
fof(f184,plain,
! [X0,X1] :
( relation_field(X0) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ subset(sK8(X0,X1),sK9(X0,X1))
| ~ in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) )
& ( subset(sK8(X0,X1),sK9(X0,X1))
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) )
& in(sK9(X0,X1),X1)
& in(sK8(X0,X1),X1) )
| relation_field(X0) != X1 )
& ( ( ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X0)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X0) ) )
| ~ in(X5,X1)
| ~ in(X4,X1) )
& relation_field(X0) = X1 )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f117,f118]) ).
fof(f118,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X0) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X0) )
& in(X3,X1)
& in(X2,X1) )
=> ( ( ~ subset(sK8(X0,X1),sK9(X0,X1))
| ~ in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) )
& ( subset(sK8(X0,X1),sK9(X0,X1))
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0) )
& in(sK9(X0,X1),X1)
& in(sK8(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X0) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X0) )
& in(X3,X1)
& in(X2,X1) )
| relation_field(X0) != X1 )
& ( ( ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X0)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X0) ) )
| ~ in(X5,X1)
| ~ in(X4,X1) )
& relation_field(X0) = X1 )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
| relation_field(X1) != X0 )
& ( ( ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X3,X0)
& in(X2,X0) )
| relation_field(X1) != X0 )
& ( ( ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X3,X0)
| ~ in(X2,X0) )
& relation_field(X1) = X0 )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f153,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',d14_relat_2) ).
fof(f92246,plain,
! [X17] :
( is_connected_in(inclusion_relation(X17),X17)
| ~ relation(inclusion_relation(X17))
| ~ ordinal(X17)
| ~ sP1(inclusion_relation(X17)) ),
inference(resolution,[],[f92235,f155]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| is_connected_in(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ is_connected_in(X0,X1) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f92235,plain,
! [X0] :
( sP0(inclusion_relation(X0),X0)
| ~ ordinal(X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f92234,f570]) ).
fof(f92234,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sP0(X0,X1)
| ~ ordinal(X1) ),
inference(duplicate_literal_removal,[],[f92215]) ).
fof(f92215,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ sP2(X0,X1)
| ~ ordinal(X1)
| sP0(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f90400,f560]) ).
fof(f560,plain,
! [X0,X1] :
( ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f157,f192]) ).
fof(f192,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t23_ordinal1) ).
fof(f157,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
& ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& sK5(X0,X1) != sK6(X0,X1)
& in(sK6(X0,X1),X1)
& in(sK5(X0,X1),X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
& ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& sK5(X0,X1) != sK6(X0,X1)
& in(sK6(X0,X1),X1)
& in(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
& ~ in(ordered_pair(X2,X3),X0)
& X2 != X3
& in(X3,X1)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( sP0(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) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f90400,plain,
! [X0,X1] :
( ~ ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ sP2(X0,X1)
| ~ ordinal(X1) ),
inference(duplicate_literal_removal,[],[f90379]) ).
fof(f90379,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ ordinal(sK5(X0,X1))
| ~ sP2(X0,X1)
| sP0(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f90371,f564]) ).
fof(f564,plain,
! [X0,X1] :
( ordinal(sK6(X0,X1))
| sP0(X0,X1)
| ~ ordinal(X1) ),
inference(resolution,[],[f158,f192]) ).
fof(f158,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f90371,plain,
! [X0,X1] :
( ~ ordinal(sK6(X0,X1))
| sP0(X0,X1)
| ~ ordinal(sK5(X0,X1))
| ~ sP2(X0,X1) ),
inference(duplicate_literal_removal,[],[f90357]) ).
fof(f90357,plain,
! [X0,X1] :
( ~ ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ sP2(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f90337,f157]) ).
fof(f90337,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| ~ ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ sP2(X0,X1) ),
inference(duplicate_literal_removal,[],[f90311]) ).
fof(f90311,plain,
! [X0,X1] :
( ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X1)
| ~ sP2(X0,X1)
| ~ sP2(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f13582,f158]) ).
fof(f13582,plain,
! [X2,X0,X1] :
( ~ in(sK6(X0,X1),X2)
| ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| sP0(X0,X1)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK5(X0,X1),X1)
| ~ sP2(X0,X2)
| ~ sP2(X0,X1) ),
inference(duplicate_literal_removal,[],[f13570]) ).
fof(f13570,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| ~ in(sK6(X0,X1),X2)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK5(X0,X1),X1)
| ~ sP2(X0,X2)
| ~ sP2(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f2720,f158]) ).
fof(f2720,plain,
! [X2,X3,X0,X1] :
( ~ in(sK6(X0,X2),X3)
| sP0(X0,X2)
| ~ ordinal(sK6(X0,X2))
| ~ ordinal(sK5(X0,X2))
| ~ in(sK6(X0,X2),X1)
| ~ in(sK5(X0,X2),X1)
| ~ in(sK5(X0,X2),X3)
| ~ sP2(X0,X1)
| ~ sP2(X0,X3) ),
inference(duplicate_literal_removal,[],[f2711]) ).
fof(f2711,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1)
| sP0(X0,X2)
| ~ ordinal(sK6(X0,X2))
| ~ ordinal(sK5(X0,X2))
| ~ in(sK6(X0,X2),X1)
| ~ in(sK5(X0,X2),X1)
| ~ in(sK5(X0,X2),X3)
| ~ in(sK6(X0,X2),X3)
| ~ sP2(X0,X3)
| sP0(X0,X2) ),
inference(resolution,[],[f1367,f800]) ).
fof(f800,plain,
! [X2,X0,X1] :
( ~ subset(sK6(X0,X1),sK5(X0,X1))
| ~ in(sK5(X0,X1),X2)
| ~ in(sK6(X0,X1),X2)
| ~ sP2(X0,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f615,f602]) ).
fof(f602,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK5(X0,X1),sK6(X0,X1))),X0)
| sP0(X0,X1) ),
inference(forward_demodulation,[],[f601,f177]) ).
fof(f177,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',commutativity_k2_tarski) ).
fof(f601,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0)
| sP0(X0,X1) ),
inference(forward_demodulation,[],[f230,f177]) ).
fof(f230,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK6(X0,X1),sK5(X0,X1)),singleton(sK6(X0,X1))),X0) ),
inference(definition_unfolding,[],[f161,f179]) ).
fof(f179,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',d5_tarski) ).
fof(f161,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f615,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),X2)
| ~ subset(X0,X1)
| ~ in(X1,X3)
| ~ in(X0,X3)
| ~ sP2(X2,X3) ),
inference(superposition,[],[f606,f177]) ).
fof(f606,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| ~ subset(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f236,f177]) ).
fof(f236,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ subset(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f186,f179]) ).
fof(f186,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X0)
| ~ subset(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f1367,plain,
! [X2,X0,X1] :
( subset(sK6(X0,X1),sK5(X0,X1))
| ~ sP2(X0,X2)
| sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| ~ in(sK6(X0,X1),X2)
| ~ in(sK5(X0,X1),X2) ),
inference(duplicate_literal_removal,[],[f1364]) ).
fof(f1364,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0,X1),X2)
| ~ sP2(X0,X2)
| sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| ~ in(sK6(X0,X1),X2)
| subset(sK6(X0,X1),sK5(X0,X1))
| ~ ordinal(sK5(X0,X1))
| ~ ordinal(sK6(X0,X1)) ),
inference(resolution,[],[f843,f198]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ordinal_subset(X0,X1)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',redefinition_r1_ordinal1) ).
fof(f843,plain,
! [X2,X0,X1] :
( ordinal_subset(sK6(X0,X1),sK5(X0,X1))
| ~ in(sK5(X0,X1),X2)
| ~ sP2(X0,X2)
| sP0(X0,X1)
| ~ ordinal(sK6(X0,X1))
| ~ ordinal(sK5(X0,X1))
| ~ in(sK6(X0,X1),X2) ),
inference(resolution,[],[f610,f585]) ).
fof(f585,plain,
! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ),
inference(duplicate_literal_removal,[],[f584]) ).
fof(f584,plain,
! [X2,X1] :
( subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(resolution,[],[f198,f197]) ).
fof(f197,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',connectedness_r1_ordinal1) ).
fof(f610,plain,
! [X2,X0,X1] :
( ~ subset(sK5(X0,X1),sK6(X0,X1))
| ~ in(sK6(X0,X1),X2)
| ~ in(sK5(X0,X1),X2)
| ~ sP2(X0,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f606,f605]) ).
fof(f605,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK5(X0,X1)),unordered_pair(sK5(X0,X1),sK6(X0,X1))),X0)
| sP0(X0,X1) ),
inference(forward_demodulation,[],[f231,f177]) ).
fof(f231,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK5(X0,X1),sK6(X0,X1)),singleton(sK5(X0,X1))),X0) ),
inference(definition_unfolding,[],[f160,f179]) ).
fof(f160,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f91900,plain,
( ~ spl19_80
| spl19_100
| spl19_95 ),
inference(avatar_split_clause,[],[f91898,f89745,f91839,f70012]) ).
fof(f70012,plain,
( spl19_80
<=> relation(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_80])]) ).
fof(f91839,plain,
( spl19_100
<=> ! [X0] :
( ~ empty(X0)
| ~ relation(X0)
| ~ sP2(X0,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_100])]) ).
fof(f89745,plain,
( spl19_95
<=> empty(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_95])]) ).
fof(f91898,plain,
( ! [X0] :
( ~ empty(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_95 ),
inference(superposition,[],[f89747,f2069]) ).
fof(f2069,plain,
! [X0,X1] :
( inclusion_relation(X1) = X0
| ~ sP2(X0,X1)
| ~ relation(X0)
| ~ relation(inclusion_relation(X1)) ),
inference(duplicate_literal_removal,[],[f2067]) ).
fof(f2067,plain,
! [X0,X1] :
( inclusion_relation(X1) = X0
| ~ sP2(X0,X1)
| ~ relation(X0)
| ~ relation(inclusion_relation(X1))
| ~ relation(inclusion_relation(X1)) ),
inference(resolution,[],[f1062,f570]) ).
fof(f1062,plain,
! [X2,X0,X1] :
( ~ sP2(X1,X2)
| X0 = X1
| ~ sP2(X0,X2)
| ~ relation(X0)
| ~ relation(X1) ),
inference(resolution,[],[f783,f191]) ).
fof(f783,plain,
! [X2,X0,X1] :
( ~ sP3(X1,X2)
| X0 = X2
| ~ sP2(X2,X1)
| ~ sP2(X0,X1)
| ~ relation(X0) ),
inference(resolution,[],[f575,f191]) ).
fof(f575,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X2)
| ~ sP2(X2,X0)
| X1 = X2
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(superposition,[],[f183,f183]) ).
fof(f183,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f89747,plain,
( ~ empty(inclusion_relation(powerset(sK4)))
| spl19_95 ),
inference(avatar_component_clause,[],[f89745]) ).
fof(f91874,plain,
( ~ spl19_80
| spl19_105
| ~ spl19_95 ),
inference(avatar_split_clause,[],[f91849,f89745,f91872,f70012]) ).
fof(f91872,plain,
( spl19_105
<=> ! [X0] :
( empty(X0)
| ~ relation(X0)
| ~ sP2(X0,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_105])]) ).
fof(f91849,plain,
( ! [X0] :
( empty(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| ~ spl19_95 ),
inference(superposition,[],[f89746,f2069]) ).
fof(f89746,plain,
( empty(inclusion_relation(powerset(sK4)))
| ~ spl19_95 ),
inference(avatar_component_clause,[],[f89745]) ).
fof(f91870,plain,
( spl19_104
| ~ spl19_95 ),
inference(avatar_split_clause,[],[f91846,f89745,f91867]) ).
fof(f91867,plain,
( spl19_104
<=> ordinal(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_104])]) ).
fof(f91846,plain,
( ordinal(inclusion_relation(powerset(sK4)))
| ~ spl19_95 ),
inference(resolution,[],[f89746,f169]) ).
fof(f169,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',cc3_ordinal1) ).
fof(f91865,plain,
( spl19_103
| ~ spl19_95 ),
inference(avatar_split_clause,[],[f91845,f89745,f91862]) ).
fof(f91862,plain,
( spl19_103
<=> epsilon_connected(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_103])]) ).
fof(f91845,plain,
( epsilon_connected(inclusion_relation(powerset(sK4)))
| ~ spl19_95 ),
inference(resolution,[],[f89746,f168]) ).
fof(f168,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f91860,plain,
( spl19_102
| ~ spl19_95 ),
inference(avatar_split_clause,[],[f91844,f89745,f91857]) ).
fof(f91857,plain,
( spl19_102
<=> epsilon_transitive(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_102])]) ).
fof(f91844,plain,
( epsilon_transitive(inclusion_relation(powerset(sK4)))
| ~ spl19_95 ),
inference(resolution,[],[f89746,f167]) ).
fof(f167,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f91855,plain,
( spl19_101
| ~ spl19_95 ),
inference(avatar_split_clause,[],[f91843,f89745,f91852]) ).
fof(f91852,plain,
( spl19_101
<=> function(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_101])]) ).
fof(f91843,plain,
( function(inclusion_relation(powerset(sK4)))
| ~ spl19_95 ),
inference(resolution,[],[f89746,f165]) ).
fof(f165,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',cc1_funct_1) ).
fof(f91841,plain,
( ~ spl19_80
| spl19_100
| spl19_95 ),
inference(avatar_split_clause,[],[f91836,f89745,f91839,f70012]) ).
fof(f91836,plain,
( ! [X0] :
( ~ empty(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_95 ),
inference(superposition,[],[f89747,f2069]) ).
fof(f91835,plain,
( ~ spl19_80
| spl19_85
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f91830,f70016,f70047,f70012]) ).
fof(f70047,plain,
( spl19_85
<=> ! [X0] :
( connected(X0)
| ~ relation(X0)
| ~ sP2(X0,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_85])]) ).
fof(f70016,plain,
( spl19_81
<=> connected(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_81])]) ).
fof(f91830,plain,
( ! [X0] :
( connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| ~ spl19_81 ),
inference(superposition,[],[f70017,f2069]) ).
fof(f70017,plain,
( connected(inclusion_relation(powerset(sK4)))
| ~ spl19_81 ),
inference(avatar_component_clause,[],[f70016]) ).
fof(f91834,plain,
( spl19_96
| ~ spl19_80
| ~ spl19_95
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f91829,f70016,f89745,f70012,f89750]) ).
fof(f89750,plain,
( spl19_96
<=> ! [X3] : sP0(X3,powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_96])]) ).
fof(f91829,plain,
( ! [X3] :
( ~ empty(inclusion_relation(powerset(sK4)))
| ~ relation(inclusion_relation(powerset(sK4)))
| sP0(X3,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f71207]) ).
fof(f71207,plain,
! [X0,X1] :
( ~ connected(inclusion_relation(X0))
| ~ empty(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| sP0(X1,X0) ),
inference(resolution,[],[f71029,f415]) ).
fof(f71029,plain,
! [X0,X1] :
( ~ sP1(inclusion_relation(X0))
| ~ empty(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| sP0(X1,X0) ),
inference(duplicate_literal_removal,[],[f71026]) ).
fof(f71026,plain,
! [X0,X1] :
( ~ empty(inclusion_relation(X0))
| ~ sP1(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| sP0(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f71015,f570]) ).
fof(f71015,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ empty(X0)
| ~ sP1(X0)
| ~ connected(X0)
| ~ relation(X0)
| sP0(X2,X1) ),
inference(superposition,[],[f70880,f184]) ).
fof(f70880,plain,
! [X0,X1] :
( sP0(X0,relation_field(X1))
| ~ empty(X1)
| ~ sP1(X1)
| ~ connected(X1)
| ~ relation(X1) ),
inference(duplicate_literal_removal,[],[f70872]) ).
fof(f70872,plain,
! [X0,X1] :
( sP0(X0,relation_field(X1))
| ~ empty(X1)
| ~ sP1(X1)
| ~ connected(X1)
| ~ relation(X1)
| sP0(X0,relation_field(X1)) ),
inference(resolution,[],[f70869,f157]) ).
fof(f70869,plain,
! [X0,X1] :
( ~ in(sK5(X0,relation_field(X1)),relation_field(X1))
| sP0(X0,relation_field(X1))
| ~ empty(X1)
| ~ sP1(X1)
| ~ connected(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f7705]) ).
fof(f7705,plain,
! [X3,X4,X5] :
( sK5(X3,relation_field(X4)) != X5
| sP0(X3,relation_field(X4))
| ~ in(X5,relation_field(X4))
| ~ empty(X4)
| ~ sP1(X4)
| ~ connected(X4)
| ~ relation(X4) ),
inference(duplicate_literal_removal,[],[f7660]) ).
fof(f7660,plain,
! [X3,X4,X5] :
( sK5(X3,relation_field(X4)) != X5
| sP0(X3,relation_field(X4))
| ~ in(X5,relation_field(X4))
| ~ empty(X4)
| ~ sP1(X4)
| ~ connected(X4)
| ~ relation(X4)
| sP0(X3,relation_field(X4)) ),
inference(superposition,[],[f159,f2167]) ).
fof(f2167,plain,
! [X18,X19,X20] :
( sK6(X20,relation_field(X19)) = X18
| ~ in(X18,relation_field(X19))
| ~ empty(X19)
| ~ sP1(X19)
| ~ connected(X19)
| ~ relation(X19)
| sP0(X20,relation_field(X19)) ),
inference(resolution,[],[f1064,f158]) ).
fof(f1064,plain,
! [X6,X4,X5] :
( ~ in(X6,relation_field(X5))
| ~ in(X4,relation_field(X5))
| X4 = X6
| ~ empty(X5)
| ~ sP1(X5)
| ~ connected(X5)
| ~ relation(X5) ),
inference(resolution,[],[f841,f559]) ).
fof(f559,plain,
! [X0] :
( sP0(X0,relation_field(X0))
| ~ sP1(X0)
| ~ connected(X0)
| ~ relation(X0) ),
inference(resolution,[],[f154,f152]) ).
fof(f152,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f154,plain,
! [X0,X1] :
( ~ is_connected_in(X0,X1)
| sP0(X0,X1)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f841,plain,
! [X28,X29,X26,X27] :
( ~ sP0(X29,X28)
| ~ in(X27,X28)
| ~ in(X26,X28)
| X26 = X27
| ~ empty(X29) ),
inference(duplicate_literal_removal,[],[f833]) ).
fof(f833,plain,
! [X28,X29,X26,X27] :
( X26 = X27
| ~ in(X27,X28)
| ~ in(X26,X28)
| ~ sP0(X29,X28)
| ~ empty(X29)
| ~ empty(X29) ),
inference(resolution,[],[f629,f203]) ).
fof(f203,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t7_boole) ).
fof(f629,plain,
! [X21,X22,X23,X20] :
( in(unordered_pair(singleton(X20),unordered_pair(X20,X21)),X22)
| X20 = X21
| ~ in(X21,X23)
| ~ in(X20,X23)
| ~ sP0(X22,X23)
| ~ empty(X22) ),
inference(resolution,[],[f621,f203]) ).
fof(f621,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f620,f177]) ).
fof(f620,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f232,f177]) ).
fof(f232,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP0(X0,X1) ),
inference(definition_unfolding,[],[f156,f179,f179]) ).
fof(f156,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f159,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f91833,plain,
( spl19_94
| ~ spl19_95
| ~ spl19_80
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f91828,f70016,f70012,f89745,f89742]) ).
fof(f89742,plain,
( spl19_94
<=> ! [X2] :
( ~ sP1(X2)
| is_connected_in(X2,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_94])]) ).
fof(f91828,plain,
( ! [X2] :
( ~ relation(inclusion_relation(powerset(sK4)))
| ~ empty(inclusion_relation(powerset(sK4)))
| ~ sP1(X2)
| is_connected_in(X2,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f72348]) ).
fof(f72348,plain,
! [X0,X1] :
( ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ empty(inclusion_relation(X0))
| ~ sP1(X1)
| is_connected_in(X1,X0) ),
inference(resolution,[],[f72347,f415]) ).
fof(f72347,plain,
! [X0,X1] :
( ~ sP1(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ empty(inclusion_relation(X0))
| ~ sP1(X1)
| is_connected_in(X1,X0) ),
inference(duplicate_literal_removal,[],[f72344]) ).
fof(f72344,plain,
! [X0,X1] :
( ~ sP1(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ empty(inclusion_relation(X0))
| ~ sP1(X1)
| is_connected_in(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f71021,f570]) ).
fof(f71021,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ sP1(X0)
| ~ connected(X0)
| ~ relation(X0)
| ~ empty(X0)
| ~ sP1(X2)
| is_connected_in(X2,X1) ),
inference(superposition,[],[f70884,f184]) ).
fof(f70884,plain,
! [X14,X13] :
( is_connected_in(X14,relation_field(X13))
| ~ sP1(X13)
| ~ connected(X13)
| ~ relation(X13)
| ~ empty(X13)
| ~ sP1(X14) ),
inference(resolution,[],[f70880,f155]) ).
fof(f91832,plain,
( ~ spl19_80
| spl19_93
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f91827,f70016,f89738,f70012]) ).
fof(f89738,plain,
( spl19_93
<=> ! [X0,X1] :
( ~ in(X0,powerset(sK4))
| ~ in(X1,powerset(sK4))
| subset(X0,X1)
| X0 = X1
| subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_93])]) ).
fof(f91827,plain,
( ! [X0,X1] :
( ~ in(X0,powerset(sK4))
| subset(X1,X0)
| X0 = X1
| ~ relation(inclusion_relation(powerset(sK4)))
| subset(X0,X1)
| ~ in(X1,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f77831]) ).
fof(f77831,plain,
! [X2,X0,X1] :
( ~ connected(inclusion_relation(X2))
| ~ in(X0,X2)
| subset(X1,X0)
| X0 = X1
| ~ relation(inclusion_relation(X2))
| subset(X0,X1)
| ~ in(X1,X2) ),
inference(resolution,[],[f8519,f415]) ).
fof(f8519,plain,
! [X2,X0,X1] :
( ~ sP1(inclusion_relation(X1))
| subset(X2,X0)
| ~ in(X2,X1)
| subset(X0,X2)
| X0 = X2
| ~ relation(inclusion_relation(X1))
| ~ connected(inclusion_relation(X1))
| ~ in(X0,X1) ),
inference(duplicate_literal_removal,[],[f8503]) ).
fof(f8503,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| subset(X2,X0)
| ~ in(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X1)
| subset(X0,X2)
| X0 = X2
| ~ relation(inclusion_relation(X1))
| ~ connected(inclusion_relation(X1))
| ~ relation(inclusion_relation(X1))
| ~ sP1(inclusion_relation(X1)) ),
inference(resolution,[],[f3036,f1002]) ).
fof(f1002,plain,
! [X0] :
( sP0(inclusion_relation(X0),X0)
| ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ sP1(inclusion_relation(X0)) ),
inference(resolution,[],[f747,f154]) ).
fof(f747,plain,
! [X0] :
( is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0)) ),
inference(duplicate_literal_removal,[],[f745]) ).
fof(f745,plain,
! [X0] :
( ~ connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| is_connected_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f555,f570]) ).
fof(f555,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ connected(X0)
| ~ relation(X0)
| is_connected_in(X0,X1) ),
inference(superposition,[],[f152,f184]) ).
fof(f3036,plain,
! [X2,X3,X0,X1] :
( ~ sP0(inclusion_relation(X2),X1)
| ~ in(X0,X1)
| subset(X3,X0)
| ~ in(X0,X2)
| ~ in(X3,X2)
| ~ in(X3,X1)
| subset(X0,X3)
| X0 = X3
| ~ relation(inclusion_relation(X2)) ),
inference(duplicate_literal_removal,[],[f3030]) ).
fof(f3030,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ sP0(inclusion_relation(X2),X1)
| subset(X3,X0)
| ~ in(X0,X2)
| ~ in(X3,X2)
| ~ in(X3,X1)
| subset(X0,X3)
| ~ in(X3,X2)
| ~ in(X0,X2)
| X0 = X3
| ~ relation(inclusion_relation(X2))
| ~ relation(inclusion_relation(X2)) ),
inference(resolution,[],[f1436,f570]) ).
fof(f1436,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP2(inclusion_relation(X3),X4)
| ~ in(X2,X1)
| ~ sP0(inclusion_relation(X3),X1)
| subset(X0,X2)
| ~ in(X2,X4)
| ~ in(X0,X4)
| ~ in(X0,X1)
| subset(X2,X0)
| ~ in(X0,X3)
| ~ in(X2,X3)
| X0 = X2
| ~ relation(inclusion_relation(X3)) ),
inference(resolution,[],[f927,f570]) ).
fof(f927,plain,
! [X10,X11,X8,X9,X7,X12] :
( ~ sP2(X10,X12)
| ~ in(X8,X9)
| ~ in(X7,X9)
| ~ sP0(X10,X9)
| subset(X8,X7)
| ~ in(X7,X11)
| ~ in(X8,X11)
| ~ sP2(X10,X11)
| subset(X7,X8)
| ~ in(X8,X12)
| ~ in(X7,X12)
| X7 = X8 ),
inference(resolution,[],[f625,f609]) ).
fof(f609,plain,
! [X0,X1,X4,X5] :
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| subset(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f237,f177]) ).
fof(f237,plain,
! [X0,X1,X4,X5] :
( subset(X4,X5)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f185,f179]) ).
fof(f185,plain,
! [X0,X1,X4,X5] :
( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(X5,X1)
| ~ in(X4,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f625,plain,
! [X3,X6,X7,X4,X5] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),X5)
| X3 = X4
| ~ in(X4,X6)
| ~ in(X3,X6)
| ~ sP0(X5,X6)
| subset(X4,X3)
| ~ in(X3,X7)
| ~ in(X4,X7)
| ~ sP2(X5,X7) ),
inference(resolution,[],[f621,f609]) ).
fof(f91035,plain,
( spl19_65
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f91033,f40431,f42193]) ).
fof(f42193,plain,
( spl19_65
<=> epsilon_connected(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_65])]) ).
fof(f40431,plain,
( spl19_60
<=> ordinal(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_60])]) ).
fof(f91033,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_60 ),
inference(resolution,[],[f40432,f164]) ).
fof(f164,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',cc1_ordinal1) ).
fof(f40432,plain,
( ordinal(powerset(sK4))
| ~ spl19_60 ),
inference(avatar_component_clause,[],[f40431]) ).
fof(f90482,plain,
( spl19_60
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f90478,f31105,f40431]) ).
fof(f31105,plain,
( spl19_55
<=> empty(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_55])]) ).
fof(f90478,plain,
( ordinal(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f169]) ).
fof(f31107,plain,
( empty(powerset(sK4))
| ~ spl19_55 ),
inference(avatar_component_clause,[],[f31105]) ).
fof(f90481,plain,
( spl19_65
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f90477,f31105,f42193]) ).
fof(f90477,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f168]) ).
fof(f90461,plain,
( ~ spl19_2
| spl19_52
| spl19_55
| spl19_99
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f90419,f30818,f90459,f31105,f1759,f249]) ).
fof(f1759,plain,
( spl19_52
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_52])]) ).
fof(f90459,plain,
( spl19_99
<=> ! [X39] :
( ~ empty(X39)
| ~ empty(sK8(X39,relation_field(X39)))
| ~ ordinal(sK8(X39,relation_field(X39)))
| ~ ordinal(sK9(X39,relation_field(X39)))
| ~ empty(sK9(X39,relation_field(X39)))
| ~ sP2(X39,powerset(sK4))
| sP2(X39,relation_field(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_99])]) ).
fof(f30818,plain,
( spl19_54
<=> ! [X0] :
( ~ ordinal(X0)
| subset(X0,sK4)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_54])]) ).
fof(f90419,plain,
( ! [X39] :
( ~ empty(X39)
| empty(powerset(sK4))
| sP2(X39,relation_field(X39))
| ~ sP2(X39,powerset(sK4))
| ~ empty(sK9(X39,relation_field(X39)))
| ~ ordinal(sK9(X39,relation_field(X39)))
| empty(sK4)
| ~ ordinal(sK4)
| ~ ordinal(sK8(X39,relation_field(X39)))
| ~ empty(sK8(X39,relation_field(X39))) )
| ~ spl19_54 ),
inference(resolution,[],[f8208,f30819]) ).
fof(f30819,plain,
( ! [X0] :
( subset(X0,sK4)
| ~ ordinal(X0)
| ~ empty(X0) )
| ~ spl19_54 ),
inference(avatar_component_clause,[],[f30818]) ).
fof(f8208,plain,
! [X3,X4] :
( ~ subset(sK8(X3,relation_field(X3)),X4)
| ~ empty(X3)
| empty(powerset(X4))
| sP2(X3,relation_field(X3))
| ~ sP2(X3,powerset(X4))
| ~ empty(sK9(X3,relation_field(X3)))
| ~ ordinal(sK9(X3,relation_field(X3)))
| empty(X4)
| ~ ordinal(X4) ),
inference(resolution,[],[f2341,f1917]) ).
fof(f1917,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ empty(X1)
| ~ ordinal(X1)
| empty(X0)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f1916]) ).
fof(f1916,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ empty(X1)
| ~ ordinal(X1)
| empty(X0)
| subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(resolution,[],[f1024,f198]) ).
fof(f1024,plain,
! [X10,X9] :
( ordinal_subset(X10,X9)
| ~ ordinal(X9)
| ~ empty(X10)
| ~ ordinal(X10)
| empty(X9) ),
inference(resolution,[],[f766,f568]) ).
fof(f568,plain,
! [X0] :
( in(sK7(X0),X0)
| empty(X0) ),
inference(resolution,[],[f195,f173]) ).
fof(f173,plain,
! [X0] : element(sK7(X0),X0),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] : element(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f112]) ).
fof(f112,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',existence_m1_subset_1) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t2_subset) ).
fof(f766,plain,
! [X6,X7,X5] :
( ~ in(X7,X6)
| ~ ordinal(X6)
| ordinal_subset(X5,X6)
| ~ empty(X5)
| ~ ordinal(X5) ),
inference(resolution,[],[f585,f571]) ).
fof(f571,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(forward_literal_rewriting,[],[f205,f201]) ).
fof(f201,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t3_subset) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t5_subset) ).
fof(f2341,plain,
! [X0,X1] :
( ~ subset(sK9(X0,relation_field(X0)),X1)
| ~ sP2(X0,powerset(X1))
| ~ empty(X0)
| empty(powerset(X1))
| sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(duplicate_literal_removal,[],[f2338]) ).
fof(f2338,plain,
! [X0,X1] :
( sP2(X0,relation_field(X0))
| ~ sP2(X0,powerset(X1))
| ~ empty(X0)
| empty(powerset(X1))
| ~ subset(sK9(X0,relation_field(X0)),X1)
| empty(powerset(X1))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(resolution,[],[f1157,f569]) ).
fof(f569,plain,
! [X2,X1] :
( in(X2,powerset(X1))
| empty(powerset(X1))
| ~ subset(X2,X1) ),
inference(resolution,[],[f195,f201]) ).
fof(f1157,plain,
! [X2,X1] :
( ~ in(sK8(X1,relation_field(X1)),powerset(X2))
| sP2(X1,relation_field(X1))
| ~ sP2(X1,powerset(X2))
| ~ empty(X1)
| empty(powerset(X2))
| ~ subset(sK9(X1,relation_field(X1)),X2) ),
inference(resolution,[],[f880,f569]) ).
fof(f880,plain,
! [X0,X1] :
( ~ in(sK9(X0,relation_field(X0)),X1)
| sP2(X0,relation_field(X0))
| ~ in(sK8(X0,relation_field(X0)),X1)
| ~ sP2(X0,X1)
| ~ empty(X0) ),
inference(duplicate_literal_removal,[],[f877]) ).
fof(f877,plain,
! [X0,X1] :
( sP2(X0,relation_field(X0))
| ~ in(sK9(X0,relation_field(X0)),X1)
| ~ in(sK8(X0,relation_field(X0)),X1)
| ~ sP2(X0,X1)
| sP2(X0,relation_field(X0))
| ~ empty(X0) ),
inference(resolution,[],[f640,f649]) ).
fof(f649,plain,
! [X6] :
( subset(sK8(X6,relation_field(X6)),sK9(X6,relation_field(X6)))
| sP2(X6,relation_field(X6))
| ~ empty(X6) ),
inference(resolution,[],[f636,f203]) ).
fof(f636,plain,
! [X0] :
( in(unordered_pair(singleton(sK8(X0,relation_field(X0))),unordered_pair(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0)))),X0)
| sP2(X0,relation_field(X0))
| subset(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0))) ),
inference(forward_demodulation,[],[f240,f177]) ).
fof(f240,plain,
! [X0] :
( sP2(X0,relation_field(X0))
| subset(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0)))
| in(unordered_pair(unordered_pair(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0))),singleton(sK8(X0,relation_field(X0)))),X0) ),
inference(equality_resolution,[],[f235]) ).
fof(f235,plain,
! [X0,X1] :
( sP2(X0,X1)
| subset(sK8(X0,X1),sK9(X0,X1))
| in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X0)
| relation_field(X0) != X1 ),
inference(definition_unfolding,[],[f189,f179]) ).
fof(f189,plain,
! [X0,X1] :
( sP2(X0,X1)
| subset(sK8(X0,X1),sK9(X0,X1))
| in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0)
| relation_field(X0) != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f640,plain,
! [X2,X3] :
( ~ subset(sK8(X2,relation_field(X2)),sK9(X2,relation_field(X2)))
| sP2(X2,relation_field(X2))
| ~ in(sK9(X2,relation_field(X2)),X3)
| ~ in(sK8(X2,relation_field(X2)),X3)
| ~ sP2(X2,X3) ),
inference(duplicate_literal_removal,[],[f638]) ).
fof(f638,plain,
! [X2,X3] :
( sP2(X2,relation_field(X2))
| ~ subset(sK8(X2,relation_field(X2)),sK9(X2,relation_field(X2)))
| ~ subset(sK8(X2,relation_field(X2)),sK9(X2,relation_field(X2)))
| ~ in(sK9(X2,relation_field(X2)),X3)
| ~ in(sK8(X2,relation_field(X2)),X3)
| ~ sP2(X2,X3) ),
inference(resolution,[],[f635,f606]) ).
fof(f635,plain,
! [X0] :
( ~ in(unordered_pair(singleton(sK8(X0,relation_field(X0))),unordered_pair(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0)))),X0)
| sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0))) ),
inference(forward_demodulation,[],[f239,f177]) ).
fof(f239,plain,
! [X0] :
( sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0)))
| ~ in(unordered_pair(unordered_pair(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0))),singleton(sK8(X0,relation_field(X0)))),X0) ),
inference(equality_resolution,[],[f234]) ).
fof(f234,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ subset(sK8(X0,X1),sK9(X0,X1))
| ~ in(unordered_pair(unordered_pair(sK8(X0,X1),sK9(X0,X1)),singleton(sK8(X0,X1))),X0)
| relation_field(X0) != X1 ),
inference(definition_unfolding,[],[f190,f179]) ).
fof(f190,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ subset(sK8(X0,X1),sK9(X0,X1))
| ~ in(ordered_pair(sK8(X0,X1),sK9(X0,X1)),X0)
| relation_field(X0) != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f90265,plain,
( ~ spl19_80
| spl19_84
| spl19_81 ),
inference(avatar_split_clause,[],[f90263,f70016,f70041,f70012]) ).
fof(f70041,plain,
( spl19_84
<=> ! [X0] :
( ~ connected(X0)
| ~ relation(X0)
| ~ sP2(X0,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_84])]) ).
fof(f90263,plain,
( ! [X0] :
( ~ connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_81 ),
inference(superposition,[],[f70018,f2069]) ).
fof(f70018,plain,
( ~ connected(inclusion_relation(powerset(sK4)))
| spl19_81 ),
inference(avatar_component_clause,[],[f70016]) ).
fof(f89762,plain,
( ~ spl19_66
| spl19_60
| ~ spl19_65 ),
inference(avatar_split_clause,[],[f89731,f42193,f40431,f42198]) ).
fof(f42198,plain,
( spl19_66
<=> epsilon_transitive(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_66])]) ).
fof(f89731,plain,
( ordinal(powerset(sK4))
| ~ epsilon_transitive(powerset(sK4))
| ~ spl19_65 ),
inference(resolution,[],[f42195,f170]) ).
fof(f170,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',cc2_ordinal1) ).
fof(f42195,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_65 ),
inference(avatar_component_clause,[],[f42193]) ).
fof(f89761,plain,
( spl19_55
| spl19_98
| ~ spl19_2
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f88545,f40431,f249,f89759,f31105]) ).
fof(f89759,plain,
( spl19_98
<=> ! [X0] :
( subset(X0,sK4)
| ~ in(X0,sK4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_98])]) ).
fof(f88545,plain,
( ! [X0] :
( ~ ordinal(sK4)
| subset(X0,sK4)
| empty(powerset(sK4))
| ~ in(X0,sK4) )
| ~ spl19_60 ),
inference(resolution,[],[f40432,f77067]) ).
fof(f77067,plain,
! [X6,X7] :
( ~ ordinal(powerset(X6))
| ~ ordinal(X6)
| subset(X7,X6)
| empty(powerset(X6))
| ~ in(X7,X6) ),
inference(forward_literal_rewriting,[],[f77054,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f77054,plain,
! [X6,X7] :
( ~ ordinal(X6)
| ~ ordinal(powerset(X6))
| empty(powerset(X6))
| element(X7,powerset(X6))
| ~ in(X7,X6) ),
inference(resolution,[],[f76895,f589]) ).
fof(f589,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(forward_literal_rewriting,[],[f204,f201]) ).
fof(f204,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t4_subset) ).
fof(f76895,plain,
! [X0] :
( subset(X0,powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| empty(powerset(X0)) ),
inference(duplicate_literal_removal,[],[f76894]) ).
fof(f76894,plain,
! [X0] :
( empty(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| subset(X0,powerset(X0))
| ~ ordinal(powerset(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f76892,f198]) ).
fof(f76892,plain,
! [X0] :
( ordinal_subset(X0,powerset(X0))
| empty(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(powerset(X0)) ),
inference(duplicate_literal_removal,[],[f76891]) ).
fof(f76891,plain,
! [X0] :
( ordinal_subset(X0,powerset(X0))
| empty(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| ~ ordinal(X0)
| ~ ordinal(powerset(X0))
| empty(powerset(X0)) ),
inference(factoring,[],[f6975]) ).
fof(f6975,plain,
! [X3,X4] :
( ordinal_subset(X4,powerset(X3))
| empty(powerset(X4))
| ~ ordinal(X3)
| ~ ordinal(powerset(X4))
| ordinal_subset(X3,powerset(X4))
| ~ ordinal(X4)
| ~ ordinal(powerset(X3))
| empty(powerset(X3)) ),
inference(resolution,[],[f2078,f585]) ).
fof(f2078,plain,
! [X3,X4] :
( ~ subset(powerset(X4),X3)
| empty(powerset(X4))
| empty(powerset(X3))
| ~ ordinal(X4)
| ~ ordinal(powerset(X3))
| ordinal_subset(X4,powerset(X3)) ),
inference(resolution,[],[f1008,f585]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ subset(powerset(X1),X0)
| empty(powerset(X1))
| empty(powerset(X0))
| ~ subset(powerset(X0),X1) ),
inference(resolution,[],[f756,f569]) ).
fof(f756,plain,
! [X4,X5] :
( ~ in(powerset(X4),X5)
| ~ subset(X5,X4)
| empty(powerset(X4)) ),
inference(resolution,[],[f569,f193]) ).
fof(f193,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',antisymmetry_r2_hidden) ).
fof(f89757,plain,
( spl19_55
| spl19_97
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f88547,f40431,f89755,f31105]) ).
fof(f89755,plain,
( spl19_97
<=> ! [X2,X1] :
( ~ ordinal(X1)
| element(sK4,X1)
| subset(X2,sK4)
| ~ in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_97])]) ).
fof(f88547,plain,
( ! [X2,X1] :
( ~ ordinal(X1)
| empty(powerset(sK4))
| subset(X2,sK4)
| element(sK4,X1)
| ~ in(X2,X1) )
| ~ spl19_60 ),
inference(resolution,[],[f40432,f40336]) ).
fof(f40336,plain,
! [X2,X0,X1] :
( ~ ordinal(powerset(X0))
| ~ ordinal(X1)
| empty(powerset(X0))
| subset(X2,X0)
| element(X0,X1)
| ~ in(X2,X1) ),
inference(resolution,[],[f6970,f174]) ).
fof(f174,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',reflexivity_r1_tarski) ).
fof(f6970,plain,
! [X10,X8,X9,X7] :
( ~ subset(X7,X9)
| element(X7,X8)
| ~ ordinal(X8)
| empty(powerset(X9))
| subset(X10,X9)
| ~ ordinal(powerset(X9))
| ~ in(X10,X8) ),
inference(forward_literal_rewriting,[],[f6959,f200]) ).
fof(f6959,plain,
! [X10,X8,X9,X7] :
( element(X7,X8)
| ~ ordinal(X8)
| empty(powerset(X9))
| ~ subset(X7,X9)
| ~ ordinal(powerset(X9))
| element(X10,powerset(X9))
| ~ in(X10,X8) ),
inference(resolution,[],[f2149,f589]) ).
fof(f2149,plain,
! [X2,X0,X1] :
( subset(X2,powerset(X0))
| element(X1,X2)
| ~ ordinal(X2)
| empty(powerset(X0))
| ~ subset(X1,X0)
| ~ ordinal(powerset(X0)) ),
inference(duplicate_literal_removal,[],[f2148]) ).
fof(f2148,plain,
! [X2,X0,X1] :
( ~ ordinal(powerset(X0))
| element(X1,X2)
| ~ ordinal(X2)
| empty(powerset(X0))
| ~ subset(X1,X0)
| subset(X2,powerset(X0))
| ~ ordinal(powerset(X0))
| ~ ordinal(X2) ),
inference(resolution,[],[f1060,f198]) ).
fof(f1060,plain,
! [X58,X59,X57] :
( ordinal_subset(X58,powerset(X57))
| ~ ordinal(powerset(X57))
| element(X59,X58)
| ~ ordinal(X58)
| empty(powerset(X57))
| ~ subset(X59,X57) ),
inference(resolution,[],[f764,f569]) ).
fof(f764,plain,
! [X2,X0,X1] :
( ~ in(X2,X1)
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| element(X2,X0)
| ~ ordinal(X0) ),
inference(resolution,[],[f585,f589]) ).
fof(f89753,plain,
( ~ spl19_80
| spl19_85
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f89735,f70016,f70047,f70012]) ).
fof(f89735,plain,
( ! [X0] :
( connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| ~ spl19_81 ),
inference(superposition,[],[f70017,f2069]) ).
fof(f89752,plain,
( spl19_96
| ~ spl19_80
| ~ spl19_95
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f89734,f70016,f89745,f70012,f89750]) ).
fof(f89734,plain,
( ! [X3] :
( ~ empty(inclusion_relation(powerset(sK4)))
| ~ relation(inclusion_relation(powerset(sK4)))
| sP0(X3,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f71207]) ).
fof(f89748,plain,
( spl19_94
| ~ spl19_95
| ~ spl19_80
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f89733,f70016,f70012,f89745,f89742]) ).
fof(f89733,plain,
( ! [X2] :
( ~ relation(inclusion_relation(powerset(sK4)))
| ~ empty(inclusion_relation(powerset(sK4)))
| ~ sP1(X2)
| is_connected_in(X2,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f72348]) ).
fof(f89740,plain,
( ~ spl19_80
| spl19_93
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f89732,f70016,f89738,f70012]) ).
fof(f89732,plain,
( ! [X0,X1] :
( ~ in(X0,powerset(sK4))
| subset(X1,X0)
| X0 = X1
| ~ relation(inclusion_relation(powerset(sK4)))
| subset(X0,X1)
| ~ in(X1,powerset(sK4)) )
| ~ spl19_81 ),
inference(resolution,[],[f70017,f77831]) ).
fof(f88552,plain,
( spl19_66
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f88550,f40431,f42198]) ).
fof(f88550,plain,
( epsilon_transitive(powerset(sK4))
| ~ spl19_60 ),
inference(resolution,[],[f40432,f163]) ).
fof(f163,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f88551,plain,
( spl19_65
| ~ spl19_60 ),
inference(avatar_split_clause,[],[f88549,f40431,f42193]) ).
fof(f88549,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_60 ),
inference(resolution,[],[f40432,f164]) ).
fof(f88086,plain,
( spl19_63
| ~ spl19_35
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88080,f31105,f423,f42182]) ).
fof(f42182,plain,
( spl19_63
<=> sP1(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_63])]) ).
fof(f423,plain,
( spl19_35
<=> sP1(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_35])]) ).
fof(f88080,plain,
( sP1(powerset(sK4))
| ~ spl19_35
| ~ spl19_55 ),
inference(resolution,[],[f31107,f531]) ).
fof(f531,plain,
( ! [X0] :
( ~ empty(X0)
| sP1(X0) )
| ~ spl19_35 ),
inference(superposition,[],[f425,f166]) ).
fof(f166,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t6_boole) ).
fof(f425,plain,
( sP1(empty_set)
| ~ spl19_35 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f88085,plain,
( spl19_64
| ~ spl19_8
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88079,f31105,f280,f42187]) ).
fof(f42187,plain,
( spl19_64
<=> relation(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_64])]) ).
fof(f280,plain,
( spl19_8
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f88079,plain,
( relation(powerset(sK4))
| ~ spl19_8
| ~ spl19_55 ),
inference(resolution,[],[f31107,f530]) ).
fof(f530,plain,
( ! [X7] :
( ~ empty(X7)
| relation(X7) )
| ~ spl19_8 ),
inference(superposition,[],[f282,f166]) ).
fof(f282,plain,
( relation(empty_set)
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f88084,plain,
( spl19_60
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88078,f31105,f40431]) ).
fof(f88078,plain,
( ordinal(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f169]) ).
fof(f88083,plain,
( spl19_65
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88077,f31105,f42193]) ).
fof(f88077,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f168]) ).
fof(f88082,plain,
( spl19_66
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88076,f31105,f42198]) ).
fof(f88076,plain,
( epsilon_transitive(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f167]) ).
fof(f88081,plain,
( spl19_67
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f88075,f31105,f42203]) ).
fof(f42203,plain,
( spl19_67
<=> function(powerset(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_67])]) ).
fof(f88075,plain,
( function(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f165]) ).
fof(f88074,plain,
( spl19_55
| spl19_92
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f88046,f30818,f88072,f31105]) ).
fof(f88072,plain,
( spl19_92
<=> ! [X57,X58] :
( ~ sP2(X57,powerset(sK4))
| ~ empty(sK8(X57,relation_field(X57)))
| ~ ordinal(sK8(X57,relation_field(X57)))
| ~ relation(X57)
| ~ connected(X57)
| ~ sP1(X57)
| ~ subset(X58,sK4)
| ~ in(X58,relation_field(X57))
| sP2(X57,relation_field(X57))
| ~ empty(X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_92])]) ).
fof(f88046,plain,
( ! [X58,X57] :
( ~ sP2(X57,powerset(sK4))
| ~ empty(X57)
| empty(powerset(sK4))
| sP2(X57,relation_field(X57))
| ~ subset(X58,sK4)
| ~ in(X58,relation_field(X57))
| ~ sP1(X57)
| ~ connected(X57)
| ~ relation(X57)
| ~ ordinal(sK8(X57,relation_field(X57)))
| ~ empty(sK8(X57,relation_field(X57))) )
| ~ spl19_54 ),
inference(resolution,[],[f8215,f30819]) ).
fof(f8215,plain,
! [X2,X0,X1] :
( ~ subset(sK8(X0,relation_field(X0)),X2)
| ~ sP2(X0,powerset(X2))
| ~ empty(X0)
| empty(powerset(X2))
| sP2(X0,relation_field(X0))
| ~ subset(X1,X2)
| ~ in(X1,relation_field(X0))
| ~ sP1(X0)
| ~ connected(X0)
| ~ relation(X0) ),
inference(duplicate_literal_removal,[],[f8214]) ).
fof(f8214,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ sP2(X0,powerset(X2))
| ~ empty(X0)
| empty(powerset(X2))
| sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),X2)
| ~ in(X1,relation_field(X0))
| ~ empty(X0)
| ~ sP1(X0)
| ~ connected(X0)
| ~ relation(X0)
| sP2(X0,relation_field(X0)) ),
inference(superposition,[],[f2341,f2160]) ).
fof(f2160,plain,
! [X0,X1] :
( sK9(X1,relation_field(X1)) = X0
| ~ in(X0,relation_field(X1))
| ~ empty(X1)
| ~ sP1(X1)
| ~ connected(X1)
| ~ relation(X1)
| sP2(X1,relation_field(X1)) ),
inference(resolution,[],[f1064,f241]) ).
fof(f241,plain,
! [X0] :
( in(sK9(X0,relation_field(X0)),relation_field(X0))
| sP2(X0,relation_field(X0)) ),
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X0,X1] :
( sP2(X0,X1)
| in(sK9(X0,X1),X1)
| relation_field(X0) != X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f88027,plain,
( ~ spl19_60
| spl19_91
| spl19_89
| ~ spl19_68 ),
inference(avatar_split_clause,[],[f70004,f42835,f88016,f88024,f40431]) ).
fof(f88024,plain,
( spl19_91
<=> ! [X0] :
( ordinal_subset(X0,powerset(sK4))
| ~ ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_91])]) ).
fof(f88016,plain,
( spl19_89
<=> ! [X4,X3] :
( ~ ordinal(sK5(X3,X4))
| ~ ordinal(sK6(X3,X4))
| ~ empty(sK6(X3,X4))
| sP0(X3,X4)
| ~ empty(sK5(X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_89])]) ).
fof(f42835,plain,
( spl19_68
<=> ! [X4,X5] :
( ~ empty(sK6(X4,X5))
| ~ ordinal(sK5(X4,X5))
| ~ empty(sK5(X4,X5))
| sP0(X4,X5)
| ~ sP0(X4,powerset(sK4))
| ~ ordinal(sK6(X4,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_68])]) ).
fof(f70004,plain,
( ! [X2,X0,X1] :
( ~ ordinal(sK5(X0,X1))
| ~ empty(sK5(X0,X1))
| sP0(X0,X1)
| ~ empty(sK6(X0,X1))
| ~ ordinal(sK6(X0,X1))
| ordinal_subset(X2,powerset(sK4))
| ~ empty(X2)
| ~ ordinal(X2)
| ~ ordinal(powerset(sK4)) )
| ~ spl19_68 ),
inference(resolution,[],[f42836,f1025]) ).
fof(f1025,plain,
! [X11,X12,X13] :
( sP0(X13,X11)
| ordinal_subset(X12,X11)
| ~ empty(X12)
| ~ ordinal(X12)
| ~ ordinal(X11) ),
inference(resolution,[],[f766,f157]) ).
fof(f42836,plain,
( ! [X4,X5] :
( ~ sP0(X4,powerset(sK4))
| ~ ordinal(sK5(X4,X5))
| ~ empty(sK5(X4,X5))
| sP0(X4,X5)
| ~ empty(sK6(X4,X5))
| ~ ordinal(sK6(X4,X5)) )
| ~ spl19_68 ),
inference(avatar_component_clause,[],[f42835]) ).
fof(f88026,plain,
( ~ spl19_60
| spl19_91
| spl19_81 ),
inference(avatar_split_clause,[],[f70094,f70016,f88024,f40431]) ).
fof(f70094,plain,
( ! [X0] :
( ordinal_subset(X0,powerset(sK4))
| ~ empty(X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(sK4)) )
| spl19_81 ),
inference(resolution,[],[f70018,f30502]) ).
fof(f30502,plain,
! [X0,X1] :
( connected(inclusion_relation(X0))
| ordinal_subset(X1,X0)
| ~ empty(X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f30234,f149]) ).
fof(f30234,plain,
! [X0,X1] :
( ~ relation(inclusion_relation(X1))
| ~ ordinal(X1)
| ordinal_subset(X0,X1)
| ~ empty(X0)
| ~ ordinal(X0)
| connected(inclusion_relation(X1)) ),
inference(resolution,[],[f6277,f415]) ).
fof(f6277,plain,
! [X6,X5] :
( ~ sP1(inclusion_relation(X6))
| ~ ordinal(X5)
| ~ ordinal(X6)
| ordinal_subset(X5,X6)
| ~ empty(X5)
| ~ relation(inclusion_relation(X6))
| connected(inclusion_relation(X6)) ),
inference(resolution,[],[f2011,f750]) ).
fof(f2011,plain,
! [X6,X7,X5] :
( is_connected_in(X7,X6)
| ~ empty(X5)
| ~ ordinal(X5)
| ~ ordinal(X6)
| ordinal_subset(X5,X6)
| ~ sP1(X7) ),
inference(resolution,[],[f1025,f155]) ).
fof(f88022,plain,
( ~ spl19_60
| spl19_90
| ~ spl19_68 ),
inference(avatar_split_clause,[],[f80425,f42835,f88020,f40431]) ).
fof(f88020,plain,
( spl19_90
<=> ! [X25,X24] :
( empty(X24)
| ~ ordinal(sK6(inclusion_relation(X24),X25))
| ~ empty(sK6(inclusion_relation(X24),X25))
| sP0(inclusion_relation(X24),X25)
| ~ empty(sK5(inclusion_relation(X24),X25))
| ~ ordinal(sK5(inclusion_relation(X24),X25))
| ~ sP1(inclusion_relation(X24))
| ~ relation(inclusion_relation(X24))
| ~ connected(inclusion_relation(X24))
| ~ ordinal(X24)
| ordinal_subset(X24,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_90])]) ).
fof(f80425,plain,
( ! [X24,X25] :
( empty(X24)
| ordinal_subset(X24,powerset(sK4))
| ~ ordinal(powerset(sK4))
| ~ ordinal(X24)
| ~ connected(inclusion_relation(X24))
| ~ relation(inclusion_relation(X24))
| ~ sP1(inclusion_relation(X24))
| ~ ordinal(sK5(inclusion_relation(X24),X25))
| ~ empty(sK5(inclusion_relation(X24),X25))
| sP0(inclusion_relation(X24),X25)
| ~ empty(sK6(inclusion_relation(X24),X25))
| ~ ordinal(sK6(inclusion_relation(X24),X25)) )
| ~ spl19_68 ),
inference(resolution,[],[f38779,f42836]) ).
fof(f38779,plain,
! [X60,X61] :
( sP0(inclusion_relation(X60),X61)
| empty(X60)
| ordinal_subset(X60,X61)
| ~ ordinal(X61)
| ~ ordinal(X60)
| ~ connected(inclusion_relation(X60))
| ~ relation(inclusion_relation(X60))
| ~ sP1(inclusion_relation(X60)) ),
inference(resolution,[],[f38739,f1002]) ).
fof(f38739,plain,
! [X6,X4,X5] :
( ~ sP0(X5,X4)
| sP0(X5,X6)
| empty(X4)
| ordinal_subset(X4,X6)
| ~ ordinal(X6)
| ~ ordinal(X4) ),
inference(duplicate_literal_removal,[],[f38732]) ).
fof(f38732,plain,
! [X6,X4,X5] :
( ~ ordinal(X4)
| sP0(X5,X6)
| empty(X4)
| ordinal_subset(X4,X6)
| ~ ordinal(X6)
| ~ sP0(X5,X4)
| ~ ordinal(X6)
| ~ ordinal(X4)
| sP0(X5,X6)
| empty(X4)
| ordinal_subset(X4,X6) ),
inference(resolution,[],[f6916,f2116]) ).
fof(f2116,plain,
! [X3,X4,X5] :
( in(sK5(X5,X4),X3)
| ~ ordinal(X4)
| ~ ordinal(X3)
| sP0(X5,X4)
| empty(X3)
| ordinal_subset(X3,X4) ),
inference(resolution,[],[f1049,f195]) ).
fof(f1049,plain,
! [X11,X12,X13] :
( element(sK5(X13,X11),X12)
| ordinal_subset(X12,X11)
| ~ ordinal(X11)
| ~ ordinal(X12)
| sP0(X13,X11) ),
inference(resolution,[],[f764,f157]) ).
fof(f6916,plain,
! [X2,X0,X1] :
( ~ in(sK5(X2,X0),X1)
| ~ ordinal(X1)
| sP0(X2,X0)
| empty(X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ sP0(X2,X1) ),
inference(duplicate_literal_removal,[],[f6869]) ).
fof(f6869,plain,
! [X2,X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| sP0(X2,X0)
| empty(X1)
| ordinal_subset(X1,X0)
| ~ in(sK5(X2,X0),X1)
| sP0(X2,X0)
| ~ sP0(X2,X1) ),
inference(resolution,[],[f2118,f1189]) ).
fof(f1189,plain,
! [X3,X4,X5] :
( ~ in(sK6(X3,X4),X5)
| ~ in(sK5(X3,X4),X5)
| sP0(X3,X4)
| ~ sP0(X3,X5) ),
inference(trivial_inequality_removal,[],[f1188]) ).
fof(f1188,plain,
! [X3,X4,X5] :
( sK5(X3,X4) != sK5(X3,X4)
| sP0(X3,X4)
| ~ in(sK5(X3,X4),X5)
| ~ in(sK6(X3,X4),X5)
| ~ sP0(X3,X5) ),
inference(duplicate_literal_removal,[],[f1166]) ).
fof(f1166,plain,
! [X3,X4,X5] :
( sK5(X3,X4) != sK5(X3,X4)
| sP0(X3,X4)
| ~ in(sK5(X3,X4),X5)
| ~ in(sK6(X3,X4),X5)
| ~ sP0(X3,X5)
| sP0(X3,X4) ),
inference(superposition,[],[f159,f952]) ).
fof(f952,plain,
! [X2,X0,X1] :
( sK5(X0,X1) = sK6(X0,X1)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK6(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f943]) ).
fof(f943,plain,
! [X2,X0,X1] :
( sK5(X0,X1) = sK6(X0,X1)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK6(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1)
| sP0(X0,X1) ),
inference(resolution,[],[f634,f602]) ).
fof(f634,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK5(X0,X1),sK6(X0,X1))),X0)
| sK5(X0,X1) = sK6(X0,X1)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK6(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(forward_demodulation,[],[f624,f177]) ).
fof(f624,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(sK6(X0,X1)),unordered_pair(sK6(X0,X1),sK5(X0,X1))),X0)
| sK5(X0,X1) = sK6(X0,X1)
| ~ in(sK5(X0,X1),X2)
| ~ in(sK6(X0,X1),X2)
| ~ sP0(X0,X2)
| sP0(X0,X1) ),
inference(resolution,[],[f621,f605]) ).
fof(f2118,plain,
! [X3,X4,X5] :
( in(sK6(X5,X4),X3)
| ~ ordinal(X4)
| ~ ordinal(X3)
| sP0(X5,X4)
| empty(X3)
| ordinal_subset(X3,X4) ),
inference(resolution,[],[f1050,f195]) ).
fof(f1050,plain,
! [X16,X14,X15] :
( element(sK6(X16,X14),X15)
| ordinal_subset(X15,X14)
| ~ ordinal(X14)
| ~ ordinal(X15)
| sP0(X16,X14) ),
inference(resolution,[],[f764,f158]) ).
fof(f88018,plain,
( ~ spl19_55
| spl19_89
| ~ spl19_68 ),
inference(avatar_split_clause,[],[f70005,f42835,f88016,f31105]) ).
fof(f70005,plain,
( ! [X3,X4] :
( ~ ordinal(sK5(X3,X4))
| ~ empty(sK5(X3,X4))
| sP0(X3,X4)
| ~ empty(sK6(X3,X4))
| ~ ordinal(sK6(X3,X4))
| ~ empty(powerset(sK4)) )
| ~ spl19_68 ),
inference(resolution,[],[f42836,f563]) ).
fof(f563,plain,
! [X6,X7] :
( sP0(X6,X7)
| ~ empty(X7) ),
inference(resolution,[],[f157,f203]) ).
fof(f88014,plain,
( ~ spl19_55
| spl19_81 ),
inference(avatar_split_clause,[],[f70095,f70016,f31105]) ).
fof(f70095,plain,
( ~ empty(powerset(sK4))
| spl19_81 ),
inference(resolution,[],[f70018,f1684]) ).
fof(f1684,plain,
! [X0] :
( connected(inclusion_relation(X0))
| ~ empty(X0) ),
inference(resolution,[],[f1665,f149]) ).
fof(f1665,plain,
! [X0] :
( ~ relation(inclusion_relation(X0))
| ~ empty(X0)
| connected(inclusion_relation(X0)) ),
inference(resolution,[],[f1005,f415]) ).
fof(f1005,plain,
! [X1] :
( ~ sP1(inclusion_relation(X1))
| connected(inclusion_relation(X1))
| ~ empty(X1)
| ~ relation(inclusion_relation(X1)) ),
inference(resolution,[],[f750,f678]) ).
fof(f678,plain,
! [X0,X1] :
( is_connected_in(X1,X0)
| ~ empty(X0)
| ~ sP1(X1) ),
inference(resolution,[],[f563,f155]) ).
fof(f88013,plain,
( ~ spl19_2
| spl19_55
| spl19_88
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f87971,f30818,f88011,f31105,f249]) ).
fof(f88011,plain,
( spl19_88
<=> ! [X39] :
( ~ empty(X39)
| ~ empty(sK8(X39,relation_field(X39)))
| ~ ordinal(sK8(X39,relation_field(X39)))
| ordinal_subset(sK4,sK9(X39,relation_field(X39)))
| ~ ordinal(sK9(X39,relation_field(X39)))
| ~ sP2(X39,powerset(sK4))
| sP2(X39,relation_field(X39)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_88])]) ).
fof(f87971,plain,
( ! [X39] :
( ~ empty(X39)
| empty(powerset(sK4))
| sP2(X39,relation_field(X39))
| ~ sP2(X39,powerset(sK4))
| ~ ordinal(sK4)
| ~ ordinal(sK9(X39,relation_field(X39)))
| ordinal_subset(sK4,sK9(X39,relation_field(X39)))
| ~ ordinal(sK8(X39,relation_field(X39)))
| ~ empty(sK8(X39,relation_field(X39))) )
| ~ spl19_54 ),
inference(resolution,[],[f8209,f30819]) ).
fof(f8209,plain,
! [X6,X5] :
( ~ subset(sK8(X5,relation_field(X5)),X6)
| ~ empty(X5)
| empty(powerset(X6))
| sP2(X5,relation_field(X5))
| ~ sP2(X5,powerset(X6))
| ~ ordinal(X6)
| ~ ordinal(sK9(X5,relation_field(X5)))
| ordinal_subset(X6,sK9(X5,relation_field(X5))) ),
inference(resolution,[],[f2341,f585]) ).
fof(f80350,plain,
( ~ spl19_3
| ~ spl19_86 ),
inference(avatar_contradiction_clause,[],[f80334]) ).
fof(f80334,plain,
( $false
| ~ spl19_3
| ~ spl19_86 ),
inference(resolution,[],[f80255,f256]) ).
fof(f256,plain,
( empty(empty_set)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f254,plain,
( spl19_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f80255,plain,
( ! [X26] : ~ empty(X26)
| ~ spl19_86 ),
inference(avatar_component_clause,[],[f80254]) ).
fof(f80254,plain,
( spl19_86
<=> ! [X26] : ~ empty(X26) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_86])]) ).
fof(f80349,plain,
( ~ spl19_12
| ~ spl19_86 ),
inference(avatar_contradiction_clause,[],[f80344]) ).
fof(f80344,plain,
( $false
| ~ spl19_12
| ~ spl19_86 ),
inference(resolution,[],[f80255,f299]) ).
fof(f299,plain,
( empty(sK11)
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f297,plain,
( spl19_12
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
fof(f80348,plain,
( ~ spl19_29
| ~ spl19_86 ),
inference(avatar_contradiction_clause,[],[f80345]) ).
fof(f80345,plain,
( $false
| ~ spl19_29
| ~ spl19_86 ),
inference(resolution,[],[f80255,f384]) ).
fof(f384,plain,
( empty(sK17)
| ~ spl19_29 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f382,plain,
( spl19_29
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_29])]) ).
fof(f80347,plain,
( ~ spl19_33
| ~ spl19_86 ),
inference(avatar_contradiction_clause,[],[f80346]) ).
fof(f80346,plain,
( $false
| ~ spl19_33
| ~ spl19_86 ),
inference(resolution,[],[f80255,f404]) ).
fof(f404,plain,
( empty(sK18)
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f402,plain,
( spl19_33
<=> empty(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_33])]) ).
fof(f80259,plain,
( spl19_86
| spl19_87 ),
inference(avatar_split_clause,[],[f80238,f80257,f80254]) ).
fof(f80257,plain,
( spl19_87
<=> ! [X24,X25,X23] :
( empty(relation_field(X23))
| ~ relation(X23)
| ~ connected(X23)
| ~ sP1(X23)
| ~ empty(X23)
| ~ in(X24,sK7(powerset(relation_field(X23))))
| X24 = X25
| ~ in(X25,sK7(powerset(relation_field(X23)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_87])]) ).
fof(f80238,plain,
! [X26,X24,X25,X23] :
( empty(relation_field(X23))
| X24 = X25
| ~ in(X25,sK7(powerset(relation_field(X23))))
| ~ in(X24,sK7(powerset(relation_field(X23))))
| ~ empty(X26)
| ~ empty(X23)
| ~ sP1(X23)
| ~ connected(X23)
| ~ relation(X23) ),
inference(resolution,[],[f27758,f70880]) ).
fof(f27758,plain,
! [X291,X290,X289,X288] :
( ~ sP0(sK7(powerset(X289)),X288)
| empty(X288)
| X290 = X291
| ~ in(X291,sK7(powerset(X288)))
| ~ in(X290,sK7(powerset(X288)))
| ~ empty(X289) ),
inference(resolution,[],[f27633,f2317]) ).
fof(f2317,plain,
! [X21,X18,X19,X20] :
( ~ sP0(sK7(powerset(X18)),X21)
| X19 = X20
| ~ in(X20,X21)
| ~ in(X19,X21)
| ~ empty(X18) ),
inference(duplicate_literal_removal,[],[f2308]) ).
fof(f2308,plain,
! [X21,X18,X19,X20] :
( ~ empty(X18)
| X19 = X20
| ~ in(X20,X21)
| ~ in(X19,X21)
| ~ sP0(sK7(powerset(X18)),X21)
| ~ empty(X18) ),
inference(resolution,[],[f730,f677]) ).
fof(f677,plain,
! [X3,X4] :
( ~ in(X4,sK7(powerset(X3)))
| ~ empty(X3) ),
inference(resolution,[],[f550,f571]) ).
fof(f550,plain,
! [X0] : subset(sK7(powerset(X0)),X0),
inference(resolution,[],[f200,f173]) ).
fof(f730,plain,
! [X8,X6,X9,X7] :
( in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),sK7(powerset(X6)))
| ~ empty(X6)
| X7 = X8
| ~ in(X8,X9)
| ~ in(X7,X9)
| ~ sP0(sK7(powerset(X6)),X9) ),
inference(resolution,[],[f677,f621]) ).
fof(f27633,plain,
! [X0,X1] :
( sP0(X0,sK7(powerset(X1)))
| empty(X1)
| ~ sP0(X0,X1) ),
inference(duplicate_literal_removal,[],[f27628]) ).
fof(f27628,plain,
! [X0,X1] :
( sP0(X0,sK7(powerset(X1)))
| empty(X1)
| ~ sP0(X0,X1)
| empty(X1)
| sP0(X0,sK7(powerset(X1))) ),
inference(resolution,[],[f6254,f1919]) ).
fof(f1919,plain,
! [X2,X3] :
( in(sK5(X2,sK7(powerset(X3))),X3)
| empty(X3)
| sP0(X2,sK7(powerset(X3))) ),
inference(resolution,[],[f970,f195]) ).
fof(f970,plain,
! [X8,X7] :
( element(sK5(X7,sK7(powerset(X8))),X8)
| sP0(X7,sK7(powerset(X8))) ),
inference(resolution,[],[f675,f157]) ).
fof(f675,plain,
! [X0,X1] :
( ~ in(X0,sK7(powerset(X1)))
| element(X0,X1) ),
inference(resolution,[],[f550,f589]) ).
fof(f6254,plain,
! [X0,X1] :
( ~ in(sK5(X1,sK7(powerset(X0))),X0)
| sP0(X1,sK7(powerset(X0)))
| empty(X0)
| ~ sP0(X1,X0) ),
inference(duplicate_literal_removal,[],[f6223]) ).
fof(f6223,plain,
! [X0,X1] :
( empty(X0)
| sP0(X1,sK7(powerset(X0)))
| ~ in(sK5(X1,sK7(powerset(X0))),X0)
| sP0(X1,sK7(powerset(X0)))
| ~ sP0(X1,X0) ),
inference(resolution,[],[f1922,f1189]) ).
fof(f1922,plain,
! [X2,X3] :
( in(sK6(X2,sK7(powerset(X3))),X3)
| empty(X3)
| sP0(X2,sK7(powerset(X3))) ),
inference(resolution,[],[f971,f195]) ).
fof(f971,plain,
! [X10,X9] :
( element(sK6(X9,sK7(powerset(X10))),X10)
| sP0(X9,sK7(powerset(X10))) ),
inference(resolution,[],[f675,f158]) ).
fof(f70098,plain,
( ~ spl19_80
| spl19_84
| spl19_81 ),
inference(avatar_split_clause,[],[f70096,f70016,f70041,f70012]) ).
fof(f70096,plain,
( ! [X0] :
( ~ connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_81 ),
inference(superposition,[],[f70018,f2069]) ).
fof(f70049,plain,
( ~ spl19_80
| spl19_85
| ~ spl19_81 ),
inference(avatar_split_clause,[],[f70044,f70016,f70047,f70012]) ).
fof(f70044,plain,
( ! [X0] :
( connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| ~ spl19_81 ),
inference(superposition,[],[f70017,f2069]) ).
fof(f70043,plain,
( ~ spl19_80
| spl19_84
| spl19_81 ),
inference(avatar_split_clause,[],[f70038,f70016,f70041,f70012]) ).
fof(f70038,plain,
( ! [X0] :
( ~ connected(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_81 ),
inference(superposition,[],[f70018,f2069]) ).
fof(f70035,plain,
spl19_80,
inference(avatar_contradiction_clause,[],[f70031]) ).
fof(f70031,plain,
( $false
| spl19_80 ),
inference(resolution,[],[f70014,f149]) ).
fof(f70014,plain,
( ~ relation(inclusion_relation(powerset(sK4)))
| spl19_80 ),
inference(avatar_component_clause,[],[f70012]) ).
fof(f70030,plain,
( ~ spl19_80
| spl19_83
| spl19_79 ),
inference(avatar_split_clause,[],[f70024,f70008,f70028,f70012]) ).
fof(f70028,plain,
( spl19_83
<=> ! [X0] :
( ~ sP1(X0)
| ~ relation(X0)
| ~ sP2(X0,powerset(sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_83])]) ).
fof(f70008,plain,
( spl19_79
<=> sP1(inclusion_relation(powerset(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_79])]) ).
fof(f70024,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP2(X0,powerset(sK4))
| ~ relation(X0)
| ~ relation(inclusion_relation(powerset(sK4))) )
| spl19_79 ),
inference(superposition,[],[f70010,f2069]) ).
fof(f70010,plain,
( ~ sP1(inclusion_relation(powerset(sK4)))
| spl19_79 ),
inference(avatar_component_clause,[],[f70008]) ).
fof(f70026,plain,
spl19_79,
inference(avatar_contradiction_clause,[],[f70023]) ).
fof(f70023,plain,
( $false
| spl19_79 ),
inference(resolution,[],[f70010,f415]) ).
fof(f70022,plain,
( ~ spl19_79
| ~ spl19_80
| ~ spl19_81
| spl19_82
| ~ spl19_68 ),
inference(avatar_split_clause,[],[f70006,f42835,f70020,f70016,f70012,f70008]) ).
fof(f70020,plain,
( spl19_82
<=> ! [X5] :
( ~ ordinal(sK5(inclusion_relation(powerset(sK4)),X5))
| ~ ordinal(sK6(inclusion_relation(powerset(sK4)),X5))
| ~ empty(sK6(inclusion_relation(powerset(sK4)),X5))
| sP0(inclusion_relation(powerset(sK4)),X5)
| ~ empty(sK5(inclusion_relation(powerset(sK4)),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_82])]) ).
fof(f70006,plain,
( ! [X5] :
( ~ ordinal(sK5(inclusion_relation(powerset(sK4)),X5))
| ~ empty(sK5(inclusion_relation(powerset(sK4)),X5))
| sP0(inclusion_relation(powerset(sK4)),X5)
| ~ empty(sK6(inclusion_relation(powerset(sK4)),X5))
| ~ ordinal(sK6(inclusion_relation(powerset(sK4)),X5))
| ~ connected(inclusion_relation(powerset(sK4)))
| ~ relation(inclusion_relation(powerset(sK4)))
| ~ sP1(inclusion_relation(powerset(sK4))) )
| ~ spl19_68 ),
inference(resolution,[],[f42836,f1002]) ).
fof(f48674,plain,
( spl19_70
| spl19_78 ),
inference(avatar_split_clause,[],[f48633,f48672,f48641]) ).
fof(f48641,plain,
( spl19_70
<=> ! [X69] :
( ~ empty(X69)
| empty(powerset(X69))
| ~ ordinal(powerset(X69)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_70])]) ).
fof(f48672,plain,
( spl19_78
<=> ! [X294] :
( empty(sK7(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294))))))
| ~ empty(sK9(X294,relation_field(X294)))
| ~ empty(sK9(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294)))))
| ~ empty(X294)
| sP2(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294))))
| sP2(X294,relation_field(X294))
| ~ ordinal(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294)))))
| empty(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_78])]) ).
fof(f48633,plain,
! [X295,X294] :
( empty(sK7(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294))))))
| empty(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294)))))
| ~ empty(X295)
| ~ ordinal(powerset(X295))
| empty(powerset(X295))
| ~ ordinal(sK8(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294)))))
| sP2(X294,relation_field(X294))
| sP2(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294))))
| ~ empty(X294)
| ~ empty(sK9(sK8(X294,relation_field(X294)),relation_field(sK8(X294,relation_field(X294)))))
| ~ empty(sK9(X294,relation_field(X294))) ),
inference(resolution,[],[f48135,f3163]) ).
fof(f3163,plain,
! [X8,X9] :
( ~ in(X9,sK8(sK8(X8,relation_field(X8)),relation_field(sK8(X8,relation_field(X8)))))
| sP2(X8,relation_field(X8))
| sP2(sK8(X8,relation_field(X8)),relation_field(sK8(X8,relation_field(X8))))
| ~ empty(X8)
| ~ empty(sK9(sK8(X8,relation_field(X8)),relation_field(sK8(X8,relation_field(X8)))))
| ~ empty(sK9(X8,relation_field(X8))) ),
inference(resolution,[],[f1075,f571]) ).
fof(f1075,plain,
! [X0] :
( subset(sK8(sK8(X0,relation_field(X0)),relation_field(sK8(X0,relation_field(X0)))),sK9(sK8(X0,relation_field(X0)),relation_field(sK8(X0,relation_field(X0)))))
| ~ empty(sK9(X0,relation_field(X0)))
| sP2(X0,relation_field(X0))
| sP2(sK8(X0,relation_field(X0)),relation_field(sK8(X0,relation_field(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f786,f636]) ).
fof(f786,plain,
! [X3,X4] :
( ~ in(X4,sK8(X3,relation_field(X3)))
| ~ empty(X3)
| ~ empty(sK9(X3,relation_field(X3)))
| sP2(X3,relation_field(X3)) ),
inference(resolution,[],[f649,f571]) ).
fof(f48135,plain,
! [X2,X3] :
( in(sK7(powerset(X3)),X2)
| empty(sK7(X2))
| empty(X2)
| ~ empty(X3)
| ~ ordinal(powerset(X3))
| empty(powerset(X3))
| ~ ordinal(X2) ),
inference(duplicate_literal_removal,[],[f48134]) ).
fof(f48134,plain,
! [X2,X3] :
( ~ ordinal(X2)
| empty(sK7(X2))
| empty(X2)
| ~ empty(X3)
| ~ ordinal(powerset(X3))
| empty(powerset(X3))
| empty(X2)
| in(sK7(powerset(X3)),X2) ),
inference(resolution,[],[f37880,f195]) ).
fof(f37880,plain,
! [X29,X30] :
( element(sK7(powerset(X29)),X30)
| ~ ordinal(X30)
| empty(sK7(X30))
| empty(X30)
| ~ empty(X29)
| ~ ordinal(powerset(X29))
| empty(powerset(X29)) ),
inference(resolution,[],[f28625,f568]) ).
fof(f28625,plain,
! [X10,X11,X12] :
( ~ in(X12,powerset(X10))
| ~ empty(X10)
| ~ ordinal(X11)
| empty(sK7(X11))
| empty(X11)
| element(X12,X11)
| ~ ordinal(powerset(X10)) ),
inference(resolution,[],[f28560,f589]) ).
fof(f28560,plain,
! [X0,X1] :
( subset(powerset(X1),X0)
| ~ ordinal(powerset(X1))
| ~ empty(X1)
| ~ ordinal(X0)
| empty(sK7(X0))
| empty(X0) ),
inference(duplicate_literal_removal,[],[f28559]) ).
fof(f28559,plain,
! [X0,X1] :
( empty(X0)
| ~ ordinal(powerset(X1))
| ~ empty(X1)
| ~ ordinal(X0)
| empty(sK7(X0))
| subset(powerset(X1),X0)
| ~ ordinal(X0)
| ~ ordinal(powerset(X1)) ),
inference(resolution,[],[f28156,f198]) ).
fof(f28156,plain,
! [X48,X49] :
( ordinal_subset(powerset(X48),X49)
| empty(X49)
| ~ ordinal(powerset(X48))
| ~ empty(X48)
| ~ ordinal(X49)
| empty(sK7(X49)) ),
inference(resolution,[],[f6740,f568]) ).
fof(f6740,plain,
! [X10,X11,X12] :
( ~ in(X12,sK7(X10))
| ~ ordinal(powerset(X11))
| empty(X10)
| ordinal_subset(powerset(X11),X10)
| ~ empty(X11)
| ~ ordinal(X10) ),
inference(resolution,[],[f2065,f571]) ).
fof(f2065,plain,
! [X0,X1] :
( subset(sK7(X1),X0)
| ~ ordinal(X1)
| ~ ordinal(powerset(X0))
| empty(X1)
| ordinal_subset(powerset(X0),X1) ),
inference(resolution,[],[f1048,f200]) ).
fof(f1048,plain,
! [X10,X9] :
( element(sK7(X9),X10)
| ordinal_subset(X10,X9)
| ~ ordinal(X9)
| ~ ordinal(X10)
| empty(X9) ),
inference(resolution,[],[f764,f568]) ).
fof(f48670,plain,
( spl19_70
| spl19_77 ),
inference(avatar_split_clause,[],[f48631,f48668,f48641]) ).
fof(f48668,plain,
( spl19_77
<=> ! [X290] :
( empty(sK7(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290))))))
| sP2(sK7(powerset(X290)),relation_field(sK7(powerset(X290))))
| ~ empty(sK9(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))))
| ~ empty(X290)
| ~ ordinal(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))))
| empty(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_77])]) ).
fof(f48631,plain,
! [X291,X290] :
( empty(sK7(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290))))))
| empty(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))))
| ~ empty(X291)
| ~ ordinal(powerset(X291))
| empty(powerset(X291))
| ~ ordinal(sK8(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))))
| ~ empty(X290)
| ~ empty(sK9(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))))
| sP2(sK7(powerset(X290)),relation_field(sK7(powerset(X290)))) ),
inference(resolution,[],[f48135,f2355]) ).
fof(f2355,plain,
! [X8,X9] :
( ~ in(X9,sK8(sK7(powerset(X8)),relation_field(sK7(powerset(X8)))))
| ~ empty(X8)
| ~ empty(sK9(sK7(powerset(X8)),relation_field(sK7(powerset(X8)))))
| sP2(sK7(powerset(X8)),relation_field(sK7(powerset(X8)))) ),
inference(resolution,[],[f726,f571]) ).
fof(f726,plain,
! [X0] :
( subset(sK8(sK7(powerset(X0)),relation_field(sK7(powerset(X0)))),sK9(sK7(powerset(X0)),relation_field(sK7(powerset(X0)))))
| sP2(sK7(powerset(X0)),relation_field(sK7(powerset(X0))))
| ~ empty(X0) ),
inference(resolution,[],[f677,f636]) ).
fof(f48666,plain,
( spl19_70
| spl19_76 ),
inference(avatar_split_clause,[],[f48627,f48664,f48641]) ).
fof(f48664,plain,
( spl19_76
<=> ! [X283,X281] :
( empty(sK7(sK8(X281,relation_field(X281))))
| ~ empty(sK9(X281,relation_field(X281)))
| ~ ordinal(X281)
| sP2(X281,relation_field(X281))
| ~ empty(X283)
| ordinal_subset(X283,X281)
| ~ ordinal(X283)
| ~ ordinal(sK8(X281,relation_field(X281)))
| empty(sK8(X281,relation_field(X281))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_76])]) ).
fof(f48627,plain,
! [X283,X282,X281] :
( empty(sK7(sK8(X281,relation_field(X281))))
| empty(sK8(X281,relation_field(X281)))
| ~ empty(X282)
| ~ ordinal(powerset(X282))
| empty(powerset(X282))
| ~ ordinal(sK8(X281,relation_field(X281)))
| ~ empty(X283)
| ~ ordinal(X283)
| sP2(X281,relation_field(X281))
| ~ ordinal(X281)
| ~ empty(sK9(X281,relation_field(X281)))
| ordinal_subset(X283,X281) ),
inference(resolution,[],[f48135,f2223]) ).
fof(f2223,plain,
! [X14,X15,X13] :
( ~ in(X15,sK8(X14,relation_field(X14)))
| ~ empty(X13)
| ~ ordinal(X13)
| sP2(X14,relation_field(X14))
| ~ ordinal(X14)
| ~ empty(sK9(X14,relation_field(X14)))
| ordinal_subset(X13,X14) ),
inference(resolution,[],[f1021,f571]) ).
fof(f1021,plain,
! [X0,X1] :
( subset(sK8(X0,relation_field(X0)),sK9(X0,relation_field(X0)))
| ordinal_subset(X1,X0)
| ~ empty(X1)
| ~ ordinal(X1)
| sP2(X0,relation_field(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f766,f636]) ).
fof(f48662,plain,
( spl19_70
| spl19_75 ),
inference(avatar_split_clause,[],[f48576,f48660,f48641]) ).
fof(f48660,plain,
( spl19_75
<=> ! [X145,X147] :
( empty(sK7(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145)))))))
| ~ in(sK9(powerset(X145),relation_field(powerset(X145))),X147)
| ~ empty(X145)
| ~ subset(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145))))
| sP2(powerset(X145),relation_field(powerset(X145)))
| sK9(powerset(X145),relation_field(powerset(X145))) = sK8(powerset(X145),relation_field(powerset(X145)))
| ~ sP0(powerset(X145),X147)
| ~ in(sK8(powerset(X145),relation_field(powerset(X145))),X147)
| ~ ordinal(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145))))))
| empty(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_75])]) ).
fof(f48576,plain,
! [X145,X146,X147] :
( empty(sK7(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145)))))))
| empty(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145))))))
| ~ empty(X146)
| ~ ordinal(powerset(X146))
| empty(powerset(X146))
| ~ ordinal(unordered_pair(singleton(sK9(powerset(X145),relation_field(powerset(X145)))),unordered_pair(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145))))))
| ~ in(sK8(powerset(X145),relation_field(powerset(X145))),X147)
| ~ sP0(powerset(X145),X147)
| sK9(powerset(X145),relation_field(powerset(X145))) = sK8(powerset(X145),relation_field(powerset(X145)))
| sP2(powerset(X145),relation_field(powerset(X145)))
| ~ subset(sK8(powerset(X145),relation_field(powerset(X145))),sK9(powerset(X145),relation_field(powerset(X145))))
| ~ empty(X145)
| ~ in(sK9(powerset(X145),relation_field(powerset(X145))),X147) ),
inference(resolution,[],[f48135,f5679]) ).
fof(f5679,plain,
! [X14,X15,X13] :
( ~ in(X15,unordered_pair(singleton(sK9(powerset(X13),relation_field(powerset(X13)))),unordered_pair(sK8(powerset(X13),relation_field(powerset(X13))),sK9(powerset(X13),relation_field(powerset(X13))))))
| ~ in(sK8(powerset(X13),relation_field(powerset(X13))),X14)
| ~ sP0(powerset(X13),X14)
| sK9(powerset(X13),relation_field(powerset(X13))) = sK8(powerset(X13),relation_field(powerset(X13)))
| sP2(powerset(X13),relation_field(powerset(X13)))
| ~ subset(sK8(powerset(X13),relation_field(powerset(X13))),sK9(powerset(X13),relation_field(powerset(X13))))
| ~ empty(X13)
| ~ in(sK9(powerset(X13),relation_field(powerset(X13))),X14) ),
inference(resolution,[],[f1358,f571]) ).
fof(f1358,plain,
! [X3,X4] :
( subset(unordered_pair(singleton(sK9(powerset(X3),relation_field(powerset(X3)))),unordered_pair(sK8(powerset(X3),relation_field(powerset(X3))),sK9(powerset(X3),relation_field(powerset(X3))))),X3)
| ~ in(sK9(powerset(X3),relation_field(powerset(X3))),X4)
| ~ in(sK8(powerset(X3),relation_field(powerset(X3))),X4)
| ~ sP0(powerset(X3),X4)
| sK9(powerset(X3),relation_field(powerset(X3))) = sK8(powerset(X3),relation_field(powerset(X3)))
| sP2(powerset(X3),relation_field(powerset(X3)))
| ~ subset(sK8(powerset(X3),relation_field(powerset(X3))),sK9(powerset(X3),relation_field(powerset(X3)))) ),
inference(forward_demodulation,[],[f1346,f177]) ).
fof(f1346,plain,
! [X3,X4] :
( ~ in(sK9(powerset(X3),relation_field(powerset(X3))),X4)
| ~ in(sK8(powerset(X3),relation_field(powerset(X3))),X4)
| ~ sP0(powerset(X3),X4)
| sK9(powerset(X3),relation_field(powerset(X3))) = sK8(powerset(X3),relation_field(powerset(X3)))
| subset(unordered_pair(singleton(sK9(powerset(X3),relation_field(powerset(X3)))),unordered_pair(sK9(powerset(X3),relation_field(powerset(X3))),sK8(powerset(X3),relation_field(powerset(X3))))),X3)
| sP2(powerset(X3),relation_field(powerset(X3)))
| ~ subset(sK8(powerset(X3),relation_field(powerset(X3))),sK9(powerset(X3),relation_field(powerset(X3)))) ),
inference(resolution,[],[f844,f635]) ).
fof(f844,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),powerset(X3))
| ~ in(X1,X2)
| ~ in(X0,X2)
| ~ sP0(powerset(X3),X2)
| X0 = X1
| subset(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X3) ),
inference(resolution,[],[f627,f200]) ).
fof(f627,plain,
! [X14,X15,X12,X13] :
( element(unordered_pair(singleton(X13),unordered_pair(X13,X12)),X14)
| X12 = X13
| ~ in(X13,X15)
| ~ in(X12,X15)
| ~ sP0(X14,X15)
| in(unordered_pair(singleton(X12),unordered_pair(X12,X13)),X14) ),
inference(resolution,[],[f621,f194]) ).
fof(f194,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t1_subset) ).
fof(f48658,plain,
( spl19_70
| spl19_74 ),
inference(avatar_split_clause,[],[f48564,f48656,f48641]) ).
fof(f48656,plain,
( spl19_74
<=> ! [X101,X105,X104,X100,X103] :
( empty(sK7(unordered_pair(singleton(X100),unordered_pair(X100,X101))))
| ~ in(X101,X104)
| ~ empty(X103)
| ~ sP2(powerset(X103),X105)
| ~ in(X101,X105)
| ~ in(X100,X105)
| subset(X101,X100)
| ~ in(X100,X104)
| X100 = X101
| ~ sP0(powerset(X103),X104)
| ~ ordinal(unordered_pair(singleton(X100),unordered_pair(X100,X101)))
| empty(unordered_pair(singleton(X100),unordered_pair(X100,X101))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_74])]) ).
fof(f48564,plain,
! [X101,X104,X102,X105,X103,X100] :
( empty(sK7(unordered_pair(singleton(X100),unordered_pair(X100,X101))))
| empty(unordered_pair(singleton(X100),unordered_pair(X100,X101)))
| ~ empty(X102)
| ~ ordinal(powerset(X102))
| empty(powerset(X102))
| ~ ordinal(unordered_pair(singleton(X100),unordered_pair(X100,X101)))
| ~ sP0(powerset(X103),X104)
| X100 = X101
| ~ in(X100,X104)
| subset(X101,X100)
| ~ in(X100,X105)
| ~ in(X101,X105)
| ~ sP2(powerset(X103),X105)
| ~ empty(X103)
| ~ in(X101,X104) ),
inference(resolution,[],[f48135,f2931]) ).
fof(f2931,plain,
! [X40,X41,X44,X45,X42,X43] :
( ~ in(X45,unordered_pair(singleton(X43),unordered_pair(X43,X40)))
| ~ sP0(powerset(X42),X41)
| X40 = X43
| ~ in(X43,X41)
| subset(X40,X43)
| ~ in(X43,X44)
| ~ in(X40,X44)
| ~ sP2(powerset(X42),X44)
| ~ empty(X42)
| ~ in(X40,X41) ),
inference(resolution,[],[f1347,f571]) ).
fof(f1347,plain,
! [X8,X6,X9,X7,X5] :
( subset(unordered_pair(singleton(X5),unordered_pair(X5,X7)),X8)
| ~ in(X7,X6)
| ~ sP0(powerset(X8),X6)
| X5 = X7
| ~ in(X5,X6)
| subset(X7,X5)
| ~ in(X5,X9)
| ~ in(X7,X9)
| ~ sP2(powerset(X8),X9) ),
inference(resolution,[],[f844,f609]) ).
fof(f48654,plain,
( spl19_70
| spl19_73 ),
inference(avatar_split_clause,[],[f48562,f48652,f48641]) ).
fof(f48652,plain,
( spl19_73
<=> ! [X92,X88,X91,X93,X89] :
( empty(sK7(unordered_pair(singleton(X88),unordered_pair(X88,X89))))
| ~ in(X89,X92)
| ~ empty(X91)
| ~ ordinal(X93)
| ~ empty(X93)
| ordinal_subset(X93,powerset(X91))
| ~ ordinal(powerset(X91))
| ~ in(X88,X92)
| X88 = X89
| ~ sP0(powerset(X91),X92)
| ~ ordinal(unordered_pair(singleton(X88),unordered_pair(X88,X89)))
| empty(unordered_pair(singleton(X88),unordered_pair(X88,X89))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_73])]) ).
fof(f48562,plain,
! [X90,X91,X88,X89,X92,X93] :
( empty(sK7(unordered_pair(singleton(X88),unordered_pair(X88,X89))))
| empty(unordered_pair(singleton(X88),unordered_pair(X88,X89)))
| ~ empty(X90)
| ~ ordinal(powerset(X90))
| empty(powerset(X90))
| ~ ordinal(unordered_pair(singleton(X88),unordered_pair(X88,X89)))
| ~ sP0(powerset(X91),X92)
| X88 = X89
| ~ in(X88,X92)
| ~ ordinal(powerset(X91))
| ordinal_subset(X93,powerset(X91))
| ~ empty(X93)
| ~ ordinal(X93)
| ~ empty(X91)
| ~ in(X89,X92) ),
inference(resolution,[],[f48135,f2784]) ).
fof(f2784,plain,
! [X40,X41,X44,X45,X42,X43] :
( ~ in(X45,unordered_pair(singleton(X43),unordered_pair(X43,X40)))
| ~ sP0(powerset(X42),X41)
| X40 = X43
| ~ in(X43,X41)
| ~ ordinal(powerset(X42))
| ordinal_subset(X44,powerset(X42))
| ~ empty(X44)
| ~ ordinal(X44)
| ~ empty(X42)
| ~ in(X40,X41) ),
inference(resolution,[],[f1350,f571]) ).
fof(f1350,plain,
! [X21,X19,X22,X23,X20] :
( subset(unordered_pair(singleton(X19),unordered_pair(X19,X21)),X22)
| ~ in(X21,X20)
| ~ sP0(powerset(X22),X20)
| X19 = X21
| ~ in(X19,X20)
| ~ ordinal(powerset(X22))
| ordinal_subset(X23,powerset(X22))
| ~ empty(X23)
| ~ ordinal(X23) ),
inference(resolution,[],[f844,f766]) ).
fof(f48650,plain,
( spl19_70
| spl19_72 ),
inference(avatar_split_clause,[],[f48560,f48648,f48641]) ).
fof(f48648,plain,
( spl19_72
<=> ! [X81,X77,X78,X80] :
( empty(sK7(unordered_pair(singleton(X77),unordered_pair(X77,X78))))
| ~ in(X77,X81)
| ~ empty(X80)
| ~ in(X78,X81)
| X77 = X78
| ordinal(unordered_pair(singleton(X78),unordered_pair(X78,X77)))
| ~ sP0(powerset(X80),X81)
| ~ ordinal(powerset(X80))
| ~ ordinal(unordered_pair(singleton(X77),unordered_pair(X77,X78)))
| empty(unordered_pair(singleton(X77),unordered_pair(X77,X78))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_72])]) ).
fof(f48560,plain,
! [X80,X78,X81,X79,X77] :
( empty(sK7(unordered_pair(singleton(X77),unordered_pair(X77,X78))))
| empty(unordered_pair(singleton(X77),unordered_pair(X77,X78)))
| ~ empty(X79)
| ~ ordinal(powerset(X79))
| empty(powerset(X79))
| ~ ordinal(unordered_pair(singleton(X77),unordered_pair(X77,X78)))
| ~ sP0(powerset(X80),X81)
| ordinal(unordered_pair(singleton(X78),unordered_pair(X78,X77)))
| ~ ordinal(powerset(X80))
| X77 = X78
| ~ in(X78,X81)
| ~ empty(X80)
| ~ in(X77,X81) ),
inference(resolution,[],[f48135,f2705]) ).
fof(f2705,plain,
! [X36,X34,X35,X32,X33] :
( ~ in(X36,unordered_pair(singleton(X32),unordered_pair(X32,X35)))
| ~ sP0(powerset(X34),X33)
| ordinal(unordered_pair(singleton(X35),unordered_pair(X35,X32)))
| ~ ordinal(powerset(X34))
| X32 = X35
| ~ in(X35,X33)
| ~ empty(X34)
| ~ in(X32,X33) ),
inference(resolution,[],[f1322,f571]) ).
fof(f1322,plain,
! [X2,X3,X0,X1] :
( subset(unordered_pair(singleton(X2),unordered_pair(X2,X0)),X3)
| ~ in(X2,X1)
| ~ sP0(powerset(X3),X1)
| ordinal(unordered_pair(singleton(X0),unordered_pair(X0,X2)))
| ~ ordinal(powerset(X3))
| X0 = X2
| ~ in(X0,X1) ),
inference(resolution,[],[f895,f200]) ).
fof(f895,plain,
! [X21,X18,X19,X20] :
( element(unordered_pair(singleton(X18),unordered_pair(X18,X19)),X21)
| ~ in(X19,X20)
| ~ in(X18,X20)
| ~ sP0(X21,X20)
| ordinal(unordered_pair(singleton(X19),unordered_pair(X19,X18)))
| ~ ordinal(X21)
| X18 = X19 ),
inference(resolution,[],[f626,f194]) ).
fof(f626,plain,
! [X10,X11,X8,X9] :
( in(unordered_pair(singleton(X8),unordered_pair(X8,X9)),X10)
| X8 = X9
| ~ in(X9,X11)
| ~ in(X8,X11)
| ~ sP0(X10,X11)
| ordinal(unordered_pair(singleton(X9),unordered_pair(X9,X8)))
| ~ ordinal(X10) ),
inference(resolution,[],[f621,f192]) ).
fof(f48646,plain,
( spl19_70
| spl19_71 ),
inference(avatar_split_clause,[],[f48558,f48644,f48641]) ).
fof(f48644,plain,
( spl19_71
<=> ! [X71,X70,X67,X68] :
( empty(sK7(unordered_pair(singleton(X67),unordered_pair(X67,X68))))
| ~ in(X68,X70)
| ~ empty(X71)
| subset(unordered_pair(singleton(X68),unordered_pair(X68,X67)),X71)
| X67 = X68
| ~ sP0(powerset(X71),X70)
| ~ in(X67,X70)
| ~ ordinal(unordered_pair(singleton(X67),unordered_pair(X67,X68)))
| empty(unordered_pair(singleton(X67),unordered_pair(X67,X68))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_71])]) ).
fof(f48558,plain,
! [X70,X71,X68,X69,X67] :
( empty(sK7(unordered_pair(singleton(X67),unordered_pair(X67,X68))))
| empty(unordered_pair(singleton(X67),unordered_pair(X67,X68)))
| ~ empty(X69)
| ~ ordinal(powerset(X69))
| empty(powerset(X69))
| ~ ordinal(unordered_pair(singleton(X67),unordered_pair(X67,X68)))
| ~ in(X67,X70)
| ~ sP0(powerset(X71),X70)
| X67 = X68
| subset(unordered_pair(singleton(X68),unordered_pair(X68,X67)),X71)
| ~ empty(X71)
| ~ in(X68,X70) ),
inference(resolution,[],[f48135,f2648]) ).
fof(f2648,plain,
! [X36,X34,X35,X32,X33] :
( ~ in(X36,unordered_pair(singleton(X34),unordered_pair(X34,X32)))
| ~ in(X34,X33)
| ~ sP0(powerset(X35),X33)
| X32 = X34
| subset(unordered_pair(singleton(X32),unordered_pair(X32,X34)),X35)
| ~ empty(X35)
| ~ in(X32,X33) ),
inference(resolution,[],[f1359,f571]) ).
fof(f1359,plain,
! [X31,X28,X29,X30] :
( subset(unordered_pair(singleton(X30),unordered_pair(X30,X28)),X31)
| ~ in(X28,X29)
| ~ in(X30,X29)
| ~ sP0(powerset(X31),X29)
| X28 = X30
| subset(unordered_pair(singleton(X28),unordered_pair(X28,X30)),X31) ),
inference(forward_literal_rewriting,[],[f1352,f200]) ).
fof(f1352,plain,
! [X31,X28,X29,X30] :
( ~ in(X28,X29)
| ~ in(X30,X29)
| ~ sP0(powerset(X31),X29)
| X28 = X30
| subset(unordered_pair(singleton(X28),unordered_pair(X28,X30)),X31)
| element(unordered_pair(singleton(X30),unordered_pair(X30,X28)),powerset(X31)) ),
inference(resolution,[],[f844,f194]) ).
fof(f42842,plain,
( ~ spl19_2
| spl19_69
| ~ spl19_62 ),
inference(avatar_split_clause,[],[f42827,f42088,f42840,f249]) ).
fof(f42840,plain,
( spl19_69
<=> ! [X9,X8] :
( ~ empty(sK6(X8,X9))
| ordinal_subset(sK4,sK5(X8,X9))
| ~ ordinal(sK5(X8,X9))
| sP0(X8,X9)
| ~ sP0(X8,powerset(sK4))
| ~ ordinal(sK6(X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_69])]) ).
fof(f42088,plain,
( spl19_62
<=> ! [X45,X46] :
( ~ sP0(X45,powerset(sK4))
| ~ empty(sK6(X45,X46))
| ~ ordinal(sK6(X45,X46))
| ~ subset(sK5(X45,X46),sK4)
| sP0(X45,X46) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_62])]) ).
fof(f42827,plain,
( ! [X8,X9] :
( ~ empty(sK6(X8,X9))
| ~ ordinal(sK6(X8,X9))
| ~ sP0(X8,powerset(sK4))
| sP0(X8,X9)
| ~ ordinal(sK4)
| ~ ordinal(sK5(X8,X9))
| ordinal_subset(sK4,sK5(X8,X9)) )
| ~ spl19_62 ),
inference(resolution,[],[f42089,f585]) ).
fof(f42089,plain,
( ! [X46,X45] :
( ~ subset(sK5(X45,X46),sK4)
| ~ empty(sK6(X45,X46))
| ~ ordinal(sK6(X45,X46))
| ~ sP0(X45,powerset(sK4))
| sP0(X45,X46) )
| ~ spl19_62 ),
inference(avatar_component_clause,[],[f42088]) ).
fof(f42838,plain,
( ~ spl19_2
| spl19_52
| spl19_68
| ~ spl19_62 ),
inference(avatar_split_clause,[],[f42826,f42088,f42835,f1759,f249]) ).
fof(f42826,plain,
( ! [X6,X7] :
( ~ empty(sK6(X6,X7))
| ~ ordinal(sK6(X6,X7))
| ~ sP0(X6,powerset(sK4))
| sP0(X6,X7)
| ~ empty(sK5(X6,X7))
| ~ ordinal(sK5(X6,X7))
| empty(sK4)
| ~ ordinal(sK4) )
| ~ spl19_62 ),
inference(resolution,[],[f42089,f1917]) ).
fof(f42837,plain,
( ~ spl19_2
| spl19_1
| spl19_68
| ~ spl19_62 ),
inference(avatar_split_clause,[],[f42825,f42088,f42835,f244,f249]) ).
fof(f42825,plain,
( ! [X4,X5] :
( ~ empty(sK6(X4,X5))
| ~ ordinal(sK6(X4,X5))
| ~ sP0(X4,powerset(sK4))
| sP0(X4,X5)
| connected(inclusion_relation(sK4))
| ~ empty(sK5(X4,X5))
| ~ ordinal(sK5(X4,X5))
| ~ ordinal(sK4) )
| ~ spl19_62 ),
inference(resolution,[],[f42089,f33322]) ).
fof(f33322,plain,
! [X0,X1] :
( subset(X1,X0)
| connected(inclusion_relation(X0))
| ~ empty(X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[],[f33046,f149]) ).
fof(f33046,plain,
! [X0,X1] :
( ~ relation(inclusion_relation(X1))
| ~ ordinal(X1)
| connected(inclusion_relation(X1))
| ~ empty(X0)
| ~ ordinal(X0)
| subset(X0,X1) ),
inference(resolution,[],[f32798,f415]) ).
fof(f32798,plain,
! [X0,X1] :
( ~ sP1(inclusion_relation(X0))
| ~ empty(X1)
| ~ ordinal(X0)
| connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X1)
| subset(X1,X0) ),
inference(duplicate_literal_removal,[],[f32794]) ).
fof(f32794,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ empty(X1)
| ~ sP1(inclusion_relation(X0))
| connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ ordinal(X1)
| subset(X1,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f29472,f570]) ).
fof(f29472,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1)
| ~ ordinal(X1)
| ~ empty(X2)
| ~ sP1(X0)
| connected(X0)
| ~ relation(X0)
| ~ ordinal(X2)
| subset(X2,X1) ),
inference(superposition,[],[f28143,f184]) ).
fof(f28143,plain,
! [X0,X1] :
( subset(X0,relation_field(X1))
| ~ ordinal(relation_field(X1))
| ~ empty(X0)
| ~ sP1(X1)
| connected(X1)
| ~ relation(X1)
| ~ ordinal(X0) ),
inference(duplicate_literal_removal,[],[f28139]) ).
fof(f28139,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(relation_field(X1))
| ~ empty(X0)
| ~ sP1(X1)
| connected(X1)
| ~ relation(X1)
| subset(X0,relation_field(X1))
| ~ ordinal(relation_field(X1))
| ~ ordinal(X0) ),
inference(resolution,[],[f6275,f198]) ).
fof(f6275,plain,
! [X0,X1] :
( ordinal_subset(X0,relation_field(X1))
| ~ ordinal(X0)
| ~ ordinal(relation_field(X1))
| ~ empty(X0)
| ~ sP1(X1)
| connected(X1)
| ~ relation(X1) ),
inference(resolution,[],[f2011,f153]) ).
fof(f42206,plain,
( spl19_67
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42180,f31105,f42203]) ).
fof(f42180,plain,
( function(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f165]) ).
fof(f42201,plain,
( spl19_66
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42179,f31105,f42198]) ).
fof(f42179,plain,
( epsilon_transitive(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f167]) ).
fof(f42196,plain,
( spl19_65
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42178,f31105,f42193]) ).
fof(f42178,plain,
( epsilon_connected(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f168]) ).
fof(f42191,plain,
( spl19_60
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42177,f31105,f40431]) ).
fof(f42177,plain,
( ordinal(powerset(sK4))
| ~ spl19_55 ),
inference(resolution,[],[f31107,f169]) ).
fof(f42190,plain,
( spl19_64
| ~ spl19_8
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42176,f31105,f280,f42187]) ).
fof(f42176,plain,
( relation(powerset(sK4))
| ~ spl19_8
| ~ spl19_55 ),
inference(resolution,[],[f31107,f530]) ).
fof(f42185,plain,
( spl19_63
| ~ spl19_35
| ~ spl19_55 ),
inference(avatar_split_clause,[],[f42175,f31105,f423,f42182]) ).
fof(f42175,plain,
( sP1(powerset(sK4))
| ~ spl19_35
| ~ spl19_55 ),
inference(resolution,[],[f31107,f531]) ).
fof(f42090,plain,
( spl19_55
| spl19_62
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f42077,f30818,f42088,f31105]) ).
fof(f42077,plain,
( ! [X46,X45] :
( ~ sP0(X45,powerset(sK4))
| empty(powerset(sK4))
| sP0(X45,X46)
| ~ subset(sK5(X45,X46),sK4)
| ~ ordinal(sK6(X45,X46))
| ~ empty(sK6(X45,X46)) )
| ~ spl19_54 ),
inference(resolution,[],[f7033,f30819]) ).
fof(f7033,plain,
! [X2,X0,X1] :
( ~ subset(sK6(X0,X1),X2)
| ~ sP0(X0,powerset(X2))
| empty(powerset(X2))
| sP0(X0,X1)
| ~ subset(sK5(X0,X1),X2) ),
inference(duplicate_literal_removal,[],[f7026]) ).
fof(f7026,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ sP0(X0,powerset(X2))
| empty(powerset(X2))
| ~ subset(sK6(X0,X1),X2)
| empty(powerset(X2))
| ~ subset(sK5(X0,X1),X2) ),
inference(resolution,[],[f2127,f569]) ).
fof(f2127,plain,
! [X2,X3,X4] :
( ~ in(sK5(X2,X3),powerset(X4))
| sP0(X2,X3)
| ~ sP0(X2,powerset(X4))
| empty(powerset(X4))
| ~ subset(sK6(X2,X3),X4) ),
inference(resolution,[],[f1189,f569]) ).
fof(f40437,plain,
( ~ spl19_60
| spl19_55
| spl19_61
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f40397,f30818,f40435,f31105,f40431]) ).
fof(f40435,plain,
( spl19_61
<=> ! [X323,X321,X322] :
( element(X321,X322)
| ~ empty(X321)
| ~ ordinal(X321)
| subset(X323,sK4)
| ~ in(X323,X322)
| ~ ordinal(X322) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_61])]) ).
fof(f40397,plain,
( ! [X323,X322,X321] :
( element(X321,X322)
| ~ ordinal(X322)
| empty(powerset(sK4))
| subset(X323,sK4)
| ~ ordinal(powerset(sK4))
| ~ in(X323,X322)
| ~ ordinal(X321)
| ~ empty(X321) )
| ~ spl19_54 ),
inference(resolution,[],[f6970,f30819]) ).
fof(f31123,plain,
( spl19_55
| spl19_59
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f31101,f30818,f31121,f31105]) ).
fof(f31121,plain,
( spl19_59
<=> ! [X24] :
( ~ ordinal(sK9(X24,relation_field(X24)))
| ~ subset(sK8(X24,relation_field(X24)),sK4)
| sP2(X24,relation_field(X24))
| ~ empty(X24)
| ~ sP2(X24,powerset(sK4))
| ~ empty(sK9(X24,relation_field(X24))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_59])]) ).
fof(f31101,plain,
( ! [X24] :
( ~ ordinal(sK9(X24,relation_field(X24)))
| ~ empty(sK9(X24,relation_field(X24)))
| ~ sP2(X24,powerset(sK4))
| ~ empty(X24)
| empty(powerset(sK4))
| sP2(X24,relation_field(X24))
| ~ subset(sK8(X24,relation_field(X24)),sK4) )
| ~ spl19_54 ),
inference(resolution,[],[f30819,f2341]) ).
fof(f31119,plain,
( spl19_55
| spl19_58
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f31102,f30818,f31117,f31105]) ).
fof(f31117,plain,
( spl19_58
<=> ! [X22,X23] :
( ~ ordinal(sK9(X22,relation_field(X22)))
| ~ subset(sK8(X22,relation_field(X22)),sK4)
| sP2(X22,relation_field(X22))
| ~ in(X23,sK8(X22,relation_field(X22)))
| ~ sP2(X22,powerset(sK4))
| ~ empty(sK9(X22,relation_field(X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_58])]) ).
fof(f31102,plain,
( ! [X22,X23] :
( ~ ordinal(sK9(X22,relation_field(X22)))
| ~ empty(sK9(X22,relation_field(X22)))
| ~ sP2(X22,powerset(sK4))
| ~ in(X23,sK8(X22,relation_field(X22)))
| empty(powerset(sK4))
| sP2(X22,relation_field(X22))
| ~ subset(sK8(X22,relation_field(X22)),sK4) )
| ~ spl19_54 ),
inference(duplicate_literal_removal,[],[f31100]) ).
fof(f31100,plain,
( ! [X22,X23] :
( ~ ordinal(sK9(X22,relation_field(X22)))
| ~ empty(sK9(X22,relation_field(X22)))
| ~ sP2(X22,powerset(sK4))
| ~ empty(sK9(X22,relation_field(X22)))
| ~ in(X23,sK8(X22,relation_field(X22)))
| empty(powerset(sK4))
| sP2(X22,relation_field(X22))
| ~ subset(sK8(X22,relation_field(X22)),sK4) )
| ~ spl19_54 ),
inference(resolution,[],[f30819,f2946]) ).
fof(f2946,plain,
! [X2,X0,X1] :
( ~ subset(sK9(X0,relation_field(X0)),X1)
| ~ sP2(X0,powerset(X1))
| ~ empty(sK9(X0,relation_field(X0)))
| ~ in(X2,sK8(X0,relation_field(X0)))
| empty(powerset(X1))
| sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(duplicate_literal_removal,[],[f2943]) ).
fof(f2943,plain,
! [X2,X0,X1] :
( sP2(X0,relation_field(X0))
| ~ sP2(X0,powerset(X1))
| ~ empty(sK9(X0,relation_field(X0)))
| ~ in(X2,sK8(X0,relation_field(X0)))
| empty(powerset(X1))
| ~ subset(sK9(X0,relation_field(X0)),X1)
| empty(powerset(X1))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(resolution,[],[f1361,f569]) ).
fof(f1361,plain,
! [X2,X3,X4] :
( ~ in(sK8(X2,relation_field(X2)),powerset(X3))
| sP2(X2,relation_field(X2))
| ~ sP2(X2,powerset(X3))
| ~ empty(sK9(X2,relation_field(X2)))
| ~ in(X4,sK8(X2,relation_field(X2)))
| empty(powerset(X3))
| ~ subset(sK9(X2,relation_field(X2)),X3) ),
inference(resolution,[],[f887,f569]) ).
fof(f887,plain,
! [X10,X8,X9] :
( ~ in(sK9(X8,relation_field(X8)),X9)
| sP2(X8,relation_field(X8))
| ~ in(sK8(X8,relation_field(X8)),X9)
| ~ sP2(X8,X9)
| ~ empty(sK9(X8,relation_field(X8)))
| ~ in(X10,sK8(X8,relation_field(X8))) ),
inference(resolution,[],[f651,f571]) ).
fof(f651,plain,
! [X2,X1] :
( subset(sK8(X1,relation_field(X1)),sK9(X1,relation_field(X1)))
| sP2(X1,relation_field(X1))
| ~ in(sK9(X1,relation_field(X1)),X2)
| ~ in(sK8(X1,relation_field(X1)),X2)
| ~ sP2(X1,X2) ),
inference(duplicate_literal_removal,[],[f645]) ).
fof(f645,plain,
! [X2,X1] :
( sP2(X1,relation_field(X1))
| subset(sK8(X1,relation_field(X1)),sK9(X1,relation_field(X1)))
| subset(sK8(X1,relation_field(X1)),sK9(X1,relation_field(X1)))
| ~ in(sK9(X1,relation_field(X1)),X2)
| ~ in(sK8(X1,relation_field(X1)),X2)
| ~ sP2(X1,X2) ),
inference(resolution,[],[f636,f609]) ).
fof(f31115,plain,
( spl19_55
| spl19_57
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f31099,f30818,f31113,f31105]) ).
fof(f31113,plain,
( spl19_57
<=> ! [X20,X21] :
( ~ ordinal(sK9(X20,relation_field(X20)))
| ~ subset(sK8(X20,relation_field(X20)),sK4)
| sP2(X20,relation_field(X20))
| ~ in(X21,sK8(X20,relation_field(X20)))
| element(X21,sK9(X20,relation_field(X20)))
| ~ sP2(X20,powerset(sK4))
| ~ empty(sK9(X20,relation_field(X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_57])]) ).
fof(f31099,plain,
( ! [X21,X20] :
( ~ ordinal(sK9(X20,relation_field(X20)))
| ~ empty(sK9(X20,relation_field(X20)))
| ~ sP2(X20,powerset(sK4))
| element(X21,sK9(X20,relation_field(X20)))
| ~ in(X21,sK8(X20,relation_field(X20)))
| empty(powerset(sK4))
| sP2(X20,relation_field(X20))
| ~ subset(sK8(X20,relation_field(X20)),sK4) )
| ~ spl19_54 ),
inference(resolution,[],[f30819,f2956]) ).
fof(f2956,plain,
! [X2,X0,X1] :
( ~ subset(sK9(X0,relation_field(X0)),X1)
| ~ sP2(X0,powerset(X1))
| element(X2,sK9(X0,relation_field(X0)))
| ~ in(X2,sK8(X0,relation_field(X0)))
| empty(powerset(X1))
| sP2(X0,relation_field(X0))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(duplicate_literal_removal,[],[f2953]) ).
fof(f2953,plain,
! [X2,X0,X1] :
( sP2(X0,relation_field(X0))
| ~ sP2(X0,powerset(X1))
| element(X2,sK9(X0,relation_field(X0)))
| ~ in(X2,sK8(X0,relation_field(X0)))
| empty(powerset(X1))
| ~ subset(sK9(X0,relation_field(X0)),X1)
| empty(powerset(X1))
| ~ subset(sK8(X0,relation_field(X0)),X1) ),
inference(resolution,[],[f1369,f569]) ).
fof(f1369,plain,
! [X2,X3,X4] :
( ~ in(sK8(X2,relation_field(X2)),powerset(X3))
| sP2(X2,relation_field(X2))
| ~ sP2(X2,powerset(X3))
| element(X4,sK9(X2,relation_field(X2)))
| ~ in(X4,sK8(X2,relation_field(X2)))
| empty(powerset(X3))
| ~ subset(sK9(X2,relation_field(X2)),X3) ),
inference(resolution,[],[f885,f569]) ).
fof(f885,plain,
! [X3,X4,X5] :
( ~ in(sK9(X3,relation_field(X3)),X4)
| sP2(X3,relation_field(X3))
| ~ in(sK8(X3,relation_field(X3)),X4)
| ~ sP2(X3,X4)
| element(X5,sK9(X3,relation_field(X3)))
| ~ in(X5,sK8(X3,relation_field(X3))) ),
inference(resolution,[],[f651,f589]) ).
fof(f31111,plain,
( spl19_55
| spl19_56
| ~ spl19_54 ),
inference(avatar_split_clause,[],[f31098,f30818,f31109,f31105]) ).
fof(f31109,plain,
( spl19_56
<=> ! [X18,X19] :
( ~ ordinal(sK9(X18,relation_field(X18)))
| ~ subset(sK8(X18,relation_field(X18)),sK4)
| ~ in(sK8(X18,relation_field(X18)),X19)
| ~ sP2(X18,powerset(sK4))
| ~ in(sK9(X18,relation_field(X18)),X19)
| sP2(X18,relation_field(X18))
| ~ sP2(X18,X19)
| ~ empty(sK9(X18,relation_field(X18))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_56])]) ).
fof(f31098,plain,
( ! [X18,X19] :
( ~ ordinal(sK9(X18,relation_field(X18)))
| ~ empty(sK9(X18,relation_field(X18)))
| ~ sP2(X18,X19)
| sP2(X18,relation_field(X18))
| ~ in(sK9(X18,relation_field(X18)),X19)
| ~ sP2(X18,powerset(sK4))
| empty(powerset(sK4))
| ~ in(sK8(X18,relation_field(X18)),X19)
| ~ subset(sK8(X18,relation_field(X18)),sK4) )
| ~ spl19_54 ),
inference(resolution,[],[f30819,f3096]) ).
fof(f3096,plain,
! [X2,X0,X1] :
( ~ subset(sK9(X0,relation_field(X0)),X2)
| ~ sP2(X0,X1)
| sP2(X0,relation_field(X0))
| ~ in(sK9(X0,relation_field(X0)),X1)
| ~ sP2(X0,powerset(X2))
| empty(powerset(X2))
| ~ in(sK8(X0,relation_field(X0)),X1)
| ~ subset(sK8(X0,relation_field(X0)),X2) ),
inference(duplicate_literal_removal,[],[f3093]) ).
fof(f3093,plain,
! [X2,X0,X1] :
( ~ in(sK8(X0,relation_field(X0)),X1)
| ~ sP2(X0,X1)
| sP2(X0,relation_field(X0))
| ~ in(sK9(X0,relation_field(X0)),X1)
| ~ sP2(X0,powerset(X2))
| empty(powerset(X2))
| ~ subset(sK9(X0,relation_field(X0)),X2)
| empty(powerset(X2))
| ~ subset(sK8(X0,relation_field(X0)),X2) ),
inference(resolution,[],[f1433,f569]) ).
fof(f1433,plain,
! [X2,X3,X4] :
( ~ in(sK8(X2,relation_field(X2)),powerset(X4))
| ~ in(sK8(X2,relation_field(X2)),X3)
| ~ sP2(X2,X3)
| sP2(X2,relation_field(X2))
| ~ in(sK9(X2,relation_field(X2)),X3)
| ~ sP2(X2,powerset(X4))
| empty(powerset(X4))
| ~ subset(sK9(X2,relation_field(X2)),X4) ),
inference(resolution,[],[f889,f569]) ).
fof(f889,plain,
! [X2,X0,X1] :
( ~ in(sK9(X0,relation_field(X0)),X2)
| ~ in(sK9(X0,relation_field(X0)),X1)
| ~ in(sK8(X0,relation_field(X0)),X1)
| ~ sP2(X0,X1)
| sP2(X0,relation_field(X0))
| ~ in(sK8(X0,relation_field(X0)),X2)
| ~ sP2(X0,X2) ),
inference(duplicate_literal_removal,[],[f884]) ).
fof(f884,plain,
! [X2,X0,X1] :
( sP2(X0,relation_field(X0))
| ~ in(sK9(X0,relation_field(X0)),X1)
| ~ in(sK8(X0,relation_field(X0)),X1)
| ~ sP2(X0,X1)
| sP2(X0,relation_field(X0))
| ~ in(sK9(X0,relation_field(X0)),X2)
| ~ in(sK8(X0,relation_field(X0)),X2)
| ~ sP2(X0,X2) ),
inference(resolution,[],[f651,f640]) ).
fof(f30820,plain,
( ~ spl19_2
| spl19_54
| ~ spl19_53 ),
inference(avatar_split_clause,[],[f30816,f30753,f30818,f249]) ).
fof(f30753,plain,
( spl19_53
<=> ! [X0] :
( ordinal_subset(X0,sK4)
| ~ ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_53])]) ).
fof(f30816,plain,
( ! [X0] :
( ~ ordinal(X0)
| ~ empty(X0)
| subset(X0,sK4)
| ~ ordinal(sK4) )
| ~ spl19_53 ),
inference(duplicate_literal_removal,[],[f30815]) ).
fof(f30815,plain,
( ! [X0] :
( ~ ordinal(X0)
| ~ empty(X0)
| subset(X0,sK4)
| ~ ordinal(sK4)
| ~ ordinal(X0) )
| ~ spl19_53 ),
inference(resolution,[],[f30754,f198]) ).
fof(f30754,plain,
( ! [X0] :
( ordinal_subset(X0,sK4)
| ~ ordinal(X0)
| ~ empty(X0) )
| ~ spl19_53 ),
inference(avatar_component_clause,[],[f30753]) ).
fof(f30755,plain,
( ~ spl19_2
| spl19_53
| spl19_1 ),
inference(avatar_split_clause,[],[f30748,f244,f30753,f249]) ).
fof(f30748,plain,
( ! [X0] :
( ordinal_subset(X0,sK4)
| ~ empty(X0)
| ~ ordinal(X0)
| ~ ordinal(sK4) )
| spl19_1 ),
inference(resolution,[],[f30502,f246]) ).
fof(f1762,plain,
( ~ spl19_52
| spl19_1 ),
inference(avatar_split_clause,[],[f1756,f244,f1759]) ).
fof(f1756,plain,
( ~ empty(sK4)
| spl19_1 ),
inference(resolution,[],[f1684,f246]) ).
fof(f674,plain,
( spl19_51
| ~ spl19_50 ),
inference(avatar_split_clause,[],[f669,f658,f671]) ).
fof(f671,plain,
( spl19_51
<=> sP1(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_51])]) ).
fof(f658,plain,
( spl19_50
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_50])]) ).
fof(f669,plain,
( sP1(sK11)
| ~ spl19_50 ),
inference(resolution,[],[f660,f162]) ).
fof(f660,plain,
( relation(sK11)
| ~ spl19_50 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f661,plain,
( spl19_50
| ~ spl19_8
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f654,f297,f280,f658]) ).
fof(f654,plain,
( relation(sK11)
| ~ spl19_8
| ~ spl19_12 ),
inference(resolution,[],[f530,f299]) ).
fof(f608,plain,
( ~ spl19_45
| spl19_49
| ~ spl19_47 ),
inference(avatar_split_clause,[],[f607,f505,f519,f491]) ).
fof(f491,plain,
( spl19_45
<=> epsilon_transitive(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_45])]) ).
fof(f519,plain,
( spl19_49
<=> ordinal(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_49])]) ).
fof(f505,plain,
( spl19_47
<=> epsilon_connected(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_47])]) ).
fof(f607,plain,
( ordinal(sK18)
| ~ epsilon_transitive(sK18)
| ~ spl19_47 ),
inference(resolution,[],[f507,f170]) ).
fof(f507,plain,
( epsilon_connected(sK18)
| ~ spl19_47 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f604,plain,
( ~ spl19_44
| spl19_48
| ~ spl19_46 ),
inference(avatar_split_clause,[],[f603,f500,f514,f486]) ).
fof(f486,plain,
( spl19_44
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_44])]) ).
fof(f514,plain,
( spl19_48
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_48])]) ).
fof(f500,plain,
( spl19_46
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_46])]) ).
fof(f603,plain,
( ordinal(sK11)
| ~ epsilon_transitive(sK11)
| ~ spl19_46 ),
inference(resolution,[],[f502,f170]) ).
fof(f502,plain,
( epsilon_connected(sK11)
| ~ spl19_46 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f522,plain,
( spl19_49
| ~ spl19_33 ),
inference(avatar_split_clause,[],[f512,f402,f519]) ).
fof(f512,plain,
( ordinal(sK18)
| ~ spl19_33 ),
inference(resolution,[],[f169,f404]) ).
fof(f517,plain,
( spl19_48
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f510,f297,f514]) ).
fof(f510,plain,
( ordinal(sK11)
| ~ spl19_12 ),
inference(resolution,[],[f169,f299]) ).
fof(f508,plain,
( spl19_47
| ~ spl19_33 ),
inference(avatar_split_clause,[],[f498,f402,f505]) ).
fof(f498,plain,
( epsilon_connected(sK18)
| ~ spl19_33 ),
inference(resolution,[],[f168,f404]) ).
fof(f503,plain,
( spl19_46
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f496,f297,f500]) ).
fof(f496,plain,
( epsilon_connected(sK11)
| ~ spl19_12 ),
inference(resolution,[],[f168,f299]) ).
fof(f494,plain,
( spl19_45
| ~ spl19_33 ),
inference(avatar_split_clause,[],[f484,f402,f491]) ).
fof(f484,plain,
( epsilon_transitive(sK18)
| ~ spl19_33 ),
inference(resolution,[],[f167,f404]) ).
fof(f489,plain,
( spl19_44
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f482,f297,f486]) ).
fof(f482,plain,
( epsilon_transitive(sK11)
| ~ spl19_12 ),
inference(resolution,[],[f167,f299]) ).
fof(f480,plain,
( spl19_43
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f473,f297,f477]) ).
fof(f477,plain,
( spl19_43
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_43])]) ).
fof(f473,plain,
( function(sK11)
| ~ spl19_12 ),
inference(resolution,[],[f165,f299]) ).
fof(f471,plain,
( spl19_42
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f463,f249,f468]) ).
fof(f468,plain,
( spl19_42
<=> epsilon_connected(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_42])]) ).
fof(f463,plain,
( epsilon_connected(sK4)
| ~ spl19_2 ),
inference(resolution,[],[f164,f251]) ).
fof(f251,plain,
( ordinal(sK4)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f461,plain,
( spl19_41
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f453,f249,f458]) ).
fof(f458,plain,
( spl19_41
<=> epsilon_transitive(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_41])]) ).
fof(f453,plain,
( epsilon_transitive(sK4)
| ~ spl19_2 ),
inference(resolution,[],[f163,f251]) ).
fof(f451,plain,
( spl19_40
| ~ spl19_34 ),
inference(avatar_split_clause,[],[f421,f407,f448]) ).
fof(f448,plain,
( spl19_40
<=> sP1(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_40])]) ).
fof(f407,plain,
( spl19_34
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_34])]) ).
fof(f421,plain,
( sP1(sK18)
| ~ spl19_34 ),
inference(resolution,[],[f162,f409]) ).
fof(f409,plain,
( relation(sK18)
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f446,plain,
( spl19_39
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f420,f392,f443]) ).
fof(f443,plain,
( spl19_39
<=> sP1(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_39])]) ).
fof(f392,plain,
( spl19_31
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_31])]) ).
fof(f420,plain,
( sP1(sK17)
| ~ spl19_31 ),
inference(resolution,[],[f162,f394]) ).
fof(f394,plain,
( relation(sK17)
| ~ spl19_31 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f441,plain,
( spl19_38
| ~ spl19_25 ),
inference(avatar_split_clause,[],[f419,f362,f438]) ).
fof(f438,plain,
( spl19_38
<=> sP1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_38])]) ).
fof(f362,plain,
( spl19_25
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
fof(f419,plain,
( sP1(sK16)
| ~ spl19_25 ),
inference(resolution,[],[f162,f364]) ).
fof(f364,plain,
( relation(sK16)
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f436,plain,
( spl19_37
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f418,f352,f433]) ).
fof(f433,plain,
( spl19_37
<=> sP1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_37])]) ).
fof(f352,plain,
( spl19_23
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
fof(f418,plain,
( sP1(sK15)
| ~ spl19_23 ),
inference(resolution,[],[f162,f354]) ).
fof(f354,plain,
( relation(sK15)
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f431,plain,
( spl19_36
| ~ spl19_21 ),
inference(avatar_split_clause,[],[f417,f342,f428]) ).
fof(f428,plain,
( spl19_36
<=> sP1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_36])]) ).
fof(f342,plain,
( spl19_21
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
fof(f417,plain,
( sP1(sK14)
| ~ spl19_21 ),
inference(resolution,[],[f162,f344]) ).
fof(f344,plain,
( relation(sK14)
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f426,plain,
( spl19_35
| ~ spl19_8 ),
inference(avatar_split_clause,[],[f416,f280,f423]) ).
fof(f416,plain,
( sP1(empty_set)
| ~ spl19_8 ),
inference(resolution,[],[f162,f282]) ).
fof(f414,plain,
( ~ spl19_2
| ~ spl19_9 ),
inference(avatar_contradiction_clause,[],[f411]) ).
fof(f411,plain,
( $false
| ~ spl19_2
| ~ spl19_9 ),
inference(resolution,[],[f286,f251]) ).
fof(f286,plain,
( ! [X1] : ~ ordinal(X1)
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f285,plain,
( spl19_9
<=> ! [X1] : ~ ordinal(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
fof(f413,plain,
( ~ spl19_4
| ~ spl19_9 ),
inference(avatar_contradiction_clause,[],[f412]) ).
fof(f412,plain,
( $false
| ~ spl19_4
| ~ spl19_9 ),
inference(resolution,[],[f286,f261]) ).
fof(f261,plain,
( ordinal(empty_set)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f259,plain,
( spl19_4
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f410,plain,
spl19_34,
inference(avatar_split_clause,[],[f227,f407]) ).
fof(f227,plain,
relation(sK18),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( function(sK18)
& empty(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f36,f138]) ).
fof(f138,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK18)
& empty(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc2_funct_1) ).
fof(f405,plain,
spl19_33,
inference(avatar_split_clause,[],[f228,f402]) ).
fof(f228,plain,
empty(sK18),
inference(cnf_transformation,[],[f139]) ).
fof(f400,plain,
spl19_32,
inference(avatar_split_clause,[],[f229,f397]) ).
fof(f397,plain,
( spl19_32
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_32])]) ).
fof(f229,plain,
function(sK18),
inference(cnf_transformation,[],[f139]) ).
fof(f395,plain,
spl19_31,
inference(avatar_split_clause,[],[f221,f392]) ).
fof(f221,plain,
relation(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f62,f136]) ).
fof(f136,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK17)
& epsilon_connected(sK17)
& epsilon_transitive(sK17)
& empty(sK17)
& function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc2_ordinal1) ).
fof(f390,plain,
spl19_30,
inference(avatar_split_clause,[],[f222,f387]) ).
fof(f387,plain,
( spl19_30
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_30])]) ).
fof(f222,plain,
function(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f385,plain,
spl19_29,
inference(avatar_split_clause,[],[f223,f382]) ).
fof(f223,plain,
empty(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f380,plain,
spl19_28,
inference(avatar_split_clause,[],[f224,f377]) ).
fof(f377,plain,
( spl19_28
<=> epsilon_transitive(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_28])]) ).
fof(f224,plain,
epsilon_transitive(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f375,plain,
spl19_27,
inference(avatar_split_clause,[],[f225,f372]) ).
fof(f372,plain,
( spl19_27
<=> epsilon_connected(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_27])]) ).
fof(f225,plain,
epsilon_connected(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f370,plain,
spl19_26,
inference(avatar_split_clause,[],[f226,f367]) ).
fof(f367,plain,
( spl19_26
<=> ordinal(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_26])]) ).
fof(f226,plain,
ordinal(sK17),
inference(cnf_transformation,[],[f137]) ).
fof(f365,plain,
spl19_25,
inference(avatar_split_clause,[],[f219,f362]) ).
fof(f219,plain,
relation(sK16),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f61,f134]) ).
fof(f134,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f39]) ).
fof(f39,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc3_funct_1) ).
fof(f360,plain,
spl19_24,
inference(avatar_split_clause,[],[f220,f357]) ).
fof(f357,plain,
( spl19_24
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
fof(f220,plain,
function(sK16),
inference(cnf_transformation,[],[f135]) ).
fof(f355,plain,
spl19_23,
inference(avatar_split_clause,[],[f217,f352]) ).
fof(f217,plain,
relation(sK15),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f33,f132]) ).
fof(f132,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc1_funct_1) ).
fof(f350,plain,
spl19_22,
inference(avatar_split_clause,[],[f218,f347]) ).
fof(f347,plain,
( spl19_22
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
fof(f218,plain,
function(sK15),
inference(cnf_transformation,[],[f133]) ).
fof(f345,plain,
spl19_21,
inference(avatar_split_clause,[],[f215,f342]) ).
fof(f215,plain,
relation(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f59,f130]) ).
fof(f130,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f41]) ).
fof(f41,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc4_funct_1) ).
fof(f340,plain,
spl19_20,
inference(avatar_split_clause,[],[f216,f337]) ).
fof(f337,plain,
( spl19_20
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
fof(f216,plain,
function(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f335,plain,
spl19_19,
inference(avatar_split_clause,[],[f212,f332]) ).
fof(f332,plain,
( spl19_19
<=> epsilon_transitive(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
fof(f212,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f34,f128]) ).
fof(f128,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc1_ordinal1) ).
fof(f330,plain,
spl19_18,
inference(avatar_split_clause,[],[f213,f327]) ).
fof(f327,plain,
( spl19_18
<=> epsilon_connected(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
fof(f213,plain,
epsilon_connected(sK13),
inference(cnf_transformation,[],[f129]) ).
fof(f325,plain,
spl19_17,
inference(avatar_split_clause,[],[f214,f322]) ).
fof(f322,plain,
( spl19_17
<=> ordinal(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
fof(f214,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f129]) ).
fof(f320,plain,
~ spl19_16,
inference(avatar_split_clause,[],[f208,f317]) ).
fof(f317,plain,
( spl19_16
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
fof(f208,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f40,f126]) ).
fof(f126,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc3_ordinal1) ).
fof(f315,plain,
spl19_15,
inference(avatar_split_clause,[],[f209,f312]) ).
fof(f312,plain,
( spl19_15
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
fof(f209,plain,
epsilon_transitive(sK12),
inference(cnf_transformation,[],[f127]) ).
fof(f310,plain,
spl19_14,
inference(avatar_split_clause,[],[f210,f307]) ).
fof(f307,plain,
( spl19_14
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
fof(f210,plain,
epsilon_connected(sK12),
inference(cnf_transformation,[],[f127]) ).
fof(f305,plain,
spl19_13,
inference(avatar_split_clause,[],[f211,f302]) ).
fof(f302,plain,
( spl19_13
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
fof(f211,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f127]) ).
fof(f300,plain,
spl19_12,
inference(avatar_split_clause,[],[f207,f297]) ).
fof(f207,plain,
empty(sK11),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f35,f124]) ).
fof(f124,plain,
( ? [X0] : empty(X0)
=> empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc1_xboole_0) ).
fof(f295,plain,
~ spl19_11,
inference(avatar_split_clause,[],[f206,f292]) ).
fof(f292,plain,
( spl19_11
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
fof(f206,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
~ empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f38,f122]) ).
fof(f122,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',rc2_xboole_0) ).
fof(f290,plain,
( spl19_9
| spl19_10 ),
inference(avatar_split_clause,[],[f196,f288,f285]) ).
fof(f288,plain,
( spl19_10
<=> ! [X0] :
( ordinal_subset(X0,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
fof(f196,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ordinal_subset(X0,X0)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ordinal_subset(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',reflexivity_r1_ordinal1) ).
fof(f283,plain,
spl19_8,
inference(avatar_split_clause,[],[f143,f280]) ).
fof(f143,plain,
relation(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f60]) ).
fof(f60,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',fc2_ordinal1) ).
fof(f278,plain,
spl19_7,
inference(avatar_split_clause,[],[f144,f275]) ).
fof(f275,plain,
( spl19_7
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f144,plain,
function(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f273,plain,
spl19_3,
inference(avatar_split_clause,[],[f145,f254]) ).
fof(f145,plain,
empty(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f272,plain,
spl19_6,
inference(avatar_split_clause,[],[f146,f269]) ).
fof(f269,plain,
( spl19_6
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f146,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f267,plain,
spl19_5,
inference(avatar_split_clause,[],[f147,f264]) ).
fof(f264,plain,
( spl19_5
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f147,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f262,plain,
spl19_4,
inference(avatar_split_clause,[],[f148,f259]) ).
fof(f148,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f257,plain,
spl19_3,
inference(avatar_split_clause,[],[f142,f254]) ).
fof(f142,plain,
empty(empty_set),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',fc1_xboole_0) ).
fof(f252,plain,
spl19_2,
inference(avatar_split_clause,[],[f140,f249]) ).
fof(f140,plain,
ordinal(sK4),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
( ~ connected(inclusion_relation(sK4))
& ordinal(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f65,f104]) ).
fof(f104,plain,
( ? [X0] :
( ~ connected(inclusion_relation(X0))
& ordinal(X0) )
=> ( ~ connected(inclusion_relation(sK4))
& ordinal(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
? [X0] :
( ~ connected(inclusion_relation(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
inference(negated_conjecture,[],[f51]) ).
fof(f51,conjecture,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452',t4_wellord2) ).
fof(f247,plain,
~ spl19_1,
inference(avatar_split_clause,[],[f141,f244]) ).
fof(f141,plain,
~ connected(inclusion_relation(sK4)),
inference(cnf_transformation,[],[f105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU270+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Wed Aug 23 21:25:53 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.20/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.yLYGJae5MJ/Vampire---4.8_452
% 0.20/0.36 % (578)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (580)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.22/0.42 % (582)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.22/0.42 % (581)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.22/0.42 % (583)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.22/0.42 % (579)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.22/0.42 % (584)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.42 % (585)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.22/0.48 % (581)Refutation not found, incomplete strategy% (581)------------------------------
% 0.22/0.48 % (581)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.48 % (581)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.48 % (581)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.48
% 0.22/0.48 % (581)Memory used [KB]: 1151
% 0.22/0.48 % (581)Time elapsed: 0.060 s
% 0.22/0.48 % (581)------------------------------
% 0.22/0.48 % (581)------------------------------
% 0.22/0.52 % (586)ott+10_5_av=off:bsr=on:br=off:drc=off:fsd=off:fsr=off:fde=unused:gsp=on:lcm=predicate:lma=on:nwc=2.5:sos=all:sp=occurrence:tgt=full:urr=on_375 on Vampire---4 for (375ds/0Mi)
% 0.22/0.52 % (586)Refutation not found, incomplete strategy% (586)------------------------------
% 0.22/0.52 % (586)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.52 % (586)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.52 % (586)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.52
% 0.22/0.52 % (586)Memory used [KB]: 1151
% 0.22/0.52 % (586)Time elapsed: 0.003 s
% 0.22/0.52 % (586)------------------------------
% 0.22/0.52 % (586)------------------------------
% 0.22/0.56 % (587)lrs-1010_3_aac=none:anc=none:er=known:fsd=off:fde=unused:gs=on:lcm=predicate:sos=on:sp=weighted_frequency:tgt=ground:stl=62_365 on Vampire---4 for (365ds/0Mi)
% 0.22/0.56 % (587)Refutation not found, incomplete strategy% (587)------------------------------
% 0.22/0.56 % (587)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.56 % (587)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.56 % (587)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.56
% 0.22/0.56 % (587)Memory used [KB]: 9978
% 0.22/0.56 % (587)Time elapsed: 0.003 s
% 0.22/0.56 % (587)------------------------------
% 0.22/0.56 % (587)------------------------------
% 0.22/0.59 % (588)ott+10_128_aac=none:add=large:afr=on:anc=all_dependent:bsr=on:bce=on:fsd=off:irw=on:nm=2:nwc=1.5:sp=scramble:tgt=full_251 on Vampire---4 for (251ds/0Mi)
% 76.58/11.34 % (580)First to succeed.
% 77.13/11.36 % (580)Refutation found. Thanks to Tanya!
% 77.13/11.36 % SZS status Theorem for Vampire---4
% 77.13/11.36 % SZS output start Proof for Vampire---4
% See solution above
% 77.13/11.36 % (580)------------------------------
% 77.13/11.36 % (580)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 77.13/11.36 % (580)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 77.13/11.36 % (580)Termination reason: Refutation
% 77.13/11.36
% 77.13/11.36 % (580)Memory used [KB]: 125626
% 77.13/11.36 % (580)Time elapsed: 10.923 s
% 77.13/11.36 % (580)------------------------------
% 77.13/11.36 % (580)------------------------------
% 77.13/11.36 % (578)Success in time 10.973 s
% 77.13/11.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------