TSTP Solution File: SEU161+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU161+2 : 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 : n005.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 : Sat Sep 2 00:06:56 EDT 2023
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 160
% Syntax : Number of formulae : 433 ( 135 unt; 0 def)
% Number of atoms : 1004 ( 216 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1004 ( 433 ~; 356 |; 77 &)
% ( 111 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 99 ( 97 usr; 91 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 623 (; 595 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f997,plain,
$false,
inference(avatar_sat_refutation,[],[f401,f406,f411,f416,f421,f425,f429,f433,f437,f441,f446,f450,f454,f458,f463,f467,f471,f475,f479,f483,f488,f492,f496,f510,f514,f518,f524,f528,f542,f547,f551,f555,f559,f563,f567,f571,f575,f579,f587,f595,f599,f603,f608,f613,f617,f621,f630,f651,f656,f660,f664,f668,f672,f676,f680,f711,f720,f724,f728,f732,f736,f740,f744,f748,f752,f757,f762,f766,f813,f817,f844,f848,f853,f858,f862,f866,f882,f886,f890,f894,f898,f902,f906,f910,f914,f918,f983,f987,f991,f995,f996]) ).
fof(f996,plain,
( spl29_2
| ~ spl29_1
| ~ spl29_82 ),
inference(avatar_split_clause,[],[f956,f900,f398,f403]) ).
fof(f403,plain,
( spl29_2
<=> sK7 = set_union2(singleton(sK6),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
fof(f398,plain,
( spl29_1
<=> in(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
fof(f900,plain,
( spl29_82
<=> ! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_82])]) ).
fof(f956,plain,
( sK7 = set_union2(singleton(sK6),sK7)
| ~ spl29_1
| ~ spl29_82 ),
inference(resolution,[],[f901,f400]) ).
fof(f400,plain,
( in(sK6,sK7)
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f901,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 )
| ~ spl29_82 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f995,plain,
spl29_90,
inference(avatar_split_clause,[],[f357,f993]) ).
fof(f993,plain,
( spl29_90
<=> ! [X2,X0,X1] :
( sP1(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_90])]) ).
fof(f357,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f12,f140]) ).
fof(f140,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d2_zfmisc_1) ).
fof(f991,plain,
spl29_89,
inference(avatar_split_clause,[],[f328,f989]) ).
fof(f989,plain,
( spl29_89
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_89])]) ).
fof(f328,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK12(X0,X1),X1)
& in(sK12(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f182,f183]) ).
fof(f183,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK12(X0,X1),X1)
& in(sK12(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f182,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f181]) ).
fof(f181,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d3_tarski) ).
fof(f987,plain,
spl29_88,
inference(avatar_split_clause,[],[f325,f985]) ).
fof(f985,plain,
( spl29_88
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_88])]) ).
fof(f325,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(flattening,[],[f178]) ).
fof(f178,plain,
! [X0,X1] :
( ( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) )
& ( ( X0 != X1
& subset(X0,X1) )
| ~ proper_subset(X0,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d8_xboole_0) ).
fof(f983,plain,
spl29_87,
inference(avatar_split_clause,[],[f322,f981]) ).
fof(f981,plain,
( spl29_87
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_87])]) ).
fof(f322,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f176]) ).
fof(f176,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d10_xboole_0) ).
fof(f918,plain,
spl29_86,
inference(avatar_split_clause,[],[f284,f916]) ).
fof(f916,plain,
( spl29_86
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_86])]) ).
fof(f284,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t1_xboole_1) ).
fof(f914,plain,
spl29_85,
inference(avatar_split_clause,[],[f283,f912]) ).
fof(f912,plain,
( spl29_85
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_85])]) ).
fof(f283,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t63_xboole_1) ).
fof(f910,plain,
spl29_84,
inference(avatar_split_clause,[],[f282,f908]) ).
fof(f908,plain,
( spl29_84
<=> ! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_84])]) ).
fof(f282,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t9_zfmisc_1) ).
fof(f906,plain,
spl29_83,
inference(avatar_split_clause,[],[f281,f904]) ).
fof(f904,plain,
( spl29_83
<=> ! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_83])]) ).
fof(f281,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t8_zfmisc_1) ).
fof(f902,plain,
spl29_82,
inference(avatar_split_clause,[],[f255,f900]) ).
fof(f255,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l23_zfmisc_1) ).
fof(f898,plain,
spl29_81,
inference(avatar_split_clause,[],[f252,f896]) ).
fof(f896,plain,
( spl29_81
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_81])]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f102,f154]) ).
fof(f154,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK9(X0,X1),X1)
& in(sK9(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f72]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t3_xboole_0) ).
fof(f894,plain,
spl29_80,
inference(avatar_split_clause,[],[f247,f892]) ).
fof(f892,plain,
( spl29_80
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_80])]) ).
fof(f247,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t40_xboole_1) ).
fof(f890,plain,
( spl29_79
| ~ spl29_5
| ~ spl29_18
| ~ spl29_19
| ~ spl29_64 ),
inference(avatar_split_clause,[],[f809,f746,f477,f473,f418,f888]) ).
fof(f888,plain,
( spl29_79
<=> ! [X1] : disjoint(X1,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_79])]) ).
fof(f418,plain,
( spl29_5
<=> empty(sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).
fof(f473,plain,
( spl29_18
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl29_18])]) ).
fof(f477,plain,
( spl29_19
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_19])]) ).
fof(f746,plain,
( spl29_64
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_64])]) ).
fof(f809,plain,
( ! [X1] : disjoint(X1,sK28)
| ~ spl29_5
| ~ spl29_18
| ~ spl29_19
| ~ spl29_64 ),
inference(forward_demodulation,[],[f806,f502]) ).
fof(f502,plain,
( empty_set = sK28
| ~ spl29_5
| ~ spl29_19 ),
inference(resolution,[],[f478,f420]) ).
fof(f420,plain,
( empty(sK28)
| ~ spl29_5 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f478,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl29_19 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f806,plain,
( ! [X1] : disjoint(X1,empty_set)
| ~ spl29_18
| ~ spl29_64 ),
inference(trivial_inequality_removal,[],[f805]) ).
fof(f805,plain,
( ! [X1] :
( X1 != X1
| disjoint(X1,empty_set) )
| ~ spl29_18
| ~ spl29_64 ),
inference(superposition,[],[f747,f474]) ).
fof(f474,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl29_18 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f747,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) )
| ~ spl29_64 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f886,plain,
spl29_78,
inference(avatar_split_clause,[],[f246,f884]) ).
fof(f884,plain,
( spl29_78
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_78])]) ).
fof(f246,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t39_xboole_1) ).
fof(f882,plain,
spl29_77,
inference(avatar_split_clause,[],[f245,f880]) ).
fof(f880,plain,
( spl29_77
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_77])]) ).
fof(f245,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t48_xboole_1) ).
fof(f866,plain,
( spl29_76
| ~ spl29_5
| ~ spl29_19
| ~ spl29_73 ),
inference(avatar_split_clause,[],[f854,f851,f477,f418,f864]) ).
fof(f864,plain,
( spl29_76
<=> ! [X0,X1] :
( set_intersection2(X0,X1) != sK28
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_76])]) ).
fof(f851,plain,
( spl29_73
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_73])]) ).
fof(f854,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK28
| disjoint(X0,X1) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_73 ),
inference(forward_demodulation,[],[f852,f502]) ).
fof(f852,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
| ~ spl29_73 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f862,plain,
spl29_75,
inference(avatar_split_clause,[],[f330,f860]) ).
fof(f860,plain,
( spl29_75
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK12(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_75])]) ).
fof(f330,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f858,plain,
spl29_74,
inference(avatar_split_clause,[],[f329,f856]) ).
fof(f856,plain,
( spl29_74
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK12(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_74])]) ).
fof(f329,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f853,plain,
spl29_73,
inference(avatar_split_clause,[],[f327,f851]) ).
fof(f327,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d7_xboole_0) ).
fof(f848,plain,
spl29_72,
inference(avatar_split_clause,[],[f326,f846]) ).
fof(f846,plain,
( spl29_72
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_72])]) ).
fof(f326,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f844,plain,
( spl29_71
| ~ spl29_5
| ~ spl29_16
| ~ spl29_19
| ~ spl29_64 ),
inference(avatar_split_clause,[],[f808,f746,f477,f465,f418,f842]) ).
fof(f842,plain,
( spl29_71
<=> ! [X0] : disjoint(sK28,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_71])]) ).
fof(f465,plain,
( spl29_16
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).
fof(f808,plain,
( ! [X0] : disjoint(sK28,X0)
| ~ spl29_5
| ~ spl29_16
| ~ spl29_19
| ~ spl29_64 ),
inference(forward_demodulation,[],[f807,f502]) ).
fof(f807,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl29_16
| ~ spl29_64 ),
inference(trivial_inequality_removal,[],[f804]) ).
fof(f804,plain,
( ! [X0] :
( empty_set != empty_set
| disjoint(empty_set,X0) )
| ~ spl29_16
| ~ spl29_64 ),
inference(superposition,[],[f747,f466]) ).
fof(f466,plain,
( ! [X0] : empty_set = set_difference(empty_set,X0)
| ~ spl29_16 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f817,plain,
( spl29_70
| ~ spl29_5
| ~ spl29_19
| ~ spl29_66 ),
inference(avatar_split_clause,[],[f758,f755,f477,f418,f815]) ).
fof(f815,plain,
( spl29_70
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK28
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_70])]) ).
fof(f755,plain,
( spl29_66
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_66])]) ).
fof(f758,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK28
| ~ subset(X0,X1) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_66 ),
inference(forward_demodulation,[],[f756,f502]) ).
fof(f756,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl29_66 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f813,plain,
( spl29_69
| ~ spl29_5
| ~ spl29_19
| ~ spl29_65 ),
inference(avatar_split_clause,[],[f753,f750,f477,f418,f811]) ).
fof(f811,plain,
( spl29_69
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK28
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_69])]) ).
fof(f750,plain,
( spl29_65
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_65])]) ).
fof(f753,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK28
| subset(X0,X1) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_65 ),
inference(forward_demodulation,[],[f751,f502]) ).
fof(f751,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl29_65 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f766,plain,
spl29_68,
inference(avatar_split_clause,[],[f288,f764]) ).
fof(f764,plain,
( spl29_68
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_68])]) ).
fof(f288,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t38_zfmisc_1) ).
fof(f762,plain,
spl29_67,
inference(avatar_split_clause,[],[f287,f760]) ).
fof(f760,plain,
( spl29_67
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_67])]) ).
fof(f287,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f166]) ).
fof(f757,plain,
spl29_66,
inference(avatar_split_clause,[],[f273,f755]) ).
fof(f273,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l32_xboole_1) ).
fof(f752,plain,
spl29_65,
inference(avatar_split_clause,[],[f272,f750]) ).
fof(f272,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f748,plain,
spl29_64,
inference(avatar_split_clause,[],[f261,f746]) ).
fof(f261,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t83_xboole_1) ).
fof(f744,plain,
spl29_63,
inference(avatar_split_clause,[],[f260,f742]) ).
fof(f742,plain,
( spl29_63
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_63])]) ).
fof(f260,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
fof(f740,plain,
spl29_62,
inference(avatar_split_clause,[],[f259,f738]) ).
fof(f738,plain,
( spl29_62
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_62])]) ).
fof(f259,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t6_zfmisc_1) ).
fof(f736,plain,
spl29_61,
inference(avatar_split_clause,[],[f257,f734]) ).
fof(f734,plain,
( spl29_61
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_61])]) ).
fof(f257,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t12_xboole_1) ).
fof(f732,plain,
spl29_60,
inference(avatar_split_clause,[],[f256,f730]) ).
fof(f730,plain,
( spl29_60
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_60])]) ).
fof(f256,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t28_xboole_1) ).
fof(f728,plain,
spl29_59,
inference(avatar_split_clause,[],[f251,f726]) ).
fof(f726,plain,
( spl29_59
<=> ! [X0,X1] :
( in(sK9(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_59])]) ).
fof(f251,plain,
! [X0,X1] :
( in(sK9(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f724,plain,
spl29_58,
inference(avatar_split_clause,[],[f250,f722]) ).
fof(f722,plain,
( spl29_58
<=> ! [X0,X1] :
( in(sK9(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_58])]) ).
fof(f250,plain,
! [X0,X1] :
( in(sK9(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f720,plain,
spl29_57,
inference(avatar_split_clause,[],[f249,f718]) ).
fof(f718,plain,
( spl29_57
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_57])]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f101,f152]) ).
fof(f152,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK8(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t4_xboole_0) ).
fof(f711,plain,
( ~ spl29_56
| spl29_2
| ~ spl29_51 ),
inference(avatar_split_clause,[],[f693,f662,f403,f708]) ).
fof(f708,plain,
( spl29_56
<=> sK7 = set_union2(sK7,singleton(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_56])]) ).
fof(f662,plain,
( spl29_51
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_51])]) ).
fof(f693,plain,
( sK7 != set_union2(sK7,singleton(sK6))
| spl29_2
| ~ spl29_51 ),
inference(superposition,[],[f405,f663]) ).
fof(f663,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl29_51 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f405,plain,
( sK7 != set_union2(singleton(sK6),sK7)
| spl29_2 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f680,plain,
( spl29_55
| ~ spl29_5
| ~ spl29_19
| ~ spl29_48 ),
inference(avatar_split_clause,[],[f652,f649,f477,f418,f678]) ).
fof(f678,plain,
( spl29_55
<=> ! [X0] :
( sK28 = X0
| in(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_55])]) ).
fof(f649,plain,
( spl29_48
<=> ! [X0] :
( empty_set = X0
| in(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_48])]) ).
fof(f652,plain,
( ! [X0] :
( sK28 = X0
| in(sK10(X0),X0) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_48 ),
inference(forward_demodulation,[],[f650,f502]) ).
fof(f650,plain,
( ! [X0] :
( empty_set = X0
| in(sK10(X0),X0) )
| ~ spl29_48 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f676,plain,
spl29_54,
inference(avatar_split_clause,[],[f347,f674]) ).
fof(f674,plain,
( spl29_54
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_54])]) ).
fof(f347,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t8_boole) ).
fof(f672,plain,
spl29_53,
inference(avatar_split_clause,[],[f342,f670]) ).
fof(f670,plain,
( spl29_53
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_53])]) ).
fof(f342,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f15,f138]) ).
fof(f138,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f15,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d4_tarski) ).
fof(f668,plain,
spl29_52,
inference(avatar_split_clause,[],[f341,f666]) ).
fof(f666,plain,
( spl29_52
<=> ! [X0,X1] :
( sP0(X0,X1)
| union(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_52])]) ).
fof(f341,plain,
! [X0,X1] :
( sP0(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f195]) ).
fof(f664,plain,
spl29_51,
inference(avatar_split_clause,[],[f311,f662]) ).
fof(f311,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',commutativity_k2_xboole_0) ).
fof(f660,plain,
spl29_50,
inference(avatar_split_clause,[],[f310,f658]) ).
fof(f658,plain,
( spl29_50
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_50])]) ).
fof(f310,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',commutativity_k3_xboole_0) ).
fof(f656,plain,
spl29_49,
inference(avatar_split_clause,[],[f309,f654]) ).
fof(f654,plain,
( spl29_49
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_49])]) ).
fof(f309,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',commutativity_k2_tarski) ).
fof(f651,plain,
spl29_48,
inference(avatar_split_clause,[],[f303,f649]) ).
fof(f303,plain,
! [X0] :
( empty_set = X0
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( empty_set = X0
| in(sK10(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f170,f171]) ).
fof(f171,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f170,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f169]) ).
fof(f169,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',d1_xboole_0) ).
fof(f630,plain,
( spl29_47
| ~ spl29_5
| ~ spl29_19
| ~ spl29_42 ),
inference(avatar_split_clause,[],[f604,f601,f477,f418,f628]) ).
fof(f628,plain,
( spl29_47
<=> ! [X0,X1] :
( sK28 != X0
| subset(X0,singleton(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_47])]) ).
fof(f601,plain,
( spl29_42
<=> ! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_42])]) ).
fof(f604,plain,
( ! [X0,X1] :
( sK28 != X0
| subset(X0,singleton(X1)) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_42 ),
inference(forward_demodulation,[],[f602,f502]) ).
fof(f602,plain,
( ! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 )
| ~ spl29_42 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f621,plain,
spl29_46,
inference(avatar_split_clause,[],[f277,f619]) ).
fof(f619,plain,
( spl29_46
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_46])]) ).
fof(f277,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l25_zfmisc_1) ).
fof(f617,plain,
spl29_45,
inference(avatar_split_clause,[],[f269,f615]) ).
fof(f615,plain,
( spl29_45
<=> ! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_45])]) ).
fof(f269,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t37_zfmisc_1) ).
fof(f613,plain,
( ~ spl29_44
| ~ spl29_1
| ~ spl29_34 ),
inference(avatar_split_clause,[],[f588,f561,f398,f610]) ).
fof(f610,plain,
( spl29_44
<=> in(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_44])]) ).
fof(f561,plain,
( spl29_34
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_34])]) ).
fof(f588,plain,
( ~ in(sK7,sK6)
| ~ spl29_1
| ~ spl29_34 ),
inference(resolution,[],[f562,f400]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl29_34 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f608,plain,
spl29_43,
inference(avatar_split_clause,[],[f268,f606]) ).
fof(f606,plain,
( spl29_43
<=> ! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_43])]) ).
fof(f268,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f603,plain,
spl29_42,
inference(avatar_split_clause,[],[f263,f601]) ).
fof(f263,plain,
! [X0,X1] :
( subset(X0,singleton(X1))
| empty_set != X0 ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l4_zfmisc_1) ).
fof(f599,plain,
spl29_41,
inference(avatar_split_clause,[],[f254,f597]) ).
fof(f597,plain,
( spl29_41
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_41])]) ).
fof(f254,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l50_zfmisc_1) ).
fof(f595,plain,
spl29_40,
inference(avatar_split_clause,[],[f253,f593]) ).
fof(f593,plain,
( spl29_40
<=> ! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_40])]) ).
fof(f253,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l28_zfmisc_1) ).
fof(f587,plain,
( spl29_39
| ~ spl29_5
| ~ spl29_6
| ~ spl29_19
| ~ spl29_27 ),
inference(avatar_split_clause,[],[f534,f522,f477,f423,f418,f585]) ).
fof(f585,plain,
( spl29_39
<=> ! [X3] : ~ proper_subset(X3,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_39])]) ).
fof(f423,plain,
( spl29_6
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).
fof(f522,plain,
( spl29_27
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).
fof(f534,plain,
( ! [X3] : ~ proper_subset(X3,sK28)
| ~ spl29_5
| ~ spl29_6
| ~ spl29_19
| ~ spl29_27 ),
inference(forward_demodulation,[],[f531,f502]) ).
fof(f531,plain,
( ! [X3] : ~ proper_subset(X3,empty_set)
| ~ spl29_6
| ~ spl29_27 ),
inference(resolution,[],[f523,f424]) ).
fof(f424,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl29_6 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f523,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl29_27 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f579,plain,
( spl29_38
| ~ spl29_5
| ~ spl29_19
| ~ spl29_29 ),
inference(avatar_split_clause,[],[f543,f540,f477,f418,f577]) ).
fof(f577,plain,
( spl29_38
<=> ! [X2,X0] :
( sK28 != X0
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_38])]) ).
fof(f540,plain,
( spl29_29
<=> ! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_29])]) ).
fof(f543,plain,
( ! [X2,X0] :
( sK28 != X0
| ~ in(X2,X0) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_29 ),
inference(forward_demodulation,[],[f541,f502]) ).
fof(f541,plain,
( ! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 )
| ~ spl29_29 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f575,plain,
spl29_37,
inference(avatar_split_clause,[],[f324,f573]) ).
fof(f573,plain,
( spl29_37
<=> ! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_37])]) ).
fof(f324,plain,
! [X0,X1] :
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f571,plain,
spl29_36,
inference(avatar_split_clause,[],[f323,f569]) ).
fof(f569,plain,
( spl29_36
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_36])]) ).
fof(f323,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
fof(f567,plain,
spl29_35,
inference(avatar_split_clause,[],[f321,f565]) ).
fof(f565,plain,
( spl29_35
<=> ! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_35])]) ).
fof(f321,plain,
! [X0,X1] :
( subset(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f177]) ).
fof(f563,plain,
spl29_34,
inference(avatar_split_clause,[],[f317,f561]) ).
fof(f317,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,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/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',antisymmetry_r2_hidden) ).
fof(f559,plain,
spl29_33,
inference(avatar_split_clause,[],[f316,f557]) ).
fof(f557,plain,
( spl29_33
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_33])]) ).
fof(f316,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',symmetry_r1_xboole_0) ).
fof(f555,plain,
spl29_32,
inference(avatar_split_clause,[],[f315,f553]) ).
fof(f553,plain,
( spl29_32
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_32])]) ).
fof(f315,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',antisymmetry_r2_xboole_0) ).
fof(f551,plain,
spl29_31,
inference(avatar_split_clause,[],[f314,f549]) ).
fof(f549,plain,
( spl29_31
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_31])]) ).
fof(f314,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',fc2_xboole_0) ).
fof(f547,plain,
spl29_30,
inference(avatar_split_clause,[],[f313,f545]) ).
fof(f545,plain,
( spl29_30
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_30])]) ).
fof(f313,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',fc3_xboole_0) ).
fof(f542,plain,
spl29_29,
inference(avatar_split_clause,[],[f302,f540]) ).
fof(f302,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f172]) ).
fof(f528,plain,
( spl29_28
| ~ spl29_5
| ~ spl29_19
| ~ spl29_26 ),
inference(avatar_split_clause,[],[f520,f516,f477,f418,f526]) ).
fof(f526,plain,
( spl29_28
<=> ! [X0] :
( ~ subset(X0,sK28)
| sK28 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_28])]) ).
fof(f516,plain,
( spl29_26
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_26])]) ).
fof(f520,plain,
( ! [X0] :
( ~ subset(X0,sK28)
| sK28 = X0 )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_26 ),
inference(forward_demodulation,[],[f519,f502]) ).
fof(f519,plain,
( ! [X0] :
( sK28 = X0
| ~ subset(X0,empty_set) )
| ~ spl29_5
| ~ spl29_19
| ~ spl29_26 ),
inference(forward_demodulation,[],[f517,f502]) ).
fof(f517,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl29_26 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f524,plain,
spl29_27,
inference(avatar_split_clause,[],[f276,f522]) ).
fof(f276,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t60_xboole_1) ).
fof(f518,plain,
spl29_26,
inference(avatar_split_clause,[],[f241,f516]) ).
fof(f241,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t3_xboole_1) ).
fof(f514,plain,
spl29_25,
inference(avatar_split_clause,[],[f240,f512]) ).
fof(f512,plain,
( spl29_25
<=> ! [X0] : singleton(X0) = unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_25])]) ).
fof(f240,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t69_enumset1) ).
fof(f510,plain,
( ~ spl29_24
| ~ spl29_1
| ~ spl29_23 ),
inference(avatar_split_clause,[],[f505,f494,f398,f507]) ).
fof(f507,plain,
( spl29_24
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_24])]) ).
fof(f494,plain,
( spl29_23
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_23])]) ).
fof(f505,plain,
( ~ empty(sK7)
| ~ spl29_1
| ~ spl29_23 ),
inference(resolution,[],[f495,f400]) ).
fof(f495,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl29_23 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f496,plain,
spl29_23,
inference(avatar_split_clause,[],[f348,f494]) ).
fof(f348,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t7_boole) ).
fof(f492,plain,
spl29_22,
inference(avatar_split_clause,[],[f308,f490]) ).
fof(f490,plain,
( spl29_22
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).
fof(f308,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',idempotence_k2_xboole_0) ).
fof(f488,plain,
( ~ spl29_21
| ~ spl29_9
| ~ spl29_11 ),
inference(avatar_split_clause,[],[f459,f443,f435,f485]) ).
fof(f485,plain,
( spl29_21
<=> empty_set = powerset(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_21])]) ).
fof(f435,plain,
( spl29_9
<=> ! [X0] : singleton(X0) != empty_set ),
introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).
fof(f443,plain,
( spl29_11
<=> powerset(empty_set) = singleton(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_11])]) ).
fof(f459,plain,
( empty_set != powerset(empty_set)
| ~ spl29_9
| ~ spl29_11 ),
inference(superposition,[],[f436,f445]) ).
fof(f445,plain,
( powerset(empty_set) = singleton(empty_set)
| ~ spl29_11 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f436,plain,
( ! [X0] : singleton(X0) != empty_set
| ~ spl29_9 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f483,plain,
spl29_20,
inference(avatar_split_clause,[],[f307,f481]) ).
fof(f481,plain,
( spl29_20
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).
fof(f307,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',idempotence_k3_xboole_0) ).
fof(f479,plain,
spl29_19,
inference(avatar_split_clause,[],[f301,f477]) ).
fof(f301,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t6_boole) ).
fof(f475,plain,
spl29_18,
inference(avatar_split_clause,[],[f300,f473]) ).
fof(f300,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t3_boole) ).
fof(f471,plain,
spl29_17,
inference(avatar_split_clause,[],[f299,f469]) ).
fof(f469,plain,
( spl29_17
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).
fof(f299,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t1_boole) ).
fof(f467,plain,
spl29_16,
inference(avatar_split_clause,[],[f298,f465]) ).
fof(f298,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t4_boole) ).
fof(f463,plain,
spl29_15,
inference(avatar_split_clause,[],[f297,f461]) ).
fof(f461,plain,
( spl29_15
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).
fof(f297,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t2_boole) ).
fof(f458,plain,
spl29_14,
inference(avatar_split_clause,[],[f244,f456]) ).
fof(f456,plain,
( spl29_14
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).
fof(f244,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t36_xboole_1) ).
fof(f454,plain,
spl29_13,
inference(avatar_split_clause,[],[f243,f452]) ).
fof(f452,plain,
( spl29_13
<=> ! [X0,X1] : subset(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_13])]) ).
fof(f243,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t17_xboole_1) ).
fof(f450,plain,
spl29_12,
inference(avatar_split_clause,[],[f242,f448]) ).
fof(f448,plain,
( spl29_12
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_12])]) ).
fof(f242,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t7_xboole_1) ).
fof(f446,plain,
spl29_11,
inference(avatar_split_clause,[],[f237,f443]) ).
fof(f237,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t1_zfmisc_1) ).
fof(f441,plain,
spl29_10,
inference(avatar_split_clause,[],[f306,f439]) ).
fof(f439,plain,
( spl29_10
<=> ! [X0,X1] : ~ empty(ordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_10])]) ).
fof(f306,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',fc1_zfmisc_1) ).
fof(f437,plain,
spl29_9,
inference(avatar_split_clause,[],[f239,f435]) ).
fof(f239,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',l1_zfmisc_1) ).
fof(f433,plain,
spl29_8,
inference(avatar_split_clause,[],[f305,f431]) ).
fof(f431,plain,
( spl29_8
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).
fof(f305,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',reflexivity_r1_tarski) ).
fof(f429,plain,
spl29_7,
inference(avatar_split_clause,[],[f304,f427]) ).
fof(f427,plain,
( spl29_7
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).
fof(f304,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',irreflexivity_r2_xboole_0) ).
fof(f425,plain,
spl29_6,
inference(avatar_split_clause,[],[f238,f423]) ).
fof(f238,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t2_xboole_1) ).
fof(f421,plain,
spl29_5,
inference(avatar_split_clause,[],[f392,f418]) ).
fof(f392,plain,
empty(sK28),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
empty(sK28),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f47,f233]) ).
fof(f233,plain,
( ? [X0] : empty(X0)
=> empty(sK28) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',rc1_xboole_0) ).
fof(f416,plain,
~ spl29_4,
inference(avatar_split_clause,[],[f391,f413]) ).
fof(f413,plain,
( spl29_4
<=> empty(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).
fof(f391,plain,
~ empty(sK27),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
~ empty(sK27),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f48,f231]) ).
fof(f231,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK27) ),
introduced(choice_axiom,[]) ).
fof(f48,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',rc2_xboole_0) ).
fof(f411,plain,
spl29_3,
inference(avatar_split_clause,[],[f296,f408]) ).
fof(f408,plain,
( spl29_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
fof(f296,plain,
empty(empty_set),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
empty(empty_set),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',fc1_xboole_0) ).
fof(f406,plain,
~ spl29_2,
inference(avatar_split_clause,[],[f236,f403]) ).
fof(f236,plain,
sK7 != set_union2(singleton(sK6),sK7),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( sK7 != set_union2(singleton(sK6),sK7)
& in(sK6,sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f99,f150]) ).
fof(f150,plain,
( ? [X0,X1] :
( set_union2(singleton(X0),X1) != X1
& in(X0,X1) )
=> ( sK7 != set_union2(singleton(sK6),sK7)
& in(sK6,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0,X1] :
( set_union2(singleton(X0),X1) != X1
& in(X0,X1) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[],[f76]) ).
fof(f76,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.PYUmobVYkf/Vampire---4.8_8334',t46_zfmisc_1) ).
fof(f401,plain,
spl29_1,
inference(avatar_split_clause,[],[f235,f398]) ).
fof(f235,plain,
in(sK6,sK7),
inference(cnf_transformation,[],[f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 30 14:07:07 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.43 % (8623)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (8669)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (8667)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.43 % (8666)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.43 % (8668)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.22/0.43 % (8670)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.22/0.43 % (8671)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.22/0.43 % (8672)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.22/0.44 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.45 TRYING [3]
% 0.22/0.45 % (8670)First to succeed.
% 0.22/0.45 TRYING [1]
% 0.22/0.45 TRYING [2]
% 0.22/0.46 % (8670)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Theorem for Vampire---4
% 0.22/0.46 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.46 % (8670)------------------------------
% 0.22/0.46 % (8670)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.46 % (8670)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.46 % (8670)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (8670)Memory used [KB]: 6012
% 0.22/0.46 % (8670)Time elapsed: 0.025 s
% 0.22/0.46 % (8670)------------------------------
% 0.22/0.46 % (8670)------------------------------
% 0.22/0.46 % (8623)Success in time 0.086 s
% 0.22/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------