TSTP Solution File: NUM386+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Tue Apr 30 14:21:56 EDT 2024
% Result : Theorem 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 148
% Syntax : Number of formulae : 453 ( 93 unt; 0 def)
% Number of atoms : 1274 ( 135 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1336 ( 515 ~; 597 |; 90 &)
% ( 110 <=>; 23 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 112 ( 110 usr; 102 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 13 con; 0-3 aty)
% Number of variables : 468 ( 427 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1054,plain,
$false,
inference(avatar_sat_refutation,[],[f168,f173,f178,f183,f188,f193,f198,f203,f208,f213,f218,f223,f228,f233,f238,f243,f248,f253,f258,f263,f272,f281,f282,f288,f292,f296,f300,f313,f317,f321,f325,f329,f333,f344,f348,f352,f356,f360,f374,f379,f383,f387,f412,f416,f427,f431,f436,f440,f446,f450,f456,f461,f469,f473,f477,f505,f510,f515,f520,f524,f536,f540,f544,f548,f562,f566,f585,f589,f593,f611,f615,f647,f651,f669,f683,f687,f692,f696,f700,f736,f744,f749,f758,f763,f764,f774,f779,f801,f824,f828,f832,f836,f893,f897,f901,f905,f915,f919,f979,f983,f984,f994,f999,f1053]) ).
fof(f1053,plain,
( ~ spl16_22
| spl16_21
| ~ spl16_71 ),
inference(avatar_split_clause,[],[f620,f609,f265,f269]) ).
fof(f269,plain,
( spl16_22
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
fof(f265,plain,
( spl16_21
<=> in(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_21])]) ).
fof(f609,plain,
( spl16_71
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_71])]) ).
fof(f620,plain,
( ~ in(sK1,sK2)
| spl16_21
| ~ spl16_71 ),
inference(resolution,[],[f610,f267]) ).
fof(f267,plain,
( ~ in(sK1,set_union2(sK2,singleton(sK2)))
| spl16_21 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f610,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) )
| ~ spl16_71 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f999,plain,
( spl16_101
| ~ spl16_43
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f495,f475,f385,f997]) ).
fof(f997,plain,
( spl16_101
<=> ! [X2,X0,X1] :
( in(sK5(singleton(X0),X1,X2),X2)
| in(sK5(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK5(singleton(X0),X1,X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_101])]) ).
fof(f385,plain,
( spl16_43
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_43])]) ).
fof(f475,plain,
( spl16_56
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_56])]) ).
fof(f495,plain,
( ! [X2,X0,X1] :
( in(sK5(singleton(X0),X1,X2),X2)
| in(sK5(singleton(X0),X1,X2),X1)
| sP0(singleton(X0),X1,X2)
| sK5(singleton(X0),X1,X2) = X0 )
| ~ spl16_43
| ~ spl16_56 ),
inference(resolution,[],[f476,f386]) ).
fof(f386,plain,
( ! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 )
| ~ spl16_43 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2) )
| ~ spl16_56 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f994,plain,
( ~ spl16_100
| ~ spl16_22
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f738,f350,f269,f991]) ).
fof(f991,plain,
( spl16_100
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_100])]) ).
fof(f350,plain,
( spl16_37
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_37])]) ).
fof(f738,plain,
( ~ in(sK2,sK1)
| ~ spl16_22
| ~ spl16_37 ),
inference(resolution,[],[f270,f351]) ).
fof(f351,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl16_37 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f270,plain,
( in(sK1,sK2)
| ~ spl16_22 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f984,plain,
( spl16_24
| ~ spl16_43
| ~ spl16_88 ),
inference(avatar_split_clause,[],[f906,f821,f385,f278]) ).
fof(f278,plain,
( spl16_24
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
fof(f821,plain,
( spl16_88
<=> in(sK1,singleton(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_88])]) ).
fof(f906,plain,
( sK1 = sK2
| ~ spl16_43
| ~ spl16_88 ),
inference(resolution,[],[f823,f386]) ).
fof(f823,plain,
( in(sK1,singleton(sK2))
| ~ spl16_88 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f983,plain,
( spl16_99
| ~ spl16_43
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f489,f475,f385,f981]) ).
fof(f981,plain,
( spl16_99
<=> ! [X2,X0,X1] :
( in(sK5(X0,singleton(X1),X2),X2)
| in(sK5(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK5(X0,singleton(X1),X2) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_99])]) ).
fof(f489,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,singleton(X1),X2),X2)
| in(sK5(X0,singleton(X1),X2),X0)
| sP0(X0,singleton(X1),X2)
| sK5(X0,singleton(X1),X2) = X1 )
| ~ spl16_43
| ~ spl16_56 ),
inference(resolution,[],[f476,f386]) ).
fof(f979,plain,
( spl16_98
| ~ spl16_43
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f483,f475,f385,f977]) ).
fof(f977,plain,
( spl16_98
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,singleton(X2)),X1)
| in(sK5(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK5(X0,X1,singleton(X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_98])]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,singleton(X2)),X1)
| in(sK5(X0,X1,singleton(X2)),X0)
| sP0(X0,X1,singleton(X2))
| sK5(X0,X1,singleton(X2)) = X2 )
| ~ spl16_43
| ~ spl16_56 ),
inference(resolution,[],[f476,f386]) ).
fof(f919,plain,
( spl16_97
| ~ spl16_37
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f493,f475,f350,f917]) ).
fof(f917,plain,
( spl16_97
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_97])]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ in(X0,sK5(X0,X1,X2)) )
| ~ spl16_37
| ~ spl16_56 ),
inference(resolution,[],[f476,f351]) ).
fof(f915,plain,
( spl16_96
| ~ spl16_38
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f492,f475,f354,f913]) ).
fof(f913,plain,
( spl16_96
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_96])]) ).
fof(f354,plain,
( spl16_38
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_38])]) ).
fof(f492,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X0) )
| ~ spl16_38
| ~ spl16_56 ),
inference(resolution,[],[f476,f355]) ).
fof(f355,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl16_38 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f905,plain,
( spl16_95
| ~ spl16_37
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f487,f475,f350,f903]) ).
fof(f903,plain,
( spl16_95
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_95])]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X1,sK5(X0,X1,X2)) )
| ~ spl16_37
| ~ spl16_56 ),
inference(resolution,[],[f476,f351]) ).
fof(f901,plain,
( spl16_94
| ~ spl16_38
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f486,f475,f354,f899]) ).
fof(f899,plain,
( spl16_94
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_94])]) ).
fof(f486,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X1) )
| ~ spl16_38
| ~ spl16_56 ),
inference(resolution,[],[f476,f355]) ).
fof(f897,plain,
( spl16_93
| ~ spl16_37
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f481,f475,f350,f895]) ).
fof(f895,plain,
( spl16_93
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK5(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_93])]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ in(X2,sK5(X0,X1,X2)) )
| ~ spl16_37
| ~ spl16_56 ),
inference(resolution,[],[f476,f351]) ).
fof(f893,plain,
( spl16_92
| ~ spl16_38
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f480,f475,f354,f891]) ).
fof(f891,plain,
( spl16_92
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_92])]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| element(sK5(X0,X1,X2),X2) )
| ~ spl16_38
| ~ spl16_56 ),
inference(resolution,[],[f476,f355]) ).
fof(f836,plain,
( spl16_91
| ~ spl16_33
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f494,f475,f327,f834]) ).
fof(f834,plain,
( spl16_91
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_91])]) ).
fof(f327,plain,
( spl16_33
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_33])]) ).
fof(f494,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| sP0(X0,X1,X2)
| ~ empty(X0) )
| ~ spl16_33
| ~ spl16_56 ),
inference(resolution,[],[f476,f328]) ).
fof(f328,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl16_33 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f832,plain,
( spl16_90
| ~ spl16_33
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f488,f475,f327,f830]) ).
fof(f830,plain,
( spl16_90
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_90])]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X1) )
| ~ spl16_33
| ~ spl16_56 ),
inference(resolution,[],[f476,f328]) ).
fof(f828,plain,
( spl16_89
| ~ spl16_33
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f482,f475,f327,f826]) ).
fof(f826,plain,
( spl16_89
<=> ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_89])]) ).
fof(f482,plain,
( ! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| sP0(X0,X1,X2)
| ~ empty(X2) )
| ~ spl16_33
| ~ spl16_56 ),
inference(resolution,[],[f476,f328]) ).
fof(f824,plain,
( spl16_88
| spl16_22
| ~ spl16_21
| ~ spl16_73 ),
inference(avatar_split_clause,[],[f750,f645,f265,f269,f821]) ).
fof(f645,plain,
( spl16_73
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_73])]) ).
fof(f750,plain,
( in(sK1,sK2)
| in(sK1,singleton(sK2))
| ~ spl16_21
| ~ spl16_73 ),
inference(resolution,[],[f266,f646]) ).
fof(f646,plain,
( ! [X2,X0,X1] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) )
| ~ spl16_73 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f266,plain,
( in(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f801,plain,
( spl16_87
| ~ spl16_43
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f465,f459,f385,f799]) ).
fof(f799,plain,
( spl16_87
<=> ! [X0,X1] :
( sK4(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1)
| sK4(X0,singleton(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_87])]) ).
fof(f459,plain,
( spl16_53
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_53])]) ).
fof(f465,plain,
( ! [X0,X1] :
( sK4(X0,singleton(X1)) = X0
| singleton(X0) = singleton(X1)
| sK4(X0,singleton(X1)) = X1 )
| ~ spl16_43
| ~ spl16_53 ),
inference(resolution,[],[f460,f386]) ).
fof(f460,plain,
( ! [X0,X1] :
( in(sK4(X0,X1),X1)
| sK4(X0,X1) = X0
| singleton(X0) = X1 )
| ~ spl16_53 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f779,plain,
( ~ spl16_86
| ~ spl16_23
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f767,f350,f274,f776]) ).
fof(f776,plain,
( spl16_86
<=> in(set_union2(sK1,singleton(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_86])]) ).
fof(f274,plain,
( spl16_23
<=> in(sK1,set_union2(sK1,singleton(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
fof(f767,plain,
( ~ in(set_union2(sK1,singleton(sK1)),sK1)
| ~ spl16_23
| ~ spl16_37 ),
inference(resolution,[],[f275,f351]) ).
fof(f275,plain,
( in(sK1,set_union2(sK1,singleton(sK1)))
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f774,plain,
( spl16_85
| ~ spl16_23
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f766,f354,f274,f771]) ).
fof(f771,plain,
( spl16_85
<=> element(sK1,set_union2(sK1,singleton(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_85])]) ).
fof(f766,plain,
( element(sK1,set_union2(sK1,singleton(sK1)))
| ~ spl16_23
| ~ spl16_38 ),
inference(resolution,[],[f275,f355]) ).
fof(f764,plain,
( ~ spl16_75
| spl16_23
| ~ spl16_72 ),
inference(avatar_split_clause,[],[f634,f613,f274,f666]) ).
fof(f666,plain,
( spl16_75
<=> in(sK1,singleton(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_75])]) ).
fof(f613,plain,
( spl16_72
<=> ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_72])]) ).
fof(f634,plain,
( ~ in(sK1,singleton(sK1))
| spl16_23
| ~ spl16_72 ),
inference(resolution,[],[f614,f276]) ).
fof(f276,plain,
( ~ in(sK1,set_union2(sK1,singleton(sK1)))
| spl16_23 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) )
| ~ spl16_72 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f763,plain,
( ~ spl16_84
| ~ spl16_21
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f752,f350,f265,f760]) ).
fof(f760,plain,
( spl16_84
<=> in(set_union2(sK2,singleton(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_84])]) ).
fof(f752,plain,
( ~ in(set_union2(sK2,singleton(sK2)),sK1)
| ~ spl16_21
| ~ spl16_37 ),
inference(resolution,[],[f266,f351]) ).
fof(f758,plain,
( spl16_83
| ~ spl16_21
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f751,f354,f265,f755]) ).
fof(f755,plain,
( spl16_83
<=> element(sK1,set_union2(sK2,singleton(sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_83])]) ).
fof(f751,plain,
( element(sK1,set_union2(sK2,singleton(sK2)))
| ~ spl16_21
| ~ spl16_38 ),
inference(resolution,[],[f266,f355]) ).
fof(f749,plain,
( spl16_82
| ~ spl16_22
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f737,f354,f269,f746]) ).
fof(f746,plain,
( spl16_82
<=> element(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_82])]) ).
fof(f737,plain,
( element(sK1,sK2)
| ~ spl16_22
| ~ spl16_38 ),
inference(resolution,[],[f270,f355]) ).
fof(f744,plain,
( ~ spl16_81
| ~ spl16_22
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f739,f327,f269,f741]) ).
fof(f741,plain,
( spl16_81
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_81])]) ).
fof(f739,plain,
( ~ empty(sK2)
| ~ spl16_22
| ~ spl16_33 ),
inference(resolution,[],[f270,f328]) ).
fof(f736,plain,
( ~ spl16_28
| spl16_75 ),
inference(avatar_contradiction_clause,[],[f735]) ).
fof(f735,plain,
( $false
| ~ spl16_28
| spl16_75 ),
inference(resolution,[],[f668,f299]) ).
fof(f299,plain,
( ! [X3] : in(X3,singleton(X3))
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f298,plain,
( spl16_28
<=> ! [X3] : in(X3,singleton(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_28])]) ).
fof(f668,plain,
( ~ in(sK1,singleton(sK1))
| spl16_75 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f700,plain,
( spl16_80
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f498,f475,f698]) ).
fof(f698,plain,
( spl16_80
<=> ! [X4,X5] :
( in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4)
| sP0(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_80])]) ).
fof(f498,plain,
( ! [X4,X5] :
( in(sK5(X4,X4,X5),X5)
| in(sK5(X4,X4,X5),X4)
| sP0(X4,X4,X5) )
| ~ spl16_56 ),
inference(factoring,[],[f476]) ).
fof(f696,plain,
( spl16_79
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f497,f475,f694]) ).
fof(f694,plain,
( spl16_79
<=> ! [X2,X3] :
( in(sK5(X2,X3,X2),X2)
| in(sK5(X2,X3,X2),X3)
| sP0(X2,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_79])]) ).
fof(f497,plain,
( ! [X2,X3] :
( in(sK5(X2,X3,X2),X2)
| in(sK5(X2,X3,X2),X3)
| sP0(X2,X3,X2) )
| ~ spl16_56 ),
inference(factoring,[],[f476]) ).
fof(f692,plain,
( spl16_78
| ~ spl16_56 ),
inference(avatar_split_clause,[],[f496,f475,f690]) ).
fof(f690,plain,
( spl16_78
<=> ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_78])]) ).
fof(f496,plain,
( ! [X0,X1] :
( in(sK5(X0,X1,X1),X1)
| in(sK5(X0,X1,X1),X0)
| sP0(X0,X1,X1) )
| ~ spl16_56 ),
inference(factoring,[],[f476]) ).
fof(f687,plain,
( spl16_77
| ~ spl16_37
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f463,f459,f350,f685]) ).
fof(f685,plain,
( spl16_77
<=> ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_77])]) ).
fof(f463,plain,
( ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ in(X1,sK4(X0,X1)) )
| ~ spl16_37
| ~ spl16_53 ),
inference(resolution,[],[f460,f351]) ).
fof(f683,plain,
( spl16_76
| ~ spl16_38
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f462,f459,f354,f681]) ).
fof(f681,plain,
( spl16_76
<=> ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| element(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_76])]) ).
fof(f462,plain,
( ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| element(sK4(X0,X1),X1) )
| ~ spl16_38
| ~ spl16_53 ),
inference(resolution,[],[f460,f355]) ).
fof(f669,plain,
( ~ spl16_75
| spl16_21
| ~ spl16_24
| ~ spl16_72 ),
inference(avatar_split_clause,[],[f642,f613,f278,f265,f666]) ).
fof(f642,plain,
( ~ in(sK1,singleton(sK1))
| spl16_21
| ~ spl16_24
| ~ spl16_72 ),
inference(forward_demodulation,[],[f633,f279]) ).
fof(f279,plain,
( sK1 = sK2
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f633,plain,
( ~ in(sK1,singleton(sK2))
| spl16_21
| ~ spl16_72 ),
inference(resolution,[],[f614,f267]) ).
fof(f651,plain,
( spl16_74
| ~ spl16_33
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f464,f459,f327,f649]) ).
fof(f649,plain,
( spl16_74
<=> ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_74])]) ).
fof(f464,plain,
( ! [X0,X1] :
( sK4(X0,X1) = X0
| singleton(X0) = X1
| ~ empty(X1) )
| ~ spl16_33
| ~ spl16_53 ),
inference(resolution,[],[f460,f328]) ).
fof(f647,plain,
( spl16_73
| ~ spl16_39
| ~ spl16_51 ),
inference(avatar_split_clause,[],[f451,f448,f358,f645]) ).
fof(f358,plain,
( spl16_39
<=> ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_39])]) ).
fof(f448,plain,
( spl16_51
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_51])]) ).
fof(f451,plain,
( ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,set_union2(X1,X2))
| in(X0,X2) )
| ~ spl16_39
| ~ spl16_51 ),
inference(resolution,[],[f449,f359]) ).
fof(f359,plain,
( ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1))
| ~ spl16_39 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f449,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| in(X4,X1)
| ~ in(X4,X2)
| in(X4,X0) )
| ~ spl16_51 ),
inference(avatar_component_clause,[],[f448]) ).
fof(f615,plain,
( spl16_72
| ~ spl16_39
| ~ spl16_49 ),
inference(avatar_split_clause,[],[f442,f438,f358,f613]) ).
fof(f438,plain,
( spl16_49
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_49])]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) )
| ~ spl16_39
| ~ spl16_49 ),
inference(resolution,[],[f439,f359]) ).
fof(f439,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl16_49 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f611,plain,
( spl16_71
| ~ spl16_39
| ~ spl16_48 ),
inference(avatar_split_clause,[],[f441,f434,f358,f609]) ).
fof(f434,plain,
( spl16_48
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_48])]) ).
fof(f441,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) )
| ~ spl16_39
| ~ spl16_48 ),
inference(resolution,[],[f435,f359]) ).
fof(f435,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X1)
| in(X4,X2) )
| ~ spl16_48 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f593,plain,
( spl16_70
| ~ spl16_27
| ~ spl16_44 ),
inference(avatar_split_clause,[],[f417,f410,f294,f591]) ).
fof(f591,plain,
( spl16_70
<=> ! [X0] :
( empty(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_70])]) ).
fof(f294,plain,
( spl16_27
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_27])]) ).
fof(f410,plain,
( spl16_44
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_44])]) ).
fof(f417,plain,
( ! [X0] :
( empty(X0)
| in(sK3(X0),X0) )
| ~ spl16_27
| ~ spl16_44 ),
inference(resolution,[],[f411,f295]) ).
fof(f295,plain,
( ! [X0] : element(sK3(X0),X0)
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f411,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl16_44 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f589,plain,
( spl16_69
| ~ spl16_39
| ~ spl16_66 ),
inference(avatar_split_clause,[],[f573,f560,f358,f587]) ).
fof(f587,plain,
( spl16_69
<=> ! [X0] : sP0(X0,sK7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_69])]) ).
fof(f560,plain,
( spl16_66
<=> ! [X0] : set_union2(sK7,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_66])]) ).
fof(f573,plain,
( ! [X0] : sP0(X0,sK7,X0)
| ~ spl16_39
| ~ spl16_66 ),
inference(superposition,[],[f359,f561]) ).
fof(f561,plain,
( ! [X0] : set_union2(sK7,X0) = X0
| ~ spl16_66 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f585,plain,
( spl16_68
| ~ spl16_39
| ~ spl16_41 ),
inference(avatar_split_clause,[],[f390,f377,f358,f583]) ).
fof(f583,plain,
( spl16_68
<=> ! [X0,X1] : sP0(X1,X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_68])]) ).
fof(f377,plain,
( spl16_41
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
fof(f390,plain,
( ! [X0,X1] : sP0(X1,X0,set_union2(X1,X0))
| ~ spl16_39
| ~ spl16_41 ),
inference(superposition,[],[f359,f378]) ).
fof(f378,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl16_41 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f566,plain,
( spl16_67
| ~ spl16_4
| ~ spl16_42 ),
inference(avatar_split_clause,[],[f403,f381,f180,f564]) ).
fof(f564,plain,
( spl16_67
<=> ! [X0] :
( sK7 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_67])]) ).
fof(f180,plain,
( spl16_4
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f381,plain,
( spl16_42
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f403,plain,
( ! [X0] :
( sK7 = X0
| ~ empty(X0) )
| ~ spl16_4
| ~ spl16_42 ),
inference(resolution,[],[f382,f182]) ).
fof(f182,plain,
( empty(sK7)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f382,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl16_42 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f562,plain,
( spl16_66
| ~ spl16_4
| ~ spl16_30
| ~ spl16_31
| ~ spl16_41 ),
inference(avatar_split_clause,[],[f398,f377,f319,f315,f180,f560]) ).
fof(f315,plain,
( spl16_30
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_30])]) ).
fof(f319,plain,
( spl16_31
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_31])]) ).
fof(f398,plain,
( ! [X0] : set_union2(sK7,X0) = X0
| ~ spl16_4
| ~ spl16_30
| ~ spl16_31
| ~ spl16_41 ),
inference(forward_demodulation,[],[f388,f335]) ).
fof(f335,plain,
( empty_set = sK7
| ~ spl16_4
| ~ spl16_31 ),
inference(resolution,[],[f320,f182]) ).
fof(f320,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl16_31 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f388,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl16_30
| ~ spl16_41 ),
inference(superposition,[],[f378,f316]) ).
fof(f316,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl16_30 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f548,plain,
( spl16_65
| ~ spl16_4
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(avatar_split_clause,[],[f369,f358,f319,f315,f180,f546]) ).
fof(f546,plain,
( spl16_65
<=> ! [X0] : sP0(sK7,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_65])]) ).
fof(f369,plain,
( ! [X0] : sP0(sK7,X0,X0)
| ~ spl16_4
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(forward_demodulation,[],[f367,f335]) ).
fof(f367,plain,
( ! [X0] : sP0(empty_set,X0,X0)
| ~ spl16_30
| ~ spl16_39 ),
inference(superposition,[],[f359,f316]) ).
fof(f544,plain,
( spl16_64
| ~ spl16_32
| ~ spl16_39 ),
inference(avatar_split_clause,[],[f368,f358,f323,f542]) ).
fof(f542,plain,
( spl16_64
<=> ! [X0] : sP0(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_64])]) ).
fof(f323,plain,
( spl16_32
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_32])]) ).
fof(f368,plain,
( ! [X0] : sP0(X0,X0,X0)
| ~ spl16_32
| ~ spl16_39 ),
inference(superposition,[],[f359,f324]) ).
fof(f324,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f540,plain,
( spl16_63
| ~ spl16_28
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f366,f354,f298,f538]) ).
fof(f538,plain,
( spl16_63
<=> ! [X0] : element(X0,singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_63])]) ).
fof(f366,plain,
( ! [X0] : element(X0,singleton(X0))
| ~ spl16_28
| ~ spl16_38 ),
inference(resolution,[],[f355,f299]) ).
fof(f536,plain,
( spl16_62
| ~ spl16_28
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f365,f350,f298,f534]) ).
fof(f534,plain,
( spl16_62
<=> ! [X0] : ~ in(singleton(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_62])]) ).
fof(f365,plain,
( ! [X0] : ~ in(singleton(X0),X0)
| ~ spl16_28
| ~ spl16_37 ),
inference(resolution,[],[f351,f299]) ).
fof(f524,plain,
( spl16_61
| ~ spl16_28
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f340,f327,f298,f522]) ).
fof(f522,plain,
( spl16_61
<=> ! [X0] : ~ empty(singleton(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_61])]) ).
fof(f340,plain,
( ! [X0] : ~ empty(singleton(X0))
| ~ spl16_28
| ~ spl16_33 ),
inference(resolution,[],[f328,f299]) ).
fof(f520,plain,
( spl16_60
| ~ spl16_4
| ~ spl16_19
| ~ spl16_31 ),
inference(avatar_split_clause,[],[f339,f319,f255,f180,f517]) ).
fof(f517,plain,
( spl16_60
<=> sK7 = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_60])]) ).
fof(f255,plain,
( spl16_19
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_19])]) ).
fof(f339,plain,
( sK7 = sK15
| ~ spl16_4
| ~ spl16_19
| ~ spl16_31 ),
inference(forward_demodulation,[],[f337,f335]) ).
fof(f337,plain,
( empty_set = sK15
| ~ spl16_19
| ~ spl16_31 ),
inference(resolution,[],[f320,f257]) ).
fof(f257,plain,
( empty(sK15)
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f515,plain,
( spl16_59
| ~ spl16_4
| ~ spl16_7
| ~ spl16_31 ),
inference(avatar_split_clause,[],[f338,f319,f195,f180,f512]) ).
fof(f512,plain,
( spl16_59
<=> sK7 = sK9 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_59])]) ).
fof(f195,plain,
( spl16_7
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
fof(f338,plain,
( sK7 = sK9
| ~ spl16_4
| ~ spl16_7
| ~ spl16_31 ),
inference(forward_demodulation,[],[f336,f335]) ).
fof(f336,plain,
( empty_set = sK9
| ~ spl16_7
| ~ spl16_31 ),
inference(resolution,[],[f320,f197]) ).
fof(f197,plain,
( empty(sK9)
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f510,plain,
( spl16_58
| ~ spl16_4
| ~ spl16_31 ),
inference(avatar_split_clause,[],[f335,f319,f180,f507]) ).
fof(f507,plain,
( spl16_58
<=> empty_set = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl16_58])]) ).
fof(f505,plain,
( spl16_57
| ~ spl16_4
| ~ spl16_26 ),
inference(avatar_split_clause,[],[f306,f290,f180,f502]) ).
fof(f502,plain,
( spl16_57
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_57])]) ).
fof(f290,plain,
( spl16_26
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_26])]) ).
fof(f306,plain,
( relation(sK7)
| ~ spl16_4
| ~ spl16_26 ),
inference(resolution,[],[f291,f182]) ).
fof(f291,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f477,plain,
spl16_56,
inference(avatar_split_clause,[],[f131,f475]) ).
fof(f131,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( ~ in(sK5(X0,X1,X2),X0)
& ~ in(sK5(X0,X1,X2),X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK5(X0,X1,X2),X0)
& ~ in(sK5(X0,X1,X2),X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f473,plain,
spl16_55,
inference(avatar_split_clause,[],[f133,f471]) ).
fof(f471,plain,
( spl16_55
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_55])]) ).
fof(f133,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f469,plain,
spl16_54,
inference(avatar_split_clause,[],[f132,f467]) ).
fof(f467,plain,
( spl16_54
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_54])]) ).
fof(f132,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f461,plain,
spl16_53,
inference(avatar_split_clause,[],[f124,f459]) ).
fof(f124,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f68,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f456,plain,
( spl16_52
| ~ spl16_7
| ~ spl16_25 ),
inference(avatar_split_clause,[],[f303,f286,f195,f453]) ).
fof(f453,plain,
( spl16_52
<=> function(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_52])]) ).
fof(f286,plain,
( spl16_25
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_25])]) ).
fof(f303,plain,
( function(sK9)
| ~ spl16_7
| ~ spl16_25 ),
inference(resolution,[],[f287,f197]) ).
fof(f287,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl16_25 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f450,plain,
spl16_51,
inference(avatar_split_clause,[],[f128,f448]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f446,plain,
spl16_50,
inference(avatar_split_clause,[],[f163,f444]) ).
fof(f444,plain,
( spl16_50
<=> ! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_50])]) ).
fof(f163,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f440,plain,
spl16_49,
inference(avatar_split_clause,[],[f130,f438]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f436,plain,
spl16_48,
inference(avatar_split_clause,[],[f129,f434]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f431,plain,
spl16_47,
inference(avatar_split_clause,[],[f135,f429]) ).
fof(f429,plain,
( spl16_47
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_47])]) ).
fof(f135,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f8,f59]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f427,plain,
( spl16_46
| ~ spl16_4
| ~ spl16_25 ),
inference(avatar_split_clause,[],[f302,f286,f180,f424]) ).
fof(f424,plain,
( spl16_46
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_46])]) ).
fof(f302,plain,
( function(sK7)
| ~ spl16_4
| ~ spl16_25 ),
inference(resolution,[],[f287,f182]) ).
fof(f416,plain,
spl16_45,
inference(avatar_split_clause,[],[f121,f414]) ).
fof(f414,plain,
( spl16_45
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_45])]) ).
fof(f121,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f412,plain,
spl16_44,
inference(avatar_split_clause,[],[f120,f410]) ).
fof(f120,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f387,plain,
spl16_43,
inference(avatar_split_clause,[],[f160,f385]) ).
fof(f160,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f122]) ).
fof(f122,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f383,plain,
spl16_42,
inference(avatar_split_clause,[],[f126,f381]) ).
fof(f126,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f379,plain,
spl16_41,
inference(avatar_split_clause,[],[f115,f377]) ).
fof(f115,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f374,plain,
( spl16_40
| ~ spl16_1
| ~ spl16_25 ),
inference(avatar_split_clause,[],[f301,f286,f165,f371]) ).
fof(f371,plain,
( spl16_40
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_40])]) ).
fof(f165,plain,
( spl16_1
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f301,plain,
( function(empty_set)
| ~ spl16_1
| ~ spl16_25 ),
inference(resolution,[],[f287,f167]) ).
fof(f167,plain,
( empty(empty_set)
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f360,plain,
spl16_39,
inference(avatar_split_clause,[],[f161,f358]) ).
fof(f161,plain,
! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f134]) ).
fof(f134,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f76]) ).
fof(f356,plain,
spl16_38,
inference(avatar_split_clause,[],[f119,f354]) ).
fof(f119,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f352,plain,
spl16_37,
inference(avatar_split_clause,[],[f118,f350]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,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/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f348,plain,
spl16_36,
inference(avatar_split_clause,[],[f117,f346]) ).
fof(f346,plain,
( spl16_36
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_36])]) ).
fof(f117,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f344,plain,
spl16_35,
inference(avatar_split_clause,[],[f116,f342]) ).
fof(f342,plain,
( spl16_35
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_35])]) ).
fof(f116,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f333,plain,
spl16_34,
inference(avatar_split_clause,[],[f157,f331]) ).
fof(f331,plain,
( spl16_34
<=> ! [X0] : ~ empty(set_union2(X0,singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_34])]) ).
fof(f157,plain,
! [X0] : ~ empty(set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f105,f107]) ).
fof(f107,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f105,plain,
! [X0] : ~ empty(succ(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : ~ empty(succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f329,plain,
spl16_33,
inference(avatar_split_clause,[],[f127,f327]) ).
fof(f127,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f325,plain,
spl16_32,
inference(avatar_split_clause,[],[f114,f323]) ).
fof(f114,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f321,plain,
spl16_31,
inference(avatar_split_clause,[],[f110,f319]) ).
fof(f110,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f317,plain,
spl16_30,
inference(avatar_split_clause,[],[f106,f315]) ).
fof(f106,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f313,plain,
( ~ spl16_29
| spl16_22
| ~ spl16_24 ),
inference(avatar_split_clause,[],[f284,f278,f269,f310]) ).
fof(f310,plain,
( spl16_29
<=> in(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_29])]) ).
fof(f284,plain,
( ~ in(sK1,sK1)
| spl16_22
| ~ spl16_24 ),
inference(superposition,[],[f271,f279]) ).
fof(f271,plain,
( ~ in(sK1,sK2)
| spl16_22 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f300,plain,
spl16_28,
inference(avatar_split_clause,[],[f159,f298]) ).
fof(f159,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f158]) ).
fof(f158,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f70]) ).
fof(f296,plain,
spl16_27,
inference(avatar_split_clause,[],[f113,f294]) ).
fof(f113,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f9,f65]) ).
fof(f65,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f292,plain,
spl16_26,
inference(avatar_split_clause,[],[f109,f290]) ).
fof(f109,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f288,plain,
spl16_25,
inference(avatar_split_clause,[],[f108,f286]) ).
fof(f108,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f282,plain,
( spl16_21
| spl16_22
| spl16_24 ),
inference(avatar_split_clause,[],[f156,f278,f269,f265]) ).
fof(f156,plain,
( sK1 = sK2
| in(sK1,sK2)
| in(sK1,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f97,f107]) ).
fof(f97,plain,
( sK1 = sK2
| in(sK1,sK2)
| in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ( ( sK1 != sK2
& ~ in(sK1,sK2) )
| ~ in(sK1,succ(sK2)) )
& ( sK1 = sK2
| in(sK1,sK2)
| in(sK1,succ(sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f62,f63]) ).
fof(f63,plain,
( ? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) )
=> ( ( ( sK1 != sK2
& ~ in(sK1,sK2) )
| ~ in(sK1,succ(sK2)) )
& ( sK1 = sK2
| in(sK1,sK2)
| in(sK1,succ(sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
? [X0,X1] :
( in(X0,succ(X1))
<~> ( X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f281,plain,
( ~ spl16_23
| ~ spl16_24 ),
inference(avatar_split_clause,[],[f162,f278,f274]) ).
fof(f162,plain,
( sK1 != sK2
| ~ in(sK1,set_union2(sK1,singleton(sK1))) ),
inference(inner_rewriting,[],[f154]) ).
fof(f154,plain,
( sK1 != sK2
| ~ in(sK1,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f99,f107]) ).
fof(f99,plain,
( sK1 != sK2
| ~ in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f272,plain,
( ~ spl16_21
| ~ spl16_22 ),
inference(avatar_split_clause,[],[f155,f269,f265]) ).
fof(f155,plain,
( ~ in(sK1,sK2)
| ~ in(sK1,set_union2(sK2,singleton(sK2))) ),
inference(definition_unfolding,[],[f98,f107]) ).
fof(f98,plain,
( ~ in(sK1,sK2)
| ~ in(sK1,succ(sK2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f263,plain,
spl16_20,
inference(avatar_split_clause,[],[f153,f260]) ).
fof(f260,plain,
( spl16_20
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_20])]) ).
fof(f153,plain,
function(sK15),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( function(sK15)
& empty(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f21,f95]) ).
fof(f95,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK15)
& empty(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f258,plain,
spl16_19,
inference(avatar_split_clause,[],[f152,f255]) ).
fof(f152,plain,
empty(sK15),
inference(cnf_transformation,[],[f96]) ).
fof(f253,plain,
spl16_18,
inference(avatar_split_clause,[],[f151,f250]) ).
fof(f250,plain,
( spl16_18
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_18])]) ).
fof(f151,plain,
relation(sK15),
inference(cnf_transformation,[],[f96]) ).
fof(f248,plain,
spl16_17,
inference(avatar_split_clause,[],[f150,f245]) ).
fof(f245,plain,
( spl16_17
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_17])]) ).
fof(f150,plain,
function(sK14),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f42,f93]) ).
fof(f93,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f24]) ).
fof(f24,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f243,plain,
spl16_16,
inference(avatar_split_clause,[],[f149,f240]) ).
fof(f240,plain,
( spl16_16
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_16])]) ).
fof(f149,plain,
relation(sK14),
inference(cnf_transformation,[],[f94]) ).
fof(f238,plain,
spl16_15,
inference(avatar_split_clause,[],[f148,f235]) ).
fof(f235,plain,
( spl16_15
<=> function(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_15])]) ).
fof(f148,plain,
function(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( function(sK13)
& relation(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f18,f91]) ).
fof(f91,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK13)
& relation(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f233,plain,
spl16_14,
inference(avatar_split_clause,[],[f147,f230]) ).
fof(f230,plain,
( spl16_14
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
fof(f147,plain,
relation(sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f228,plain,
spl16_13,
inference(avatar_split_clause,[],[f146,f225]) ).
fof(f225,plain,
( spl16_13
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
fof(f146,plain,
function(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( function(sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f39,f89]) ).
fof(f89,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f223,plain,
spl16_12,
inference(avatar_split_clause,[],[f145,f220]) ).
fof(f220,plain,
( spl16_12
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_12])]) ).
fof(f145,plain,
relation(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f218,plain,
spl16_11,
inference(avatar_split_clause,[],[f144,f215]) ).
fof(f215,plain,
( spl16_11
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
fof(f144,plain,
relation(sK11),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
relation(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f40,f87]) ).
fof(f87,plain,
( ? [X0] : relation(X0)
=> relation(sK11) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f25]) ).
fof(f25,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f213,plain,
spl16_10,
inference(avatar_split_clause,[],[f143,f210]) ).
fof(f210,plain,
( spl16_10
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f143,plain,
function(sK10),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f37,f85]) ).
fof(f85,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f208,plain,
spl16_9,
inference(avatar_split_clause,[],[f142,f205]) ).
fof(f205,plain,
( spl16_9
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f142,plain,
relation(sK10),
inference(cnf_transformation,[],[f86]) ).
fof(f203,plain,
spl16_8,
inference(avatar_split_clause,[],[f141,f200]) ).
fof(f200,plain,
( spl16_8
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f141,plain,
relation(sK9),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
( relation(sK9)
& empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f19,f83]) ).
fof(f83,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK9)
& empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f198,plain,
spl16_7,
inference(avatar_split_clause,[],[f140,f195]) ).
fof(f140,plain,
empty(sK9),
inference(cnf_transformation,[],[f84]) ).
fof(f193,plain,
spl16_6,
inference(avatar_split_clause,[],[f139,f190]) ).
fof(f190,plain,
( spl16_6
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f139,plain,
relation(sK8),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f81]) ).
fof(f81,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK8)
& ~ empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f188,plain,
~ spl16_5,
inference(avatar_split_clause,[],[f138,f185]) ).
fof(f185,plain,
( spl16_5
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f138,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f82]) ).
fof(f183,plain,
spl16_4,
inference(avatar_split_clause,[],[f137,f180]) ).
fof(f137,plain,
empty(sK7),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f20,f79]) ).
fof(f79,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f178,plain,
~ spl16_3,
inference(avatar_split_clause,[],[f136,f175]) ).
fof(f175,plain,
( spl16_3
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f136,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f23,f77]) ).
fof(f77,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f173,plain,
spl16_2,
inference(avatar_split_clause,[],[f102,f170]) ).
fof(f170,plain,
( spl16_2
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f102,plain,
relation(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f168,plain,
spl16_1,
inference(avatar_split_clause,[],[f100,f165]) ).
fof(f100,plain,
empty(empty_set),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n022.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Apr 29 23:48:58 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (10766)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (10769)WARNING: value z3 for option sas not known
% 0.14/0.39 % (10769)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 theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (10770)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (10768)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (10772)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 theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (10773)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 theBenchmark for (497ds/0Mi)
% 0.14/0.39 % (10771)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 theBenchmark for (531ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 % (10767)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [3]
% 0.14/0.40 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [5]
% 0.14/0.41 % (10771)First to succeed.
% 0.14/0.41 TRYING [5]
% 0.14/0.41 TRYING [3]
% 0.14/0.41 % (10771)Refutation found. Thanks to Tanya!
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42 % (10771)------------------------------
% 0.14/0.42 % (10771)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.42 % (10771)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (10771)Memory used [KB]: 1219
% 0.14/0.42 % (10771)Time elapsed: 0.025 s
% 0.14/0.42 % (10771)Instructions burned: 43 (million)
% 0.14/0.42 % (10771)------------------------------
% 0.14/0.42 % (10771)------------------------------
% 0.14/0.42 % (10766)Success in time 0.04 s
%------------------------------------------------------------------------------