TSTP Solution File: LCL187-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL187-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 13:40:48 EDT 2024
% Result : Unsatisfiable 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 112
% Syntax : Number of formulae : 376 ( 22 unt; 0 def)
% Number of atoms : 1082 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1311 ( 605 ~; 603 |; 0 &)
% ( 103 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 107 ( 105 usr; 104 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 575 ( 575 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1490,plain,
$false,
inference(avatar_sat_refutation,[],[f21,f25,f29,f33,f39,f43,f48,f52,f57,f62,f68,f73,f77,f82,f87,f94,f104,f115,f119,f127,f137,f141,f145,f153,f161,f165,f173,f182,f186,f190,f194,f219,f223,f232,f237,f241,f251,f256,f262,f270,f277,f281,f288,f298,f302,f312,f316,f320,f324,f359,f363,f367,f419,f444,f448,f452,f477,f481,f485,f489,f524,f528,f533,f537,f541,f590,f623,f656,f660,f664,f704,f708,f737,f741,f767,f771,f775,f779,f813,f832,f836,f840,f844,f904,f908,f912,f916,f920,f924,f931,f935,f939,f943,f954,f1030,f1034,f1038,f1043,f1047,f1051,f1059,f1060,f1061,f1285,f1489]) ).
fof(f1489,plain,
( ~ spl0_40
| spl0_103 ),
inference(avatar_contradiction_clause,[],[f1484]) ).
fof(f1484,plain,
( $false
| ~ spl0_40
| spl0_103 ),
inference(resolution,[],[f269,f1284]) ).
fof(f1284,plain,
( ~ theorem(or(not(p),not(not(p))))
| spl0_103 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f1282,plain,
( spl0_103
<=> theorem(or(not(p),not(not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f269,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl0_40
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1285,plain,
( ~ spl0_103
| spl0_1
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f998,f937,f18,f1282]) ).
fof(f18,plain,
( spl0_1
<=> theorem(or(not(p),or(not(not(p)),q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f937,plain,
( spl0_94
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f998,plain,
( ~ theorem(or(not(p),not(not(p))))
| spl0_1
| ~ spl0_94 ),
inference(resolution,[],[f938,f20]) ).
fof(f20,plain,
( ~ theorem(or(not(p),or(not(not(p)),q)))
| spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f938,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f937]) ).
fof(f1061,plain,
( spl0_1
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f1052]) ).
fof(f1052,plain,
( $false
| spl0_1
| ~ spl0_92 ),
inference(resolution,[],[f930,f20]) ).
fof(f930,plain,
( ! [X0,X1] : theorem(or(X0,X1))
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f929,plain,
( spl0_92
<=> ! [X0,X1] : theorem(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1060,plain,
( spl0_38
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f1053]) ).
fof(f1053,plain,
( $false
| spl0_38
| ~ spl0_92 ),
inference(resolution,[],[f930,f255]) ).
fof(f255,plain,
( ~ theorem(or(not(p),q))
| spl0_38 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f253,plain,
( spl0_38
<=> theorem(or(not(p),q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1059,plain,
( spl0_18
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f1056]) ).
fof(f1056,plain,
( $false
| spl0_18
| ~ spl0_92 ),
inference(resolution,[],[f930,f114]) ).
fof(f114,plain,
( ~ theorem(or(not(not(p)),q))
| spl0_18 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f112,plain,
( spl0_18
<=> theorem(or(not(not(p)),q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1051,plain,
( spl0_102
| spl0_92
| ~ spl0_44
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f406,f361,f286,f929,f1049]) ).
fof(f1049,plain,
( spl0_102
<=> ! [X2,X3] :
( ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f286,plain,
( spl0_44
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f361,plain,
( spl0_52
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) )
| ~ spl0_44
| ~ spl0_52 ),
inference(resolution,[],[f362,f287]) ).
fof(f287,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f362,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,X1))
| ~ theorem(not(X2)) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f1047,plain,
( spl0_101
| ~ spl0_22
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f379,f357,f139,f1045]) ).
fof(f1045,plain,
( spl0_101
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f139,plain,
( spl0_22
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f357,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f379,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) )
| ~ spl0_22
| ~ spl0_51 ),
inference(resolution,[],[f358,f140]) ).
fof(f140,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f1043,plain,
( ~ spl0_100
| spl0_1
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f955,f910,f18,f1040]) ).
fof(f1040,plain,
( spl0_100
<=> theorem(or(q,not(not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f910,plain,
( spl0_87
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f955,plain,
( ~ theorem(or(q,not(not(p))))
| spl0_1
| ~ spl0_87 ),
inference(resolution,[],[f911,f20]) ).
fof(f911,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f1038,plain,
( spl0_99
| ~ spl0_47
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f371,f357,f310,f1036]) ).
fof(f1036,plain,
( spl0_99
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f310,plain,
( spl0_47
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f371,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) )
| ~ spl0_47
| ~ spl0_51 ),
inference(resolution,[],[f358,f311]) ).
fof(f311,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f1034,plain,
( spl0_98
| ~ spl0_46
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f354,f322,f300,f1032]) ).
fof(f1032,plain,
( spl0_98
<=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f300,plain,
( spl0_46
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f322,plain,
( spl0_50
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f354,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
| ~ spl0_46
| ~ spl0_50 ),
inference(resolution,[],[f323,f301]) ).
fof(f301,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f1030,plain,
( spl0_97
| ~ spl0_10
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f346,f322,f60,f1028]) ).
fof(f1028,plain,
( spl0_97
<=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f60,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f346,plain,
( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
| ~ spl0_10
| ~ spl0_50 ),
inference(resolution,[],[f323,f61]) ).
fof(f61,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f954,plain,
( spl0_96
| ~ spl0_17
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f759,f739,f102,f952]) ).
fof(f952,plain,
( spl0_96
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f102,plain,
( spl0_17
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f739,plain,
( spl0_75
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f759,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X0))))
| ~ spl0_17
| ~ spl0_75 ),
inference(resolution,[],[f740,f103]) ).
fof(f103,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f740,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f943,plain,
( spl0_95
| ~ spl0_44
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f610,f588,f286,f941]) ).
fof(f941,plain,
( spl0_95
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f588,plain,
( spl0_67
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f610,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) )
| ~ spl0_44
| ~ spl0_67 ),
inference(resolution,[],[f589,f287]) ).
fof(f589,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X2,or(X1,X3))))
| theorem(or(X0,or(X1,or(X2,X3)))) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f939,plain,
( spl0_94
| ~ spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f435,f417,f171,f937]) ).
fof(f171,plain,
( spl0_27
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f417,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f435,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_27
| ~ spl0_54 ),
inference(resolution,[],[f418,f172]) ).
fof(f172,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f935,plain,
( spl0_93
| ~ spl0_21
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f408,f361,f135,f933]) ).
fof(f933,plain,
( spl0_93
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f135,plain,
( spl0_21
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_21
| ~ spl0_52 ),
inference(resolution,[],[f362,f136]) ).
fof(f136,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f931,plain,
( spl0_91
| spl0_92
| ~ spl0_23
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f401,f361,f143,f929,f926]) ).
fof(f926,plain,
( spl0_91
<=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f143,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(X2),X2))) )
| ~ spl0_23
| ~ spl0_52 ),
inference(resolution,[],[f362,f144]) ).
fof(f144,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f924,plain,
( spl0_90
| ~ spl0_22
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f399,f361,f139,f922]) ).
fof(f922,plain,
( spl0_90
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f399,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) )
| ~ spl0_22
| ~ spl0_52 ),
inference(resolution,[],[f362,f140]) ).
fof(f920,plain,
( spl0_89
| ~ spl0_10
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f390,f361,f60,f918]) ).
fof(f918,plain,
( spl0_89
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f390,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_10
| ~ spl0_52 ),
inference(resolution,[],[f362,f61]) ).
fof(f916,plain,
( spl0_88
| ~ spl0_7
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f388,f361,f46,f914]) ).
fof(f914,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f46,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) )
| ~ spl0_7
| ~ spl0_52 ),
inference(resolution,[],[f362,f47]) ).
fof(f47,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f912,plain,
( spl0_87
| ~ spl0_11
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f372,f357,f66,f910]) ).
fof(f66,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_11
| ~ spl0_51 ),
inference(resolution,[],[f358,f67]) ).
fof(f67,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f908,plain,
( spl0_86
| ~ spl0_16
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f752,f735,f92,f906]) ).
fof(f906,plain,
( spl0_86
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f92,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f735,plain,
( spl0_74
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f752,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X0)))
| ~ spl0_16
| ~ spl0_74 ),
inference(resolution,[],[f736,f93]) ).
fof(f93,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f736,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f904,plain,
( spl0_85
| ~ spl0_16
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f327,f310,f92,f902]) ).
fof(f902,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f327,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) )
| ~ spl0_16
| ~ spl0_47 ),
inference(resolution,[],[f311,f93]) ).
fof(f844,plain,
( spl0_84
| ~ spl0_26
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f430,f417,f163,f842]) ).
fof(f842,plain,
( spl0_84
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f163,plain,
( spl0_26
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f430,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_26
| ~ spl0_54 ),
inference(resolution,[],[f418,f164]) ).
fof(f164,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f840,plain,
( spl0_83
| ~ spl0_6
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f326,f310,f41,f838]) ).
fof(f838,plain,
( spl0_83
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f41,plain,
( spl0_6
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_47 ),
inference(resolution,[],[f311,f42]) ).
fof(f42,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f836,plain,
( spl0_82
| ~ spl0_17
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f284,f279,f102,f834]) ).
fof(f834,plain,
( spl0_82
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f279,plain,
( spl0_43
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f284,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_43 ),
inference(resolution,[],[f280,f103]) ).
fof(f280,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f832,plain,
( spl0_81
| ~ spl0_17
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f266,f260,f102,f830]) ).
fof(f830,plain,
( spl0_81
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f260,plain,
( spl0_39
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f266,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_39 ),
inference(resolution,[],[f261,f103]) ).
fof(f261,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f813,plain,
( spl0_80
| ~ spl0_17
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f748,f735,f102,f811]) ).
fof(f811,plain,
( spl0_80
<=> ! [X0,X1] : theorem(or(X0,or(not(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f748,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X0),X1)))
| ~ spl0_17
| ~ spl0_74 ),
inference(resolution,[],[f736,f103]) ).
fof(f779,plain,
( spl0_79
| ~ spl0_7
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f368,f357,f46,f777]) ).
fof(f777,plain,
( spl0_79
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f368,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_51 ),
inference(resolution,[],[f358,f47]) ).
fof(f775,plain,
( spl0_78
| ~ spl0_48
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f337,f318,f314,f773]) ).
fof(f773,plain,
( spl0_78
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f314,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f318,plain,
( spl0_49
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f337,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_48
| ~ spl0_49 ),
inference(resolution,[],[f319,f315]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f319,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f771,plain,
( spl0_77
| ~ spl0_42
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f303,f296,f275,f769]) ).
fof(f769,plain,
( spl0_77
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f275,plain,
( spl0_42
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f296,plain,
( spl0_45
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f303,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_42
| ~ spl0_45 ),
inference(resolution,[],[f297,f276]) ).
fof(f276,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f297,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f767,plain,
( spl0_76
| ~ spl0_16
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f294,f286,f92,f765]) ).
fof(f765,plain,
( spl0_76
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f294,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_44 ),
inference(resolution,[],[f287,f93]) ).
fof(f741,plain,
( spl0_75
| ~ spl0_23
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f429,f417,f143,f739]) ).
fof(f429,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_23
| ~ spl0_54 ),
inference(resolution,[],[f418,f144]) ).
fof(f737,plain,
( spl0_74
| ~ spl0_7
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f420,f417,f46,f735]) ).
fof(f420,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_54 ),
inference(resolution,[],[f418,f47]) ).
fof(f708,plain,
( spl0_73
| ~ spl0_31
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f224,f217,f192,f706]) ).
fof(f706,plain,
( spl0_73
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(not(X3),X0)),X1)))
| ~ theorem(or(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f192,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f217,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f224,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(not(X3),X0)),X1)))
| ~ theorem(or(X2,X3)) )
| ~ spl0_31
| ~ spl0_32 ),
inference(resolution,[],[f218,f193]) ).
fof(f193,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f218,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f704,plain,
( spl0_72
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f213,f192,f188,f702]) ).
fof(f702,plain,
( spl0_72
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f188,plain,
( spl0_30
<=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f213,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_30
| ~ spl0_31 ),
inference(resolution,[],[f193,f189]) ).
fof(f189,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f664,plain,
( spl0_71
| ~ spl0_31
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f243,f239,f192,f662]) ).
fof(f662,plain,
( spl0_71
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f239,plain,
( spl0_36
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f243,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) )
| ~ spl0_31
| ~ spl0_36 ),
inference(resolution,[],[f240,f193]) ).
fof(f240,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f660,plain,
( spl0_70
| ~ spl0_29
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f214,f192,f184,f658]) ).
fof(f658,plain,
( spl0_70
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f184,plain,
( spl0_29
<=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f214,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) )
| ~ spl0_29
| ~ spl0_31 ),
inference(resolution,[],[f193,f185]) ).
fof(f185,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f656,plain,
( spl0_69
| ~ spl0_14
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f207,f192,f80,f654]) ).
fof(f654,plain,
( spl0_69
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(X0,or(not(X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f80,plain,
( spl0_14
<=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
| ~ theorem(or(X0,or(not(X2),X3))) )
| ~ spl0_14
| ~ spl0_31 ),
inference(resolution,[],[f193,f81]) ).
fof(f81,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f623,plain,
( spl0_68
| ~ spl0_19
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f206,f192,f117,f621]) ).
fof(f621,plain,
( spl0_68
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X1,X3)))
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f117,plain,
( spl0_19
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f206,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X1,X3)))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_19
| ~ spl0_31 ),
inference(resolution,[],[f193,f118]) ).
fof(f118,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f590,plain,
( spl0_67
| ~ spl0_12
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f205,f192,f71,f588]) ).
fof(f71,plain,
( spl0_12
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f205,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) )
| ~ spl0_12
| ~ spl0_31 ),
inference(resolution,[],[f193,f72]) ).
fof(f72,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f541,plain,
( spl0_66
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f246,f239,f92,f539]) ).
fof(f539,plain,
( spl0_66
<=> ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f246,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
| ~ spl0_16
| ~ spl0_36 ),
inference(resolution,[],[f240,f93]) ).
fof(f537,plain,
( spl0_65
| ~ spl0_6
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f225,f217,f41,f535]) ).
fof(f535,plain,
( spl0_65
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f225,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) )
| ~ spl0_6
| ~ spl0_32 ),
inference(resolution,[],[f218,f42]) ).
fof(f533,plain,
( ~ spl0_64
| spl0_37
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f472,f365,f248,f530]) ).
fof(f530,plain,
( spl0_64
<=> theorem(p) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f248,plain,
( spl0_37
<=> theorem(not(not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f365,plain,
( spl0_53
<=> ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f472,plain,
( ~ theorem(p)
| spl0_37
| ~ spl0_53 ),
inference(resolution,[],[f366,f250]) ).
fof(f250,plain,
( ~ theorem(not(not(p)))
| spl0_37 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f366,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f528,plain,
( spl0_63
| ~ spl0_27
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f215,f192,f171,f526]) ).
fof(f526,plain,
( spl0_63
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f215,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_31 ),
inference(resolution,[],[f193,f172]) ).
fof(f524,plain,
( spl0_62
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f199,f188,f41,f522]) ).
fof(f522,plain,
( spl0_62
<=> ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f199,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_30 ),
inference(resolution,[],[f189,f42]) ).
fof(f489,plain,
( spl0_61
| ~ spl0_6
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f244,f239,f41,f487]) ).
fof(f487,plain,
( spl0_61
<=> ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f244,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_36 ),
inference(resolution,[],[f240,f42]) ).
fof(f485,plain,
( spl0_60
| ~ spl0_16
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f227,f217,f92,f483]) ).
fof(f483,plain,
( spl0_60
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f227,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_32 ),
inference(resolution,[],[f218,f93]) ).
fof(f481,plain,
( spl0_59
| ~ spl0_26
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f212,f192,f163,f479]) ).
fof(f479,plain,
( spl0_59
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f212,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26
| ~ spl0_31 ),
inference(resolution,[],[f193,f164]) ).
fof(f477,plain,
( spl0_58
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f196,f184,f41,f475]) ).
fof(f475,plain,
( spl0_58
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f196,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f185,f42]) ).
fof(f452,plain,
( spl0_57
| ~ spl0_22
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f210,f192,f139,f450]) ).
fof(f450,plain,
( spl0_57
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f210,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_22
| ~ spl0_31 ),
inference(resolution,[],[f193,f140]) ).
fof(f448,plain,
( spl0_56
| ~ spl0_16
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f201,f188,f92,f446]) ).
fof(f446,plain,
( spl0_56
<=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f201,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_30 ),
inference(resolution,[],[f189,f93]) ).
fof(f444,plain,
( spl0_55
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f198,f184,f92,f442]) ).
fof(f442,plain,
( spl0_55
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f198,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f185,f93]) ).
fof(f419,plain,
( spl0_54
| ~ spl0_11
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f204,f192,f66,f417]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_31 ),
inference(resolution,[],[f193,f67]) ).
fof(f367,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f307,f268,f41,f365]) ).
fof(f307,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_40 ),
inference(resolution,[],[f269,f42]) ).
fof(f363,plain,
( spl0_52
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f208,f192,f125,f361]) ).
fof(f125,plain,
( spl0_20
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f208,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_20
| ~ spl0_31 ),
inference(resolution,[],[f193,f126]) ).
fof(f126,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f359,plain,
( spl0_51
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f175,f171,f41,f357]) ).
fof(f175,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_27 ),
inference(resolution,[],[f172,f42]) ).
fof(f324,plain,
( spl0_50
| ~ spl0_10
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f203,f192,f60,f322]) ).
fof(f203,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_31 ),
inference(resolution,[],[f193,f61]) ).
fof(f320,plain,
( spl0_49
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f178,f171,f92,f318]) ).
fof(f178,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_27 ),
inference(resolution,[],[f172,f93]) ).
fof(f316,plain,
( spl0_48
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f177,f171,f85,f314]) ).
fof(f85,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f172,f86]) ).
fof(f86,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f312,plain,
( spl0_47
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f163,f41,f310]) ).
fof(f167,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f164,f42]) ).
fof(f302,plain,
( spl0_46
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f169,f163,f92,f300]) ).
fof(f169,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f164,f93]) ).
fof(f298,plain,
( spl0_45
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f147,f139,f41,f296]) ).
fof(f147,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f140,f42]) ).
fof(f288,plain,
( spl0_44
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f133,f125,f102,f286]) ).
fof(f133,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f126,f103]) ).
fof(f281,plain,
( spl0_43
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f143,f92,f279]) ).
fof(f157,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f144,f93]) ).
fof(f277,plain,
( spl0_41
| spl0_42
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f129,f125,f41,f275,f272]) ).
fof(f272,plain,
( spl0_41
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f129,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f126,f42]) ).
fof(f270,plain,
( spl0_40
| ~ spl0_16
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f265,f260,f92,f268]) ).
fof(f265,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_39 ),
inference(resolution,[],[f261,f93]) ).
fof(f262,plain,
( spl0_39
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f156,f143,f85,f260]) ).
fof(f156,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f144,f86]) ).
fof(f256,plain,
( ~ spl0_38
| spl0_1
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f174,f171,f18,f253]) ).
fof(f174,plain,
( ~ theorem(or(not(p),q))
| spl0_1
| ~ spl0_27 ),
inference(resolution,[],[f172,f20]) ).
fof(f251,plain,
( ~ spl0_37
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f125,f112,f248]) ).
fof(f130,plain,
( ~ theorem(not(not(p)))
| spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f126,f114]) ).
fof(f241,plain,
( spl0_36
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f102,f80,f239]) ).
fof(f109,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_14
| ~ spl0_17 ),
inference(resolution,[],[f103,f81]) ).
fof(f237,plain,
( ~ spl0_35
| spl0_1
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f128,f125,f18,f234]) ).
fof(f234,plain,
( spl0_35
<=> theorem(not(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f128,plain,
( ~ theorem(not(p))
| spl0_1
| ~ spl0_20 ),
inference(resolution,[],[f126,f20]) ).
fof(f232,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f92,f80,f230]) ).
fof(f230,plain,
( spl0_34
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f99,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[],[f93,f81]) ).
fof(f223,plain,
( spl0_33
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f117,f92,f221]) ).
fof(f221,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) )
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f118,f93]) ).
fof(f219,plain,
( spl0_32
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f117,f102,f217]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) )
| ~ spl0_17
| ~ spl0_19 ),
inference(resolution,[],[f118,f103]) ).
fof(f194,plain,
( spl0_31
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f120,f117,f41,f192]) ).
fof(f120,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[],[f118,f42]) ).
fof(f190,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f102,f60,f188]) ).
fof(f108,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f103,f61]) ).
fof(f186,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f102,f71,f184]) ).
fof(f107,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f103,f72]) ).
fof(f182,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f92,f71,f180]) ).
fof(f180,plain,
( spl0_28
<=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f98,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f93,f72]) ).
fof(f173,plain,
( spl0_27
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f102,f75,f171]) ).
fof(f75,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f110,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f103,f76]) ).
fof(f76,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f165,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f106,f102,f66,f163]) ).
fof(f106,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f103,f67]) ).
fof(f161,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f92,f66,f159]) ).
fof(f159,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f97,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f93,f67]) ).
fof(f153,plain,
( ~ spl0_24
| ~ spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f123,f112,f75,f150]) ).
fof(f150,plain,
( spl0_24
<=> theorem(q) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f123,plain,
( ~ theorem(q)
| ~ spl0_13
| spl0_18 ),
inference(resolution,[],[f114,f76]) ).
fof(f145,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f105,f102,f46,f143]) ).
fof(f105,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f103,f47]) ).
fof(f141,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f96,f92,f60,f139]) ).
fof(f96,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f93,f61]) ).
fof(f137,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f95,f92,f46,f135]) ).
fof(f95,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f93,f47]) ).
fof(f127,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f92,f75,f125]) ).
fof(f100,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f93,f76]) ).
fof(f119,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f83,f80,f41,f117]) ).
fof(f83,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f81,f42]) ).
fof(f115,plain,
( ~ spl0_18
| spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f88,f75,f18,f112]) ).
fof(f88,plain,
( ~ theorem(or(not(not(p)),q))
| spl0_1
| ~ spl0_13 ),
inference(resolution,[],[f76,f20]) ).
fof(f104,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f78,f71,f41,f102]) ).
fof(f78,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_6
| ~ spl0_12 ),
inference(resolution,[],[f72,f42]) ).
fof(f94,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f69,f66,f41,f92]) ).
fof(f69,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f67,f42]) ).
fof(f87,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f64,f60,f41,f85]) ).
fof(f64,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f61,f42]) ).
fof(f82,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f58,f55,f23,f80]) ).
fof(f23,plain,
( spl0_2
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f55,plain,
( spl0_9
<=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f58,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_2
| ~ spl0_9 ),
inference(resolution,[],[f56,f24]) ).
fof(f24,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f56,plain,
( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f77,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f63,f46,f41,f75]) ).
fof(f63,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f47,f42]) ).
fof(f73,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f53,f50,f23,f71]) ).
fof(f50,plain,
( spl0_8
<=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f53,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_2
| ~ spl0_8 ),
inference(resolution,[],[f51,f24]) ).
fof(f51,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f68,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f44,f37,f23,f66]) ).
fof(f37,plain,
( spl0_5
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f44,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f38,f24]) ).
fof(f38,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f62,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f31,f23,f60]) ).
fof(f31,plain,
( spl0_4
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f35,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f32,f24]) ).
fof(f32,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f57,plain,
spl0_9,
inference(avatar_split_clause,[],[f14,f55]) ).
fof(f14,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f6,axiom,
! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f52,plain,
spl0_8,
inference(avatar_split_clause,[],[f15,f50]) ).
fof(f15,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f48,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f34,f27,f23,f46]) ).
fof(f27,plain,
( spl0_3
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f34,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f28,f24]) ).
fof(f28,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f43,plain,
spl0_6,
inference(avatar_split_clause,[],[f16,f41]) ).
fof(f16,plain,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f8,axiom,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(implies(X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f39,plain,
spl0_5,
inference(avatar_split_clause,[],[f13,f37]) ).
fof(f13,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f33,plain,
spl0_4,
inference(avatar_split_clause,[],[f12,f31]) ).
fof(f12,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f29,plain,
spl0_3,
inference(avatar_split_clause,[],[f11,f27]) ).
fof(f11,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f7,f23]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f21,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f10,f18]) ).
fof(f10,plain,
~ theorem(or(not(p),or(not(not(p)),q))),
inference(definition_unfolding,[],[f9,f6,f6]) ).
fof(f9,axiom,
~ theorem(implies(p,implies(not(p),q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL187-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n011.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 : Mon Apr 29 23:04:31 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (4134)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (4137)WARNING: value z3 for option sas not known
% 0.15/0.38 % (4136)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (4138)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (4135)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (4137)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)
% 0.15/0.38 % (4139)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)
% 0.15/0.38 % (4140)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)
% 0.15/0.38 % (4141)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [4]
% 0.22/0.40 TRYING [4]
% 0.22/0.42 TRYING [5]
% 0.22/0.43 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [5]
% 0.22/0.45 TRYING [4]
% 0.22/0.46 % (4139)First to succeed.
% 0.22/0.46 % (4139)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.47 % (4139)------------------------------
% 0.22/0.47 % (4139)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.47 % (4139)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (4139)Memory used [KB]: 1413
% 0.22/0.47 % (4139)Time elapsed: 0.083 s
% 0.22/0.47 % (4139)Instructions burned: 139 (million)
% 0.22/0.47 % (4139)------------------------------
% 0.22/0.47 % (4139)------------------------------
% 0.22/0.47 % (4134)Success in time 0.099 s
%------------------------------------------------------------------------------