TSTP Solution File: LCL237-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL237-3 : 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 : n003.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 : Sun May 5 07:44:53 EDT 2024
% Result : Unsatisfiable 0.16s 0.36s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 93
% Syntax : Number of formulae : 301 ( 23 unt; 0 def)
% Number of atoms : 855 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1030 ( 476 ~; 471 |; 0 &)
% ( 83 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 87 ( 85 usr; 84 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 475 ( 475 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f898,plain,
$false,
inference(avatar_sat_refutation,[],[f22,f26,f30,f34,f40,f44,f49,f53,f58,f63,f69,f74,f78,f83,f88,f95,f105,f116,f120,f128,f138,f142,f146,f154,f162,f166,f174,f183,f187,f191,f196,f200,f225,f229,f238,f242,f252,f257,f263,f271,f278,f282,f289,f299,f303,f313,f317,f321,f325,f360,f364,f368,f420,f445,f449,f453,f477,f481,f485,f489,f524,f528,f532,f536,f540,f589,f622,f655,f659,f663,f667,f707,f711,f762,f766,f770,f774,f823,f827,f831,f835,f839,f897]) ).
fof(f897,plain,
( spl0_1
| ~ spl0_83 ),
inference(avatar_contradiction_clause,[],[f887]) ).
fof(f887,plain,
( $false
| spl0_1
| ~ spl0_83 ),
inference(resolution,[],[f838,f21]) ).
fof(f21,plain,
( ~ theorem(or(not(q),or(not(p),not(or(not(p),not(q))))))
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f19,plain,
( spl0_1
<=> theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f838,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f837,plain,
( spl0_83
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f839,plain,
( spl0_83
| ~ spl0_26
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f431,f418,f164,f837]) ).
fof(f164,plain,
( spl0_26
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f418,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(f431,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_26
| ~ spl0_54 ),
inference(resolution,[],[f419,f165]) ).
fof(f165,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f419,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f835,plain,
( spl0_82
| ~ spl0_6
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f327,f311,f42,f833]) ).
fof(f833,plain,
( spl0_82
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f42,plain,
( spl0_6
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f311,plain,
( spl0_47
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f327,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_47 ),
inference(resolution,[],[f312,f43]) ).
fof(f43,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f312,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f831,plain,
( spl0_81
| ~ spl0_17
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f285,f280,f103,f829]) ).
fof(f829,plain,
( spl0_81
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f103,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(f280,plain,
( spl0_43
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f285,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_43 ),
inference(resolution,[],[f281,f104]) ).
fof(f104,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f281,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f827,plain,
( spl0_80
| ~ spl0_17
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f743,f530,f103,f825]) ).
fof(f825,plain,
( spl0_80
<=> ! [X0,X1] : theorem(or(X0,or(not(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f530,plain,
( spl0_64
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f743,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X0),X1)))
| ~ spl0_17
| ~ spl0_64 ),
inference(resolution,[],[f531,f104]) ).
fof(f531,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f823,plain,
( spl0_79
| ~ spl0_17
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f267,f261,f103,f821]) ).
fof(f821,plain,
( spl0_79
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f261,plain,
( spl0_39
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f267,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_39 ),
inference(resolution,[],[f262,f104]) ).
fof(f262,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f774,plain,
( spl0_78
| ~ spl0_7
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f369,f358,f47,f772]) ).
fof(f772,plain,
( spl0_78
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f47,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f358,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(f369,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_51 ),
inference(resolution,[],[f359,f48]) ).
fof(f48,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f359,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f770,plain,
( spl0_77
| ~ spl0_48
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f338,f319,f315,f768]) ).
fof(f768,plain,
( spl0_77
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f315,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f319,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(f338,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_48
| ~ spl0_49 ),
inference(resolution,[],[f320,f316]) ).
fof(f316,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f320,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f766,plain,
( spl0_76
| ~ spl0_42
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f304,f297,f276,f764]) ).
fof(f764,plain,
( spl0_76
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f276,plain,
( spl0_42
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f297,plain,
( spl0_45
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f304,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_42
| ~ spl0_45 ),
inference(resolution,[],[f298,f277]) ).
fof(f277,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f298,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f762,plain,
( spl0_75
| ~ spl0_16
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f295,f287,f93,f760]) ).
fof(f760,plain,
( spl0_75
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f93,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f287,plain,
( spl0_44
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f295,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_44 ),
inference(resolution,[],[f288,f94]) ).
fof(f94,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f288,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f711,plain,
( spl0_74
| ~ spl0_32
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f230,f223,f198,f709]) ).
fof(f709,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f198,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f223,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f230,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_32
| ~ spl0_33 ),
inference(resolution,[],[f224,f199]) ).
fof(f199,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f224,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f707,plain,
( spl0_73
| ~ spl0_30
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f219,f198,f189,f705]) ).
fof(f705,plain,
( spl0_73
<=> ! [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_73])]) ).
fof(f189,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(f219,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_32 ),
inference(resolution,[],[f199,f190]) ).
fof(f190,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f667,plain,
( spl0_72
| ~ spl0_32
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f244,f240,f198,f665]) ).
fof(f665,plain,
( spl0_72
<=> ! [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_72])]) ).
fof(f240,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(f244,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) )
| ~ spl0_32
| ~ spl0_36 ),
inference(resolution,[],[f241,f199]) ).
fof(f241,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,[],[f240]) ).
fof(f663,plain,
( spl0_71
| ~ spl0_29
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f220,f198,f185,f661]) ).
fof(f661,plain,
( spl0_71
<=> ! [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_71])]) ).
fof(f185,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(f220,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_32 ),
inference(resolution,[],[f199,f186]) ).
fof(f186,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f659,plain,
( spl0_70
| ~ spl0_14
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f213,f198,f81,f657]) ).
fof(f657,plain,
( spl0_70
<=> ! [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_70])]) ).
fof(f81,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(f213,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_32 ),
inference(resolution,[],[f199,f82]) ).
fof(f82,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,[],[f81]) ).
fof(f655,plain,
( spl0_69
| ~ spl0_23
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f430,f418,f144,f653]) ).
fof(f653,plain,
( spl0_69
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f144,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f430,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_23
| ~ spl0_54 ),
inference(resolution,[],[f419,f145]) ).
fof(f145,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f622,plain,
( spl0_68
| ~ spl0_19
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f212,f198,f118,f620]) ).
fof(f620,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(f118,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(f212,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_32 ),
inference(resolution,[],[f199,f119]) ).
fof(f119,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f589,plain,
( spl0_67
| ~ spl0_12
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f211,f198,f72,f587]) ).
fof(f587,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(f72,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(f211,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) )
| ~ spl0_12
| ~ spl0_32 ),
inference(resolution,[],[f199,f73]) ).
fof(f73,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f540,plain,
( spl0_66
| ~ spl0_16
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f247,f240,f93,f538]) ).
fof(f538,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(f247,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,[],[f241,f94]) ).
fof(f536,plain,
( spl0_65
| ~ spl0_6
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f231,f223,f42,f534]) ).
fof(f534,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(f231,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) )
| ~ spl0_6
| ~ spl0_33 ),
inference(resolution,[],[f224,f43]) ).
fof(f532,plain,
( spl0_64
| ~ spl0_7
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f421,f418,f47,f530]) ).
fof(f421,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_54 ),
inference(resolution,[],[f419,f48]) ).
fof(f528,plain,
( spl0_63
| ~ spl0_27
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f221,f198,f172,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(f172,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(f221,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_27
| ~ spl0_32 ),
inference(resolution,[],[f199,f173]) ).
fof(f173,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f524,plain,
( spl0_62
| ~ spl0_6
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f205,f189,f42,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(f205,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_30 ),
inference(resolution,[],[f190,f43]) ).
fof(f489,plain,
( spl0_61
| ~ spl0_6
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f245,f240,f42,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(f245,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_36 ),
inference(resolution,[],[f241,f43]) ).
fof(f485,plain,
( spl0_60
| ~ spl0_16
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f233,f223,f93,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(f233,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_33 ),
inference(resolution,[],[f224,f94]) ).
fof(f481,plain,
( spl0_59
| ~ spl0_26
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f218,f198,f164,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(f218,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26
| ~ spl0_32 ),
inference(resolution,[],[f199,f165]) ).
fof(f477,plain,
( spl0_58
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f202,f185,f42,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(f202,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f186,f43]) ).
fof(f453,plain,
( spl0_57
| ~ spl0_22
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f216,f198,f140,f451]) ).
fof(f451,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(f140,plain,
( spl0_22
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f216,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_22
| ~ spl0_32 ),
inference(resolution,[],[f199,f141]) ).
fof(f141,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f449,plain,
( spl0_56
| ~ spl0_16
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f207,f189,f93,f447]) ).
fof(f447,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(f207,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_30 ),
inference(resolution,[],[f190,f94]) ).
fof(f445,plain,
( spl0_55
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f204,f185,f93,f443]) ).
fof(f443,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(f204,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f186,f94]) ).
fof(f420,plain,
( spl0_54
| ~ spl0_11
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f210,f198,f67,f418]) ).
fof(f67,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f210,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_32 ),
inference(resolution,[],[f199,f68]) ).
fof(f68,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f368,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f308,f269,f42,f366]) ).
fof(f366,plain,
( spl0_53
<=> ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f269,plain,
( spl0_40
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f308,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_40 ),
inference(resolution,[],[f270,f43]) ).
fof(f270,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f364,plain,
( spl0_52
| ~ spl0_20
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f214,f198,f126,f362]) ).
fof(f362,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(f126,plain,
( spl0_20
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f214,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_20
| ~ spl0_32 ),
inference(resolution,[],[f199,f127]) ).
fof(f127,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f360,plain,
( spl0_51
| ~ spl0_6
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f176,f172,f42,f358]) ).
fof(f176,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_27 ),
inference(resolution,[],[f173,f43]) ).
fof(f325,plain,
( spl0_50
| ~ spl0_10
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f209,f198,f61,f323]) ).
fof(f323,plain,
( spl0_50
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f61,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f209,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_32 ),
inference(resolution,[],[f199,f62]) ).
fof(f62,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f321,plain,
( spl0_49
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f179,f172,f93,f319]) ).
fof(f179,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_27 ),
inference(resolution,[],[f173,f94]) ).
fof(f317,plain,
( spl0_48
| ~ spl0_15
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f178,f172,f86,f315]) ).
fof(f86,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f178,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_27 ),
inference(resolution,[],[f173,f87]) ).
fof(f87,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f313,plain,
( spl0_47
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f168,f164,f42,f311]) ).
fof(f168,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f165,f43]) ).
fof(f303,plain,
( spl0_46
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f170,f164,f93,f301]) ).
fof(f301,plain,
( spl0_46
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f170,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f165,f94]) ).
fof(f299,plain,
( spl0_45
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f148,f140,f42,f297]) ).
fof(f148,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f141,f43]) ).
fof(f289,plain,
( spl0_44
| ~ spl0_17
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f134,f126,f103,f287]) ).
fof(f134,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_20 ),
inference(resolution,[],[f127,f104]) ).
fof(f282,plain,
( spl0_43
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f158,f144,f93,f280]) ).
fof(f158,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f145,f94]) ).
fof(f278,plain,
( spl0_41
| spl0_42
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f130,f126,f42,f276,f273]) ).
fof(f273,plain,
( spl0_41
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f130,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_20 ),
inference(resolution,[],[f127,f43]) ).
fof(f271,plain,
( spl0_40
| ~ spl0_16
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f266,f261,f93,f269]) ).
fof(f266,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_39 ),
inference(resolution,[],[f262,f94]) ).
fof(f263,plain,
( spl0_39
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f157,f144,f86,f261]) ).
fof(f157,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f145,f87]) ).
fof(f257,plain,
( ~ spl0_38
| spl0_1
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f175,f172,f19,f254]) ).
fof(f254,plain,
( spl0_38
<=> theorem(or(not(q),not(or(not(p),not(q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f175,plain,
( ~ theorem(or(not(q),not(or(not(p),not(q)))))
| spl0_1
| ~ spl0_27 ),
inference(resolution,[],[f173,f21]) ).
fof(f252,plain,
( ~ spl0_37
| ~ spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f124,f113,f76,f249]) ).
fof(f249,plain,
( spl0_37
<=> theorem(not(or(not(p),not(q)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f76,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f113,plain,
( spl0_18
<=> theorem(or(not(p),not(or(not(p),not(q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f124,plain,
( ~ theorem(not(or(not(p),not(q))))
| ~ spl0_13
| spl0_18 ),
inference(resolution,[],[f115,f77]) ).
fof(f77,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f115,plain,
( ~ theorem(or(not(p),not(or(not(p),not(q)))))
| spl0_18 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f242,plain,
( spl0_36
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f103,f81,f240]) ).
fof(f110,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,[],[f104,f82]) ).
fof(f238,plain,
( spl0_35
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f93,f81,f236]) ).
fof(f236,plain,
( spl0_35
<=> ! [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_35])]) ).
fof(f100,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,[],[f94,f82]) ).
fof(f229,plain,
( spl0_34
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f123,f118,f93,f227]) ).
fof(f227,plain,
( spl0_34
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f123,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) )
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f119,f94]) ).
fof(f225,plain,
( spl0_33
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f118,f103,f223]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) )
| ~ spl0_17
| ~ spl0_19 ),
inference(resolution,[],[f119,f104]) ).
fof(f200,plain,
( spl0_32
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f118,f42,f198]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_19 ),
inference(resolution,[],[f119,f43]) ).
fof(f196,plain,
( ~ spl0_31
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f131,f126,f113,f193]) ).
fof(f193,plain,
( spl0_31
<=> theorem(not(p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f131,plain,
( ~ theorem(not(p))
| spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f127,f115]) ).
fof(f191,plain,
( spl0_30
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f103,f61,f189]) ).
fof(f109,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f104,f62]) ).
fof(f187,plain,
( spl0_29
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f103,f72,f185]) ).
fof(f108,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f104,f73]) ).
fof(f183,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f93,f72,f181]) ).
fof(f181,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(f99,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f94,f73]) ).
fof(f174,plain,
( spl0_27
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f111,f103,f76,f172]) ).
fof(f111,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f104,f77]) ).
fof(f166,plain,
( spl0_26
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f103,f67,f164]) ).
fof(f107,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f104,f68]) ).
fof(f162,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f93,f67,f160]) ).
fof(f160,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f98,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f94,f68]) ).
fof(f154,plain,
( ~ spl0_24
| spl0_1
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f129,f126,f19,f151]) ).
fof(f151,plain,
( spl0_24
<=> theorem(not(q)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f129,plain,
( ~ theorem(not(q))
| spl0_1
| ~ spl0_20 ),
inference(resolution,[],[f127,f21]) ).
fof(f146,plain,
( spl0_23
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f106,f103,f47,f144]) ).
fof(f106,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f104,f48]) ).
fof(f142,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f93,f61,f140]) ).
fof(f97,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f94,f62]) ).
fof(f138,plain,
( spl0_21
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f96,f93,f47,f136]) ).
fof(f136,plain,
( spl0_21
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f96,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f94,f48]) ).
fof(f128,plain,
( spl0_20
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f101,f93,f76,f126]) ).
fof(f101,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f94,f77]) ).
fof(f120,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f84,f81,f42,f118]) ).
fof(f84,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f82,f43]) ).
fof(f116,plain,
( ~ spl0_18
| spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f89,f76,f19,f113]) ).
fof(f89,plain,
( ~ theorem(or(not(p),not(or(not(p),not(q)))))
| spl0_1
| ~ spl0_13 ),
inference(resolution,[],[f77,f21]) ).
fof(f105,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f79,f72,f42,f103]) ).
fof(f79,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_6
| ~ spl0_12 ),
inference(resolution,[],[f73,f43]) ).
fof(f95,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f70,f67,f42,f93]) ).
fof(f70,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f68,f43]) ).
fof(f88,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f65,f61,f42,f86]) ).
fof(f65,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f62,f43]) ).
fof(f83,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f59,f56,f24,f81]) ).
fof(f24,plain,
( spl0_2
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f56,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(f59,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,[],[f57,f25]) ).
fof(f25,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f57,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,[],[f56]) ).
fof(f78,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f64,f47,f42,f76]) ).
fof(f64,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f48,f43]) ).
fof(f74,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f54,f51,f24,f72]) ).
fof(f51,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(f54,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_2
| ~ spl0_8 ),
inference(resolution,[],[f52,f25]) ).
fof(f52,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f69,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f45,f38,f24,f67]) ).
fof(f38,plain,
( spl0_5
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f45,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f39,f25]) ).
fof(f39,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f63,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f36,f32,f24,f61]) ).
fof(f32,plain,
( spl0_4
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f36,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f33,f25]) ).
fof(f33,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f58,plain,
spl0_9,
inference(avatar_split_clause,[],[f15,f56]) ).
fof(f15,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f53,plain,
spl0_8,
inference(avatar_split_clause,[],[f16,f51]) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f49,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f35,f28,f24,f47]) ).
fof(f28,plain,
( spl0_3
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f35,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f29,f25]) ).
fof(f29,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f44,plain,
spl0_6,
inference(avatar_split_clause,[],[f17,f42]) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f40,plain,
spl0_5,
inference(avatar_split_clause,[],[f14,f38]) ).
fof(f14,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/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f34,plain,
spl0_4,
inference(avatar_split_clause,[],[f13,f32]) ).
fof(f13,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/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f30,plain,
spl0_3,
inference(avatar_split_clause,[],[f12,f28]) ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f26,plain,
spl0_2,
inference(avatar_split_clause,[],[f7,f24]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f22,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f11,f19]) ).
fof(f11,plain,
~ theorem(or(not(q),or(not(p),not(or(not(p),not(q)))))),
inference(definition_unfolding,[],[f10,f6,f6,f9]) ).
fof(f9,axiom,
! [X6,X5] : and(X5,X6) = not(or(not(X5),not(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
~ theorem(implies(q,implies(p,and(p,q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : LCL237-3 : TPTP v8.1.2. Released v2.3.0.
% 0.05/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n003.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 13:45:35 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (15349)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (15352)WARNING: value z3 for option sas not known
% 0.16/0.32 % (15350)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32 % (15355)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)
% 0.16/0.32 % (15353)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.32 % (15352)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)
% 0.16/0.32 % (15351)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.32 % (15356)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)
% 0.16/0.32 % (15354)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)
% 0.16/0.32 TRYING [1]
% 0.16/0.32 TRYING [1]
% 0.16/0.32 TRYING [2]
% 0.16/0.32 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.33 TRYING [3]
% 0.16/0.33 TRYING [4]
% 0.16/0.33 TRYING [4]
% 0.16/0.35 % (15354)First to succeed.
% 0.16/0.36 % (15354)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15349"
% 0.16/0.36 % (15354)Refutation found. Thanks to Tanya!
% 0.16/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.36 % (15354)------------------------------
% 0.16/0.36 % (15354)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.36 % (15354)Termination reason: Refutation
% 0.16/0.36
% 0.16/0.36 % (15354)Memory used [KB]: 1307
% 0.16/0.36 % (15354)Time elapsed: 0.034 s
% 0.16/0.36 % (15354)Instructions burned: 62 (million)
% 0.16/0.36 % (15349)Success in time 0.049 s
%------------------------------------------------------------------------------