TSTP Solution File: LCL326-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL326-3 : 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 : n002.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 07:45:20 EDT 2024
% Result : Unsatisfiable 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 170
% Syntax : Number of formulae : 554 ( 25 unt; 0 def)
% Number of atoms : 1666 ( 4 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2072 ( 960 ~; 953 |; 0 &)
% ( 159 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 163 ( 161 usr; 160 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 942 ( 942 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2729,plain,
$false,
inference(avatar_sat_refutation,[],[f24,f28,f32,f36,f42,f46,f51,f55,f60,f65,f71,f76,f80,f85,f90,f96,f106,f116,f120,f131,f135,f139,f150,f154,f158,f166,f174,f178,f182,f186,f215,f219,f228,f232,f237,f248,f252,f259,f268,f272,f282,f286,f290,f294,f329,f333,f337,f389,f414,f418,f422,f447,f451,f455,f459,f494,f499,f503,f507,f511,f560,f593,f629,f633,f637,f677,f681,f698,f715,f719,f745,f749,f753,f757,f771,f810,f814,f818,f822,f883,f887,f891,f895,f899,f906,f910,f914,f919,f923,f1005,f1009,f1013,f1017,f1021,f1027,f1064,f1597,f1657,f1661,f1714,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1900,f2000,f2004,f2008,f2012,f2016,f2020,f2024,f2028,f2032,f2036,f2040,f2044,f2048,f2052,f2069,f2073,f2077,f2081,f2497,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2547,f2556,f2560,f2564,f2568,f2572,f2576,f2580,f2584,f2588,f2592,f2597,f2601,f2605,f2609,f2613,f2617,f2728]) ).
fof(f2728,plain,
( ~ spl0_35
| spl0_154 ),
inference(avatar_contradiction_clause,[],[f2725]) ).
fof(f2725,plain,
( $false
| ~ spl0_35
| spl0_154 ),
inference(resolution,[],[f2596,f236]) ).
fof(f236,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl0_35
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2596,plain,
( ~ theorem(or(p,not(p)))
| spl0_154 ),
inference(avatar_component_clause,[],[f2594]) ).
fof(f2594,plain,
( spl0_154
<=> theorem(or(p,not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2617,plain,
( spl0_159
| ~ spl0_25
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f611,f591,f156,f2615]) ).
fof(f2615,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f156,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f591,plain,
( spl0_63
<=> ! [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_63])]) ).
fof(f611,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,X0)),X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_25
| ~ spl0_63 ),
inference(resolution,[],[f592,f157]) ).
fof(f157,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f592,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X3)))
| theorem(or(X0,or(X1,X2)))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f2613,plain,
( spl0_158
| ~ spl0_11
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f599,f591,f69,f2611]) ).
fof(f2611,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f69,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f599,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X1,X2)))
| ~ theorem(or(not(X0),X2)) )
| ~ spl0_11
| ~ spl0_63 ),
inference(resolution,[],[f592,f70]) ).
fof(f70,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f2609,plain,
( spl0_157
| ~ spl0_26
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f581,f558,f164,f2607]) ).
fof(f2607,plain,
( spl0_157
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f164,plain,
( spl0_26
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f558,plain,
( spl0_62
<=> ! [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_62])]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X1,X3))) )
| ~ spl0_26
| ~ spl0_62 ),
inference(resolution,[],[f559,f165]) ).
fof(f165,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f559,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X2,or(X1,X3))))
| theorem(or(X0,or(X1,or(X2,X3)))) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f2605,plain,
( spl0_156
| ~ spl0_6
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f548,f505,f44,f2603]) ).
fof(f2603,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f44,plain,
( spl0_6
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f505,plain,
( spl0_60
<=> ! [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_60])]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| ~ theorem(X2)
| theorem(X1)
| ~ theorem(or(not(X2),X0)) )
| ~ spl0_6
| ~ spl0_60 ),
inference(resolution,[],[f506,f45]) ).
fof(f45,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f506,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(or(not(X0),X1))
| ~ theorem(X2) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f2601,plain,
( spl0_155
| ~ spl0_11
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f524,f501,f69,f2599]) ).
fof(f2599,plain,
( spl0_155
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f501,plain,
( spl0_59
<=> ! [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_59])]) ).
fof(f524,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X2)))
| theorem(or(X0,or(X3,or(X2,X1)))) )
| ~ spl0_11
| ~ spl0_59 ),
inference(resolution,[],[f502,f70]) ).
fof(f502,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(not(X3),X2))
| ~ theorem(or(X0,X3))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f2597,plain,
( ~ spl0_154
| ~ spl0_112
| spl0_134 ),
inference(avatar_split_clause,[],[f2549,f2494,f1792,f2594]) ).
fof(f1792,plain,
( spl0_112
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2494,plain,
( spl0_134
<=> theorem(or(not(or(not(not(p)),p)),p)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f2549,plain,
( ~ theorem(or(p,not(p)))
| ~ spl0_112
| spl0_134 ),
inference(resolution,[],[f2496,f1793]) ).
fof(f1793,plain,
( ! [X0,X1] :
( theorem(or(not(or(not(X1),X0)),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f2496,plain,
( ~ theorem(or(not(or(not(not(p)),p)),p))
| spl0_134 ),
inference(avatar_component_clause,[],[f2494]) ).
fof(f2592,plain,
( spl0_153
| ~ spl0_6
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f514,f492,f44,f2590]) ).
fof(f2590,plain,
( spl0_153
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f492,plain,
( spl0_57
<=> ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) )
| ~ spl0_6
| ~ spl0_57 ),
inference(resolution,[],[f493,f45]) ).
fof(f493,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f2588,plain,
( spl0_152
| ~ spl0_16
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f490,f457,f94,f2586]) ).
fof(f2586,plain,
( spl0_152
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f94,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f457,plain,
( spl0_56
<=> ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f490,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X0,X2),not(or(not(X1),X2)))) )
| ~ spl0_16
| ~ spl0_56 ),
inference(resolution,[],[f458,f95]) ).
fof(f95,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f458,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f2584,plain,
( spl0_151
| ~ spl0_17
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f487,f457,f104,f2582]) ).
fof(f2582,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f104,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(f487,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(not(or(not(X1),X2)),X2))) )
| ~ spl0_17
| ~ spl0_56 ),
inference(resolution,[],[f458,f105]) ).
fof(f105,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f2580,plain,
( spl0_150
| ~ spl0_49
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f486,f457,f387,f2578]) ).
fof(f2578,plain,
( spl0_150
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f387,plain,
( spl0_49
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f486,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X2)),or(X2,X0))) )
| ~ spl0_49
| ~ spl0_56 ),
inference(resolution,[],[f458,f388]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f2576,plain,
( spl0_149
| ~ spl0_16
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f475,f449,f94,f2574]) ).
fof(f2574,plain,
( spl0_149
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f449,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f475,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(not(or(X2,not(X1))),X2),X0)) )
| ~ spl0_16
| ~ spl0_54 ),
inference(resolution,[],[f450,f95]) ).
fof(f450,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f2572,plain,
( spl0_148
| ~ spl0_17
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f472,f449,f104,f2570]) ).
fof(f2570,plain,
( spl0_148
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(X2,not(X1))),or(X0,X2))) )
| ~ spl0_17
| ~ spl0_54 ),
inference(resolution,[],[f450,f105]) ).
fof(f2568,plain,
( spl0_147
| ~ spl0_49
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f471,f449,f387,f2566]) ).
fof(f2566,plain,
( spl0_147
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,not(or(X2,not(X1)))))) )
| ~ spl0_49
| ~ spl0_54 ),
inference(resolution,[],[f450,f388]) ).
fof(f2564,plain,
( spl0_146
| ~ spl0_16
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f467,f445,f94,f2562]) ).
fof(f2562,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f445,plain,
( spl0_53
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) )
| ~ spl0_16
| ~ spl0_53 ),
inference(resolution,[],[f446,f95]) ).
fof(f446,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f2560,plain,
( spl0_145
| ~ spl0_17
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f464,f445,f104,f2558]) ).
fof(f2558,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) )
| ~ spl0_17
| ~ spl0_53 ),
inference(resolution,[],[f446,f105]) ).
fof(f2556,plain,
( spl0_144
| ~ spl0_49
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f463,f445,f387,f2554]) ).
fof(f2554,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) )
| ~ spl0_49
| ~ spl0_53 ),
inference(resolution,[],[f446,f388]) ).
fof(f2547,plain,
( spl0_143
| ~ spl0_6
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f439,f420,f44,f2545]) ).
fof(f2545,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f420,plain,
( spl0_52
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f439,plain,
( ! [X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(not(or(not(X1),not(X1))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_52 ),
inference(resolution,[],[f421,f45]) ).
fof(f421,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f2543,plain,
( spl0_142
| ~ spl0_44
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f410,f387,f288,f2541]) ).
fof(f2541,plain,
( spl0_142
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f288,plain,
( spl0_44
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f410,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),or(X2,X3)))
| ~ theorem(or(or(X3,X2),X1)) )
| ~ spl0_44
| ~ spl0_49 ),
inference(resolution,[],[f388,f289]) ).
fof(f289,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f2539,plain,
( spl0_141
| ~ spl0_31
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f403,f387,f213,f2537]) ).
fof(f2537,plain,
( spl0_141
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f213,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,not(or(X0,X2)))))
| ~ theorem(or(not(X2),X1)) )
| ~ spl0_31
| ~ spl0_49 ),
inference(resolution,[],[f388,f214]) ).
fof(f214,plain,
( ! [X2,X0,X1] :
( theorem(or(X2,or(not(or(X2,X0)),X1)))
| ~ theorem(or(not(X0),X1)) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f2535,plain,
( spl0_140
| ~ spl0_42
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f397,f387,f280,f2533]) ).
fof(f2533,plain,
( spl0_140
<=> ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f280,plain,
( spl0_42
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f397,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
| ~ theorem(X2) )
| ~ spl0_42
| ~ spl0_49 ),
inference(resolution,[],[f388,f281]) ).
fof(f281,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f2531,plain,
( spl0_139
| ~ spl0_19
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f394,f387,f118,f2529]) ).
fof(f2529,plain,
( spl0_139
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
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(f394,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X2,X0)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19
| ~ spl0_49 ),
inference(resolution,[],[f388,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(f2527,plain,
( spl0_138
| ~ spl0_12
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f343,f327,f74,f2525]) ).
fof(f2525,plain,
( spl0_138
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f74,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(f327,plain,
( spl0_46
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f343,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X2,or(X1,X3))) )
| ~ spl0_12
| ~ spl0_46 ),
inference(resolution,[],[f328,f75]) ).
fof(f75,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f2523,plain,
( spl0_137
| ~ spl0_17
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f310,f288,f104,f2521]) ).
fof(f2521,plain,
( spl0_137
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(or(X0,X1),X2))
| theorem(or(X0,or(or(X3,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f310,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(or(X0,X1),X2))
| theorem(or(X0,or(or(X3,X2),X1))) )
| ~ spl0_17
| ~ spl0_44 ),
inference(resolution,[],[f289,f105]) ).
fof(f2519,plain,
( spl0_136
| ~ spl0_26
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f306,f284,f164,f2517]) ).
fof(f2517,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f284,plain,
( spl0_43
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f306,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(or(X0,or(X1,X2)),X2)) )
| ~ spl0_26
| ~ spl0_43 ),
inference(resolution,[],[f285,f165]) ).
fof(f285,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f2515,plain,
( spl0_135
| ~ spl0_17
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f298,f280,f104,f2513]) ).
fof(f2513,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f298,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) )
| ~ spl0_17
| ~ spl0_42 ),
inference(resolution,[],[f281,f105]) ).
fof(f2497,plain,
( ~ spl0_134
| spl0_58
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f2384,f2050,f496,f2494]) ).
fof(f496,plain,
( spl0_58
<=> theorem(or(not(or(not(p),not(p))),not(or(not(not(p)),p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2050,plain,
( spl0_129
<=> ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f2384,plain,
( ~ theorem(or(not(or(not(not(p)),p)),p))
| spl0_58
| ~ spl0_129 ),
inference(resolution,[],[f2051,f498]) ).
fof(f498,plain,
( ~ theorem(or(not(or(not(p),not(p))),not(or(not(not(p)),p))))
| spl0_58 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f2051,plain,
( ! [X0,X1] :
( theorem(or(not(or(not(X1),not(X1))),X0))
| ~ theorem(or(X0,X1)) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f2050]) ).
fof(f2081,plain,
( spl0_133
| ~ spl0_25
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f576,f558,f156,f2079]) ).
fof(f2079,plain,
( spl0_133
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f576,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2))))
| ~ spl0_25
| ~ spl0_62 ),
inference(resolution,[],[f559,f157]) ).
fof(f2077,plain,
( spl0_132
| ~ spl0_28
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f574,f558,f176,f2075]) ).
fof(f2075,plain,
( spl0_132
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f176,plain,
( spl0_28
<=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f574,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2))))
| ~ spl0_28
| ~ spl0_62 ),
inference(resolution,[],[f559,f177]) ).
fof(f177,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f2073,plain,
( spl0_131
| ~ spl0_11
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f563,f558,f69,f2071]) ).
fof(f2071,plain,
( spl0_131
<=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f563,plain,
( ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1))))
| ~ spl0_11
| ~ spl0_62 ),
inference(resolution,[],[f559,f70]) ).
fof(f2069,plain,
( spl0_130
| ~ spl0_6
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f462,f445,f44,f2067]) ).
fof(f2067,plain,
( spl0_130
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(not(X0),X2))) )
| ~ spl0_6
| ~ spl0_53 ),
inference(resolution,[],[f446,f45]) ).
fof(f2052,plain,
( spl0_129
| ~ spl0_16
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f442,f420,f94,f2050]) ).
fof(f442,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),not(X1))),X0)) )
| ~ spl0_16
| ~ spl0_52 ),
inference(resolution,[],[f421,f95]) ).
fof(f2048,plain,
( spl0_128
| ~ spl0_41
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f409,f387,f270,f2046]) ).
fof(f2046,plain,
( spl0_128
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f270,plain,
( spl0_41
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f409,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1)))
| ~ spl0_41
| ~ spl0_49 ),
inference(resolution,[],[f388,f271]) ).
fof(f271,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f2044,plain,
( spl0_127
| ~ spl0_28
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f402,f387,f176,f2042]) ).
fof(f2042,plain,
( spl0_127
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f402,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2))))))
| ~ spl0_28
| ~ spl0_49 ),
inference(resolution,[],[f388,f177]) ).
fof(f2040,plain,
( spl0_126
| ~ spl0_29
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f401,f387,f180,f2038]) ).
fof(f2038,plain,
( spl0_126
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f180,plain,
( spl0_29
<=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f401,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1))))))
| ~ spl0_29
| ~ spl0_49 ),
inference(resolution,[],[f388,f181]) ).
fof(f181,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f2036,plain,
( spl0_125
| ~ spl0_10
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f396,f387,f63,f2034]) ).
fof(f2034,plain,
( spl0_125
<=> ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f63,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f396,plain,
( ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0)))
| ~ spl0_10
| ~ spl0_49 ),
inference(resolution,[],[f388,f64]) ).
fof(f64,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f2032,plain,
( spl0_124
| ~ spl0_12
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f393,f387,f74,f2030]) ).
fof(f2030,plain,
( spl0_124
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f393,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1)))
| ~ spl0_12
| ~ spl0_49 ),
inference(resolution,[],[f388,f75]) ).
fof(f2028,plain,
( spl0_123
| ~ spl0_44
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f385,f335,f288,f2026]) ).
fof(f2026,plain,
( spl0_123
<=> ! [X0,X3,X2,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f335,plain,
( spl0_48
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f385,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(X3))
| ~ theorem(or(X3,X1)) )
| ~ spl0_44
| ~ spl0_48 ),
inference(resolution,[],[f336,f289]) ).
fof(f336,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,X1))
| ~ theorem(not(X2)) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f2024,plain,
( spl0_122
| ~ spl0_26
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f377,f335,f164,f2022]) ).
fof(f2022,plain,
( spl0_122
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f377,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(or(X0,X3)) )
| ~ spl0_26
| ~ spl0_48 ),
inference(resolution,[],[f336,f165]) ).
fof(f2020,plain,
( spl0_121
| ~ spl0_42
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f361,f335,f280,f2018]) ).
fof(f2018,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f361,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,not(X1))),X2))
| ~ theorem(not(X0))
| ~ theorem(X1) )
| ~ spl0_42
| ~ spl0_48 ),
inference(resolution,[],[f336,f281]) ).
fof(f2016,plain,
( spl0_120
| ~ spl0_26
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f357,f327,f164,f2014]) ).
fof(f2014,plain,
( spl0_120
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f357,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X3)
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_26
| ~ spl0_46 ),
inference(resolution,[],[f328,f165]) ).
fof(f2012,plain,
( spl0_119
| ~ spl0_73
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f951,f893,f747,f2010]) ).
fof(f2010,plain,
( spl0_119
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f747,plain,
( spl0_73
<=> ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f893,plain,
( spl0_84
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f951,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(or(X0,X0)) )
| ~ spl0_73
| ~ spl0_84 ),
inference(resolution,[],[f894,f748]) ).
fof(f748,plain,
( ! [X0] :
( ~ theorem(or(not(X0),not(X0)))
| ~ theorem(X0) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f894,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f893]) ).
fof(f2008,plain,
( spl0_118
| ~ spl0_12
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f314,f292,f74,f2006]) ).
fof(f2006,plain,
( spl0_118
<=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f292,plain,
( spl0_45
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f314,plain,
( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
| ~ spl0_12
| ~ spl0_45 ),
inference(resolution,[],[f293,f75]) ).
fof(f293,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f2004,plain,
( spl0_117
| ~ spl0_30
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f295,f280,f184,f2002]) ).
fof(f2002,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f184,plain,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f295,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,X2))
| ~ theorem(or(X1,or(X2,not(X0)))) )
| ~ spl0_30
| ~ spl0_42 ),
inference(resolution,[],[f281,f185]) ).
fof(f185,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f2000,plain,
( spl0_116
| ~ spl0_17
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f278,f270,f104,f1998]) ).
fof(f1998,plain,
( spl0_116
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f278,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
| ~ spl0_17
| ~ spl0_41 ),
inference(resolution,[],[f271,f105]) ).
fof(f1900,plain,
( spl0_115
| ~ spl0_16
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f740,f717,f94,f1898]) ).
fof(f1898,plain,
( spl0_115
<=> ! [X0,X1] : theorem(or(or(X0,not(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f717,plain,
( spl0_71
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f740,plain,
( ! [X0,X1] : theorem(or(or(X0,not(X0)),X1))
| ~ spl0_16
| ~ spl0_71 ),
inference(resolution,[],[f718,f95]) ).
fof(f718,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f1802,plain,
( spl0_114
| ~ spl0_10
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f522,f501,f63,f1800]) ).
fof(f1800,plain,
( spl0_114
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f522,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,or(X2,X1))) )
| ~ spl0_10
| ~ spl0_59 ),
inference(resolution,[],[f502,f64]) ).
fof(f1798,plain,
( spl0_113
| ~ spl0_7
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f520,f501,f49,f1796]) ).
fof(f1796,plain,
( spl0_113
<=> ! [X0,X3,X2,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f49,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f520,plain,
( ! [X2,X3,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,or(X2,or(X3,X1)))) )
| ~ spl0_7
| ~ spl0_59 ),
inference(resolution,[],[f502,f50]) ).
fof(f50,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f1794,plain,
( spl0_112
| ~ spl0_45
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f488,f457,f292,f1792]) ).
fof(f488,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(not(or(not(X1),X0)),X0)) )
| ~ spl0_45
| ~ spl0_56 ),
inference(resolution,[],[f458,f293]) ).
fof(f1790,plain,
( spl0_111
| ~ spl0_45
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f465,f445,f292,f1788]) ).
fof(f1788,plain,
( spl0_111
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f465,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
| ~ spl0_45
| ~ spl0_53 ),
inference(resolution,[],[f446,f293]) ).
fof(f1786,plain,
( spl0_110
| ~ spl0_41
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f384,f335,f270,f1784]) ).
fof(f1784,plain,
( spl0_110
<=> ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( theorem(or(or(not(or(X0,X1)),X0),X2))
| ~ theorem(not(X1)) )
| ~ spl0_41
| ~ spl0_48 ),
inference(resolution,[],[f336,f271]) ).
fof(f1782,plain,
( spl0_109
| ~ spl0_17
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f737,f717,f104,f1780]) ).
fof(f1780,plain,
( spl0_109
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f737,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X0))))
| ~ spl0_17
| ~ spl0_71 ),
inference(resolution,[],[f718,f105]) ).
fof(f1778,plain,
( spl0_108
| ~ spl0_23
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f379,f335,f148,f1776]) ).
fof(f1776,plain,
( spl0_108
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f148,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f379,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(or(X1,X0)))) )
| ~ spl0_23
| ~ spl0_48 ),
inference(resolution,[],[f336,f149]) ).
fof(f149,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f1774,plain,
( spl0_107
| ~ spl0_25
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f372,f335,f156,f1772]) ).
fof(f1772,plain,
( spl0_107
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f372,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(or(X2,X0)),X2))) )
| ~ spl0_25
| ~ spl0_48 ),
inference(resolution,[],[f336,f157]) ).
fof(f1770,plain,
( spl0_106
| ~ spl0_11
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f362,f335,f69,f1768]) ).
fof(f1768,plain,
( spl0_106
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f362,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),X2))
| ~ theorem(not(or(X1,X0))) )
| ~ spl0_11
| ~ spl0_48 ),
inference(resolution,[],[f336,f70]) ).
fof(f1766,plain,
( spl0_105
| ~ spl0_25
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f352,f327,f156,f1764]) ).
fof(f1764,plain,
( spl0_105
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f352,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(X2) )
| ~ spl0_25
| ~ spl0_46 ),
inference(resolution,[],[f328,f157]) ).
fof(f1762,plain,
( spl0_104
| ~ spl0_44
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f325,f292,f288,f1760]) ).
fof(f1760,plain,
( spl0_104
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(or(or(X2,X2),X1)) )
| ~ spl0_44
| ~ spl0_45 ),
inference(resolution,[],[f293,f289]) ).
fof(f1758,plain,
( spl0_103
| ~ spl0_42
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f317,f292,f280,f1756]) ).
fof(f1756,plain,
( spl0_103
<=> ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f317,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(X0,X0),not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_42
| ~ spl0_45 ),
inference(resolution,[],[f293,f281]) ).
fof(f1754,plain,
( spl0_102
| ~ spl0_19
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f315,f292,f118,f1752]) ).
fof(f1752,plain,
( spl0_102
<=> ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f315,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X1)),X0))
| ~ theorem(or(not(X1),X0)) )
| ~ spl0_19
| ~ spl0_45 ),
inference(resolution,[],[f293,f119]) ).
fof(f1714,plain,
( spl0_101
| ~ spl0_16
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f730,f713,f94,f1712]) ).
fof(f1712,plain,
( spl0_101
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f713,plain,
( spl0_70
<=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f730,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X0)))
| ~ spl0_16
| ~ spl0_70 ),
inference(resolution,[],[f714,f95]) ).
fof(f714,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1661,plain,
( spl0_100
| ~ spl0_22
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f575,f558,f137,f1659]) ).
fof(f1659,plain,
( spl0_100
<=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f137,plain,
( spl0_22
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f575,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
| ~ spl0_22
| ~ spl0_62 ),
inference(resolution,[],[f559,f138]) ).
fof(f138,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f1657,plain,
( spl0_99
| ~ spl0_7
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f561,f558,f49,f1655]) ).
fof(f1655,plain,
( spl0_99
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f561,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
| ~ spl0_7
| ~ spl0_62 ),
inference(resolution,[],[f559,f50]) ).
fof(f1597,plain,
( spl0_98
| ~ spl0_17
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f726,f713,f104,f1595]) ).
fof(f1595,plain,
( spl0_98
<=> ! [X0,X1] : theorem(or(X0,or(not(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f726,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X0),X1)))
| ~ spl0_17
| ~ spl0_70 ),
inference(resolution,[],[f714,f105]) ).
fof(f1064,plain,
( ~ spl0_97
| spl0_58
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f950,f893,f496,f1061]) ).
fof(f1061,plain,
( spl0_97
<=> theorem(not(not(p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f950,plain,
( ~ theorem(not(not(p)))
| spl0_58
| ~ spl0_84 ),
inference(resolution,[],[f894,f498]) ).
fof(f1027,plain,
( spl0_58
| ~ spl0_87 ),
inference(avatar_contradiction_clause,[],[f1023]) ).
fof(f1023,plain,
( $false
| spl0_58
| ~ spl0_87 ),
inference(resolution,[],[f905,f498]) ).
fof(f905,plain,
( ! [X0,X1] : theorem(or(X0,X1))
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f904,plain,
( spl0_87
<=> ! [X0,X1] : theorem(or(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1021,plain,
( spl0_96
| spl0_87
| ~ spl0_39
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f376,f335,f257,f904,f1019]) ).
fof(f1019,plain,
( spl0_96
<=> ! [X2,X3] :
( ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f257,plain,
( spl0_39
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f376,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(X2,X3)))
| ~ theorem(X2) )
| ~ spl0_39
| ~ spl0_48 ),
inference(resolution,[],[f336,f258]) ).
fof(f258,plain,
( ! [X2,X0,X1] :
( theorem(or(X1,or(X0,X2)))
| ~ theorem(X0) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f1017,plain,
( spl0_95
| ~ spl0_21
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f349,f327,f133,f1015]) ).
fof(f1015,plain,
( spl0_95
<=> ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f133,plain,
( spl0_21
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f349,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(X1) )
| ~ spl0_21
| ~ spl0_46 ),
inference(resolution,[],[f328,f134]) ).
fof(f134,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f1013,plain,
( spl0_94
| ~ spl0_42
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f341,f327,f280,f1011]) ).
fof(f1011,plain,
( spl0_94
<=> ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f341,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,not(X2)))
| ~ theorem(X2) )
| ~ spl0_42
| ~ spl0_46 ),
inference(resolution,[],[f328,f281]) ).
fof(f1009,plain,
( spl0_93
| ~ spl0_41
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f324,f292,f270,f1007]) ).
fof(f1007,plain,
( spl0_93
<=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f324,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
| ~ spl0_41
| ~ spl0_45 ),
inference(resolution,[],[f293,f271]) ).
fof(f1005,plain,
( spl0_92
| ~ spl0_10
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f316,f292,f63,f1003]) ).
fof(f1003,plain,
( spl0_92
<=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f316,plain,
( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
| ~ spl0_10
| ~ spl0_45 ),
inference(resolution,[],[f293,f64]) ).
fof(f923,plain,
( spl0_91
| ~ spl0_39
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f580,f558,f257,f921]) ).
fof(f921,plain,
( spl0_91
<=> ! [X0,X3,X2,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f580,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(X2) )
| ~ spl0_39
| ~ spl0_62 ),
inference(resolution,[],[f559,f258]) ).
fof(f919,plain,
( ~ spl0_90
| ~ spl0_40
| spl0_69 ),
inference(avatar_split_clause,[],[f870,f695,f266,f916]) ).
fof(f916,plain,
( spl0_90
<=> theorem(p) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f266,plain,
( spl0_40
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f695,plain,
( spl0_69
<=> theorem(not(or(not(p),not(p)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f870,plain,
( ~ theorem(p)
| ~ spl0_40
| spl0_69 ),
inference(resolution,[],[f697,f267]) ).
fof(f267,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f697,plain,
( ~ theorem(not(or(not(p),not(p))))
| spl0_69 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f914,plain,
( spl0_89
| ~ spl0_26
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f405,f387,f164,f912]) ).
fof(f912,plain,
( spl0_89
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f405,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_26
| ~ spl0_49 ),
inference(resolution,[],[f388,f165]) ).
fof(f910,plain,
( spl0_88
| ~ spl0_20
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f378,f335,f129,f908]) ).
fof(f908,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f129,plain,
( spl0_20
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f378,plain,
( ! [X2,X0,X1] :
( theorem(or(or(X0,X1),X2))
| ~ theorem(not(not(X1))) )
| ~ spl0_20
| ~ spl0_48 ),
inference(resolution,[],[f336,f130]) ).
fof(f130,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f906,plain,
( spl0_86
| spl0_87
| ~ spl0_22
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f371,f335,f137,f904,f901]) ).
fof(f901,plain,
( spl0_86
<=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f371,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(or(not(X2),X2))) )
| ~ spl0_22
| ~ spl0_48 ),
inference(resolution,[],[f336,f138]) ).
fof(f899,plain,
( spl0_85
| ~ spl0_21
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f369,f335,f133,f897]) ).
fof(f897,plain,
( spl0_85
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f369,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(not(not(or(X0,X0)))) )
| ~ spl0_21
| ~ spl0_48 ),
inference(resolution,[],[f336,f134]) ).
fof(f895,plain,
( spl0_84
| ~ spl0_10
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f360,f335,f63,f893]) ).
fof(f360,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,X0)),X1))
| ~ theorem(not(X0)) )
| ~ spl0_10
| ~ spl0_48 ),
inference(resolution,[],[f336,f64]) ).
fof(f891,plain,
( spl0_83
| ~ spl0_7
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f358,f335,f49,f889]) ).
fof(f889,plain,
( spl0_83
<=> ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(not(or(X2,X0))) )
| ~ spl0_7
| ~ spl0_48 ),
inference(resolution,[],[f336,f50]) ).
fof(f887,plain,
( spl0_82
| ~ spl0_11
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f342,f327,f69,f885]) ).
fof(f885,plain,
( spl0_82
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f342,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X2,X1)) )
| ~ spl0_11
| ~ spl0_46 ),
inference(resolution,[],[f328,f70]) ).
fof(f883,plain,
( spl0_81
| ~ spl0_16
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f297,f280,f94,f881]) ).
fof(f881,plain,
( spl0_81
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f297,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,not(or(X1,not(X0))))) )
| ~ spl0_16
| ~ spl0_42 ),
inference(resolution,[],[f281,f95]) ).
fof(f822,plain,
( spl0_80
| ~ spl0_25
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f400,f387,f156,f820]) ).
fof(f820,plain,
( spl0_80
<=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f400,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
| ~ spl0_25
| ~ spl0_49 ),
inference(resolution,[],[f388,f157]) ).
fof(f818,plain,
( spl0_79
| ~ spl0_6
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f296,f280,f44,f816]) ).
fof(f816,plain,
( spl0_79
<=> ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f296,plain,
( ! [X0,X1] :
( ~ theorem(X0)
| theorem(X1)
| ~ theorem(or(X1,not(X0))) )
| ~ spl0_6
| ~ spl0_42 ),
inference(resolution,[],[f281,f45]) ).
fof(f814,plain,
( spl0_78
| ~ spl0_17
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f255,f250,f104,f812]) ).
fof(f812,plain,
( spl0_78
<=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f250,plain,
( spl0_38
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f255,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
| ~ spl0_17
| ~ spl0_38 ),
inference(resolution,[],[f251,f105]) ).
fof(f251,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f810,plain,
( spl0_77
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f190,f152,f104,f808]) ).
fof(f808,plain,
( spl0_77
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f152,plain,
( spl0_24
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f190,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
| ~ spl0_17
| ~ spl0_24 ),
inference(resolution,[],[f153,f105]) ).
fof(f153,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f771,plain,
( ~ spl0_76
| ~ spl0_13
| spl0_58 ),
inference(avatar_split_clause,[],[f596,f496,f78,f768]) ).
fof(f768,plain,
( spl0_76
<=> theorem(not(or(not(not(p)),p))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f78,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f596,plain,
( ~ theorem(not(or(not(not(p)),p)))
| ~ spl0_13
| spl0_58 ),
inference(resolution,[],[f498,f79]) ).
fof(f79,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f757,plain,
( spl0_75
| ~ spl0_7
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f338,f327,f49,f755]) ).
fof(f755,plain,
( spl0_75
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f338,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(X2) )
| ~ spl0_7
| ~ spl0_46 ),
inference(resolution,[],[f328,f50]) ).
fof(f753,plain,
( spl0_74
| ~ spl0_43
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f307,f288,f284,f751]) ).
fof(f751,plain,
( spl0_74
<=> ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f307,plain,
( ! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(or(X1,X0)) )
| ~ spl0_43
| ~ spl0_44 ),
inference(resolution,[],[f289,f285]) ).
fof(f749,plain,
( spl0_73
| ~ spl0_37
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f273,f266,f246,f747]) ).
fof(f246,plain,
( spl0_37
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f273,plain,
( ! [X0] :
( ~ theorem(X0)
| ~ theorem(or(not(X0),not(X0))) )
| ~ spl0_37
| ~ spl0_40 ),
inference(resolution,[],[f267,f247]) ).
fof(f247,plain,
( ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f745,plain,
( spl0_72
| ~ spl0_16
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f264,f257,f94,f743]) ).
fof(f743,plain,
( spl0_72
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f264,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(or(X0,X1),X2)) )
| ~ spl0_16
| ~ spl0_39 ),
inference(resolution,[],[f258,f95]) ).
fof(f719,plain,
( spl0_71
| ~ spl0_22
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f399,f387,f137,f717]) ).
fof(f399,plain,
( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
| ~ spl0_22
| ~ spl0_49 ),
inference(resolution,[],[f388,f138]) ).
fof(f715,plain,
( spl0_70
| ~ spl0_7
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f390,f387,f49,f713]) ).
fof(f390,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
| ~ spl0_7
| ~ spl0_49 ),
inference(resolution,[],[f388,f50]) ).
fof(f698,plain,
( ~ spl0_69
| ~ spl0_18
| spl0_58 ),
inference(avatar_split_clause,[],[f595,f496,f114,f695]) ).
fof(f114,plain,
( spl0_18
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f595,plain,
( ~ theorem(not(or(not(p),not(p))))
| ~ spl0_18
| spl0_58 ),
inference(resolution,[],[f498,f115]) ).
fof(f115,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f681,plain,
( spl0_68
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f220,f213,f184,f679]) ).
fof(f679,plain,
( spl0_68
<=> ! [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_68])]) ).
fof(f220,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_30
| ~ spl0_31 ),
inference(resolution,[],[f214,f185]) ).
fof(f677,plain,
( spl0_67
| ~ spl0_29
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f209,f184,f180,f675]) ).
fof(f675,plain,
( spl0_67
<=> ! [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_67])]) ).
fof(f209,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
| ~ theorem(or(X0,X1)) )
| ~ spl0_29
| ~ spl0_30 ),
inference(resolution,[],[f185,f181]) ).
fof(f637,plain,
( spl0_66
| ~ spl0_30
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f238,f230,f184,f635]) ).
fof(f635,plain,
( spl0_66
<=> ! [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_66])]) ).
fof(f230,plain,
( spl0_34
<=> ! [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_34])]) ).
fof(f238,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
| ~ theorem(or(X0,or(X3,X1))) )
| ~ spl0_30
| ~ spl0_34 ),
inference(resolution,[],[f231,f185]) ).
fof(f231,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f633,plain,
( spl0_65
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f210,f184,f176,f631]) ).
fof(f631,plain,
( spl0_65
<=> ! [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_65])]) ).
fof(f210,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
| ~ theorem(or(X0,X2)) )
| ~ spl0_28
| ~ spl0_30 ),
inference(resolution,[],[f185,f177]) ).
fof(f629,plain,
( spl0_64
| ~ spl0_14
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f203,f184,f83,f627]) ).
fof(f627,plain,
( spl0_64
<=> ! [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_64])]) ).
fof(f83,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(f203,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_30 ),
inference(resolution,[],[f185,f84]) ).
fof(f84,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,[],[f83]) ).
fof(f593,plain,
( spl0_63
| ~ spl0_19
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f202,f184,f118,f591]) ).
fof(f202,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_30 ),
inference(resolution,[],[f185,f119]) ).
fof(f560,plain,
( spl0_62
| ~ spl0_12
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f201,f184,f74,f558]) ).
fof(f201,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,or(X2,X3))))
| ~ theorem(or(X0,or(X2,or(X1,X3)))) )
| ~ spl0_12
| ~ spl0_30 ),
inference(resolution,[],[f185,f75]) ).
fof(f511,plain,
( spl0_61
| ~ spl0_16
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f241,f230,f94,f509]) ).
fof(f509,plain,
( spl0_61
<=> ! [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_61])]) ).
fof(f241,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
| ~ spl0_16
| ~ spl0_34 ),
inference(resolution,[],[f231,f95]) ).
fof(f507,plain,
( spl0_60
| ~ spl0_6
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f221,f213,f44,f505]) ).
fof(f221,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(not(or(not(X2),X0)),X1))
| ~ theorem(X2) )
| ~ spl0_6
| ~ spl0_31 ),
inference(resolution,[],[f214,f45]) ).
fof(f503,plain,
( spl0_59
| ~ spl0_26
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f211,f184,f164,f501]) ).
fof(f211,plain,
( ! [X2,X3,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X3))
| ~ theorem(or(not(X3),X2)) )
| ~ spl0_26
| ~ spl0_30 ),
inference(resolution,[],[f185,f165]) ).
fof(f499,plain,
( ~ spl0_58
| spl0_1
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f435,f331,f21,f496]) ).
fof(f21,plain,
( spl0_1
<=> theorem(not(not(or(not(or(not(p),not(p))),not(or(not(not(p)),p)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f331,plain,
( spl0_47
<=> ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f435,plain,
( ~ theorem(or(not(or(not(p),not(p))),not(or(not(not(p)),p))))
| spl0_1
| ~ spl0_47 ),
inference(resolution,[],[f332,f23]) ).
fof(f23,plain,
( ~ theorem(not(not(or(not(or(not(p),not(p))),not(or(not(not(p)),p))))))
| spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f332,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f494,plain,
( spl0_57
| ~ spl0_6
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f194,f180,f44,f492]) ).
fof(f194,plain,
( ! [X0,X1] :
( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_29 ),
inference(resolution,[],[f181,f45]) ).
fof(f459,plain,
( spl0_56
| ~ spl0_6
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f239,f230,f44,f457]) ).
fof(f239,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
| ~ theorem(or(X2,X0)) )
| ~ spl0_6
| ~ spl0_34 ),
inference(resolution,[],[f231,f45]) ).
fof(f455,plain,
( spl0_55
| ~ spl0_16
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f223,f213,f94,f453]) ).
fof(f453,plain,
( spl0_55
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f223,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(not(or(X2,X0)),X1),X2)) )
| ~ spl0_16
| ~ spl0_31 ),
inference(resolution,[],[f214,f95]) ).
fof(f451,plain,
( spl0_54
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f208,f184,f156,f449]) ).
fof(f208,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_25
| ~ spl0_30 ),
inference(resolution,[],[f185,f157]) ).
fof(f447,plain,
( spl0_53
| ~ spl0_6
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f191,f176,f44,f445]) ).
fof(f191,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_28 ),
inference(resolution,[],[f177,f45]) ).
fof(f422,plain,
( spl0_52
| ~ spl0_21
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f206,f184,f133,f420]) ).
fof(f206,plain,
( ! [X0,X1] :
( theorem(or(X0,not(or(not(X1),not(X1)))))
| ~ theorem(or(X0,X1)) )
| ~ spl0_21
| ~ spl0_30 ),
inference(resolution,[],[f185,f134]) ).
fof(f418,plain,
( spl0_51
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f196,f180,f94,f416]) ).
fof(f416,plain,
( spl0_51
<=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f196,plain,
( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
| ~ spl0_16
| ~ spl0_29 ),
inference(resolution,[],[f181,f95]) ).
fof(f414,plain,
( spl0_50
| ~ spl0_16
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f193,f176,f94,f412]) ).
fof(f412,plain,
( spl0_50
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f193,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
| ~ spl0_16
| ~ spl0_28 ),
inference(resolution,[],[f177,f95]) ).
fof(f389,plain,
( spl0_49
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f200,f184,f69,f387]) ).
fof(f200,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,or(X2,X1))) )
| ~ spl0_11
| ~ spl0_30 ),
inference(resolution,[],[f185,f70]) ).
fof(f337,plain,
( spl0_48
| ~ spl0_18
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f204,f184,f114,f335]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,X2))
| ~ theorem(not(X2)) )
| ~ spl0_18
| ~ spl0_30 ),
inference(resolution,[],[f185,f115]) ).
fof(f333,plain,
( spl0_47
| ~ spl0_6
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f275,f235,f44,f331]) ).
fof(f275,plain,
( ! [X0] :
( theorem(not(not(X0)))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_35 ),
inference(resolution,[],[f236,f45]) ).
fof(f329,plain,
( spl0_46
| ~ spl0_6
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f164,f44,f327]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_26 ),
inference(resolution,[],[f165,f45]) ).
fof(f294,plain,
( spl0_45
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f199,f184,f63,f292]) ).
fof(f199,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_30 ),
inference(resolution,[],[f185,f64]) ).
fof(f290,plain,
( spl0_44
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f170,f164,f94,f288]) ).
fof(f170,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f165,f95]) ).
fof(f286,plain,
( spl0_43
| ~ spl0_15
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f169,f164,f88,f284]) ).
fof(f88,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f169,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_26 ),
inference(resolution,[],[f165,f89]) ).
fof(f89,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f282,plain,
( spl0_42
| ~ spl0_6
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f160,f156,f44,f280]) ).
fof(f160,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_25 ),
inference(resolution,[],[f157,f45]) ).
fof(f272,plain,
( spl0_41
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f162,f156,f94,f270]) ).
fof(f162,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f157,f95]) ).
fof(f268,plain,
( spl0_40
| ~ spl0_6
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f141,f133,f44,f266]) ).
fof(f141,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_21 ),
inference(resolution,[],[f134,f45]) ).
fof(f259,plain,
( spl0_39
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f127,f114,f104,f257]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f115,f105]) ).
fof(f252,plain,
( spl0_38
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f146,f137,f94,f250]) ).
fof(f146,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_22 ),
inference(resolution,[],[f138,f95]) ).
fof(f248,plain,
( spl0_36
| spl0_37
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f124,f114,f44,f246,f243]) ).
fof(f243,plain,
( spl0_36
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f124,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_6
| ~ spl0_18 ),
inference(resolution,[],[f115,f45]) ).
fof(f237,plain,
( spl0_35
| ~ spl0_16
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f189,f152,f94,f235]) ).
fof(f189,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_24 ),
inference(resolution,[],[f153,f95]) ).
fof(f232,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f111,f104,f83,f230]) ).
fof(f111,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,[],[f105,f84]) ).
fof(f228,plain,
( spl0_33
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f101,f94,f83,f226]) ).
fof(f226,plain,
( spl0_33
<=> ! [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_33])]) ).
fof(f101,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,[],[f95,f84]) ).
fof(f219,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f123,f118,f94,f217]) ).
fof(f217,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
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,f95]) ).
fof(f215,plain,
( spl0_31
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f118,f104,f213]) ).
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,f105]) ).
fof(f186,plain,
( spl0_30
| ~ spl0_6
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f118,f44,f184]) ).
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,f45]) ).
fof(f182,plain,
( spl0_29
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f104,f63,f180]) ).
fof(f110,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f105,f64]) ).
fof(f178,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f104,f74,f176]) ).
fof(f109,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f105,f75]) ).
fof(f174,plain,
( spl0_27
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f94,f74,f172]) ).
fof(f172,plain,
( spl0_27
<=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f100,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f95,f75]) ).
fof(f166,plain,
( spl0_26
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f112,f104,f78,f164]) ).
fof(f112,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f105,f79]) ).
fof(f158,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f104,f69,f156]) ).
fof(f108,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f105,f70]) ).
fof(f154,plain,
( spl0_24
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f137,f88,f152]) ).
fof(f145,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_22 ),
inference(resolution,[],[f138,f89]) ).
fof(f150,plain,
( spl0_23
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f94,f69,f148]) ).
fof(f99,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f95,f70]) ).
fof(f139,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f104,f49,f137]) ).
fof(f107,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f105,f50]) ).
fof(f135,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f94,f63,f133]) ).
fof(f98,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f95,f64]) ).
fof(f131,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f94,f49,f129]) ).
fof(f97,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f95,f50]) ).
fof(f120,plain,
( spl0_19
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f86,f83,f44,f118]) ).
fof(f86,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_6
| ~ spl0_14 ),
inference(resolution,[],[f84,f45]) ).
fof(f116,plain,
( spl0_18
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f102,f94,f78,f114]) ).
fof(f102,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f95,f79]) ).
fof(f106,plain,
( spl0_17
| ~ spl0_6
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f81,f74,f44,f104]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_6
| ~ spl0_12 ),
inference(resolution,[],[f75,f45]) ).
fof(f96,plain,
( spl0_16
| ~ spl0_6
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f72,f69,f44,f94]) ).
fof(f72,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_6
| ~ spl0_11 ),
inference(resolution,[],[f70,f45]) ).
fof(f90,plain,
( spl0_15
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f67,f63,f44,f88]) ).
fof(f67,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_6
| ~ spl0_10 ),
inference(resolution,[],[f64,f45]) ).
fof(f85,plain,
( spl0_14
| ~ spl0_2
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f61,f58,f26,f83]) ).
fof(f26,plain,
( spl0_2
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f58,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(f61,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,[],[f59,f27]) ).
fof(f27,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f59,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,[],[f58]) ).
fof(f80,plain,
( spl0_13
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f49,f44,f78]) ).
fof(f66,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f50,f45]) ).
fof(f76,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f56,f53,f26,f74]) ).
fof(f53,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(f56,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_2
| ~ spl0_8 ),
inference(resolution,[],[f54,f27]) ).
fof(f54,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f71,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f47,f40,f26,f69]) ).
fof(f40,plain,
( spl0_5
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f47,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_2
| ~ spl0_5 ),
inference(resolution,[],[f41,f27]) ).
fof(f41,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f65,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f38,f34,f26,f63]) ).
fof(f34,plain,
( spl0_4
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f38,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_2
| ~ spl0_4 ),
inference(resolution,[],[f35,f27]) ).
fof(f35,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f60,plain,
spl0_9,
inference(avatar_split_clause,[],[f17,f58]) ).
fof(f17,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(f55,plain,
spl0_8,
inference(avatar_split_clause,[],[f18,f53]) ).
fof(f18,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(f51,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f37,f30,f26,f49]) ).
fof(f30,plain,
( spl0_3
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f37,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f31,f27]) ).
fof(f31,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f46,plain,
spl0_6,
inference(avatar_split_clause,[],[f19,f44]) ).
fof(f19,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(f42,plain,
spl0_5,
inference(avatar_split_clause,[],[f16,f40]) ).
fof(f16,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(f36,plain,
spl0_4,
inference(avatar_split_clause,[],[f15,f34]) ).
fof(f15,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(f32,plain,
spl0_3,
inference(avatar_split_clause,[],[f14,f30]) ).
fof(f14,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(f28,plain,
spl0_2,
inference(avatar_split_clause,[],[f7,f26]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f24,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f13,f21]) ).
fof(f13,plain,
~ theorem(not(not(or(not(or(not(p),not(p))),not(or(not(not(p)),p)))))),
inference(definition_unfolding,[],[f11,f12]) ).
fof(f12,plain,
! [X6,X5] : equivalent(X5,X6) = not(or(not(or(not(X5),X6)),not(or(not(X6),X5)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f9,axiom,
! [X6,X5] : and(X5,X6) = not(or(not(X5),not(X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
! [X6,X5] : equivalent(X5,X6) = and(implies(X5,X6),implies(X6,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,axiom,
~ theorem(not(equivalent(p,not(p)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL326-3 : TPTP v8.1.2. Released v2.3.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.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 : Fri May 3 14:15:12 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (12804)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (12807)WARNING: value z3 for option sas not known
% 0.15/0.38 % (12806)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 % (12808)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (12805)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (12810)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 % (12809)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 % (12807)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 % (12811)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 [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [3]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 TRYING [4]
% 0.22/0.43 TRYING [5]
% 0.22/0.45 TRYING [5]
% 0.22/0.52 % (12809)First to succeed.
% 0.22/0.53 % (12809)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12804"
% 0.22/0.53 % (12809)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.53 % (12809)------------------------------
% 0.22/0.53 % (12809)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.53 % (12809)Termination reason: Refutation
% 0.22/0.53
% 0.22/0.53 % (12809)Memory used [KB]: 2033
% 0.22/0.53 % (12809)Time elapsed: 0.149 s
% 0.22/0.53 % (12809)Instructions burned: 264 (million)
% 0.22/0.53 % (12804)Success in time 0.166 s
%------------------------------------------------------------------------------