TSTP Solution File: LCL323-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL323-3 : 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 : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 13:41:44 EDT 2024

% Result   : Unsatisfiable 0.16s 0.52s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  136
% Syntax   : Number of formulae    :  461 (  22 unt;   0 def)
%            Number of atoms       : 1352 (   1 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 1653 ( 762   ~; 764   |;   0   &)
%                                         ( 127 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :  131 ( 129 usr; 128 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  697 ( 697   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2109,plain,
    $false,
    inference(avatar_sat_refutation,[],[f21,f25,f29,f33,f39,f43,f48,f52,f57,f62,f68,f73,f77,f82,f87,f94,f104,f115,f119,f127,f137,f141,f145,f153,f161,f165,f173,f182,f186,f190,f194,f219,f223,f232,f237,f241,f251,f258,f264,f273,f280,f284,f291,f301,f305,f312,f316,f320,f324,f361,f365,f370,f420,f445,f449,f453,f476,f480,f484,f488,f523,f527,f532,f536,f540,f588,f621,f656,f660,f664,f704,f708,f738,f745,f755,f759,f785,f789,f793,f798,f802,f854,f858,f862,f866,f928,f932,f936,f940,f944,f951,f955,f959,f963,f967,f1039,f1057,f1061,f1065,f1069,f1073,f1085,f1086,f1087,f1088,f1089,f1090,f1091,f1518,f1736,f1740,f1829,f1834,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1880,f2003,f2077,f2081,f2085,f2089,f2093,f2097,f2101,f2108]) ).

fof(f2108,plain,
    ( ~ spl0_21
    | spl0_120 ),
    inference(avatar_contradiction_clause,[],[f2102]) ).

fof(f2102,plain,
    ( $false
    | ~ spl0_21
    | spl0_120 ),
    inference(resolution,[],[f2002,f136]) ).

fof(f136,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f135,plain,
    ( spl0_21
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f2002,plain,
    ( ~ theorem(or(or(not(p),q),not(q)))
    | spl0_120 ),
    inference(avatar_component_clause,[],[f2000]) ).

fof(f2000,plain,
    ( spl0_120
  <=> theorem(or(or(not(p),q),not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f2101,plain,
    ( spl0_127
    | ~ spl0_49
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f416,f363,f318,f2099]) ).

fof(f2099,plain,
    ( spl0_127
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(X3))
        | ~ theorem(or(X3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f318,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f363,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(f416,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(X3))
        | ~ theorem(or(X3,X1)) )
    | ~ spl0_49
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f319]) ).

fof(f319,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X2,X1),X0))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f318]) ).

fof(f364,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X2))
        | theorem(or(X0,X1))
        | ~ theorem(not(X2)) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f363]) ).

fof(f2097,plain,
    ( spl0_126
    | ~ spl0_27
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f408,f363,f171,f2095]) ).

fof(f2095,plain,
    ( spl0_126
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(X2,X3)))
        | ~ theorem(or(X0,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f171,plain,
    ( spl0_27
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f408,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(X2,X3)))
        | ~ theorem(or(X0,X3)) )
    | ~ spl0_27
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f172]) ).

fof(f172,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f2093,plain,
    ( spl0_125
    | ~ spl0_47
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f393,f363,f310,f2091]) ).

fof(f2091,plain,
    ( spl0_125
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X2))
        | ~ theorem(not(X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f310,plain,
    ( spl0_47
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f393,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X2))
        | ~ theorem(not(X0))
        | ~ theorem(X1) )
    | ~ spl0_47
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f311]) ).

fof(f311,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f310]) ).

fof(f2089,plain,
    ( spl0_124
    | ~ spl0_27
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f389,f359,f171,f2087]) ).

fof(f2087,plain,
    ( spl0_124
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X3)
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f359,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(f389,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X3)
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_27
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f172]) ).

fof(f360,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f359]) ).

fof(f2085,plain,
    ( spl0_123
    | ~ spl0_12
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f346,f322,f71,f2083]) ).

fof(f2083,plain,
    ( spl0_123
  <=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f71,plain,
    ( spl0_12
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f322,plain,
    ( spl0_50
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f346,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
    | ~ spl0_12
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f72]) ).

fof(f72,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f323,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,X1)) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f2081,plain,
    ( spl0_122
    | ~ spl0_31
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f325,f310,f192,f2079]) ).

fof(f2079,plain,
    ( spl0_122
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(X2,not(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f192,plain,
    ( spl0_31
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f325,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(X2,not(X0)))) )
    | ~ spl0_31
    | ~ spl0_47 ),
    inference(resolution,[],[f311,f193]) ).

fof(f193,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f192]) ).

fof(f2077,plain,
    ( spl0_121
    | ~ spl0_17
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f308,f303,f102,f2075]) ).

fof(f2075,plain,
    ( spl0_121
  <=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f102,plain,
    ( spl0_17
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f303,plain,
    ( spl0_46
  <=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f308,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
    | ~ spl0_17
    | ~ spl0_46 ),
    inference(resolution,[],[f304,f103]) ).

fof(f103,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X1,or(X0,X2)))
        | theorem(or(X0,or(X1,X2))) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f304,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f303]) ).

fof(f2003,plain,
    ( ~ spl0_120
    | spl0_1
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1029,f961,f18,f2000]) ).

fof(f18,plain,
    ( spl0_1
  <=> theorem(or(or(not(p),q),or(not(q),r))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f961,plain,
    ( spl0_96
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1029,plain,
    ( ~ theorem(or(or(not(p),q),not(q)))
    | spl0_1
    | ~ spl0_96 ),
    inference(resolution,[],[f962,f20]) ).

fof(f20,plain,
    ( ~ theorem(or(or(not(p),q),or(not(q),r)))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f18]) ).

fof(f962,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f961]) ).

fof(f1880,plain,
    ( spl0_119
    | ~ spl0_10
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f551,f525,f60,f1878]) ).

fof(f1878,plain,
    ( spl0_119
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,or(X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f60,plain,
    ( spl0_10
  <=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f525,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(f551,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,or(X2,X1))) )
    | ~ spl0_10
    | ~ spl0_63 ),
    inference(resolution,[],[f526,f61]) ).

fof(f61,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f526,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(not(X3),X2))
        | ~ theorem(or(X0,X3))
        | theorem(or(X0,or(X1,X2))) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f525]) ).

fof(f1874,plain,
    ( spl0_118
    | ~ spl0_7
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f549,f525,f46,f1872]) ).

fof(f1872,plain,
    ( spl0_118
  <=> ! [X0,X3,X2,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(X2,or(X3,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f46,plain,
    ( spl0_7
  <=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f549,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(X2,or(X3,X1)))) )
    | ~ spl0_7
    | ~ spl0_63 ),
    inference(resolution,[],[f526,f47]) ).

fof(f47,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f1870,plain,
    ( spl0_117
    | ~ spl0_50
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f517,f486,f322,f1868]) ).

fof(f1868,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f486,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(f517,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X0)),X0)) )
    | ~ spl0_50
    | ~ spl0_61 ),
    inference(resolution,[],[f487,f323]) ).

fof(f487,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f486]) ).

fof(f1866,plain,
    ( spl0_116
    | ~ spl0_50
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f494,f474,f322,f1864]) ).

fof(f1864,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f474,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(f494,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
    | ~ spl0_50
    | ~ spl0_58 ),
    inference(resolution,[],[f475,f323]) ).

fof(f475,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f474]) ).

fof(f1862,plain,
    ( spl0_115
    | ~ spl0_46
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f415,f363,f303,f1860]) ).

fof(f1860,plain,
    ( spl0_115
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(not(or(X0,X1)),X0),X2))
        | ~ theorem(not(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f415,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(not(or(X0,X1)),X0),X2))
        | ~ theorem(not(X1)) )
    | ~ spl0_46
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f304]) ).

fof(f1858,plain,
    ( spl0_114
    | ~ spl0_25
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f410,f363,f159,f1856]) ).

fof(f1856,plain,
    ( spl0_114
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(or(X1,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f159,plain,
    ( spl0_25
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f410,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(or(X1,X0)))) )
    | ~ spl0_25
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f160]) ).

fof(f160,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f159]) ).

fof(f1854,plain,
    ( spl0_113
    | ~ spl0_26
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f403,f363,f163,f1852]) ).

fof(f1852,plain,
    ( spl0_113
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f163,plain,
    ( spl0_26
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(or(X2,X0)),X2))) )
    | ~ spl0_26
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f164]) ).

fof(f164,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f163]) ).

fof(f1850,plain,
    ( spl0_112
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f394,f363,f66,f1848]) ).

fof(f1848,plain,
    ( spl0_112
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),X2))
        | ~ theorem(not(or(X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f66,plain,
    ( spl0_11
  <=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f394,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),X2))
        | ~ theorem(not(or(X1,X0))) )
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f67]) ).

fof(f67,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f66]) ).

fof(f1846,plain,
    ( spl0_111
    | ~ spl0_26
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f384,f359,f163,f1844]) ).

fof(f1844,plain,
    ( spl0_111
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f384,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(X2) )
    | ~ spl0_26
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f164]) ).

fof(f1842,plain,
    ( spl0_110
    | ~ spl0_49
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f357,f322,f318,f1840]) ).

fof(f1840,plain,
    ( spl0_110
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(or(or(X2,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f357,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(or(or(X2,X2),X1)) )
    | ~ spl0_49
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f319]) ).

fof(f1838,plain,
    ( spl0_109
    | ~ spl0_47
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f349,f322,f310,f1836]) ).

fof(f1836,plain,
    ( spl0_109
  <=> ! [X0,X1] :
        ( theorem(or(not(or(or(X0,X0),not(X1))),X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f349,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(X0,X0),not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_47
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f311]) ).

fof(f1834,plain,
    ( ~ spl0_108
    | spl0_1
    | ~ spl0_88 ),
    inference(avatar_split_clause,[],[f984,f930,f18,f1831]) ).

fof(f1831,plain,
    ( spl0_108
  <=> theorem(or(r,not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f930,plain,
    ( spl0_88
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f984,plain,
    ( ~ theorem(or(r,not(q)))
    | spl0_1
    | ~ spl0_88 ),
    inference(resolution,[],[f931,f20]) ).

fof(f931,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) )
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f930]) ).

fof(f1829,plain,
    ( spl0_107
    | ~ spl0_19
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f347,f322,f117,f1827]) ).

fof(f1827,plain,
    ( spl0_107
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,X1)),X0))
        | ~ theorem(or(not(X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f117,plain,
    ( spl0_19
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f347,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,X1)),X0))
        | ~ theorem(or(not(X1),X0)) )
    | ~ spl0_19
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f118]) ).

fof(f118,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f1740,plain,
    ( spl0_106
    | ~ spl0_23
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f603,f586,f143,f1738]) ).

fof(f1738,plain,
    ( spl0_106
  <=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f143,plain,
    ( spl0_23
  <=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f586,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(f603,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
    | ~ spl0_23
    | ~ spl0_67 ),
    inference(resolution,[],[f587,f144]) ).

fof(f144,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f587,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(X0,or(X2,or(X1,X3))))
        | theorem(or(X0,or(X1,or(X2,X3)))) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f586]) ).

fof(f1736,plain,
    ( spl0_105
    | ~ spl0_7
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f589,f586,f46,f1734]) ).

fof(f1734,plain,
    ( spl0_105
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f589,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
    | ~ spl0_7
    | ~ spl0_67 ),
    inference(resolution,[],[f587,f47]) ).

fof(f1518,plain,
    ( ~ spl0_104
    | spl0_74
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f1008,f957,f735,f1515]) ).

fof(f1515,plain,
    ( spl0_104
  <=> theorem(not(not(r))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f735,plain,
    ( spl0_74
  <=> theorem(or(or(not(q),r),q)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f957,plain,
    ( spl0_95
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f1008,plain,
    ( ~ theorem(not(not(r)))
    | spl0_74
    | ~ spl0_95 ),
    inference(resolution,[],[f958,f737]) ).

fof(f737,plain,
    ( ~ theorem(or(or(not(q),r),q))
    | spl0_74 ),
    inference(avatar_component_clause,[],[f735]) ).

fof(f958,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(X1))) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f957]) ).

fof(f1091,plain,
    ( spl0_1
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1076]) ).

fof(f1076,plain,
    ( $false
    | spl0_1
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f20]) ).

fof(f950,plain,
    ( ! [X0,X1] : theorem(or(X0,X1))
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f949]) ).

fof(f949,plain,
    ( spl0_93
  <=> ! [X0,X1] : theorem(or(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f1090,plain,
    ( spl0_38
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1077]) ).

fof(f1077,plain,
    ( $false
    | spl0_38
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f257]) ).

fof(f257,plain,
    ( ~ theorem(or(or(not(p),q),r))
    | spl0_38 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f255,plain,
    ( spl0_38
  <=> theorem(or(or(not(p),q),r)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1089,plain,
    ( spl0_74
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1078]) ).

fof(f1078,plain,
    ( $false
    | spl0_74
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f737]) ).

fof(f1088,plain,
    ( spl0_37
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1081]) ).

fof(f1081,plain,
    ( $false
    | spl0_37
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f250]) ).

fof(f250,plain,
    ( ~ theorem(or(not(p),q))
    | spl0_37 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f248,plain,
    ( spl0_37
  <=> theorem(or(not(p),q)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1087,plain,
    ( spl0_18
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1082]) ).

fof(f1082,plain,
    ( $false
    | spl0_18
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f114]) ).

fof(f114,plain,
    ( ~ theorem(or(not(q),r))
    | spl0_18 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f112,plain,
    ( spl0_18
  <=> theorem(or(not(q),r)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1086,plain,
    ( spl0_81
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1083]) ).

fof(f1083,plain,
    ( $false
    | spl0_81
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f797]) ).

fof(f797,plain,
    ( ~ theorem(or(q,r))
    | spl0_81 ),
    inference(avatar_component_clause,[],[f795]) ).

fof(f795,plain,
    ( spl0_81
  <=> theorem(or(q,r)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1085,plain,
    ( spl0_64
    | ~ spl0_93 ),
    inference(avatar_contradiction_clause,[],[f1084]) ).

fof(f1084,plain,
    ( $false
    | spl0_64
    | ~ spl0_93 ),
    inference(resolution,[],[f950,f531]) ).

fof(f531,plain,
    ( ~ theorem(or(r,q))
    | spl0_64 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f529,plain,
    ( spl0_64
  <=> theorem(or(r,q)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1073,plain,
    ( spl0_103
    | spl0_93
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f407,f363,f289,f949,f1071]) ).

fof(f1071,plain,
    ( spl0_103
  <=> ! [X2,X3] :
        ( ~ theorem(not(or(X2,X3)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f289,plain,
    ( spl0_44
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f407,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(X2,X3)))
        | ~ theorem(X2) )
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f290]) ).

fof(f290,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X1,or(X0,X2)))
        | ~ theorem(X0) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f1069,plain,
    ( spl0_102
    | ~ spl0_22
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f382,f359,f139,f1067]) ).

fof(f1067,plain,
    ( spl0_102
  <=> ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f139,plain,
    ( spl0_22
  <=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f382,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(X1) )
    | ~ spl0_22
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f140]) ).

fof(f140,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f139]) ).

fof(f1065,plain,
    ( spl0_101
    | ~ spl0_47
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f374,f359,f310,f1063]) ).

fof(f1063,plain,
    ( spl0_101
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,not(X2)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f374,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,not(X2)))
        | ~ theorem(X2) )
    | ~ spl0_47
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f311]) ).

fof(f1061,plain,
    ( spl0_100
    | ~ spl0_46
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f356,f322,f303,f1059]) ).

fof(f1059,plain,
    ( spl0_100
  <=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f356,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
    | ~ spl0_46
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f304]) ).

fof(f1057,plain,
    ( spl0_99
    | ~ spl0_10
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f348,f322,f60,f1055]) ).

fof(f1055,plain,
    ( spl0_99
  <=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f348,plain,
    ( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
    | ~ spl0_10
    | ~ spl0_50 ),
    inference(resolution,[],[f323,f61]) ).

fof(f1039,plain,
    ( ~ spl0_98
    | spl0_1
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f1006,f957,f18,f1036]) ).

fof(f1036,plain,
    ( spl0_98
  <=> theorem(not(not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1006,plain,
    ( ~ theorem(not(not(q)))
    | spl0_1
    | ~ spl0_95 ),
    inference(resolution,[],[f958,f20]) ).

fof(f967,plain,
    ( spl0_97
    | ~ spl0_44
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f608,f586,f289,f965]) ).

fof(f965,plain,
    ( spl0_97
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f608,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(X2) )
    | ~ spl0_44
    | ~ spl0_67 ),
    inference(resolution,[],[f587,f290]) ).

fof(f963,plain,
    ( spl0_96
    | ~ spl0_27
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f436,f418,f171,f961]) ).

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(f436,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_27
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f172]) ).

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(f959,plain,
    ( spl0_95
    | ~ spl0_21
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f409,f363,f135,f957]) ).

fof(f409,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(X1))) )
    | ~ spl0_21
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f136]) ).

fof(f955,plain,
    ( spl0_94
    | ~ spl0_6
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f751,f743,f41,f953]) ).

fof(f953,plain,
    ( spl0_94
  <=> ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f41,plain,
    ( spl0_6
  <=> ! [X4,X3] :
        ( ~ theorem(X4)
        | theorem(X3)
        | ~ theorem(or(not(X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f743,plain,
    ( spl0_75
  <=> ! [X0] : theorem(or(X0,not(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f751,plain,
    ( ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_75 ),
    inference(resolution,[],[f744,f42]) ).

fof(f42,plain,
    ( ! [X3,X4] :
        ( ~ theorem(or(not(X4),X3))
        | theorem(X3)
        | ~ theorem(X4) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f744,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f743]) ).

fof(f951,plain,
    ( spl0_92
    | spl0_93
    | ~ spl0_23
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f402,f363,f143,f949,f946]) ).

fof(f946,plain,
    ( spl0_92
  <=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(X2),X2))) )
    | ~ spl0_23
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f144]) ).

fof(f944,plain,
    ( spl0_91
    | ~ spl0_22
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f401,f363,f139,f942]) ).

fof(f942,plain,
    ( spl0_91
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(not(or(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f401,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(not(or(X0,X0)))) )
    | ~ spl0_22
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f140]) ).

fof(f940,plain,
    ( spl0_90
    | ~ spl0_10
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f392,f363,f60,f938]) ).

fof(f938,plain,
    ( spl0_90
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,X0)),X1))
        | ~ theorem(not(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f392,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,X0)),X1))
        | ~ theorem(not(X0)) )
    | ~ spl0_10
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f61]) ).

fof(f936,plain,
    ( spl0_89
    | ~ spl0_7
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f390,f363,f46,f934]) ).

fof(f934,plain,
    ( spl0_89
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(X0),X1))
        | ~ theorem(not(or(X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f390,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(X0),X1))
        | ~ theorem(not(or(X2,X0))) )
    | ~ spl0_7
    | ~ spl0_52 ),
    inference(resolution,[],[f364,f47]) ).

fof(f932,plain,
    ( spl0_88
    | ~ spl0_11
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f375,f359,f66,f930]) ).

fof(f375,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) )
    | ~ spl0_11
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f67]) ).

fof(f928,plain,
    ( spl0_87
    | ~ spl0_16
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f327,f310,f92,f926]) ).

fof(f926,plain,
    ( spl0_87
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,not(or(X1,not(X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f92,plain,
    ( spl0_16
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f327,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,not(or(X1,not(X0))))) )
    | ~ spl0_16
    | ~ spl0_47 ),
    inference(resolution,[],[f311,f93]) ).

fof(f93,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X1,X0))
        | theorem(or(X0,X1)) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f866,plain,
    ( spl0_86
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f431,f418,f163,f864]) ).

fof(f864,plain,
    ( spl0_86
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f431,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f164]) ).

fof(f862,plain,
    ( spl0_85
    | ~ spl0_6
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f326,f310,f41,f860]) ).

fof(f860,plain,
    ( spl0_85
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(X1,not(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f326,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(X1,not(X0))) )
    | ~ spl0_6
    | ~ spl0_47 ),
    inference(resolution,[],[f311,f42]) ).

fof(f858,plain,
    ( spl0_84
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f287,f282,f102,f856]) ).

fof(f856,plain,
    ( spl0_84
  <=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f282,plain,
    ( spl0_43
  <=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f287,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(resolution,[],[f283,f103]) ).

fof(f283,plain,
    ( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f854,plain,
    ( spl0_83
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f268,f262,f102,f852]) ).

fof(f852,plain,
    ( spl0_83
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f262,plain,
    ( spl0_39
  <=> ! [X0] : theorem(or(not(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f268,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(resolution,[],[f263,f103]) ).

fof(f263,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f802,plain,
    ( spl0_82
    | ~ spl0_7
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f371,f359,f46,f800]) ).

fof(f800,plain,
    ( spl0_82
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f371,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X2) )
    | ~ spl0_7
    | ~ spl0_51 ),
    inference(resolution,[],[f360,f47]) ).

fof(f798,plain,
    ( ~ spl0_81
    | ~ spl0_49
    | spl0_74 ),
    inference(avatar_split_clause,[],[f739,f735,f318,f795]) ).

fof(f739,plain,
    ( ~ theorem(or(q,r))
    | ~ spl0_49
    | spl0_74 ),
    inference(resolution,[],[f737,f319]) ).

fof(f793,plain,
    ( spl0_80
    | ~ spl0_48
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f339,f318,f314,f791]) ).

fof(f791,plain,
    ( spl0_80
  <=> ! [X0,X1] :
        ( ~ theorem(or(X0,X0))
        | theorem(or(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f314,plain,
    ( spl0_48
  <=> ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f339,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,X0))
        | theorem(or(X1,X0)) )
    | ~ spl0_48
    | ~ spl0_49 ),
    inference(resolution,[],[f319,f315]) ).

fof(f315,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f314]) ).

fof(f789,plain,
    ( spl0_79
    | ~ spl0_42
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f306,f299,f278,f787]) ).

fof(f787,plain,
    ( spl0_79
  <=> ! [X0] :
        ( ~ theorem(X0)
        | ~ theorem(or(not(X0),not(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f278,plain,
    ( spl0_42
  <=> ! [X0] :
        ( ~ theorem(not(X0))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f299,plain,
    ( spl0_45
  <=> ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f306,plain,
    ( ! [X0] :
        ( ~ theorem(X0)
        | ~ theorem(or(not(X0),not(X0))) )
    | ~ spl0_42
    | ~ spl0_45 ),
    inference(resolution,[],[f300,f279]) ).

fof(f279,plain,
    ( ! [X0] :
        ( ~ theorem(not(X0))
        | ~ theorem(X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f300,plain,
    ( ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f299]) ).

fof(f785,plain,
    ( spl0_78
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f297,f289,f92,f783]) ).

fof(f783,plain,
    ( spl0_78
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f297,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X0,X1),X2)) )
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(resolution,[],[f290,f93]) ).

fof(f759,plain,
    ( spl0_77
    | ~ spl0_23
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f430,f418,f143,f757]) ).

fof(f757,plain,
    ( spl0_77
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f430,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
    | ~ spl0_23
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f144]) ).

fof(f755,plain,
    ( spl0_76
    | ~ spl0_7
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f421,f418,f46,f753]) ).

fof(f753,plain,
    ( spl0_76
  <=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f421,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
    | ~ spl0_7
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f47]) ).

fof(f745,plain,
    ( spl0_75
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f267,f262,f92,f743]) ).

fof(f267,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(resolution,[],[f263,f93]) ).

fof(f738,plain,
    ( ~ spl0_74
    | spl0_1
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f337,f318,f18,f735]) ).

fof(f337,plain,
    ( ~ theorem(or(or(not(q),r),q))
    | spl0_1
    | ~ spl0_49 ),
    inference(resolution,[],[f319,f20]) ).

fof(f708,plain,
    ( spl0_73
    | ~ spl0_31
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f224,f217,f192,f706]) ).

fof(f706,plain,
    ( spl0_73
  <=> ! [X0,X3,X2,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(not(X3),X0)),X1)))
        | ~ theorem(or(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f217,plain,
    ( spl0_32
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f224,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(not(X3),X0)),X1)))
        | ~ theorem(or(X2,X3)) )
    | ~ spl0_31
    | ~ spl0_32 ),
    inference(resolution,[],[f218,f193]) ).

fof(f218,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X2,or(not(or(X2,X0)),X1)))
        | ~ theorem(or(not(X0),X1)) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f704,plain,
    ( spl0_72
    | ~ spl0_30
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f213,f192,f188,f702]) ).

fof(f702,plain,
    ( spl0_72
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
        | ~ theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f188,plain,
    ( spl0_30
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f213,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_30
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f189]) ).

fof(f189,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f188]) ).

fof(f664,plain,
    ( spl0_71
    | ~ spl0_31
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f243,f239,f192,f662]) ).

fof(f662,plain,
    ( spl0_71
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
        | ~ theorem(or(X0,or(X3,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f239,plain,
    ( spl0_36
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f243,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
        | ~ theorem(or(X0,or(X3,X1))) )
    | ~ spl0_31
    | ~ spl0_36 ),
    inference(resolution,[],[f240,f193]) ).

fof(f240,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f239]) ).

fof(f660,plain,
    ( spl0_70
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f214,f192,f184,f658]) ).

fof(f658,plain,
    ( spl0_70
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f184,plain,
    ( spl0_29
  <=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f214,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_29
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f185]) ).

fof(f185,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f656,plain,
    ( spl0_69
    | ~ spl0_14
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f207,f192,f80,f654]) ).

fof(f654,plain,
    ( spl0_69
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
        | ~ theorem(or(X0,or(not(X2),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f80,plain,
    ( spl0_14
  <=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f207,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
        | ~ theorem(or(X0,or(not(X2),X3))) )
    | ~ spl0_14
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f81]) ).

fof(f81,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f621,plain,
    ( spl0_68
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f206,f192,f117,f619]) ).

fof(f619,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(f206,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X1,X3)))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f118]) ).

fof(f588,plain,
    ( spl0_67
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f205,f192,f71,f586]) ).

fof(f205,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X2,or(X1,X3)))) )
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f72]) ).

fof(f540,plain,
    ( spl0_66
    | ~ spl0_16
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f246,f239,f92,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(f246,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
    | ~ spl0_16
    | ~ spl0_36 ),
    inference(resolution,[],[f240,f93]) ).

fof(f536,plain,
    ( spl0_65
    | ~ spl0_6
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f225,f217,f41,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(f225,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(not(or(not(X2),X0)),X1))
        | ~ theorem(X2) )
    | ~ spl0_6
    | ~ spl0_32 ),
    inference(resolution,[],[f218,f42]) ).

fof(f532,plain,
    ( ~ spl0_64
    | spl0_38
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f338,f318,f255,f529]) ).

fof(f338,plain,
    ( ~ theorem(or(r,q))
    | spl0_38
    | ~ spl0_49 ),
    inference(resolution,[],[f319,f257]) ).

fof(f527,plain,
    ( spl0_63
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f215,f192,f171,f525]) ).

fof(f215,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X3))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f172]) ).

fof(f523,plain,
    ( spl0_62
    | ~ spl0_6
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f199,f188,f41,f521]) ).

fof(f521,plain,
    ( spl0_62
  <=> ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f199,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_30 ),
    inference(resolution,[],[f189,f42]) ).

fof(f488,plain,
    ( spl0_61
    | ~ spl0_6
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f244,f239,f41,f486]) ).

fof(f244,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_36 ),
    inference(resolution,[],[f240,f42]) ).

fof(f484,plain,
    ( spl0_60
    | ~ spl0_16
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f227,f217,f92,f482]) ).

fof(f482,plain,
    ( spl0_60
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f227,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) )
    | ~ spl0_16
    | ~ spl0_32 ),
    inference(resolution,[],[f218,f93]) ).

fof(f480,plain,
    ( spl0_59
    | ~ spl0_26
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f212,f192,f163,f478]) ).

fof(f478,plain,
    ( spl0_59
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f212,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_26
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f164]) ).

fof(f476,plain,
    ( spl0_58
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f196,f184,f41,f474]) ).

fof(f196,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(resolution,[],[f185,f42]) ).

fof(f453,plain,
    ( spl0_57
    | ~ spl0_22
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f210,f192,f139,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(f210,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f140]) ).

fof(f449,plain,
    ( spl0_56
    | ~ spl0_16
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f201,f188,f92,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(f201,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
    | ~ spl0_16
    | ~ spl0_30 ),
    inference(resolution,[],[f189,f93]) ).

fof(f445,plain,
    ( spl0_55
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f198,f184,f92,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(f198,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(resolution,[],[f185,f93]) ).

fof(f420,plain,
    ( spl0_54
    | ~ spl0_11
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f204,f192,f66,f418]) ).

fof(f204,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X2,X1))) )
    | ~ spl0_11
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f67]) ).

fof(f370,plain,
    ( ~ spl0_53
    | ~ spl0_20
    | spl0_37 ),
    inference(avatar_split_clause,[],[f252,f248,f125,f367]) ).

fof(f367,plain,
    ( spl0_53
  <=> theorem(not(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f125,plain,
    ( spl0_20
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f252,plain,
    ( ~ theorem(not(p))
    | ~ spl0_20
    | spl0_37 ),
    inference(resolution,[],[f250,f126]) ).

fof(f126,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f125]) ).

fof(f365,plain,
    ( spl0_52
    | ~ spl0_20
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f208,f192,f125,f363]) ).

fof(f208,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,X2))
        | ~ theorem(not(X2)) )
    | ~ spl0_20
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f126]) ).

fof(f361,plain,
    ( spl0_51
    | ~ spl0_6
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f175,f171,f41,f359]) ).

fof(f175,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_27 ),
    inference(resolution,[],[f172,f42]) ).

fof(f324,plain,
    ( spl0_50
    | ~ spl0_10
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f203,f192,f60,f322]) ).

fof(f203,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) )
    | ~ spl0_10
    | ~ spl0_31 ),
    inference(resolution,[],[f193,f61]) ).

fof(f320,plain,
    ( spl0_49
    | ~ spl0_16
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f178,f171,f92,f318]) ).

fof(f178,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) )
    | ~ spl0_16
    | ~ spl0_27 ),
    inference(resolution,[],[f172,f93]) ).

fof(f316,plain,
    ( spl0_48
    | ~ spl0_15
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f177,f171,f85,f314]) ).

fof(f85,plain,
    ( spl0_15
  <=> ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f177,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) )
    | ~ spl0_15
    | ~ spl0_27 ),
    inference(resolution,[],[f172,f86]) ).

fof(f86,plain,
    ( ! [X0] :
        ( ~ theorem(or(X0,X0))
        | theorem(X0) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f312,plain,
    ( spl0_47
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f167,f163,f41,f310]) ).

fof(f167,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(resolution,[],[f164,f42]) ).

fof(f305,plain,
    ( spl0_46
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f169,f163,f92,f303]) ).

fof(f169,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(resolution,[],[f164,f93]) ).

fof(f301,plain,
    ( spl0_45
    | ~ spl0_6
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f147,f139,f41,f299]) ).

fof(f147,plain,
    ( ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_22 ),
    inference(resolution,[],[f140,f42]) ).

fof(f291,plain,
    ( spl0_44
    | ~ spl0_17
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f133,f125,f102,f289]) ).

fof(f133,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) )
    | ~ spl0_17
    | ~ spl0_20 ),
    inference(resolution,[],[f126,f103]) ).

fof(f284,plain,
    ( spl0_43
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f157,f143,f92,f282]) ).

fof(f157,plain,
    ( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(resolution,[],[f144,f93]) ).

fof(f280,plain,
    ( spl0_41
    | spl0_42
    | ~ spl0_6
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f129,f125,f41,f278,f275]) ).

fof(f275,plain,
    ( spl0_41
  <=> ! [X1] : theorem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f129,plain,
    ( ! [X0,X1] :
        ( ~ theorem(not(X0))
        | theorem(X1)
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_20 ),
    inference(resolution,[],[f126,f42]) ).

fof(f273,plain,
    ( ~ spl0_40
    | ~ spl0_13
    | spl0_37 ),
    inference(avatar_split_clause,[],[f253,f248,f75,f270]) ).

fof(f270,plain,
    ( spl0_40
  <=> theorem(q) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f75,plain,
    ( spl0_13
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f253,plain,
    ( ~ theorem(q)
    | ~ spl0_13
    | spl0_37 ),
    inference(resolution,[],[f250,f76]) ).

fof(f76,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f264,plain,
    ( spl0_39
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f156,f143,f85,f262]) ).

fof(f156,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(resolution,[],[f144,f86]) ).

fof(f258,plain,
    ( ~ spl0_38
    | spl0_1
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f174,f171,f18,f255]) ).

fof(f174,plain,
    ( ~ theorem(or(or(not(p),q),r))
    | spl0_1
    | ~ spl0_27 ),
    inference(resolution,[],[f172,f20]) ).

fof(f251,plain,
    ( ~ spl0_37
    | spl0_1
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f128,f125,f18,f248]) ).

fof(f128,plain,
    ( ~ theorem(or(not(p),q))
    | spl0_1
    | ~ spl0_20 ),
    inference(resolution,[],[f126,f20]) ).

fof(f241,plain,
    ( spl0_36
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f109,f102,f80,f239]) ).

fof(f109,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f81]) ).

fof(f237,plain,
    ( ~ spl0_35
    | spl0_18
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f130,f125,f112,f234]) ).

fof(f234,plain,
    ( spl0_35
  <=> theorem(not(q)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f130,plain,
    ( ~ theorem(not(q))
    | spl0_18
    | ~ spl0_20 ),
    inference(resolution,[],[f126,f114]) ).

fof(f232,plain,
    ( spl0_34
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f99,f92,f80,f230]) ).

fof(f230,plain,
    ( spl0_34
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f99,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f81]) ).

fof(f223,plain,
    ( spl0_33
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f122,f117,f92,f221]) ).

fof(f221,plain,
    ( spl0_33
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f122,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) )
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f93]) ).

fof(f219,plain,
    ( spl0_32
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f121,f117,f102,f217]) ).

fof(f121,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) )
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f103]) ).

fof(f194,plain,
    ( spl0_31
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f120,f117,f41,f192]) ).

fof(f120,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(resolution,[],[f118,f42]) ).

fof(f190,plain,
    ( spl0_30
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f108,f102,f60,f188]) ).

fof(f108,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f61]) ).

fof(f186,plain,
    ( spl0_29
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f107,f102,f71,f184]) ).

fof(f107,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f72]) ).

fof(f182,plain,
    ( spl0_28
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f98,f92,f71,f180]) ).

fof(f180,plain,
    ( spl0_28
  <=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f98,plain,
    ( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f72]) ).

fof(f173,plain,
    ( spl0_27
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f110,f102,f75,f171]) ).

fof(f110,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f76]) ).

fof(f165,plain,
    ( spl0_26
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f106,f102,f66,f163]) ).

fof(f106,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f67]) ).

fof(f161,plain,
    ( spl0_25
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f92,f66,f159]) ).

fof(f97,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f67]) ).

fof(f153,plain,
    ( ~ spl0_24
    | ~ spl0_13
    | spl0_18 ),
    inference(avatar_split_clause,[],[f123,f112,f75,f150]) ).

fof(f150,plain,
    ( spl0_24
  <=> theorem(r) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f123,plain,
    ( ~ theorem(r)
    | ~ spl0_13
    | spl0_18 ),
    inference(resolution,[],[f114,f76]) ).

fof(f145,plain,
    ( spl0_23
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f105,f102,f46,f143]) ).

fof(f105,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f47]) ).

fof(f141,plain,
    ( spl0_22
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f96,f92,f60,f139]) ).

fof(f96,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f61]) ).

fof(f137,plain,
    ( spl0_21
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f95,f92,f46,f135]) ).

fof(f95,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f47]) ).

fof(f127,plain,
    ( spl0_20
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f100,f92,f75,f125]) ).

fof(f100,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f76]) ).

fof(f119,plain,
    ( spl0_19
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f83,f80,f41,f117]) ).

fof(f83,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(resolution,[],[f81,f42]) ).

fof(f115,plain,
    ( ~ spl0_18
    | spl0_1
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f88,f75,f18,f112]) ).

fof(f88,plain,
    ( ~ theorem(or(not(q),r))
    | spl0_1
    | ~ spl0_13 ),
    inference(resolution,[],[f76,f20]) ).

fof(f104,plain,
    ( spl0_17
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f78,f71,f41,f102]) ).

fof(f78,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) )
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(resolution,[],[f72,f42]) ).

fof(f94,plain,
    ( spl0_16
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f69,f66,f41,f92]) ).

fof(f69,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) )
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(resolution,[],[f67,f42]) ).

fof(f87,plain,
    ( spl0_15
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f64,f60,f41,f85]) ).

fof(f64,plain,
    ( ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) )
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(resolution,[],[f61,f42]) ).

fof(f82,plain,
    ( spl0_14
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f58,f55,f23,f80]) ).

fof(f23,plain,
    ( spl0_2
  <=> ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f55,plain,
    ( spl0_9
  <=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f58,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(resolution,[],[f56,f24]) ).

fof(f24,plain,
    ( ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f23]) ).

fof(f56,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f77,plain,
    ( spl0_13
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f63,f46,f41,f75]) ).

fof(f63,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(resolution,[],[f47,f42]) ).

fof(f73,plain,
    ( spl0_12
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f53,f50,f23,f71]) ).

fof(f50,plain,
    ( spl0_8
  <=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f53,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(resolution,[],[f51,f24]) ).

fof(f51,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f68,plain,
    ( spl0_11
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f44,f37,f23,f66]) ).

fof(f37,plain,
    ( spl0_5
  <=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f44,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(resolution,[],[f38,f24]) ).

fof(f38,plain,
    ( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f62,plain,
    ( spl0_10
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f35,f31,f23,f60]) ).

fof(f31,plain,
    ( spl0_4
  <=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f35,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(resolution,[],[f32,f24]) ).

fof(f32,plain,
    ( ! [X0] : axiom(or(not(or(X0,X0)),X0))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f57,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f14,f55]) ).

fof(f14,plain,
    ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
    inference(definition_unfolding,[],[f5,f6,f6,f6]) ).

fof(f6,axiom,
    ! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).

fof(f5,axiom,
    ! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).

fof(f52,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f15,f50]) ).

fof(f15,plain,
    ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
    inference(definition_unfolding,[],[f4,f6]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).

fof(f48,plain,
    ( spl0_7
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f34,f27,f23,f46]) ).

fof(f27,plain,
    ( spl0_3
  <=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f34,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f28,f24]) ).

fof(f28,plain,
    ( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f27]) ).

fof(f43,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f16,f41]) ).

fof(f16,plain,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(or(not(X4),X3)) ),
    inference(definition_unfolding,[],[f8,f6]) ).

fof(f8,axiom,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(implies(X4,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).

fof(f39,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f13,f37]) ).

fof(f13,plain,
    ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
    inference(definition_unfolding,[],[f3,f6]) ).

fof(f3,axiom,
    ! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).

fof(f33,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f12,f31]) ).

fof(f12,plain,
    ! [X0] : axiom(or(not(or(X0,X0)),X0)),
    inference(definition_unfolding,[],[f1,f6]) ).

fof(f1,axiom,
    ! [X0] : axiom(implies(or(X0,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).

fof(f29,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f11,f27]) ).

fof(f11,plain,
    ! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
    inference(definition_unfolding,[],[f2,f6]) ).

fof(f2,axiom,
    ! [X0,X1] : axiom(implies(X0,or(X1,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).

fof(f25,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f7,f23]) ).

fof(f7,axiom,
    ! [X3] :
      ( ~ axiom(X3)
      | theorem(X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).

fof(f21,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f10,f18]) ).

fof(f10,plain,
    ~ theorem(or(or(not(p),q),or(not(q),r))),
    inference(definition_unfolding,[],[f9,f6,f6]) ).

fof(f9,axiom,
    ~ theorem(or(implies(p,q),implies(q,r))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : LCL323-3 : TPTP v8.1.2. Released v2.3.0.
% 0.02/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Apr 29 22:44:50 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (1675)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33  % (1681)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)
% 0.10/0.33  % (1682)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)
% 0.10/0.34  % (1676)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [3]
% 0.10/0.34  % (1678)WARNING: value z3 for option sas not known
% 0.10/0.34  TRYING [4]
% 0.10/0.35  % (1678)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)
% 0.10/0.35  % (1679)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35  TRYING [1]
% 0.10/0.35  TRYING [2]
% 0.10/0.35  % (1677)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35  % (1680)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)
% 0.16/0.35  TRYING [3]
% 0.16/0.37  TRYING [5]
% 0.16/0.37  TRYING [4]
% 0.16/0.43  TRYING [1]
% 0.16/0.43  TRYING [2]
% 0.16/0.44  TRYING [3]
% 0.16/0.45  TRYING [4]
% 0.16/0.47  TRYING [5]
% 0.16/0.48  TRYING [6]
% 0.16/0.51  % (1680)First to succeed.
% 0.16/0.52  % (1680)Refutation found. Thanks to Tanya!
% 0.16/0.52  % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52  % (1680)------------------------------
% 0.16/0.52  % (1680)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.52  % (1680)Termination reason: Refutation
% 0.16/0.52  
% 0.16/0.52  % (1680)Memory used [KB]: 1627
% 0.16/0.52  % (1680)Time elapsed: 0.186 s
% 0.16/0.52  % (1680)Instructions burned: 180 (million)
% 0.16/0.52  % (1680)------------------------------
% 0.16/0.52  % (1680)------------------------------
% 0.16/0.52  % (1675)Success in time 0.2 s
% 0.16/0.52  1678 Aborted by signal SIGHUP on /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.52  % (1678)------------------------------
% 0.16/0.52  % (1678)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.52  % (1678)Termination reason: Unknown
% 0.16/0.52  % (1678)Termination phase: Saturation
% 0.16/0.52  
% 0.16/0.52  % (1678)Memory used [KB]: 1880
% 0.16/0.52  % (1678)Time elapsed: 0.170 s
% 0.16/0.52  % (1678)Instructions burned: 182 (million)
% 0.16/0.52  % (1678)------------------------------
% 0.16/0.52  % (1678)------------------------------
% 0.16/0.52  Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.52  ???
% 0.16/0.52   ???
% 0.16/0.52    ???
% 0.16/0.52     ???
% 0.16/0.52      ???
% 0.16/0.52       ???
% 0.16/0.52        ???
% 0.16/0.52         ???
% 0.16/0.52          ???
% 0.16/0.52           ???
% 0.16/0.52            ???
% 0.16/0.52             ???
% 0.16/0.52              ???
% 0.16/0.52               ???
% 0.16/0.52                ???
% 0.16/0.52                 ???
% 0.16/0.52                  ???
% 0.16/0.52                   ???
% 0.16/0.52                    ???
% 0.16/0.52                     ???
% 0.16/0.52                      ???
% 0.16/0.52                       ???
% 0.16/0.52                        ???
% 0.16/0.52                         ???
% 0.16/0.52                          ???
% 0.16/0.52                           ???
% 0.16/0.52                            ???
% 0.16/0.52                             ???
% 0.16/0.52                              ???
% 0.16/0.52                               ???
% 0.16/0.52                                ???
% 0.16/0.52                                 ???
%------------------------------------------------------------------------------