TSTP Solution File: LCL234-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL234-3 : TPTP v8.2.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 May 21 00:25:40 EDT 2024

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  173
% Syntax   : Number of formulae    :  569 (  23 unt;   0 def)
%            Number of atoms       : 1709 (   2 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 2119 ( 979   ~; 977   |;   0   &)
%                                         ( 163 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :  167 ( 165 usr; 164 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  944 ( 944   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2986,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f26,f30,f34,f40,f44,f49,f53,f58,f63,f69,f74,f78,f83,f88,f95,f105,f116,f120,f128,f138,f142,f146,f154,f162,f166,f174,f183,f187,f191,f196,f200,f225,f229,f238,f242,f252,f257,f263,f271,f278,f282,f289,f299,f303,f313,f317,f321,f325,f360,f364,f368,f420,f445,f449,f453,f477,f481,f485,f489,f524,f528,f532,f536,f540,f589,f622,f655,f659,f663,f667,f707,f711,f762,f766,f770,f774,f823,f827,f831,f835,f839,f899,f903,f907,f911,f915,f919,f926,f930,f934,f938,f967,f1027,f1031,f1035,f1039,f1043,f1051,f1052,f1053,f1170,f1439,f1657,f1701,f1705,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1842,f1941,f2041,f2045,f2049,f2053,f2058,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2098,f2104,f2108,f2112,f2532,f2536,f2540,f2544,f2548,f2552,f2556,f2560,f2564,f2568,f2572,f2576,f2580,f2584,f2588,f2592,f2596,f2600,f2604,f2608,f2612,f2616,f2620,f2624,f2628,f2632,f2985]) ).

fof(f2985,plain,
    ( ~ spl0_104
    | spl0_1
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f2777,f2554,f19,f1654]) ).

fof(f1654,plain,
    ( spl0_104
  <=> theorem(or(not(not(q)),not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f19,plain,
    ( spl0_1
  <=> theorem(or(not(p),or(not(q),not(or(not(p),not(q)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f2554,plain,
    ( spl0_144
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,not(or(X0,X2)))))
        | ~ theorem(or(not(X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f2777,plain,
    ( ~ theorem(or(not(not(q)),not(q)))
    | spl0_1
    | ~ spl0_144 ),
    inference(resolution,[],[f2555,f21]) ).

fof(f21,plain,
    ( ~ theorem(or(not(p),or(not(q),not(or(not(p),not(q))))))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f19]) ).

fof(f2555,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,not(or(X0,X2)))))
        | ~ theorem(or(not(X2),X1)) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f2554]) ).

fof(f2632,plain,
    ( spl0_163
    | ~ spl0_26
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f637,f620,f164,f2630]) ).

fof(f2630,plain,
    ( spl0_163
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,X0)),X2)))
        | ~ theorem(or(not(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f164,plain,
    ( spl0_26
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f620,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X1,X3)))
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f637,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,X0)),X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_26
    | ~ spl0_68 ),
    inference(resolution,[],[f621,f165]) ).

fof(f165,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f621,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X3)))
        | theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f620]) ).

fof(f2628,plain,
    ( spl0_162
    | ~ spl0_11
    | ~ spl0_68 ),
    inference(avatar_split_clause,[],[f625,f620,f67,f2626]) ).

fof(f2626,plain,
    ( spl0_162
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X1,X2)))
        | ~ theorem(or(not(X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f67,plain,
    ( spl0_11
  <=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f625,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X1,X2)))
        | ~ theorem(or(not(X0),X2)) )
    | ~ spl0_11
    | ~ spl0_68 ),
    inference(resolution,[],[f621,f68]) ).

fof(f68,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f2624,plain,
    ( spl0_161
    | ~ spl0_27
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f610,f587,f172,f2622]) ).

fof(f2622,plain,
    ( spl0_161
  <=> ! [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_161])]) ).

fof(f172,plain,
    ( spl0_27
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f587,plain,
    ( spl0_67
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X2,or(X1,X3)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f610,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X1,X3))) )
    | ~ spl0_27
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f173]) ).

fof(f173,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f172]) ).

fof(f588,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,[],[f587]) ).

fof(f2620,plain,
    ( spl0_160
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f577,f534,f42,f2618]) ).

fof(f2618,plain,
    ( spl0_160
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | ~ theorem(X2)
        | theorem(X1)
        | ~ theorem(or(not(X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f42,plain,
    ( spl0_6
  <=> ! [X4,X3] :
        ( ~ theorem(X4)
        | theorem(X3)
        | ~ theorem(or(not(X4),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(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(f577,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | ~ theorem(X2)
        | theorem(X1)
        | ~ theorem(or(not(X2),X0)) )
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(resolution,[],[f535,f43]) ).

fof(f43,plain,
    ( ! [X3,X4] :
        ( ~ theorem(or(not(X4),X3))
        | theorem(X3)
        | ~ theorem(X4) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f535,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X2),X0)),X1))
        | ~ theorem(or(not(X0),X1))
        | ~ theorem(X2) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f2616,plain,
    ( spl0_159
    | ~ spl0_16
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f757,f653,f93,f2614]) ).

fof(f2614,plain,
    ( spl0_159
  <=> ! [X0,X1] : theorem(or(or(X0,not(X0)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f93,plain,
    ( spl0_16
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f653,plain,
    ( spl0_69
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f757,plain,
    ( ! [X0,X1] : theorem(or(or(X0,not(X0)),X1))
    | ~ spl0_16
    | ~ spl0_69 ),
    inference(resolution,[],[f654,f94]) ).

fof(f94,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X1,X0))
        | theorem(or(X0,X1)) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f654,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f653]) ).

fof(f2612,plain,
    ( spl0_158
    | ~ spl0_11
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f553,f526,f67,f2610]) ).

fof(f2610,plain,
    ( spl0_158
  <=> ! [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_158])]) ).

fof(f526,plain,
    ( spl0_63
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X3))
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f553,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X2)))
        | theorem(or(X0,or(X3,or(X2,X1)))) )
    | ~ spl0_11
    | ~ spl0_63 ),
    inference(resolution,[],[f527,f68]) ).

fof(f527,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,[],[f526]) ).

fof(f2608,plain,
    ( spl0_157
    | ~ spl0_6
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f543,f522,f42,f2606]) ).

fof(f2606,plain,
    ( spl0_157
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f522,plain,
    ( spl0_62
  <=> ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f543,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(or(not(X0),X1),or(not(X0),X1))) )
    | ~ spl0_6
    | ~ spl0_62 ),
    inference(resolution,[],[f523,f43]) ).

fof(f523,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f522]) ).

fof(f2604,plain,
    ( spl0_156
    | ~ spl0_16
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f520,f487,f93,f2602]) ).

fof(f2602,plain,
    ( spl0_156
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X0,X2),not(or(not(X1),X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f487,plain,
    ( spl0_61
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f520,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X0,X2),not(or(not(X1),X2)))) )
    | ~ spl0_16
    | ~ spl0_61 ),
    inference(resolution,[],[f488,f94]) ).

fof(f488,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f487]) ).

fof(f2600,plain,
    ( spl0_155
    | ~ spl0_17
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f517,f487,f103,f2598]) ).

fof(f2598,plain,
    ( spl0_155
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(not(or(not(X1),X2)),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f103,plain,
    ( spl0_17
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f517,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(not(or(not(X1),X2)),X2))) )
    | ~ spl0_17
    | ~ spl0_61 ),
    inference(resolution,[],[f488,f104]) ).

fof(f104,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X1,or(X0,X2)))
        | theorem(or(X0,or(X1,X2))) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f2596,plain,
    ( spl0_154
    | ~ spl0_54
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f516,f487,f418,f2594]) ).

fof(f2594,plain,
    ( spl0_154
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X2)),or(X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

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(f516,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X2)),or(X2,X0))) )
    | ~ spl0_54
    | ~ spl0_61 ),
    inference(resolution,[],[f488,f419]) ).

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(f2592,plain,
    ( spl0_153
    | ~ spl0_16
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f505,f479,f93,f2590]) ).

fof(f2590,plain,
    ( spl0_153
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(not(or(X2,not(X1))),X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f479,plain,
    ( spl0_59
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f505,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(not(or(X2,not(X1))),X2),X0)) )
    | ~ spl0_16
    | ~ spl0_59 ),
    inference(resolution,[],[f480,f94]) ).

fof(f480,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f2588,plain,
    ( spl0_152
    | ~ spl0_17
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f502,f479,f103,f2586]) ).

fof(f2586,plain,
    ( spl0_152
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(X2,not(X1))),or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f502,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(X2,not(X1))),or(X0,X2))) )
    | ~ spl0_17
    | ~ spl0_59 ),
    inference(resolution,[],[f480,f104]) ).

fof(f2584,plain,
    ( spl0_151
    | ~ spl0_54
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f501,f479,f418,f2582]) ).

fof(f2582,plain,
    ( spl0_151
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(X2,not(or(X2,not(X1)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f501,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(X2,not(or(X2,not(X1)))))) )
    | ~ spl0_54
    | ~ spl0_59 ),
    inference(resolution,[],[f480,f419]) ).

fof(f2580,plain,
    ( spl0_150
    | ~ spl0_16
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f497,f475,f93,f2578]) ).

fof(f2578,plain,
    ( spl0_150
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f475,plain,
    ( spl0_58
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f497,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X1,X2),not(or(X1,or(not(X0),X2))))) )
    | ~ spl0_16
    | ~ spl0_58 ),
    inference(resolution,[],[f476,f94]) ).

fof(f476,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f475]) ).

fof(f2576,plain,
    ( spl0_149
    | ~ spl0_17
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f494,f475,f103,f2574]) ).

fof(f2574,plain,
    ( spl0_149
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f494,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(not(or(X1,or(not(X0),X2))),X2))) )
    | ~ spl0_17
    | ~ spl0_58 ),
    inference(resolution,[],[f476,f104]) ).

fof(f2572,plain,
    ( spl0_148
    | ~ spl0_17
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f754,f653,f103,f2570]) ).

fof(f2570,plain,
    ( spl0_148
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f754,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(X0))))
    | ~ spl0_17
    | ~ spl0_69 ),
    inference(resolution,[],[f654,f104]) ).

fof(f2568,plain,
    ( spl0_147
    | ~ spl0_54
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f493,f475,f418,f2566]) ).

fof(f2566,plain,
    ( spl0_147
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f493,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X2))),or(X2,X1))) )
    | ~ spl0_54
    | ~ spl0_58 ),
    inference(resolution,[],[f476,f419]) ).

fof(f2564,plain,
    ( spl0_146
    | ~ spl0_6
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f468,f451,f42,f2562]) ).

fof(f2562,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(not(or(not(X1),not(X1))))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

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(f468,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(not(or(not(X1),not(X1))))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_57 ),
    inference(resolution,[],[f452,f43]) ).

fof(f452,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f451]) ).

fof(f2560,plain,
    ( spl0_145
    | ~ spl0_49
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f441,f418,f319,f2558]) ).

fof(f2558,plain,
    ( spl0_145
  <=> ! [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_145])]) ).

fof(f319,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f441,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(or(X0,X1),or(X2,X3)))
        | ~ theorem(or(or(X3,X2),X1)) )
    | ~ spl0_49
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f320]) ).

fof(f320,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X2,X1),X0))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f319]) ).

fof(f2556,plain,
    ( spl0_144
    | ~ spl0_33
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f434,f418,f223,f2554]) ).

fof(f223,plain,
    ( spl0_33
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f434,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,not(or(X0,X2)))))
        | ~ theorem(or(not(X2),X1)) )
    | ~ spl0_33
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f224]) ).

fof(f224,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X2,or(not(or(X2,X0)),X1)))
        | ~ theorem(or(not(X0),X1)) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f2552,plain,
    ( spl0_143
    | ~ spl0_47
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f428,f418,f311,f2550]) ).

fof(f2550,plain,
    ( spl0_143
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f311,plain,
    ( spl0_47
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f428,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(or(X0,X1),not(X2))),or(X1,X0)))
        | ~ theorem(X2) )
    | ~ spl0_47
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f312]) ).

fof(f312,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f2548,plain,
    ( spl0_142
    | ~ spl0_19
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f425,f418,f118,f2546]) ).

fof(f2546,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X2,X0)))
        | ~ theorem(or(not(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

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(f425,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X2,X0)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_19
    | ~ spl0_54 ),
    inference(resolution,[],[f419,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(f2544,plain,
    ( spl0_141
    | ~ spl0_12
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f374,f358,f72,f2542]) ).

fof(f2542,plain,
    ( spl0_141
  <=> ! [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_141])]) ).

fof(f72,plain,
    ( spl0_12
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f358,plain,
    ( spl0_51
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f374,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X2,or(X1,X3))) )
    | ~ spl0_12
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f73]) ).

fof(f73,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f359,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f358]) ).

fof(f2540,plain,
    ( spl0_140
    | ~ spl0_17
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f341,f319,f103,f2538]) ).

fof(f2538,plain,
    ( spl0_140
  <=> ! [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_140])]) ).

fof(f341,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(or(X0,X1),X2))
        | theorem(or(X0,or(or(X3,X2),X1))) )
    | ~ spl0_17
    | ~ spl0_49 ),
    inference(resolution,[],[f320,f104]) ).

fof(f2536,plain,
    ( spl0_139
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f337,f315,f172,f2534]) ).

fof(f2534,plain,
    ( spl0_139
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(or(X0,or(X1,X2)),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f315,plain,
    ( spl0_48
  <=> ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f337,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(or(X0,or(X1,X2)),X2)) )
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(resolution,[],[f316,f173]) ).

fof(f316,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) )
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f2532,plain,
    ( spl0_138
    | ~ spl0_17
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f329,f311,f103,f2530]) ).

fof(f2530,plain,
    ( spl0_138
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f329,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(not(or(or(X1,X2),not(X0))),X2))) )
    | ~ spl0_17
    | ~ spl0_47 ),
    inference(resolution,[],[f312,f104]) ).

fof(f2112,plain,
    ( spl0_137
    | ~ spl0_26
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f605,f587,f164,f2110]) ).

fof(f2110,plain,
    ( spl0_137
  <=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f605,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(or(X1,X2),X0)),X2))))
    | ~ spl0_26
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f165]) ).

fof(f2108,plain,
    ( spl0_136
    | ~ spl0_29
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f603,f587,f185,f2106]) ).

fof(f2106,plain,
    ( spl0_136
  <=> ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f185,plain,
    ( spl0_29
  <=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f603,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,or(X0,X2))),X2))))
    | ~ spl0_29
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f186]) ).

fof(f186,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f2104,plain,
    ( spl0_135
    | ~ spl0_11
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f592,f587,f67,f2102]) ).

fof(f2102,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f592,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(or(X0,X1),X2)),or(X0,or(X2,X1))))
    | ~ spl0_11
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f68]) ).

fof(f2098,plain,
    ( spl0_134
    | ~ spl0_6
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f492,f475,f42,f2096]) ).

fof(f2096,plain,
    ( spl0_134
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(not(X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f492,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(not(X0),X2))) )
    | ~ spl0_6
    | ~ spl0_58 ),
    inference(resolution,[],[f476,f43]) ).

fof(f2094,plain,
    ( spl0_133
    | ~ spl0_16
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f471,f451,f93,f2092]) ).

fof(f2092,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),not(X1))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f471,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),not(X1))),X0)) )
    | ~ spl0_16
    | ~ spl0_57 ),
    inference(resolution,[],[f452,f94]) ).

fof(f2090,plain,
    ( spl0_132
    | ~ spl0_46
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f440,f418,f301,f2088]) ).

fof(f2088,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f301,plain,
    ( spl0_46
  <=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f440,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),X0),or(X2,X1)))
    | ~ spl0_46
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f302]) ).

fof(f302,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f2086,plain,
    ( spl0_131
    | ~ spl0_29
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f433,f418,f185,f2084]) ).

fof(f2084,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f433,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(or(X1,X2),not(or(X1,or(X0,X2))))))
    | ~ spl0_29
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f186]) ).

fof(f2082,plain,
    ( spl0_130
    | ~ spl0_30
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f432,f418,f189,f2080]) ).

fof(f2080,plain,
    ( spl0_130
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f189,plain,
    ( spl0_30
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f432,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(or(or(X0,X1),or(X0,X1))))))
    | ~ spl0_30
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f190]) ).

fof(f190,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f2078,plain,
    ( spl0_129
    | ~ spl0_10
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f427,f418,f61,f2076]) ).

fof(f2076,plain,
    ( spl0_129
  <=> ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f61,plain,
    ( spl0_10
  <=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f427,plain,
    ( ! [X0,X1] : theorem(or(not(or(or(X0,X1),or(X0,X1))),or(X1,X0)))
    | ~ spl0_10
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f62]) ).

fof(f62,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f61]) ).

fof(f2074,plain,
    ( spl0_128
    | ~ spl0_12
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f424,f418,f72,f2072]) ).

fof(f2072,plain,
    ( spl0_128
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f424,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(or(X0,X2),X1)))
    | ~ spl0_12
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f73]) ).

fof(f2070,plain,
    ( spl0_127
    | ~ spl0_49
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f416,f362,f319,f2068]) ).

fof(f2068,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(f362,plain,
    ( spl0_52
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,X2))
        | ~ theorem(not(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(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,[],[f363,f320]) ).

fof(f363,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X2))
        | theorem(or(X0,X1))
        | ~ theorem(not(X2)) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f362]) ).

fof(f2066,plain,
    ( spl0_126
    | ~ spl0_27
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f408,f362,f172,f2064]) ).

fof(f2064,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(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,[],[f363,f173]) ).

fof(f2062,plain,
    ( spl0_125
    | ~ spl0_47
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f392,f362,f311,f2060]) ).

fof(f2060,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(f392,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X2))
        | ~ theorem(not(X0))
        | ~ theorem(X1) )
    | ~ spl0_47
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f312]) ).

fof(f2058,plain,
    ( ~ spl0_124
    | spl0_102
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f1967,f1832,f1436,f2055]) ).

fof(f2055,plain,
    ( spl0_124
  <=> theorem(or(not(q),p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f1436,plain,
    ( spl0_102
  <=> theorem(or(not(or(not(p),not(q))),not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1832,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1967,plain,
    ( ~ theorem(or(not(q),p))
    | spl0_102
    | ~ spl0_116 ),
    inference(resolution,[],[f1833,f1438]) ).

fof(f1438,plain,
    ( ~ theorem(or(not(or(not(p),not(q))),not(q)))
    | spl0_102 ),
    inference(avatar_component_clause,[],[f1436]) ).

fof(f1833,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(not(X1),X0)),X0))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1832]) ).

fof(f2053,plain,
    ( spl0_123
    | ~ spl0_27
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f388,f358,f172,f2051]) ).

fof(f2051,plain,
    ( spl0_123
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X3)
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f388,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X3)
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_27
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f173]) ).

fof(f2049,plain,
    ( spl0_122
    | ~ spl0_12
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f345,f323,f72,f2047]) ).

fof(f2047,plain,
    ( spl0_122
  <=> ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f323,plain,
    ( spl0_50
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f345,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,or(or(X0,X1),X1))),or(X0,X1)))
    | ~ spl0_12
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f73]) ).

fof(f324,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,X1)) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f323]) ).

fof(f2045,plain,
    ( spl0_121
    | ~ spl0_32
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f326,f311,f198,f2043]) ).

fof(f2043,plain,
    ( spl0_121
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(X2,not(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f198,plain,
    ( spl0_32
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f326,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,X2))
        | ~ theorem(or(X1,or(X2,not(X0)))) )
    | ~ spl0_32
    | ~ spl0_47 ),
    inference(resolution,[],[f312,f199]) ).

fof(f199,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f2041,plain,
    ( spl0_120
    | ~ spl0_17
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f306,f301,f103,f2039]) ).

fof(f2039,plain,
    ( spl0_120
  <=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f306,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(or(not(or(X1,or(X0,X2))),X1),X2)))
    | ~ spl0_17
    | ~ spl0_46 ),
    inference(resolution,[],[f302,f104]) ).

fof(f1941,plain,
    ( ~ spl0_119
    | spl0_102
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f1920,f1808,f1436,f1938]) ).

fof(f1938,plain,
    ( spl0_119
  <=> theorem(not(or(not(q),not(p)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1808,plain,
    ( spl0_111
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),X2))
        | ~ theorem(not(or(X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1920,plain,
    ( ~ theorem(not(or(not(q),not(p))))
    | spl0_102
    | ~ spl0_111 ),
    inference(resolution,[],[f1809,f1438]) ).

fof(f1809,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),X2))
        | ~ theorem(not(or(X1,X0))) )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1808]) ).

fof(f1842,plain,
    ( spl0_118
    | ~ spl0_10
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f551,f526,f61,f1840]) ).

fof(f1840,plain,
    ( spl0_118
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,or(X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f551,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,or(X1,X1)))
        | theorem(or(X0,or(X2,X1))) )
    | ~ spl0_10
    | ~ spl0_63 ),
    inference(resolution,[],[f527,f62]) ).

fof(f1838,plain,
    ( spl0_117
    | ~ spl0_7
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f549,f526,f47,f1836]) ).

fof(f1836,plain,
    ( spl0_117
  <=> ! [X0,X3,X2,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(X0,or(X2,or(X3,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f47,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,[],[f527,f48]) ).

fof(f48,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f1834,plain,
    ( spl0_116
    | ~ spl0_50
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f518,f487,f323,f1832]) ).

fof(f518,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(not(or(not(X1),X0)),X0)) )
    | ~ spl0_50
    | ~ spl0_61 ),
    inference(resolution,[],[f488,f324]) ).

fof(f1830,plain,
    ( spl0_115
    | ~ spl0_50
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f495,f475,f323,f1828]) ).

fof(f1828,plain,
    ( spl0_115
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X1))),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f495,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(not(or(X1,or(not(X0),X1))),X1)) )
    | ~ spl0_50
    | ~ spl0_58 ),
    inference(resolution,[],[f476,f324]) ).

fof(f1826,plain,
    ( ~ spl0_39
    | spl0_104 ),
    inference(avatar_contradiction_clause,[],[f1823]) ).

fof(f1823,plain,
    ( $false
    | ~ spl0_39
    | spl0_104 ),
    inference(resolution,[],[f1656,f262]) ).

fof(f262,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl0_39
  <=> ! [X0] : theorem(or(not(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1656,plain,
    ( ~ theorem(or(not(not(q)),not(q)))
    | spl0_104 ),
    inference(avatar_component_clause,[],[f1654]) ).

fof(f1822,plain,
    ( spl0_114
    | ~ spl0_46
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f415,f362,f301,f1820]) ).

fof(f1820,plain,
    ( spl0_114
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(not(or(X0,X1)),X0),X2))
        | ~ theorem(not(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f415,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(not(or(X0,X1)),X0),X2))
        | ~ theorem(not(X1)) )
    | ~ spl0_46
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f302]) ).

fof(f1818,plain,
    ( spl0_113
    | ~ spl0_25
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f410,f362,f160,f1816]) ).

fof(f1816,plain,
    ( spl0_113
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(or(X1,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f160,plain,
    ( spl0_25
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f410,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(or(X1,X0)))) )
    | ~ spl0_25
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f161]) ).

fof(f161,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f1814,plain,
    ( spl0_112
    | ~ spl0_26
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f403,f362,f164,f1812]) ).

fof(f1812,plain,
    ( spl0_112
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(or(X2,X0)),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(or(X2,X0)),X2))) )
    | ~ spl0_26
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f165]) ).

fof(f1810,plain,
    ( spl0_111
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f393,f362,f67,f1808]) ).

fof(f393,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),X2))
        | ~ theorem(not(or(X1,X0))) )
    | ~ spl0_11
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f68]) ).

fof(f1806,plain,
    ( spl0_110
    | ~ spl0_26
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f383,f358,f164,f1804]) ).

fof(f1804,plain,
    ( spl0_110
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f383,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(X2) )
    | ~ spl0_26
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f165]) ).

fof(f1802,plain,
    ( spl0_109
    | ~ spl0_49
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f356,f323,f319,f1800]) ).

fof(f1800,plain,
    ( spl0_109
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(or(or(X2,X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f356,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(or(or(X2,X2),X1)) )
    | ~ spl0_49
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f320]) ).

fof(f1798,plain,
    ( spl0_108
    | ~ spl0_47
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f348,f323,f311,f1796]) ).

fof(f1796,plain,
    ( spl0_108
  <=> ! [X0,X1] :
        ( theorem(or(not(or(or(X0,X0),not(X1))),X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f348,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(X0,X0),not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_47
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f312]) ).

fof(f1794,plain,
    ( spl0_107
    | ~ spl0_19
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f346,f323,f118,f1792]) ).

fof(f1792,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(f346,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,X1)),X0))
        | ~ theorem(or(not(X1),X0)) )
    | ~ spl0_19
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f119]) ).

fof(f1705,plain,
    ( spl0_106
    | ~ spl0_23
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f604,f587,f144,f1703]) ).

fof(f1703,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(f144,plain,
    ( spl0_23
  <=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f604,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(X1,or(not(or(X1,X2)),X2))))
    | ~ spl0_23
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f145]) ).

fof(f145,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f1701,plain,
    ( spl0_105
    | ~ spl0_7
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f590,f587,f47,f1699]) ).

fof(f1699,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(f590,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(X0,or(X2,X1))))
    | ~ spl0_7
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f48]) ).

fof(f1657,plain,
    ( ~ spl0_103
    | ~ spl0_104
    | ~ spl0_65
    | spl0_102 ),
    inference(avatar_split_clause,[],[f1519,f1436,f534,f1654,f1650]) ).

fof(f1650,plain,
    ( spl0_103
  <=> theorem(p) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1519,plain,
    ( ~ theorem(or(not(not(q)),not(q)))
    | ~ theorem(p)
    | ~ spl0_65
    | spl0_102 ),
    inference(resolution,[],[f1438,f535]) ).

fof(f1439,plain,
    ( ~ spl0_102
    | spl0_1
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f947,f901,f19,f1436]) ).

fof(f901,plain,
    ( spl0_85
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f947,plain,
    ( ~ theorem(or(not(or(not(p),not(q))),not(q)))
    | spl0_1
    | ~ spl0_85 ),
    inference(resolution,[],[f902,f21]) ).

fof(f902,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f901]) ).

fof(f1170,plain,
    ( ~ spl0_101
    | spl0_1
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f995,f932,f19,f1167]) ).

fof(f1167,plain,
    ( spl0_101
  <=> theorem(or(not(p),not(q))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f932,plain,
    ( spl0_93
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f995,plain,
    ( ~ theorem(or(not(p),not(q)))
    | spl0_1
    | ~ spl0_93 ),
    inference(resolution,[],[f933,f21]) ).

fof(f933,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f932]) ).

fof(f1053,plain,
    ( spl0_1
    | ~ spl0_91 ),
    inference(avatar_contradiction_clause,[],[f1044]) ).

fof(f1044,plain,
    ( $false
    | spl0_1
    | ~ spl0_91 ),
    inference(resolution,[],[f925,f21]) ).

fof(f925,plain,
    ( ! [X0,X1] : theorem(or(X0,X1))
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f924]) ).

fof(f924,plain,
    ( spl0_91
  <=> ! [X0,X1] : theorem(or(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1052,plain,
    ( spl0_38
    | ~ spl0_91 ),
    inference(avatar_contradiction_clause,[],[f1045]) ).

fof(f1045,plain,
    ( $false
    | spl0_38
    | ~ spl0_91 ),
    inference(resolution,[],[f925,f256]) ).

fof(f256,plain,
    ( ~ theorem(or(not(p),not(or(not(p),not(q)))))
    | spl0_38 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f254,plain,
    ( spl0_38
  <=> theorem(or(not(p),not(or(not(p),not(q))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1051,plain,
    ( spl0_18
    | ~ spl0_91 ),
    inference(avatar_contradiction_clause,[],[f1048]) ).

fof(f1048,plain,
    ( $false
    | spl0_18
    | ~ spl0_91 ),
    inference(resolution,[],[f925,f115]) ).

fof(f115,plain,
    ( ~ theorem(or(not(q),not(or(not(p),not(q)))))
    | spl0_18 ),
    inference(avatar_component_clause,[],[f113]) ).

fof(f113,plain,
    ( spl0_18
  <=> theorem(or(not(q),not(or(not(p),not(q))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1043,plain,
    ( spl0_100
    | spl0_91
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f407,f362,f287,f924,f1041]) ).

fof(f1041,plain,
    ( spl0_100
  <=> ! [X2,X3] :
        ( ~ theorem(not(or(X2,X3)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f287,plain,
    ( spl0_44
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f407,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(X2,X3)))
        | ~ theorem(X2) )
    | ~ spl0_44
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f288]) ).

fof(f288,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X1,or(X0,X2)))
        | ~ theorem(X0) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f287]) ).

fof(f1039,plain,
    ( spl0_99
    | ~ spl0_22
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f380,f358,f140,f1037]) ).

fof(f1037,plain,
    ( spl0_99
  <=> ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f140,plain,
    ( spl0_22
  <=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f380,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(X1) )
    | ~ spl0_22
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f141]) ).

fof(f141,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f1035,plain,
    ( spl0_98
    | ~ spl0_47
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f372,f358,f311,f1033]) ).

fof(f1033,plain,
    ( spl0_98
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,not(X2)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f372,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,not(X2)))
        | ~ theorem(X2) )
    | ~ spl0_47
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f312]) ).

fof(f1031,plain,
    ( spl0_97
    | ~ spl0_46
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f355,f323,f301,f1029]) ).

fof(f1029,plain,
    ( spl0_97
  <=> ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f355,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,or(X1,X1))),X0),X1))
    | ~ spl0_46
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f302]) ).

fof(f1027,plain,
    ( spl0_96
    | ~ spl0_10
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f347,f323,f61,f1025]) ).

fof(f1025,plain,
    ( spl0_96
  <=> ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f347,plain,
    ( ! [X0] : theorem(or(not(or(or(X0,X0),or(X0,X0))),X0))
    | ~ spl0_10
    | ~ spl0_50 ),
    inference(resolution,[],[f324,f62]) ).

fof(f967,plain,
    ( ~ spl0_95
    | spl0_38
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f939,f897,f254,f964]) ).

fof(f964,plain,
    ( spl0_95
  <=> theorem(q) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f897,plain,
    ( spl0_84
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,not(or(X1,not(X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f939,plain,
    ( ~ theorem(q)
    | spl0_38
    | ~ spl0_84 ),
    inference(resolution,[],[f898,f256]) ).

fof(f898,plain,
    ( ! [X0,X1] :
        ( theorem(or(X1,not(or(X1,not(X0)))))
        | ~ theorem(X0) )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f897]) ).

fof(f938,plain,
    ( spl0_94
    | ~ spl0_44
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f609,f587,f287,f936]) ).

fof(f936,plain,
    ( spl0_94
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f609,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(X2) )
    | ~ spl0_44
    | ~ spl0_67 ),
    inference(resolution,[],[f588,f288]) ).

fof(f934,plain,
    ( spl0_93
    | ~ spl0_27
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f436,f418,f172,f932]) ).

fof(f436,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_27
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f173]) ).

fof(f930,plain,
    ( spl0_92
    | ~ spl0_21
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f409,f362,f136,f928]) ).

fof(f928,plain,
    ( spl0_92
  <=> ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f136,plain,
    ( spl0_21
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f409,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(or(X0,X1),X2))
        | ~ theorem(not(not(X1))) )
    | ~ spl0_21
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f137]) ).

fof(f137,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f926,plain,
    ( spl0_90
    | spl0_91
    | ~ spl0_23
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f402,f362,f144,f924,f921]) ).

fof(f921,plain,
    ( spl0_90
  <=> ! [X2] : ~ theorem(not(or(not(X2),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(or(not(X2),X2))) )
    | ~ spl0_23
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f145]) ).

fof(f919,plain,
    ( spl0_89
    | ~ spl0_22
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f400,f362,f140,f917]) ).

fof(f917,plain,
    ( spl0_89
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(not(or(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f400,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(not(not(or(X0,X0)))) )
    | ~ spl0_22
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f141]) ).

fof(f915,plain,
    ( spl0_88
    | ~ spl0_10
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f391,f362,f61,f913]) ).

fof(f913,plain,
    ( spl0_88
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,X0)),X1))
        | ~ theorem(not(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f391,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,X0)),X1))
        | ~ theorem(not(X0)) )
    | ~ spl0_10
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f62]) ).

fof(f911,plain,
    ( spl0_87
    | ~ spl0_16
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f747,f530,f93,f909]) ).

fof(f909,plain,
    ( spl0_87
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f530,plain,
    ( spl0_64
  <=> ! [X0,X1] : theorem(or(not(X0),or(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f747,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X0)))
    | ~ spl0_16
    | ~ spl0_64 ),
    inference(resolution,[],[f531,f94]) ).

fof(f531,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f530]) ).

fof(f907,plain,
    ( spl0_86
    | ~ spl0_7
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f389,f362,f47,f905]) ).

fof(f905,plain,
    ( spl0_86
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(X0),X1))
        | ~ theorem(not(or(X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f389,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(X0),X1))
        | ~ theorem(not(or(X2,X0))) )
    | ~ spl0_7
    | ~ spl0_52 ),
    inference(resolution,[],[f363,f48]) ).

fof(f903,plain,
    ( spl0_85
    | ~ spl0_11
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f373,f358,f67,f901]) ).

fof(f373,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X2,X1)) )
    | ~ spl0_11
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f68]) ).

fof(f899,plain,
    ( spl0_84
    | ~ spl0_16
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f328,f311,f93,f897]) ).

fof(f328,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,not(or(X1,not(X0))))) )
    | ~ spl0_16
    | ~ spl0_47 ),
    inference(resolution,[],[f312,f94]) ).

fof(f839,plain,
    ( spl0_83
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f431,f418,f164,f837]) ).

fof(f837,plain,
    ( spl0_83
  <=> ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f431,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(or(X1,X0)))))
    | ~ spl0_26
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f165]) ).

fof(f835,plain,
    ( spl0_82
    | ~ spl0_6
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f327,f311,f42,f833]) ).

fof(f833,plain,
    ( spl0_82
  <=> ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(X1,not(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f327,plain,
    ( ! [X0,X1] :
        ( ~ theorem(X0)
        | theorem(X1)
        | ~ theorem(or(X1,not(X0))) )
    | ~ spl0_6
    | ~ spl0_47 ),
    inference(resolution,[],[f312,f43]) ).

fof(f831,plain,
    ( spl0_81
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f285,f280,f103,f829]) ).

fof(f829,plain,
    ( spl0_81
  <=> ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f280,plain,
    ( spl0_43
  <=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f285,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(or(not(X1),X1),X2)))
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(resolution,[],[f281,f104]) ).

fof(f281,plain,
    ( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f827,plain,
    ( spl0_80
    | ~ spl0_17
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f743,f530,f103,f825]) ).

fof(f825,plain,
    ( spl0_80
  <=> ! [X0,X1] : theorem(or(X0,or(not(X0),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f743,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X0),X1)))
    | ~ spl0_17
    | ~ spl0_64 ),
    inference(resolution,[],[f531,f104]) ).

fof(f823,plain,
    ( spl0_79
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f267,f261,f103,f821]) ).

fof(f821,plain,
    ( spl0_79
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f267,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X0,X1)),X1)))
    | ~ spl0_17
    | ~ spl0_39 ),
    inference(resolution,[],[f262,f104]) ).

fof(f774,plain,
    ( spl0_78
    | ~ spl0_7
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f369,f358,f47,f772]) ).

fof(f772,plain,
    ( spl0_78
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f369,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(X2) )
    | ~ spl0_7
    | ~ spl0_51 ),
    inference(resolution,[],[f359,f48]) ).

fof(f770,plain,
    ( spl0_77
    | ~ spl0_48
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f338,f319,f315,f768]) ).

fof(f768,plain,
    ( spl0_77
  <=> ! [X0,X1] :
        ( ~ theorem(or(X0,X0))
        | theorem(or(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f338,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(X0,X0))
        | theorem(or(X1,X0)) )
    | ~ spl0_48
    | ~ spl0_49 ),
    inference(resolution,[],[f320,f316]) ).

fof(f766,plain,
    ( spl0_76
    | ~ spl0_42
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f304,f297,f276,f764]) ).

fof(f764,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ theorem(X0)
        | ~ theorem(or(not(X0),not(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f276,plain,
    ( spl0_42
  <=> ! [X0] :
        ( ~ theorem(not(X0))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f297,plain,
    ( spl0_45
  <=> ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f304,plain,
    ( ! [X0] :
        ( ~ theorem(X0)
        | ~ theorem(or(not(X0),not(X0))) )
    | ~ spl0_42
    | ~ spl0_45 ),
    inference(resolution,[],[f298,f277]) ).

fof(f277,plain,
    ( ! [X0] :
        ( ~ theorem(not(X0))
        | ~ theorem(X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f276]) ).

fof(f298,plain,
    ( ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f297]) ).

fof(f762,plain,
    ( spl0_75
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f295,f287,f93,f760]) ).

fof(f760,plain,
    ( spl0_75
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f295,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(or(X0,X1),X2)) )
    | ~ spl0_16
    | ~ spl0_44 ),
    inference(resolution,[],[f288,f94]) ).

fof(f711,plain,
    ( spl0_74
    | ~ spl0_32
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f230,f223,f198,f709]) ).

fof(f709,plain,
    ( spl0_74
  <=> ! [X0,X3,X2,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(not(X3),X0)),X1)))
        | ~ theorem(or(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f230,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(not(X3),X0)),X1)))
        | ~ theorem(or(X2,X3)) )
    | ~ spl0_32
    | ~ spl0_33 ),
    inference(resolution,[],[f224,f199]) ).

fof(f707,plain,
    ( spl0_73
    | ~ spl0_30
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f219,f198,f189,f705]) ).

fof(f705,plain,
    ( spl0_73
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
        | ~ theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f219,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(or(not(X1),X2),or(not(X1),X2))),X2)))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_30
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f190]) ).

fof(f667,plain,
    ( spl0_72
    | ~ spl0_32
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f244,f240,f198,f665]) ).

fof(f665,plain,
    ( spl0_72
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
        | ~ theorem(or(X0,or(X3,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f240,plain,
    ( spl0_36
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f244,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(not(X1),X2)),or(X3,X2))))
        | ~ theorem(or(X0,or(X3,X1))) )
    | ~ spl0_32
    | ~ spl0_36 ),
    inference(resolution,[],[f241,f199]) ).

fof(f241,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f240]) ).

fof(f663,plain,
    ( spl0_71
    | ~ spl0_29
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f220,f198,f185,f661]) ).

fof(f661,plain,
    ( spl0_71
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f220,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,or(not(X2),X3))),or(X1,X3))))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_29
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f186]) ).

fof(f659,plain,
    ( spl0_70
    | ~ spl0_14
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f213,f198,f81,f657]) ).

fof(f657,plain,
    ( spl0_70
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
        | ~ theorem(or(X0,or(not(X2),X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f81,plain,
    ( spl0_14
  <=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f213,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,X2)),or(X1,X3))))
        | ~ theorem(or(X0,or(not(X2),X3))) )
    | ~ spl0_14
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f82]) ).

fof(f82,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f655,plain,
    ( spl0_69
    | ~ spl0_23
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f430,f418,f144,f653]) ).

fof(f430,plain,
    ( ! [X0,X1] : theorem(or(X0,or(X1,not(X1))))
    | ~ spl0_23
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f145]) ).

fof(f622,plain,
    ( spl0_68
    | ~ spl0_19
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f212,f198,f118,f620]) ).

fof(f212,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X1,X3)))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_19
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f119]) ).

fof(f589,plain,
    ( spl0_67
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f211,f198,f72,f587]) ).

fof(f211,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X2,or(X1,X3)))) )
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f73]) ).

fof(f540,plain,
    ( spl0_66
    | ~ spl0_16
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f247,f240,f93,f538]) ).

fof(f538,plain,
    ( spl0_66
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f247,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
    | ~ spl0_16
    | ~ spl0_36 ),
    inference(resolution,[],[f241,f94]) ).

fof(f536,plain,
    ( spl0_65
    | ~ spl0_6
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f231,f223,f42,f534]) ).

fof(f231,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(not(or(not(X2),X0)),X1))
        | ~ theorem(X2) )
    | ~ spl0_6
    | ~ spl0_33 ),
    inference(resolution,[],[f224,f43]) ).

fof(f532,plain,
    ( spl0_64
    | ~ spl0_7
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f421,f418,f47,f530]) ).

fof(f421,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X0,X1)))
    | ~ spl0_7
    | ~ spl0_54 ),
    inference(resolution,[],[f419,f48]) ).

fof(f528,plain,
    ( spl0_63
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f221,f198,f172,f526]) ).

fof(f221,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X3))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f173]) ).

fof(f524,plain,
    ( spl0_62
    | ~ spl0_6
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f205,f189,f42,f522]) ).

fof(f205,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_30 ),
    inference(resolution,[],[f190,f43]) ).

fof(f489,plain,
    ( spl0_61
    | ~ spl0_6
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f245,f240,f42,f487]) ).

fof(f245,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_36 ),
    inference(resolution,[],[f241,f43]) ).

fof(f485,plain,
    ( spl0_60
    | ~ spl0_16
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f233,f223,f93,f483]) ).

fof(f483,plain,
    ( spl0_60
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f233,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) )
    | ~ spl0_16
    | ~ spl0_33 ),
    inference(resolution,[],[f224,f94]) ).

fof(f481,plain,
    ( spl0_59
    | ~ spl0_26
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f218,f198,f164,f479]) ).

fof(f218,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_26
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f165]) ).

fof(f477,plain,
    ( spl0_58
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f202,f185,f42,f475]) ).

fof(f202,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(resolution,[],[f186,f43]) ).

fof(f453,plain,
    ( spl0_57
    | ~ spl0_22
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f216,f198,f140,f451]) ).

fof(f216,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f141]) ).

fof(f449,plain,
    ( spl0_56
    | ~ spl0_16
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f207,f189,f93,f447]) ).

fof(f447,plain,
    ( spl0_56
  <=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f207,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
    | ~ spl0_16
    | ~ spl0_30 ),
    inference(resolution,[],[f190,f94]) ).

fof(f445,plain,
    ( spl0_55
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f204,f185,f93,f443]) ).

fof(f443,plain,
    ( spl0_55
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f204,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(resolution,[],[f186,f94]) ).

fof(f420,plain,
    ( spl0_54
    | ~ spl0_11
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f210,f198,f67,f418]) ).

fof(f210,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X2,X1))) )
    | ~ spl0_11
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f68]) ).

fof(f368,plain,
    ( spl0_53
    | ~ spl0_6
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f308,f269,f42,f366]) ).

fof(f366,plain,
    ( spl0_53
  <=> ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f269,plain,
    ( spl0_40
  <=> ! [X0] : theorem(or(X0,not(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f308,plain,
    ( ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_40 ),
    inference(resolution,[],[f270,f43]) ).

fof(f270,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f364,plain,
    ( spl0_52
    | ~ spl0_20
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f214,f198,f126,f362]) ).

fof(f126,plain,
    ( spl0_20
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f214,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,X2))
        | ~ theorem(not(X2)) )
    | ~ spl0_20
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f127]) ).

fof(f127,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f360,plain,
    ( spl0_51
    | ~ spl0_6
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f176,f172,f42,f358]) ).

fof(f176,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_27 ),
    inference(resolution,[],[f173,f43]) ).

fof(f325,plain,
    ( spl0_50
    | ~ spl0_10
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f209,f198,f61,f323]) ).

fof(f209,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) )
    | ~ spl0_10
    | ~ spl0_32 ),
    inference(resolution,[],[f199,f62]) ).

fof(f321,plain,
    ( spl0_49
    | ~ spl0_16
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f179,f172,f93,f319]) ).

fof(f179,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) )
    | ~ spl0_16
    | ~ spl0_27 ),
    inference(resolution,[],[f173,f94]) ).

fof(f317,plain,
    ( spl0_48
    | ~ spl0_15
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f178,f172,f86,f315]) ).

fof(f86,plain,
    ( spl0_15
  <=> ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f178,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) )
    | ~ spl0_15
    | ~ spl0_27 ),
    inference(resolution,[],[f173,f87]) ).

fof(f87,plain,
    ( ! [X0] :
        ( ~ theorem(or(X0,X0))
        | theorem(X0) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f313,plain,
    ( spl0_47
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f168,f164,f42,f311]) ).

fof(f168,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(resolution,[],[f165,f43]) ).

fof(f303,plain,
    ( spl0_46
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f170,f164,f93,f301]) ).

fof(f170,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(resolution,[],[f165,f94]) ).

fof(f299,plain,
    ( spl0_45
    | ~ spl0_6
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f148,f140,f42,f297]) ).

fof(f148,plain,
    ( ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_22 ),
    inference(resolution,[],[f141,f43]) ).

fof(f289,plain,
    ( spl0_44
    | ~ spl0_17
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f134,f126,f103,f287]) ).

fof(f134,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) )
    | ~ spl0_17
    | ~ spl0_20 ),
    inference(resolution,[],[f127,f104]) ).

fof(f282,plain,
    ( spl0_43
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f158,f144,f93,f280]) ).

fof(f158,plain,
    ( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
    | ~ spl0_16
    | ~ spl0_23 ),
    inference(resolution,[],[f145,f94]) ).

fof(f278,plain,
    ( spl0_41
    | spl0_42
    | ~ spl0_6
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f130,f126,f42,f276,f273]) ).

fof(f273,plain,
    ( spl0_41
  <=> ! [X1] : theorem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f130,plain,
    ( ! [X0,X1] :
        ( ~ theorem(not(X0))
        | theorem(X1)
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_20 ),
    inference(resolution,[],[f127,f43]) ).

fof(f271,plain,
    ( spl0_40
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f266,f261,f93,f269]) ).

fof(f266,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(resolution,[],[f262,f94]) ).

fof(f263,plain,
    ( spl0_39
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f157,f144,f86,f261]) ).

fof(f157,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_15
    | ~ spl0_23 ),
    inference(resolution,[],[f145,f87]) ).

fof(f257,plain,
    ( ~ spl0_38
    | spl0_1
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f175,f172,f19,f254]) ).

fof(f175,plain,
    ( ~ theorem(or(not(p),not(or(not(p),not(q)))))
    | spl0_1
    | ~ spl0_27 ),
    inference(resolution,[],[f173,f21]) ).

fof(f252,plain,
    ( ~ spl0_37
    | ~ spl0_13
    | spl0_18 ),
    inference(avatar_split_clause,[],[f124,f113,f76,f249]) ).

fof(f249,plain,
    ( spl0_37
  <=> theorem(not(or(not(p),not(q)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f76,plain,
    ( spl0_13
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f124,plain,
    ( ~ theorem(not(or(not(p),not(q))))
    | ~ spl0_13
    | spl0_18 ),
    inference(resolution,[],[f115,f77]) ).

fof(f77,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f242,plain,
    ( spl0_36
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f110,f103,f81,f240]) ).

fof(f110,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f82]) ).

fof(f238,plain,
    ( spl0_35
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f100,f93,f81,f236]) ).

fof(f236,plain,
    ( spl0_35
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f100,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f82]) ).

fof(f229,plain,
    ( spl0_34
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f123,f118,f93,f227]) ).

fof(f227,plain,
    ( spl0_34
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f123,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) )
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(resolution,[],[f119,f94]) ).

fof(f225,plain,
    ( spl0_33
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f122,f118,f103,f223]) ).

fof(f122,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) )
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(resolution,[],[f119,f104]) ).

fof(f200,plain,
    ( spl0_32
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f121,f118,f42,f198]) ).

fof(f121,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(resolution,[],[f119,f43]) ).

fof(f196,plain,
    ( ~ spl0_31
    | spl0_18
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f131,f126,f113,f193]) ).

fof(f193,plain,
    ( spl0_31
  <=> theorem(not(q)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f131,plain,
    ( ~ theorem(not(q))
    | spl0_18
    | ~ spl0_20 ),
    inference(resolution,[],[f127,f115]) ).

fof(f191,plain,
    ( spl0_30
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f109,f103,f61,f189]) ).

fof(f109,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f62]) ).

fof(f187,plain,
    ( spl0_29
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f108,f103,f72,f185]) ).

fof(f108,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f73]) ).

fof(f183,plain,
    ( spl0_28
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f99,f93,f72,f181]) ).

fof(f181,plain,
    ( spl0_28
  <=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f99,plain,
    ( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f73]) ).

fof(f174,plain,
    ( spl0_27
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f111,f103,f76,f172]) ).

fof(f111,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f77]) ).

fof(f166,plain,
    ( spl0_26
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f107,f103,f67,f164]) ).

fof(f107,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f68]) ).

fof(f162,plain,
    ( spl0_25
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f98,f93,f67,f160]) ).

fof(f98,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f68]) ).

fof(f154,plain,
    ( ~ spl0_24
    | spl0_1
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f129,f126,f19,f151]) ).

fof(f151,plain,
    ( spl0_24
  <=> theorem(not(p)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f129,plain,
    ( ~ theorem(not(p))
    | spl0_1
    | ~ spl0_20 ),
    inference(resolution,[],[f127,f21]) ).

fof(f146,plain,
    ( spl0_23
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f106,f103,f47,f144]) ).

fof(f106,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(resolution,[],[f104,f48]) ).

fof(f142,plain,
    ( spl0_22
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f93,f61,f140]) ).

fof(f97,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f62]) ).

fof(f138,plain,
    ( spl0_21
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f96,f93,f47,f136]) ).

fof(f96,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f48]) ).

fof(f128,plain,
    ( spl0_20
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f101,f93,f76,f126]) ).

fof(f101,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(resolution,[],[f94,f77]) ).

fof(f120,plain,
    ( spl0_19
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f84,f81,f42,f118]) ).

fof(f84,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(resolution,[],[f82,f43]) ).

fof(f116,plain,
    ( ~ spl0_18
    | spl0_1
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f89,f76,f19,f113]) ).

fof(f89,plain,
    ( ~ theorem(or(not(q),not(or(not(p),not(q)))))
    | spl0_1
    | ~ spl0_13 ),
    inference(resolution,[],[f77,f21]) ).

fof(f105,plain,
    ( spl0_17
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f79,f72,f42,f103]) ).

fof(f79,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X1,or(X0,X2))) )
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(resolution,[],[f73,f43]) ).

fof(f95,plain,
    ( spl0_16
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f70,f67,f42,f93]) ).

fof(f70,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X1,X0)) )
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(resolution,[],[f68,f43]) ).

fof(f88,plain,
    ( spl0_15
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f65,f61,f42,f86]) ).

fof(f65,plain,
    ( ! [X0] :
        ( theorem(X0)
        | ~ theorem(or(X0,X0)) )
    | ~ spl0_6
    | ~ spl0_10 ),
    inference(resolution,[],[f62,f43]) ).

fof(f83,plain,
    ( spl0_14
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f59,f56,f24,f81]) ).

fof(f24,plain,
    ( spl0_2
  <=> ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f56,plain,
    ( spl0_9
  <=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f59,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_2
    | ~ spl0_9 ),
    inference(resolution,[],[f57,f25]) ).

fof(f25,plain,
    ( ! [X3] :
        ( ~ axiom(X3)
        | theorem(X3) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f57,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f78,plain,
    ( spl0_13
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f64,f47,f42,f76]) ).

fof(f64,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(resolution,[],[f48,f43]) ).

fof(f74,plain,
    ( spl0_12
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(avatar_split_clause,[],[f54,f51,f24,f72]) ).

fof(f51,plain,
    ( spl0_8
  <=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f54,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_2
    | ~ spl0_8 ),
    inference(resolution,[],[f52,f25]) ).

fof(f52,plain,
    ( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f69,plain,
    ( spl0_11
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f45,f38,f24,f67]) ).

fof(f38,plain,
    ( spl0_5
  <=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f45,plain,
    ( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_5 ),
    inference(resolution,[],[f39,f25]) ).

fof(f39,plain,
    ( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f38]) ).

fof(f63,plain,
    ( spl0_10
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f36,f32,f24,f61]) ).

fof(f32,plain,
    ( spl0_4
  <=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f36,plain,
    ( ! [X0] : theorem(or(not(or(X0,X0)),X0))
    | ~ spl0_2
    | ~ spl0_4 ),
    inference(resolution,[],[f33,f25]) ).

fof(f33,plain,
    ( ! [X0] : axiom(or(not(or(X0,X0)),X0))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f32]) ).

fof(f58,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f15,f56]) ).

fof(f15,plain,
    ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
    inference(definition_unfolding,[],[f5,f6,f6,f6]) ).

fof(f6,axiom,
    ! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).

fof(f5,axiom,
    ! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).

fof(f53,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f16,f51]) ).

fof(f16,plain,
    ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
    inference(definition_unfolding,[],[f4,f6]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).

fof(f49,plain,
    ( spl0_7
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f35,f28,f24,f47]) ).

fof(f28,plain,
    ( spl0_3
  <=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f35,plain,
    ( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(resolution,[],[f29,f25]) ).

fof(f29,plain,
    ( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f28]) ).

fof(f44,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f17,f42]) ).

fof(f17,plain,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(or(not(X4),X3)) ),
    inference(definition_unfolding,[],[f8,f6]) ).

fof(f8,axiom,
    ! [X3,X4] :
      ( ~ theorem(X4)
      | theorem(X3)
      | ~ theorem(implies(X4,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).

fof(f40,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f14,f38]) ).

fof(f14,plain,
    ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
    inference(definition_unfolding,[],[f3,f6]) ).

fof(f3,axiom,
    ! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).

fof(f34,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f13,f32]) ).

fof(f13,plain,
    ! [X0] : axiom(or(not(or(X0,X0)),X0)),
    inference(definition_unfolding,[],[f1,f6]) ).

fof(f1,axiom,
    ! [X0] : axiom(implies(or(X0,X0),X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).

fof(f30,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f12,f28]) ).

fof(f12,plain,
    ! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
    inference(definition_unfolding,[],[f2,f6]) ).

fof(f2,axiom,
    ! [X0,X1] : axiom(implies(X0,or(X1,X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).

fof(f26,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f7,f24]) ).

fof(f7,axiom,
    ! [X3] :
      ( ~ axiom(X3)
      | theorem(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).

fof(f22,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f11,f19]) ).

fof(f11,plain,
    ~ theorem(or(not(p),or(not(q),not(or(not(p),not(q)))))),
    inference(definition_unfolding,[],[f10,f6,f6,f9]) ).

fof(f9,axiom,
    ! [X6,X5] : and(X5,X6) = not(or(not(X5),not(X6))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).

fof(f10,axiom,
    ~ theorem(implies(p,implies(q,and(p,q)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : LCL234-3 : TPTP v8.2.0. Released v2.3.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 01:01:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (8663)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38  % (8667)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38  % (8668)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)
% 0.20/0.38  % (8669)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)
% 0.20/0.38  % (8666)WARNING: value z3 for option sas not known
% 0.20/0.38  TRYING [1]
% 0.20/0.38  % (8665)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (8664)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38  TRYING [2]
% 0.20/0.38  % (8670)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)
% 0.20/0.38  % (8666)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)
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [3]
% 0.20/0.39  TRYING [3]
% 0.20/0.40  TRYING [4]
% 0.20/0.40  TRYING [4]
% 0.20/0.46  TRYING [5]
% 0.20/0.46  TRYING [5]
% 0.20/0.54  % (8668)First to succeed.
% 0.20/0.55  % (8668)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8663"
% 0.20/0.55  % (8668)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (8668)------------------------------
% 0.20/0.55  % (8668)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.55  % (8668)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (8668)Memory used [KB]: 2197
% 0.20/0.55  % (8668)Time elapsed: 0.175 s
% 0.20/0.55  % (8668)Instructions burned: 298 (million)
% 0.20/0.55  % (8663)Success in time 0.19 s
%------------------------------------------------------------------------------