TSTP Solution File: LCL239-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL239-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : 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 Apr 30 13:41:20 EDT 2024

% Result   : Unsatisfiable 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   73
% Syntax   : Number of formulae    :  231 (  23 unt;   0 def)
%            Number of atoms       :  643 (   2 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  763 ( 351   ~; 349   |;   0   &)
%                                         (  63 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   67 (  65 usr;  64 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  366 ( 366   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f596,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f26,f30,f34,f40,f44,f49,f53,f58,f63,f69,f74,f78,f83,f88,f94,f104,f114,f118,f129,f133,f137,f148,f152,f156,f164,f172,f176,f180,f184,f213,f217,f226,f230,f235,f246,f250,f257,f266,f270,f280,f284,f288,f292,f327,f331,f335,f387,f412,f416,f420,f445,f449,f453,f457,f492,f497,f501,f505,f509,f558,f591,f595]) ).

fof(f595,plain,
    ( ~ spl0_35
    | spl0_58 ),
    inference(avatar_contradiction_clause,[],[f592]) ).

fof(f592,plain,
    ( $false
    | ~ spl0_35
    | spl0_58 ),
    inference(resolution,[],[f496,f234]) ).

fof(f234,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f233,plain,
    ( spl0_35
  <=> ! [X0] : theorem(or(X0,not(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f496,plain,
    ( ~ theorem(or(not(p),not(not(p))))
    | spl0_58 ),
    inference(avatar_component_clause,[],[f494]) ).

fof(f494,plain,
    ( spl0_58
  <=> theorem(or(not(p),not(not(p)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f591,plain,
    ( spl0_63
    | ~ spl0_19
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f200,f182,f116,f589]) ).

fof(f589,plain,
    ( spl0_63
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X1,X3)))
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f116,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(f182,plain,
    ( spl0_30
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f200,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X1,X3)))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_19
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f117]) ).

fof(f117,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,X1)),or(X0,X2)))
        | ~ theorem(or(not(X1),X2)) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f116]) ).

fof(f183,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f558,plain,
    ( spl0_62
    | ~ spl0_12
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f199,f182,f72,f556]) ).

fof(f556,plain,
    ( spl0_62
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X2,or(X1,X3)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(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(f199,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,or(X2,X3))))
        | ~ theorem(or(X0,or(X2,or(X1,X3)))) )
    | ~ spl0_12
    | ~ spl0_30 ),
    inference(resolution,[],[f183,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(f509,plain,
    ( spl0_61
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f239,f228,f92,f507]) ).

fof(f507,plain,
    ( spl0_61
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

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

fof(f228,plain,
    ( spl0_34
  <=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f239,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(not(X0),X1)),or(X2,X1)),not(or(X2,X0))))
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(resolution,[],[f229,f93]) ).

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

fof(f229,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f228]) ).

fof(f505,plain,
    ( spl0_60
    | ~ spl0_6
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f219,f211,f42,f503]) ).

fof(f503,plain,
    ( spl0_60
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(not(or(not(X2),X0)),X1))
        | ~ theorem(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

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

fof(f211,plain,
    ( spl0_31
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f219,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(not(or(not(X2),X0)),X1))
        | ~ theorem(X2) )
    | ~ spl0_6
    | ~ spl0_31 ),
    inference(resolution,[],[f212,f43]) ).

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

fof(f212,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X2,or(not(or(X2,X0)),X1)))
        | ~ theorem(or(not(X0),X1)) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f501,plain,
    ( spl0_59
    | ~ spl0_26
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f209,f182,f162,f499]) ).

fof(f499,plain,
    ( spl0_59
  <=> ! [X0,X3,X2,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X3))
        | ~ theorem(or(not(X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f162,plain,
    ( spl0_26
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f209,plain,
    ( ! [X2,X3,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X3))
        | ~ theorem(or(not(X3),X2)) )
    | ~ spl0_26
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f163]) ).

fof(f163,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f162]) ).

fof(f497,plain,
    ( ~ spl0_58
    | spl0_1
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f433,f329,f19,f494]) ).

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

fof(f329,plain,
    ( spl0_47
  <=> ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f433,plain,
    ( ~ theorem(or(not(p),not(not(p))))
    | spl0_1
    | ~ spl0_47 ),
    inference(resolution,[],[f330,f21]) ).

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

fof(f330,plain,
    ( ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f329]) ).

fof(f492,plain,
    ( spl0_57
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f192,f178,f42,f490]) ).

fof(f490,plain,
    ( spl0_57
  <=> ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f178,plain,
    ( spl0_29
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f192,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(or(not(X0),X1),or(not(X0),X1))),X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_29 ),
    inference(resolution,[],[f179,f43]) ).

fof(f179,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f457,plain,
    ( spl0_56
    | ~ spl0_6
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f237,f228,f42,f455]) ).

fof(f455,plain,
    ( spl0_56
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f237,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(not(X0),X1)),or(X2,X1)))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_34 ),
    inference(resolution,[],[f229,f43]) ).

fof(f453,plain,
    ( spl0_55
    | ~ spl0_16
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f221,f211,f92,f451]) ).

fof(f451,plain,
    ( spl0_55
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f221,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(not(or(X2,X0)),X1),X2)) )
    | ~ spl0_16
    | ~ spl0_31 ),
    inference(resolution,[],[f212,f93]) ).

fof(f449,plain,
    ( spl0_54
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f206,f182,f154,f447]) ).

fof(f447,plain,
    ( spl0_54
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f154,plain,
    ( spl0_25
  <=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f206,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(not(or(X1,not(X2))),X1)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_25
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f155]) ).

fof(f155,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f154]) ).

fof(f445,plain,
    ( spl0_53
    | ~ spl0_6
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f189,f174,f42,f443]) ).

fof(f443,plain,
    ( spl0_53
  <=> ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f174,plain,
    ( spl0_28
  <=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f189,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(not(or(X0,or(not(X1),X2))),or(X0,X2)))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_28 ),
    inference(resolution,[],[f175,f43]) ).

fof(f175,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f420,plain,
    ( spl0_52
    | ~ spl0_21
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f204,f182,f131,f418]) ).

fof(f418,plain,
    ( spl0_52
  <=> ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f131,plain,
    ( spl0_21
  <=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f204,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,not(or(not(X1),not(X1)))))
        | ~ theorem(or(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f132]) ).

fof(f132,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f416,plain,
    ( spl0_51
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f194,f178,f92,f414]) ).

fof(f414,plain,
    ( spl0_51
  <=> ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f194,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(or(X0,X1),or(X0,X1))),X1),X0))
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(resolution,[],[f179,f93]) ).

fof(f412,plain,
    ( spl0_50
    | ~ spl0_16
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f191,f174,f92,f410]) ).

fof(f410,plain,
    ( spl0_50
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f191,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,or(X1,X2))),or(X0,X2)),X1))
    | ~ spl0_16
    | ~ spl0_28 ),
    inference(resolution,[],[f175,f93]) ).

fof(f387,plain,
    ( spl0_49
    | ~ spl0_11
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f198,f182,f67,f385]) ).

fof(f385,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X2,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

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

fof(f198,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,or(X2,X1))) )
    | ~ spl0_11
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f68]) ).

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

fof(f335,plain,
    ( spl0_48
    | ~ spl0_18
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f202,f182,f112,f333]) ).

fof(f333,plain,
    ( spl0_48
  <=> ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,X2))
        | ~ theorem(not(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f112,plain,
    ( spl0_18
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f202,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,X2))
        | ~ theorem(not(X2)) )
    | ~ spl0_18
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f113]) ).

fof(f113,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f331,plain,
    ( spl0_47
    | ~ spl0_6
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f273,f233,f42,f329]) ).

fof(f273,plain,
    ( ! [X0] :
        ( theorem(not(not(X0)))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_35 ),
    inference(resolution,[],[f234,f43]) ).

fof(f327,plain,
    ( spl0_46
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f165,f162,f42,f325]) ).

fof(f325,plain,
    ( spl0_46
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f165,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_26 ),
    inference(resolution,[],[f163,f43]) ).

fof(f292,plain,
    ( spl0_45
    | ~ spl0_10
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f197,f182,f61,f290]) ).

fof(f290,plain,
    ( spl0_45
  <=> ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

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

fof(f197,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(or(X0,or(X1,X1))) )
    | ~ spl0_10
    | ~ spl0_30 ),
    inference(resolution,[],[f183,f62]) ).

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

fof(f288,plain,
    ( spl0_44
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f168,f162,f92,f286]) ).

fof(f286,plain,
    ( spl0_44
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f168,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(X0,X1))
        | theorem(or(or(X2,X1),X0)) )
    | ~ spl0_16
    | ~ spl0_26 ),
    inference(resolution,[],[f163,f93]) ).

fof(f284,plain,
    ( spl0_43
    | ~ spl0_15
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f167,f162,f86,f282]) ).

fof(f282,plain,
    ( spl0_43
  <=> ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

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

fof(f167,plain,
    ( ! [X0,X1] :
        ( ~ theorem(or(or(X0,X1),X1))
        | theorem(or(X0,X1)) )
    | ~ spl0_15
    | ~ spl0_26 ),
    inference(resolution,[],[f163,f87]) ).

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

fof(f280,plain,
    ( spl0_42
    | ~ spl0_6
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f158,f154,f42,f278]) ).

fof(f278,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f158,plain,
    ( ! [X0,X1] :
        ( theorem(or(not(or(X0,not(X1))),X0))
        | ~ theorem(X1) )
    | ~ spl0_6
    | ~ spl0_25 ),
    inference(resolution,[],[f155,f43]) ).

fof(f270,plain,
    ( spl0_41
    | ~ spl0_16
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f160,f154,f92,f268]) ).

fof(f268,plain,
    ( spl0_41
  <=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f160,plain,
    ( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
    | ~ spl0_16
    | ~ spl0_25 ),
    inference(resolution,[],[f155,f93]) ).

fof(f266,plain,
    ( spl0_40
    | ~ spl0_6
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f139,f131,f42,f264]) ).

fof(f264,plain,
    ( spl0_40
  <=> ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f139,plain,
    ( ! [X0] :
        ( theorem(not(or(not(X0),not(X0))))
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_21 ),
    inference(resolution,[],[f132,f43]) ).

fof(f257,plain,
    ( spl0_39
    | ~ spl0_17
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f125,f112,f102,f255]) ).

fof(f255,plain,
    ( spl0_39
  <=> ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

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

fof(f125,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(X0)
        | theorem(or(X1,or(X0,X2))) )
    | ~ spl0_17
    | ~ spl0_18 ),
    inference(resolution,[],[f113,f103]) ).

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

fof(f250,plain,
    ( spl0_38
    | ~ spl0_16
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f144,f135,f92,f248]) ).

fof(f248,plain,
    ( spl0_38
  <=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f135,plain,
    ( spl0_22
  <=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f144,plain,
    ( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
    | ~ spl0_16
    | ~ spl0_22 ),
    inference(resolution,[],[f136,f93]) ).

fof(f136,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f246,plain,
    ( spl0_36
    | spl0_37
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f122,f112,f42,f244,f241]) ).

fof(f241,plain,
    ( spl0_36
  <=> ! [X1] : theorem(X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f244,plain,
    ( spl0_37
  <=> ! [X0] :
        ( ~ theorem(not(X0))
        | ~ theorem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f122,plain,
    ( ! [X0,X1] :
        ( ~ theorem(not(X0))
        | theorem(X1)
        | ~ theorem(X0) )
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(resolution,[],[f113,f43]) ).

fof(f235,plain,
    ( spl0_35
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f187,f150,f92,f233]) ).

fof(f150,plain,
    ( spl0_24
  <=> ! [X0] : theorem(or(not(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f187,plain,
    ( ! [X0] : theorem(or(X0,not(X0)))
    | ~ spl0_16
    | ~ spl0_24 ),
    inference(resolution,[],[f151,f93]) ).

fof(f151,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f230,plain,
    ( spl0_34
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f109,f102,f81,f228]) ).

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(f109,plain,
    ( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
    | ~ spl0_14
    | ~ spl0_17 ),
    inference(resolution,[],[f103,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(f226,plain,
    ( spl0_33
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f99,f92,f81,f224]) ).

fof(f224,plain,
    ( spl0_33
  <=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f99,plain,
    ( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f82]) ).

fof(f217,plain,
    ( spl0_32
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f121,f116,f92,f215]) ).

fof(f215,plain,
    ( spl0_32
  <=> ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f121,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(or(X2,X1),not(or(X2,X0)))) )
    | ~ spl0_16
    | ~ spl0_19 ),
    inference(resolution,[],[f117,f93]) ).

fof(f213,plain,
    ( spl0_31
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f120,f116,f102,f211]) ).

fof(f120,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,or(not(or(X2,X0)),X1))) )
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(resolution,[],[f117,f103]) ).

fof(f184,plain,
    ( spl0_30
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f119,f116,f42,f182]) ).

fof(f119,plain,
    ( ! [X2,X0,X1] :
        ( ~ theorem(or(not(X0),X1))
        | theorem(or(X2,X1))
        | ~ theorem(or(X2,X0)) )
    | ~ spl0_6
    | ~ spl0_19 ),
    inference(resolution,[],[f117,f43]) ).

fof(f180,plain,
    ( spl0_29
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f108,f102,f61,f178]) ).

fof(f108,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
    | ~ spl0_10
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f62]) ).

fof(f176,plain,
    ( spl0_28
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f107,f102,f72,f174]) ).

fof(f107,plain,
    ( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
    | ~ spl0_12
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f73]) ).

fof(f172,plain,
    ( spl0_27
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f98,f92,f72,f170]) ).

fof(f170,plain,
    ( spl0_27
  <=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f98,plain,
    ( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f73]) ).

fof(f164,plain,
    ( spl0_26
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f110,f102,f76,f162]) ).

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

fof(f110,plain,
    ( ! [X2,X0,X1] :
        ( theorem(or(X0,or(X1,X2)))
        | ~ theorem(or(X0,X2)) )
    | ~ spl0_13
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f77]) ).

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

fof(f156,plain,
    ( spl0_25
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f106,f102,f67,f154]) ).

fof(f106,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f68]) ).

fof(f152,plain,
    ( spl0_24
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f143,f135,f86,f150]) ).

fof(f143,plain,
    ( ! [X0] : theorem(or(not(X0),X0))
    | ~ spl0_15
    | ~ spl0_22 ),
    inference(resolution,[],[f136,f87]) ).

fof(f148,plain,
    ( spl0_23
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f92,f67,f146]) ).

fof(f146,plain,
    ( spl0_23
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f97,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
    | ~ spl0_11
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f68]) ).

fof(f137,plain,
    ( spl0_22
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f105,f102,f47,f135]) ).

fof(f47,plain,
    ( spl0_7
  <=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f105,plain,
    ( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
    | ~ spl0_7
    | ~ spl0_17 ),
    inference(resolution,[],[f103,f48]) ).

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

fof(f133,plain,
    ( spl0_21
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f96,f92,f61,f131]) ).

fof(f96,plain,
    ( ! [X0] : theorem(or(X0,not(or(X0,X0))))
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f62]) ).

fof(f129,plain,
    ( spl0_20
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f95,f92,f47,f127]) ).

fof(f127,plain,
    ( spl0_20
  <=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f95,plain,
    ( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
    | ~ spl0_7
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f48]) ).

fof(f118,plain,
    ( spl0_19
    | ~ spl0_6
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f84,f81,f42,f116]) ).

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(f114,plain,
    ( spl0_18
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f100,f92,f76,f112]) ).

fof(f100,plain,
    ( ! [X0,X1] :
        ( theorem(or(X0,X1))
        | ~ theorem(X0) )
    | ~ spl0_13
    | ~ spl0_16 ),
    inference(resolution,[],[f93,f77]) ).

fof(f104,plain,
    ( spl0_17
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f79,f72,f42,f102]) ).

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(f94,plain,
    ( spl0_16
    | ~ spl0_6
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f70,f67,f42,f92]) ).

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(not(not(or(not(p),not(not(p)))))),
    inference(definition_unfolding,[],[f10,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(not(and(p,not(p)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : LCL239-3 : TPTP v8.1.2. Released v2.3.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Apr 29 23:03:47 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (5313)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (5317)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (5316)WARNING: value z3 for option sas not known
% 0.15/0.37  TRYING [1]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  % (5314)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  % (5315)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (5318)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37  % (5316)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37  % (5319)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37  % (5320)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37  TRYING [1]
% 0.15/0.37  TRYING [2]
% 0.15/0.37  TRYING [3]
% 0.15/0.37  TRYING [3]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  TRYING [4]
% 0.15/0.39  % (5318)First to succeed.
% 0.15/0.39  % (5318)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (5318)------------------------------
% 0.15/0.39  % (5318)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (5318)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (5318)Memory used [KB]: 1096
% 0.15/0.39  % (5318)Time elapsed: 0.023 s
% 0.15/0.39  % (5318)Instructions burned: 36 (million)
% 0.15/0.39  % (5318)------------------------------
% 0.15/0.39  % (5318)------------------------------
% 0.15/0.40  % (5313)Success in time 0.027 s
%------------------------------------------------------------------------------