TSTP Solution File: KLE009+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KLE009+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 07:16:48 EDT 2024

% Result   : Theorem 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   93
% Syntax   : Number of formulae    :  338 (  51 unt;   0 def)
%            Number of atoms       : 1031 ( 246 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 1260 ( 567   ~; 565   |;  34   &)
%                                         (  80 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   77 (  75 usr;  73 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  381 ( 370   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1333,plain,
    $false,
    inference(avatar_sat_refutation,[],[f79,f84,f88,f92,f96,f100,f104,f108,f112,f116,f120,f124,f130,f138,f142,f146,f150,f166,f170,f182,f193,f198,f202,f206,f241,f245,f309,f313,f323,f327,f348,f352,f356,f377,f381,f386,f407,f411,f415,f422,f426,f431,f435,f439,f443,f447,f451,f476,f494,f517,f522,f526,f531,f535,f540,f544,f548,f552,f556,f560,f883,f988,f1032,f1036,f1170,f1172,f1195,f1199,f1203,f1323,f1327,f1331,f1332]) ).

fof(f1332,plain,
    ( ~ spl3_62
    | ~ spl3_1
    | ~ spl3_2
    | ~ spl3_6
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(avatar_split_clause,[],[f704,f529,f445,f243,f239,f190,f128,f98,f81,f76,f880]) ).

fof(f880,plain,
    ( spl3_62
  <=> leq(one,one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_62])]) ).

fof(f76,plain,
    ( spl3_1
  <=> test(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f81,plain,
    ( spl3_2
  <=> test(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f98,plain,
    ( spl3_6
  <=> ! [X0] : multiplication(X0,one) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f128,plain,
    ( spl3_13
  <=> ! [X0,X1] : addition(X0,X1) = addition(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f190,plain,
    ( spl3_22
  <=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

fof(f239,plain,
    ( spl3_26
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

fof(f243,plain,
    ( spl3_27
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f445,plain,
    ( spl3_47
  <=> ! [X0] :
        ( one = addition(X0,c(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_47])]) ).

fof(f529,plain,
    ( spl3_54
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_54])]) ).

fof(f704,plain,
    ( ~ leq(one,one)
    | ~ spl3_1
    | ~ spl3_2
    | ~ spl3_6
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f703,f479]) ).

fof(f479,plain,
    ( one = addition(sK0,c(sK0))
    | ~ spl3_2
    | ~ spl3_47 ),
    inference(resolution,[],[f446,f83]) ).

fof(f83,plain,
    ( test(sK0)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f446,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | one = addition(X0,c(X0)) )
    | ~ spl3_47 ),
    inference(avatar_component_clause,[],[f445]) ).

fof(f703,plain,
    ( ~ leq(addition(sK0,c(sK0)),one)
    | ~ spl3_1
    | ~ spl3_6
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f702,f99]) ).

fof(f99,plain,
    ( ! [X0] : multiplication(X0,one) = X0
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f98]) ).

fof(f702,plain,
    ( ~ leq(multiplication(addition(sK0,c(sK0)),one),one)
    | ~ spl3_1
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f701,f480]) ).

fof(f480,plain,
    ( one = addition(sK1,c(sK1))
    | ~ spl3_1
    | ~ spl3_47 ),
    inference(resolution,[],[f446,f78]) ).

fof(f78,plain,
    ( test(sK1)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f701,plain,
    ( ~ leq(multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))),one)
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f700,f244]) ).

fof(f244,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2))
    | ~ spl3_27 ),
    inference(avatar_component_clause,[],[f243]) ).

fof(f700,plain,
    ( ~ leq(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(sK1,c(sK1)))),one)
    | ~ spl3_13
    | spl3_22
    | ~ spl3_26
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f699,f129]) ).

fof(f129,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X1,X0)
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f128]) ).

fof(f699,plain,
    ( ~ leq(addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(c(sK1),sK1))),one)
    | spl3_22
    | ~ spl3_26
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f665,f610]) ).

fof(f610,plain,
    ( ! [X2,X3,X0,X1] : addition(X3,multiplication(X0,addition(X1,X2))) = addition(multiplication(X0,X2),addition(X3,multiplication(X0,X1)))
    | ~ spl3_26
    | ~ spl3_54 ),
    inference(superposition,[],[f530,f240]) ).

fof(f240,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2))
    | ~ spl3_26 ),
    inference(avatar_component_clause,[],[f239]) ).

fof(f530,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
    | ~ spl3_54 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f665,plain,
    ( ~ leq(addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),c(sK1)))),one)
    | spl3_22
    | ~ spl3_54 ),
    inference(superposition,[],[f192,f530]) ).

fof(f192,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
    | spl3_22 ),
    inference(avatar_component_clause,[],[f190]) ).

fof(f1331,plain,
    ( spl3_72
    | ~ spl3_25
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f284,f243,f204,f1329]) ).

fof(f1329,plain,
    ( spl3_72
  <=> ! [X0,X3,X2,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_72])]) ).

fof(f204,plain,
    ( spl3_25
  <=> ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

fof(f284,plain,
    ( ! [X2,X3,X0,X1] : multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2)))
    | ~ spl3_25
    | ~ spl3_27 ),
    inference(superposition,[],[f244,f205]) ).

fof(f205,plain,
    ( ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2)
    | ~ spl3_25 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f1327,plain,
    ( spl3_71
    | ~ spl3_25
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f279,f243,f204,f1325]) ).

fof(f1325,plain,
    ( spl3_71
  <=> ! [X0,X3,X2,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_71])]) ).

fof(f279,plain,
    ( ! [X2,X3,X0,X1] : multiplication(addition(multiplication(X0,X1),X3),X2) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2))
    | ~ spl3_25
    | ~ spl3_27 ),
    inference(superposition,[],[f244,f205]) ).

fof(f1323,plain,
    ( spl3_70
    | ~ spl3_24
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f260,f239,f200,f1321]) ).

fof(f1321,plain,
    ( spl3_70
  <=> ! [X0,X3,X2,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_70])]) ).

fof(f200,plain,
    ( spl3_24
  <=> ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f260,plain,
    ( ! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3)
    | ~ spl3_24
    | ~ spl3_26 ),
    inference(superposition,[],[f201,f240]) ).

fof(f201,plain,
    ( ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0)
    | ~ spl3_24 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f1203,plain,
    ( spl3_69
    | ~ spl3_10
    | ~ spl3_29 ),
    inference(avatar_split_clause,[],[f319,f311,f114,f1201]) ).

fof(f1201,plain,
    ( spl3_69
  <=> ! [X0,X1] :
        ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
        | ~ test(X0)
        | zero = c(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_69])]) ).

fof(f114,plain,
    ( spl3_10
  <=> ! [X0] :
        ( zero = c(X0)
        | test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f311,plain,
    ( spl3_29
  <=> ! [X0,X1] :
        ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
        | ~ test(X1)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_29])]) ).

fof(f319,plain,
    ( ! [X0,X1] :
        ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
        | ~ test(X0)
        | zero = c(X1) )
    | ~ spl3_10
    | ~ spl3_29 ),
    inference(resolution,[],[f312,f115]) ).

fof(f115,plain,
    ( ! [X0] :
        ( test(X0)
        | zero = c(X0) )
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f312,plain,
    ( ! [X0,X1] :
        ( ~ test(X1)
        | c(multiplication(X0,X1)) = addition(c(X0),c(X1))
        | ~ test(X0) )
    | ~ spl3_29 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f1199,plain,
    ( spl3_68
    | ~ spl3_10
    | ~ spl3_28 ),
    inference(avatar_split_clause,[],[f316,f307,f114,f1197]) ).

fof(f1197,plain,
    ( spl3_68
  <=> ! [X0,X1] :
        ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
        | ~ test(X0)
        | zero = c(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_68])]) ).

fof(f307,plain,
    ( spl3_28
  <=> ! [X0,X1] :
        ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
        | ~ test(X1)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_28])]) ).

fof(f316,plain,
    ( ! [X0,X1] :
        ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
        | ~ test(X0)
        | zero = c(X1) )
    | ~ spl3_10
    | ~ spl3_28 ),
    inference(resolution,[],[f308,f115]) ).

fof(f308,plain,
    ( ! [X0,X1] :
        ( ~ test(X1)
        | multiplication(c(X0),c(X1)) = c(addition(X0,X1))
        | ~ test(X0) )
    | ~ spl3_28 ),
    inference(avatar_component_clause,[],[f307]) ).

fof(f1195,plain,
    ( spl3_67
    | ~ spl3_17
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f293,f243,f148,f1193]) ).

fof(f1193,plain,
    ( spl3_67
  <=> ! [X2,X0,X1] :
        ( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
        | leq(multiplication(X0,X1),multiplication(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_67])]) ).

fof(f148,plain,
    ( spl3_17
  <=> ! [X0,X1] :
        ( leq(X0,X1)
        | addition(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f293,plain,
    ( ! [X2,X0,X1] :
        ( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
        | leq(multiplication(X0,X1),multiplication(X2,X1)) )
    | ~ spl3_17
    | ~ spl3_27 ),
    inference(superposition,[],[f149,f244]) ).

fof(f149,plain,
    ( ! [X0,X1] :
        ( addition(X0,X1) != X1
        | leq(X0,X1) )
    | ~ spl3_17 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f1172,plain,
    ( ~ spl3_18
    | spl3_62 ),
    inference(avatar_contradiction_clause,[],[f1171]) ).

fof(f1171,plain,
    ( $false
    | ~ spl3_18
    | spl3_62 ),
    inference(resolution,[],[f882,f165]) ).

fof(f165,plain,
    ( ! [X0] : leq(X0,X0)
    | ~ spl3_18 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f164,plain,
    ( spl3_18
  <=> ! [X0] : leq(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f882,plain,
    ( ~ leq(one,one)
    | spl3_62 ),
    inference(avatar_component_clause,[],[f880]) ).

fof(f1170,plain,
    ( spl3_66
    | ~ spl3_17
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f261,f239,f148,f1168]) ).

fof(f1168,plain,
    ( spl3_66
  <=> ! [X2,X0,X1] :
        ( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
        | leq(multiplication(X0,X1),multiplication(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_66])]) ).

fof(f261,plain,
    ( ! [X2,X0,X1] :
        ( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
        | leq(multiplication(X0,X1),multiplication(X0,X2)) )
    | ~ spl3_17
    | ~ spl3_26 ),
    inference(superposition,[],[f149,f240]) ).

fof(f1036,plain,
    ( spl3_65
    | ~ spl3_13
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f288,f243,f128,f1034]) ).

fof(f1034,plain,
    ( spl3_65
  <=> ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_65])]) ).

fof(f288,plain,
    ( ! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1))
    | ~ spl3_13
    | ~ spl3_27 ),
    inference(superposition,[],[f244,f129]) ).

fof(f1032,plain,
    ( spl3_64
    | ~ spl3_13
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f257,f239,f128,f1030]) ).

fof(f1030,plain,
    ( spl3_64
  <=> ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_64])]) ).

fof(f257,plain,
    ( ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1))
    | ~ spl3_13
    | ~ spl3_26 ),
    inference(superposition,[],[f240,f129]) ).

fof(f988,plain,
    ( spl3_63
    | ~ spl3_17
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f218,f200,f148,f986]) ).

fof(f986,plain,
    ( spl3_63
  <=> ! [X2,X0,X1] :
        ( addition(X0,addition(X1,X2)) != X2
        | leq(addition(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_63])]) ).

fof(f218,plain,
    ( ! [X2,X0,X1] :
        ( addition(X0,addition(X1,X2)) != X2
        | leq(addition(X0,X1),X2) )
    | ~ spl3_17
    | ~ spl3_24 ),
    inference(superposition,[],[f149,f201]) ).

fof(f883,plain,
    ( ~ spl3_62
    | ~ spl3_1
    | ~ spl3_2
    | ~ spl3_6
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(avatar_split_clause,[],[f698,f529,f445,f243,f239,f195,f128,f98,f81,f76,f880]) ).

fof(f195,plain,
    ( spl3_23
  <=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1)))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

fof(f698,plain,
    ( ~ leq(one,one)
    | ~ spl3_1
    | ~ spl3_2
    | ~ spl3_6
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f697,f479]) ).

fof(f697,plain,
    ( ~ leq(one,addition(sK0,c(sK0)))
    | ~ spl3_1
    | ~ spl3_6
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f696,f99]) ).

fof(f696,plain,
    ( ~ leq(one,multiplication(addition(sK0,c(sK0)),one))
    | ~ spl3_1
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_47
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f695,f480]) ).

fof(f695,plain,
    ( ~ leq(one,multiplication(addition(sK0,c(sK0)),addition(sK1,c(sK1))))
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_27
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f694,f244]) ).

fof(f694,plain,
    ( ~ leq(one,addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(sK1,c(sK1)))))
    | ~ spl3_13
    | spl3_23
    | ~ spl3_26
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f693,f129]) ).

fof(f693,plain,
    ( ~ leq(one,addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),addition(c(sK1),sK1))))
    | spl3_23
    | ~ spl3_26
    | ~ spl3_54 ),
    inference(forward_demodulation,[],[f664,f610]) ).

fof(f664,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,addition(sK1,c(sK1))),multiplication(c(sK0),c(sK1)))))
    | spl3_23
    | ~ spl3_54 ),
    inference(superposition,[],[f197,f530]) ).

fof(f197,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))))
    | spl3_23 ),
    inference(avatar_component_clause,[],[f195]) ).

fof(f560,plain,
    ( spl3_61
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(avatar_split_clause,[],[f344,f321,f102,f98,f558]) ).

fof(f558,plain,
    ( spl3_61
  <=> ! [X0] :
        ( zero != X0
        | one != addition(X0,one)
        | complement(one,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_61])]) ).

fof(f102,plain,
    ( spl3_7
  <=> ! [X0] : multiplication(one,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f321,plain,
    ( spl3_30
  <=> ! [X0,X1] :
        ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_30])]) ).

fof(f344,plain,
    ( ! [X0] :
        ( zero != X0
        | one != addition(X0,one)
        | complement(one,X0) )
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(duplicate_literal_removal,[],[f343]) ).

fof(f343,plain,
    ( ! [X0] :
        ( zero != X0
        | zero != X0
        | one != addition(X0,one)
        | complement(one,X0) )
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f332,f99]) ).

fof(f332,plain,
    ( ! [X0] :
        ( zero != X0
        | one != addition(X0,one)
        | complement(one,X0)
        | zero != multiplication(X0,one) )
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(superposition,[],[f322,f103]) ).

fof(f103,plain,
    ( ! [X0] : multiplication(one,X0) = X0
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f322,plain,
    ( ! [X0,X1] :
        ( zero != multiplication(X1,X0)
        | addition(X0,X1) != one
        | complement(X1,X0)
        | zero != multiplication(X0,X1) )
    | ~ spl3_30 ),
    inference(avatar_component_clause,[],[f321]) ).

fof(f556,plain,
    ( spl3_60
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(avatar_split_clause,[],[f339,f321,f102,f98,f554]) ).

fof(f554,plain,
    ( spl3_60
  <=> ! [X0] :
        ( zero != X0
        | one != addition(one,X0)
        | complement(X0,one) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_60])]) ).

fof(f339,plain,
    ( ! [X0] :
        ( zero != X0
        | one != addition(one,X0)
        | complement(X0,one) )
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(duplicate_literal_removal,[],[f338]) ).

fof(f338,plain,
    ( ! [X0] :
        ( zero != X0
        | zero != X0
        | one != addition(one,X0)
        | complement(X0,one) )
    | ~ spl3_6
    | ~ spl3_7
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f329,f103]) ).

fof(f329,plain,
    ( ! [X0] :
        ( zero != X0
        | one != addition(one,X0)
        | complement(X0,one)
        | zero != multiplication(one,X0) )
    | ~ spl3_6
    | ~ spl3_30 ),
    inference(superposition,[],[f322,f99]) ).

fof(f552,plain,
    ( spl3_59
    | ~ spl3_7
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f285,f243,f102,f550]) ).

fof(f550,plain,
    ( spl3_59
  <=> ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_59])]) ).

fof(f285,plain,
    ( ! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0)
    | ~ spl3_7
    | ~ spl3_27 ),
    inference(superposition,[],[f244,f103]) ).

fof(f548,plain,
    ( spl3_58
    | ~ spl3_7
    | ~ spl3_27 ),
    inference(avatar_split_clause,[],[f280,f243,f102,f546]) ).

fof(f546,plain,
    ( spl3_58
  <=> ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_58])]) ).

fof(f280,plain,
    ( ! [X0,X1] : multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0))
    | ~ spl3_7
    | ~ spl3_27 ),
    inference(superposition,[],[f244,f103]) ).

fof(f544,plain,
    ( spl3_57
    | ~ spl3_6
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f252,f239,f98,f542]) ).

fof(f542,plain,
    ( spl3_57
  <=> ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_57])]) ).

fof(f252,plain,
    ( ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0)
    | ~ spl3_6
    | ~ spl3_26 ),
    inference(superposition,[],[f240,f99]) ).

fof(f540,plain,
    ( spl3_56
    | ~ spl3_1
    | ~ spl3_41 ),
    inference(avatar_split_clause,[],[f455,f420,f76,f537]) ).

fof(f537,plain,
    ( spl3_56
  <=> zero = multiplication(sK1,sK2(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_56])]) ).

fof(f420,plain,
    ( spl3_41
  <=> ! [X0] :
        ( zero = multiplication(X0,sK2(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_41])]) ).

fof(f455,plain,
    ( zero = multiplication(sK1,sK2(sK1))
    | ~ spl3_1
    | ~ spl3_41 ),
    inference(resolution,[],[f421,f78]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | zero = multiplication(X0,sK2(X0)) )
    | ~ spl3_41 ),
    inference(avatar_component_clause,[],[f420]) ).

fof(f535,plain,
    ( spl3_55
    | ~ spl3_6
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f247,f239,f98,f533]) ).

fof(f533,plain,
    ( spl3_55
  <=> ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_55])]) ).

fof(f247,plain,
    ( ! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1))
    | ~ spl3_6
    | ~ spl3_26 ),
    inference(superposition,[],[f240,f99]) ).

fof(f531,plain,
    ( spl3_54
    | ~ spl3_13
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f214,f200,f128,f529]) ).

fof(f214,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1))
    | ~ spl3_13
    | ~ spl3_24 ),
    inference(superposition,[],[f201,f129]) ).

fof(f526,plain,
    ( spl3_53
    | ~ spl3_8
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f213,f200,f106,f524]) ).

fof(f524,plain,
    ( spl3_53
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_53])]) ).

fof(f106,plain,
    ( spl3_8
  <=> ! [X0] : addition(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f213,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1)))
    | ~ spl3_8
    | ~ spl3_24 ),
    inference(superposition,[],[f201,f107]) ).

fof(f107,plain,
    ( ! [X0] : addition(X0,X0) = X0
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f522,plain,
    ( spl3_52
    | ~ spl3_13
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f209,f200,f128,f520]) ).

fof(f520,plain,
    ( spl3_52
  <=> ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_52])]) ).

fof(f209,plain,
    ( ! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2)
    | ~ spl3_13
    | ~ spl3_24 ),
    inference(superposition,[],[f201,f129]) ).

fof(f517,plain,
    ( spl3_51
    | ~ spl3_11
    | ~ spl3_19 ),
    inference(avatar_split_clause,[],[f171,f168,f118,f515]) ).

fof(f515,plain,
    ( spl3_51
  <=> ! [X0] :
        ( c(sK2(X0)) = X0
        | ~ test(sK2(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_51])]) ).

fof(f118,plain,
    ( spl3_11
  <=> ! [X0] :
        ( complement(sK2(X0),X0)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f168,plain,
    ( spl3_19
  <=> ! [X0,X1] :
        ( c(X0) = X1
        | ~ complement(X0,X1)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f171,plain,
    ( ! [X0] :
        ( c(sK2(X0)) = X0
        | ~ test(sK2(X0))
        | ~ test(X0) )
    | ~ spl3_11
    | ~ spl3_19 ),
    inference(resolution,[],[f169,f119]) ).

fof(f119,plain,
    ( ! [X0] :
        ( complement(sK2(X0),X0)
        | ~ test(X0) )
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f169,plain,
    ( ! [X0,X1] :
        ( ~ complement(X0,X1)
        | c(X0) = X1
        | ~ test(X0) )
    | ~ spl3_19 ),
    inference(avatar_component_clause,[],[f168]) ).

fof(f494,plain,
    ( spl3_50
    | ~ spl3_8
    | ~ spl3_24 ),
    inference(avatar_split_clause,[],[f208,f200,f106,f492]) ).

fof(f492,plain,
    ( spl3_50
  <=> ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_50])]) ).

fof(f208,plain,
    ( ! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1))
    | ~ spl3_8
    | ~ spl3_24 ),
    inference(superposition,[],[f201,f107]) ).

fof(f476,plain,
    ( spl3_49
    | ~ spl3_2
    | ~ spl3_41 ),
    inference(avatar_split_clause,[],[f454,f420,f81,f473]) ).

fof(f473,plain,
    ( spl3_49
  <=> zero = multiplication(sK0,sK2(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_49])]) ).

fof(f454,plain,
    ( zero = multiplication(sK0,sK2(sK0))
    | ~ spl3_2
    | ~ spl3_41 ),
    inference(resolution,[],[f421,f83]) ).

fof(f451,plain,
    ( spl3_48
    | ~ spl3_13
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f160,f148,f128,f449]) ).

fof(f449,plain,
    ( spl3_48
  <=> ! [X0,X1] :
        ( addition(X1,X0) != X1
        | leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_48])]) ).

fof(f160,plain,
    ( ! [X0,X1] :
        ( addition(X1,X0) != X1
        | leq(X0,X1) )
    | ~ spl3_13
    | ~ spl3_17 ),
    inference(superposition,[],[f149,f129]) ).

fof(f447,plain,
    ( spl3_47
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f157,f144,f128,f122,f445]) ).

fof(f122,plain,
    ( spl3_12
  <=> ! [X0] :
        ( complement(X0,c(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f144,plain,
    ( spl3_16
  <=> ! [X0,X1] :
        ( addition(X0,X1) = one
        | ~ complement(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f157,plain,
    ( ! [X0] :
        ( one = addition(X0,c(X0))
        | ~ test(X0) )
    | ~ spl3_12
    | ~ spl3_13
    | ~ spl3_16 ),
    inference(forward_demodulation,[],[f156,f129]) ).

fof(f156,plain,
    ( ! [X0] :
        ( one = addition(c(X0),X0)
        | ~ test(X0) )
    | ~ spl3_12
    | ~ spl3_16 ),
    inference(resolution,[],[f145,f123]) ).

fof(f123,plain,
    ( ! [X0] :
        ( complement(X0,c(X0))
        | ~ test(X0) )
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f145,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | addition(X0,X1) = one )
    | ~ spl3_16 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f443,plain,
    ( spl3_46
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(avatar_split_clause,[],[f155,f144,f118,f441]) ).

fof(f441,plain,
    ( spl3_46
  <=> ! [X0] :
        ( one = addition(X0,sK2(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_46])]) ).

fof(f155,plain,
    ( ! [X0] :
        ( one = addition(X0,sK2(X0))
        | ~ test(X0) )
    | ~ spl3_11
    | ~ spl3_16 ),
    inference(resolution,[],[f145,f119]) ).

fof(f439,plain,
    ( spl3_45
    | ~ spl3_12
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f154,f140,f122,f437]) ).

fof(f437,plain,
    ( spl3_45
  <=> ! [X0] :
        ( zero = multiplication(X0,c(X0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_45])]) ).

fof(f140,plain,
    ( spl3_15
  <=> ! [X0,X1] :
        ( zero = multiplication(X1,X0)
        | ~ complement(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f154,plain,
    ( ! [X0] :
        ( zero = multiplication(X0,c(X0))
        | ~ test(X0) )
    | ~ spl3_12
    | ~ spl3_15 ),
    inference(resolution,[],[f141,f123]) ).

fof(f141,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | zero = multiplication(X1,X0) )
    | ~ spl3_15 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f435,plain,
    ( spl3_44
    | ~ spl3_11
    | ~ spl3_15 ),
    inference(avatar_split_clause,[],[f153,f140,f118,f433]) ).

fof(f433,plain,
    ( spl3_44
  <=> ! [X0] :
        ( zero = multiplication(sK2(X0),X0)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_44])]) ).

fof(f153,plain,
    ( ! [X0] :
        ( zero = multiplication(sK2(X0),X0)
        | ~ test(X0) )
    | ~ spl3_11
    | ~ spl3_15 ),
    inference(resolution,[],[f141,f119]) ).

fof(f431,plain,
    ( spl3_43
    | ~ spl3_2
    | ~ spl3_8
    | ~ spl3_34 ),
    inference(avatar_split_clause,[],[f373,f354,f106,f81,f428]) ).

fof(f428,plain,
    ( spl3_43
  <=> c(sK0) = c(multiplication(sK0,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_43])]) ).

fof(f354,plain,
    ( spl3_34
  <=> ! [X0] :
        ( c(multiplication(X0,sK0)) = addition(c(X0),c(sK0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_34])]) ).

fof(f373,plain,
    ( c(sK0) = c(multiplication(sK0,sK0))
    | ~ spl3_2
    | ~ spl3_8
    | ~ spl3_34 ),
    inference(forward_demodulation,[],[f371,f107]) ).

fof(f371,plain,
    ( c(multiplication(sK0,sK0)) = addition(c(sK0),c(sK0))
    | ~ spl3_2
    | ~ spl3_34 ),
    inference(resolution,[],[f355,f83]) ).

fof(f355,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | c(multiplication(X0,sK0)) = addition(c(X0),c(sK0)) )
    | ~ spl3_34 ),
    inference(avatar_component_clause,[],[f354]) ).

fof(f426,plain,
    ( spl3_42
    | ~ spl3_12
    | ~ spl3_14 ),
    inference(avatar_split_clause,[],[f152,f136,f122,f424]) ).

fof(f424,plain,
    ( spl3_42
  <=> ! [X0] :
        ( zero = multiplication(c(X0),X0)
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_42])]) ).

fof(f136,plain,
    ( spl3_14
  <=> ! [X0,X1] :
        ( zero = multiplication(X0,X1)
        | ~ complement(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f152,plain,
    ( ! [X0] :
        ( zero = multiplication(c(X0),X0)
        | ~ test(X0) )
    | ~ spl3_12
    | ~ spl3_14 ),
    inference(resolution,[],[f137,f123]) ).

fof(f137,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | zero = multiplication(X0,X1) )
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f422,plain,
    ( spl3_41
    | ~ spl3_11
    | ~ spl3_14 ),
    inference(avatar_split_clause,[],[f151,f136,f118,f420]) ).

fof(f151,plain,
    ( ! [X0] :
        ( zero = multiplication(X0,sK2(X0))
        | ~ test(X0) )
    | ~ spl3_11
    | ~ spl3_14 ),
    inference(resolution,[],[f137,f119]) ).

fof(f415,plain,
    ( spl3_40
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_30 ),
    inference(avatar_split_clause,[],[f342,f321,f94,f90,f86,f413]) ).

fof(f413,plain,
    ( spl3_40
  <=> ! [X0] :
        ( one != X0
        | complement(zero,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_40])]) ).

fof(f86,plain,
    ( spl3_3
  <=> ! [X0] : zero = multiplication(X0,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f90,plain,
    ( spl3_4
  <=> ! [X0] : zero = multiplication(zero,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f94,plain,
    ( spl3_5
  <=> ! [X0] : addition(X0,zero) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f342,plain,
    ( ! [X0] :
        ( one != X0
        | complement(zero,X0) )
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_30 ),
    inference(trivial_inequality_removal,[],[f341]) ).

fof(f341,plain,
    ( ! [X0] :
        ( zero != zero
        | one != X0
        | complement(zero,X0) )
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f340,f87]) ).

fof(f87,plain,
    ( ! [X0] : zero = multiplication(X0,zero)
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f340,plain,
    ( ! [X0] :
        ( one != X0
        | complement(zero,X0)
        | zero != multiplication(X0,zero) )
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f333,f95]) ).

fof(f95,plain,
    ( ! [X0] : addition(X0,zero) = X0
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f333,plain,
    ( ! [X0] :
        ( addition(X0,zero) != one
        | complement(zero,X0)
        | zero != multiplication(X0,zero) )
    | ~ spl3_4
    | ~ spl3_30 ),
    inference(trivial_inequality_removal,[],[f330]) ).

fof(f330,plain,
    ( ! [X0] :
        ( zero != zero
        | addition(X0,zero) != one
        | complement(zero,X0)
        | zero != multiplication(X0,zero) )
    | ~ spl3_4
    | ~ spl3_30 ),
    inference(superposition,[],[f322,f91]) ).

fof(f91,plain,
    ( ! [X0] : zero = multiplication(zero,X0)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f411,plain,
    ( spl3_39
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_13
    | ~ spl3_30 ),
    inference(avatar_split_clause,[],[f337,f321,f128,f94,f90,f86,f409]) ).

fof(f409,plain,
    ( spl3_39
  <=> ! [X0] :
        ( one != X0
        | complement(X0,zero) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_39])]) ).

fof(f337,plain,
    ( ! [X0] :
        ( one != X0
        | complement(X0,zero) )
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_13
    | ~ spl3_30 ),
    inference(trivial_inequality_removal,[],[f336]) ).

fof(f336,plain,
    ( ! [X0] :
        ( zero != zero
        | one != X0
        | complement(X0,zero) )
    | ~ spl3_3
    | ~ spl3_4
    | ~ spl3_5
    | ~ spl3_13
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f335,f91]) ).

fof(f335,plain,
    ( ! [X0] :
        ( one != X0
        | complement(X0,zero)
        | zero != multiplication(zero,X0) )
    | ~ spl3_3
    | ~ spl3_5
    | ~ spl3_13
    | ~ spl3_30 ),
    inference(forward_demodulation,[],[f334,f131]) ).

fof(f131,plain,
    ( ! [X0] : addition(zero,X0) = X0
    | ~ spl3_5
    | ~ spl3_13 ),
    inference(superposition,[],[f129,f95]) ).

fof(f334,plain,
    ( ! [X0] :
        ( one != addition(zero,X0)
        | complement(X0,zero)
        | zero != multiplication(zero,X0) )
    | ~ spl3_3
    | ~ spl3_30 ),
    inference(trivial_inequality_removal,[],[f328]) ).

fof(f328,plain,
    ( ! [X0] :
        ( zero != zero
        | one != addition(zero,X0)
        | complement(X0,zero)
        | zero != multiplication(zero,X0) )
    | ~ spl3_3
    | ~ spl3_30 ),
    inference(superposition,[],[f322,f87]) ).

fof(f407,plain,
    ( spl3_38
    | ~ spl3_5
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f158,f148,f94,f405]) ).

fof(f405,plain,
    ( spl3_38
  <=> ! [X0] :
        ( zero != X0
        | leq(X0,zero) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_38])]) ).

fof(f158,plain,
    ( ! [X0] :
        ( zero != X0
        | leq(X0,zero) )
    | ~ spl3_5
    | ~ spl3_17 ),
    inference(superposition,[],[f149,f95]) ).

fof(f386,plain,
    ( spl3_37
    | ~ spl3_1
    | ~ spl3_8
    | ~ spl3_33 ),
    inference(avatar_split_clause,[],[f369,f350,f106,f76,f383]) ).

fof(f383,plain,
    ( spl3_37
  <=> c(sK1) = c(multiplication(sK1,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_37])]) ).

fof(f350,plain,
    ( spl3_33
  <=> ! [X0] :
        ( c(multiplication(X0,sK1)) = addition(c(X0),c(sK1))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_33])]) ).

fof(f369,plain,
    ( c(sK1) = c(multiplication(sK1,sK1))
    | ~ spl3_1
    | ~ spl3_8
    | ~ spl3_33 ),
    inference(forward_demodulation,[],[f366,f107]) ).

fof(f366,plain,
    ( c(multiplication(sK1,sK1)) = addition(c(sK1),c(sK1))
    | ~ spl3_1
    | ~ spl3_33 ),
    inference(resolution,[],[f351,f78]) ).

fof(f351,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | c(multiplication(X0,sK1)) = addition(c(X0),c(sK1)) )
    | ~ spl3_33 ),
    inference(avatar_component_clause,[],[f350]) ).

fof(f381,plain,
    ( spl3_36
    | ~ spl3_5
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f131,f128,f94,f379]) ).

fof(f379,plain,
    ( spl3_36
  <=> ! [X0] : addition(zero,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_36])]) ).

fof(f377,plain,
    ( spl3_35
    | ~ spl3_9
    | ~ spl3_12 ),
    inference(avatar_split_clause,[],[f126,f122,f110,f375]) ).

fof(f375,plain,
    ( spl3_35
  <=> ! [X0] :
        ( ~ test(X0)
        | test(c(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_35])]) ).

fof(f110,plain,
    ( spl3_9
  <=> ! [X0,X1] :
        ( test(X0)
        | ~ complement(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f126,plain,
    ( ! [X0] :
        ( ~ test(X0)
        | test(c(X0)) )
    | ~ spl3_9
    | ~ spl3_12 ),
    inference(resolution,[],[f123,f111]) ).

fof(f111,plain,
    ( ! [X0,X1] :
        ( ~ complement(X1,X0)
        | test(X0) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f356,plain,
    ( spl3_34
    | ~ spl3_2
    | ~ spl3_29 ),
    inference(avatar_split_clause,[],[f318,f311,f81,f354]) ).

fof(f318,plain,
    ( ! [X0] :
        ( c(multiplication(X0,sK0)) = addition(c(X0),c(sK0))
        | ~ test(X0) )
    | ~ spl3_2
    | ~ spl3_29 ),
    inference(resolution,[],[f312,f83]) ).

fof(f352,plain,
    ( spl3_33
    | ~ spl3_1
    | ~ spl3_29 ),
    inference(avatar_split_clause,[],[f317,f311,f76,f350]) ).

fof(f317,plain,
    ( ! [X0] :
        ( c(multiplication(X0,sK1)) = addition(c(X0),c(sK1))
        | ~ test(X0) )
    | ~ spl3_1
    | ~ spl3_29 ),
    inference(resolution,[],[f312,f78]) ).

fof(f348,plain,
    ( spl3_32
    | ~ spl3_2
    | ~ spl3_28 ),
    inference(avatar_split_clause,[],[f315,f307,f81,f346]) ).

fof(f346,plain,
    ( spl3_32
  <=> ! [X0] :
        ( multiplication(c(X0),c(sK0)) = c(addition(X0,sK0))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_32])]) ).

fof(f315,plain,
    ( ! [X0] :
        ( multiplication(c(X0),c(sK0)) = c(addition(X0,sK0))
        | ~ test(X0) )
    | ~ spl3_2
    | ~ spl3_28 ),
    inference(resolution,[],[f308,f83]) ).

fof(f327,plain,
    ( spl3_31
    | ~ spl3_1
    | ~ spl3_28 ),
    inference(avatar_split_clause,[],[f314,f307,f76,f325]) ).

fof(f325,plain,
    ( spl3_31
  <=> ! [X0] :
        ( multiplication(c(X0),c(sK1)) = c(addition(X0,sK1))
        | ~ test(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_31])]) ).

fof(f314,plain,
    ( ! [X0] :
        ( multiplication(c(X0),c(sK1)) = c(addition(X0,sK1))
        | ~ test(X0) )
    | ~ spl3_1
    | ~ spl3_28 ),
    inference(resolution,[],[f308,f78]) ).

fof(f323,plain,
    spl3_30,
    inference(avatar_split_clause,[],[f68,f321]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
      | addition(X0,X1) != one
      | zero != multiplication(X1,X0)
      | zero != multiplication(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( complement(X1,X0)
        | addition(X0,X1) != one
        | zero != multiplication(X1,X0)
        | zero != multiplication(X0,X1) )
      & ( ( addition(X0,X1) = one
          & zero = multiplication(X1,X0)
          & zero = multiplication(X0,X1) )
        | ~ complement(X1,X0) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( complement(X1,X0)
    <=> ( addition(X0,X1) = one
        & zero = multiplication(X1,X0)
        & zero = multiplication(X0,X1) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X3,X4] :
      ( complement(X4,X3)
    <=> ( one = addition(X3,X4)
        & zero = multiplication(X4,X3)
        & zero = multiplication(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).

fof(f313,plain,
    spl3_29,
    inference(avatar_split_clause,[],[f64,f311]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( c(multiplication(X0,X1)) = addition(c(X0),c(X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( test(X1)
        & test(X0) )
     => c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X3,X4] :
      ( ( test(X4)
        & test(X3) )
     => c(multiplication(X3,X4)) = addition(c(X3),c(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).

fof(f309,plain,
    spl3_28,
    inference(avatar_split_clause,[],[f63,f307]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( multiplication(c(X0),c(X1)) = c(addition(X0,X1))
      | ~ test(X1)
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( test(X1)
        & test(X0) )
     => multiplication(c(X0),c(X1)) = c(addition(X0,X1)) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X3,X4] :
      ( ( test(X4)
        & test(X3) )
     => c(addition(X3,X4)) = multiplication(c(X3),c(X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).

fof(f245,plain,
    spl3_27,
    inference(avatar_split_clause,[],[f73,f243]) ).

fof(f73,plain,
    ! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).

fof(f241,plain,
    spl3_26,
    inference(avatar_split_clause,[],[f72,f239]) ).

fof(f72,plain,
    ! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).

fof(f206,plain,
    spl3_25,
    inference(avatar_split_clause,[],[f71,f204]) ).

fof(f71,plain,
    ! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).

fof(f202,plain,
    spl3_24,
    inference(avatar_split_clause,[],[f70,f200]) ).

fof(f70,plain,
    ! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).

fof(f198,plain,
    ( ~ spl3_23
    | ~ spl3_13
    | spl3_20 ),
    inference(avatar_split_clause,[],[f188,f175,f128,f195]) ).

fof(f175,plain,
    ( spl3_20
  <=> leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f188,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))))
    | ~ spl3_13
    | spl3_20 ),
    inference(forward_demodulation,[],[f187,f72]) ).

fof(f187,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))))))
    | ~ spl3_13
    | spl3_20 ),
    inference(forward_demodulation,[],[f186,f129]) ).

fof(f186,plain,
    ( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1))))
    | ~ spl3_13
    | spl3_20 ),
    inference(forward_demodulation,[],[f177,f129]) ).

fof(f177,plain,
    ( ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))))
    | spl3_20 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f193,plain,
    ( ~ spl3_22
    | ~ spl3_13
    | spl3_21 ),
    inference(avatar_split_clause,[],[f185,f179,f128,f190]) ).

fof(f179,plain,
    ( spl3_21
  <=> leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f185,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),multiplication(sK0,addition(sK1,c(sK1))))),one)
    | ~ spl3_13
    | spl3_21 ),
    inference(forward_demodulation,[],[f184,f72]) ).

fof(f184,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))))),one)
    | ~ spl3_13
    | spl3_21 ),
    inference(forward_demodulation,[],[f183,f129]) ).

fof(f183,plain,
    ( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1))),one)
    | ~ spl3_13
    | spl3_21 ),
    inference(forward_demodulation,[],[f181,f129]) ).

fof(f181,plain,
    ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
    | spl3_21 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f182,plain,
    ( ~ spl3_20
    | ~ spl3_21 ),
    inference(avatar_split_clause,[],[f50,f179,f175]) ).

fof(f50,plain,
    ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
    | ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
      | ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
    & test(sK0)
    & test(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f39]) ).

fof(f39,plain,
    ( ? [X0,X1] :
        ( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
          | ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
        & test(X0)
        & test(X1) )
   => ( ( ~ leq(addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
        | ~ leq(one,addition(addition(addition(multiplication(sK0,sK1),multiplication(sK0,c(sK1))),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
      & test(sK0)
      & test(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
        | ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ? [X0,X1] :
      ( ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
        | ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
      & test(X0)
      & test(X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0,X1] :
        ( ( test(X0)
          & test(X1) )
       => ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
          & leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,negated_conjecture,
    ~ ! [X3,X4] :
        ( ( test(X3)
          & test(X4) )
       => ( leq(addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
          & leq(one,addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f19,conjecture,
    ! [X3,X4] :
      ( ( test(X3)
        & test(X4) )
     => ( leq(addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
        & leq(one,addition(addition(addition(multiplication(X3,X4),multiplication(X3,c(X4))),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f170,plain,
    spl3_19,
    inference(avatar_split_clause,[],[f62,f168]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( c(X0) = X1
      | ~ complement(X0,X1)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ( ( c(X0) = X1
          | ~ complement(X0,X1) )
        & ( complement(X0,X1)
          | c(X0) != X1 ) )
      | ~ test(X0) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( c(X0) = X1
      <=> complement(X0,X1) )
      | ~ test(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( test(X0)
     => ( c(X0) = X1
      <=> complement(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X3,X4] :
      ( test(X3)
     => ( c(X3) = X4
      <=> complement(X3,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).

fof(f166,plain,
    ( spl3_18
    | ~ spl3_8
    | ~ spl3_17 ),
    inference(avatar_split_clause,[],[f162,f148,f106,f164]) ).

fof(f162,plain,
    ( ! [X0] : leq(X0,X0)
    | ~ spl3_8
    | ~ spl3_17 ),
    inference(trivial_inequality_removal,[],[f159]) ).

fof(f159,plain,
    ( ! [X0] :
        ( X0 != X0
        | leq(X0,X0) )
    | ~ spl3_8
    | ~ spl3_17 ),
    inference(superposition,[],[f149,f107]) ).

fof(f150,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f69,f148]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = X1
     => leq(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

fof(f146,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f67,f144]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( addition(X0,X1) = one
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f142,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f66,f140]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( zero = multiplication(X1,X0)
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f138,plain,
    spl3_14,
    inference(avatar_split_clause,[],[f65,f136]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( zero = multiplication(X0,X1)
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f130,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f60,f128]) ).

fof(f60,plain,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : addition(X0,X1) = addition(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).

fof(f124,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f74,f122]) ).

fof(f74,plain,
    ! [X0] :
      ( complement(X0,c(X0))
      | ~ test(X0) ),
    inference(equality_resolution,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( complement(X0,X1)
      | c(X0) != X1
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f120,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f58,f118]) ).

fof(f58,plain,
    ! [X0] :
      ( complement(sK2(X0),X0)
      | ~ test(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( complement(sK2(X0),X0)
        | ~ test(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ? [X2] : complement(X2,X0)
     => complement(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X2] : complement(X2,X0)
        | ~ test(X0) ) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( test(X0)
        | ! [X1] : ~ complement(X1,X0) )
      & ( ? [X1] : complement(X1,X0)
        | ~ test(X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( test(X0)
    <=> ? [X1] : complement(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X3] :
      ( test(X3)
    <=> ? [X4] : complement(X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).

fof(f116,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f57,f114]) ).

fof(f57,plain,
    ! [X0] :
      ( zero = c(X0)
      | test(X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( zero = c(X0)
      | test(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ~ test(X0)
     => zero = c(X0) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X3] :
      ( ~ test(X3)
     => zero = c(X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).

fof(f112,plain,
    spl3_9,
    inference(avatar_split_clause,[],[f59,f110]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( test(X0)
      | ~ complement(X1,X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f108,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f56,f106]) ).

fof(f56,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f104,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f55,f102]) ).

fof(f55,plain,
    ! [X0] : multiplication(one,X0) = X0,
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : multiplication(one,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).

fof(f100,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f54,f98]) ).

fof(f54,plain,
    ! [X0] : multiplication(X0,one) = X0,
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : multiplication(X0,one) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).

fof(f96,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f53,f94]) ).

fof(f53,plain,
    ! [X0] : addition(X0,zero) = X0,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : addition(X0,zero) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).

fof(f92,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f52,f90]) ).

fof(f52,plain,
    ! [X0] : zero = multiplication(zero,X0),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : zero = multiplication(zero,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).

fof(f88,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f51,f86]) ).

fof(f51,plain,
    ! [X0] : zero = multiplication(X0,zero),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : zero = multiplication(X0,zero),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).

fof(f84,plain,
    spl3_2,
    inference(avatar_split_clause,[],[f49,f81]) ).

fof(f49,plain,
    test(sK0),
    inference(cnf_transformation,[],[f40]) ).

fof(f79,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f48,f76]) ).

fof(f48,plain,
    test(sK1),
    inference(cnf_transformation,[],[f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : KLE009+4 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 21:23:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (2280)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (2285)WARNING: value z3 for option sas not known
% 0.14/0.38  % (2286)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (2284)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (2287)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)
% 0.14/0.38  % (2285)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)
% 0.14/0.38  % (2283)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (2288)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)
% 0.14/0.38  % (2289)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [4]
% 0.14/0.39  TRYING [3]
% 0.14/0.40  TRYING [3]
% 0.21/0.41  TRYING [4]
% 0.21/0.42  % (2287)First to succeed.
% 0.21/0.42  % (2288)Also succeeded, but the first one will report.
% 0.21/0.43  % (2287)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2280"
% 0.21/0.43  TRYING [5]
% 0.21/0.43  % (2287)Refutation found. Thanks to Tanya!
% 0.21/0.43  % SZS status Theorem for theBenchmark
% 0.21/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43  % (2287)------------------------------
% 0.21/0.43  % (2287)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43  % (2287)Termination reason: Refutation
% 0.21/0.43  
% 0.21/0.43  % (2287)Memory used [KB]: 1466
% 0.21/0.43  % (2287)Time elapsed: 0.052 s
% 0.21/0.43  % (2287)Instructions burned: 85 (million)
% 0.21/0.43  % (2280)Success in time 0.067 s
%------------------------------------------------------------------------------