TSTP Solution File: NUM840+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 14:37:49 EDT 2024

% Result   : Theorem 0.22s 0.48s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   97
% Syntax   : Number of formulae    :  318 (  66 unt;   0 def)
%            Number of atoms       :  731 ( 170 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  718 ( 305   ~; 293   |;  25   &)
%                                         (  69 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   67 (  65 usr;  62 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :  469 ( 447   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f710,plain,
    $false,
    inference(avatar_sat_refutation,[],[f179,f183,f187,f191,f195,f199,f203,f207,f211,f215,f219,f223,f227,f231,f235,f239,f251,f255,f259,f263,f281,f285,f289,f293,f297,f301,f305,f309,f313,f339,f344,f348,f352,f356,f360,f364,f403,f407,f476,f518,f523,f528,f534,f549,f553,f605,f609,f624,f630,f636,f642,f648,f656,f660,f664,f668,f672,f676,f680,f685,f689,f703,f708,f709]) ).

fof(f709,plain,
    ( ~ spl4_17
    | ~ spl4_10
    | ~ spl4_43 ),
    inference(avatar_split_clause,[],[f652,f525,f213,f248]) ).

fof(f248,plain,
    ( spl4_17
  <=> less(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).

fof(f213,plain,
    ( spl4_10
  <=> ! [X0,X1] :
        ( ~ less(X0,X1)
        | ~ greater(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f525,plain,
    ( spl4_43
  <=> greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).

fof(f652,plain,
    ( ~ less(vplus(vd328,vd330),vplus(vd329,vd330))
    | ~ spl4_10
    | ~ spl4_43 ),
    inference(resolution,[],[f526,f214]) ).

fof(f214,plain,
    ( ! [X0,X1] :
        ( ~ greater(X0,X1)
        | ~ less(X0,X1) )
    | ~ spl4_10 ),
    inference(avatar_component_clause,[],[f213]) ).

fof(f526,plain,
    ( greater(vplus(vd328,vd330),vplus(vd329,vd330))
    | ~ spl4_43 ),
    inference(avatar_component_clause,[],[f525]) ).

fof(f708,plain,
    ( spl4_61
    | ~ spl4_13
    | ~ spl4_43 ),
    inference(avatar_split_clause,[],[f651,f525,f225,f705]) ).

fof(f705,plain,
    ( spl4_61
  <=> less(vplus(vd329,vd330),vplus(vd328,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).

fof(f225,plain,
    ( spl4_13
  <=> ! [X0,X1] :
        ( less(X1,X0)
        | ~ greater(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f651,plain,
    ( less(vplus(vd329,vd330),vplus(vd328,vd330))
    | ~ spl4_13
    | ~ spl4_43 ),
    inference(resolution,[],[f526,f226]) ).

fof(f226,plain,
    ( ! [X0,X1] :
        ( ~ greater(X0,X1)
        | less(X1,X0) )
    | ~ spl4_13 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f703,plain,
    ( spl4_60
    | ~ spl4_15
    | ~ spl4_43 ),
    inference(avatar_split_clause,[],[f650,f525,f233,f700]) ).

fof(f700,plain,
    ( spl4_60
  <=> geq(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).

fof(f233,plain,
    ( spl4_15
  <=> ! [X0,X1] :
        ( geq(X1,X0)
        | ~ greater(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).

fof(f650,plain,
    ( geq(vplus(vd328,vd330),vplus(vd329,vd330))
    | ~ spl4_15
    | ~ spl4_43 ),
    inference(resolution,[],[f526,f234]) ).

fof(f234,plain,
    ( ! [X0,X1] :
        ( ~ greater(X1,X0)
        | geq(X1,X0) )
    | ~ spl4_15 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f689,plain,
    ( spl4_59
    | ~ spl4_9
    | ~ spl4_39 ),
    inference(avatar_split_clause,[],[f455,f405,f209,f687]) ).

fof(f687,plain,
    ( spl4_59
  <=> ! [X0,X1] : less(X0,vplus(v1,vplus(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).

fof(f209,plain,
    ( spl4_9
  <=> ! [X2,X1] : less(X1,vplus(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f405,plain,
    ( spl4_39
  <=> ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).

fof(f455,plain,
    ( ! [X0,X1] : less(X0,vplus(v1,vplus(X0,X1)))
    | ~ spl4_9
    | ~ spl4_39 ),
    inference(superposition,[],[f210,f406]) ).

fof(f406,plain,
    ( ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1))
    | ~ spl4_39 ),
    inference(avatar_component_clause,[],[f405]) ).

fof(f210,plain,
    ( ! [X2,X1] : less(X1,vplus(X1,X2))
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f209]) ).

fof(f685,plain,
    ( spl4_58
    | ~ spl4_13
    | ~ spl4_31 ),
    inference(avatar_split_clause,[],[f513,f336,f225,f682]) ).

fof(f682,plain,
    ( spl4_58
  <=> less(vd329,vd328) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).

fof(f336,plain,
    ( spl4_31
  <=> greater(vd328,vd329) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).

fof(f513,plain,
    ( less(vd329,vd328)
    | ~ spl4_13
    | ~ spl4_31 ),
    inference(resolution,[],[f338,f226]) ).

fof(f338,plain,
    ( greater(vd328,vd329)
    | ~ spl4_31 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f680,plain,
    ( spl4_57
    | ~ spl4_7
    | ~ spl4_39 ),
    inference(avatar_split_clause,[],[f453,f405,f201,f678]) ).

fof(f678,plain,
    ( spl4_57
  <=> ! [X0,X1] : greater(vplus(v1,vplus(X0,X1)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).

fof(f201,plain,
    ( spl4_7
  <=> ! [X0,X1] : greater(vplus(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f453,plain,
    ( ! [X0,X1] : greater(vplus(v1,vplus(X0,X1)),X0)
    | ~ spl4_7
    | ~ spl4_39 ),
    inference(superposition,[],[f202,f406]) ).

fof(f202,plain,
    ( ! [X0,X1] : greater(vplus(X0,X1),X0)
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f676,plain,
    ( spl4_56
    | ~ spl4_9
    | ~ spl4_39 ),
    inference(avatar_split_clause,[],[f443,f405,f209,f674]) ).

fof(f674,plain,
    ( spl4_56
  <=> ! [X0,X1] : less(v1,vplus(X0,vplus(v1,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).

fof(f443,plain,
    ( ! [X0,X1] : less(v1,vplus(X0,vplus(v1,X1)))
    | ~ spl4_9
    | ~ spl4_39 ),
    inference(superposition,[],[f210,f406]) ).

fof(f672,plain,
    ( spl4_55
    | ~ spl4_7
    | ~ spl4_39 ),
    inference(avatar_split_clause,[],[f441,f405,f201,f670]) ).

fof(f670,plain,
    ( spl4_55
  <=> ! [X0,X1] : greater(vplus(X0,vplus(v1,X1)),v1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).

fof(f441,plain,
    ( ! [X0,X1] : greater(vplus(X0,vplus(v1,X1)),v1)
    | ~ spl4_7
    | ~ spl4_39 ),
    inference(superposition,[],[f202,f406]) ).

fof(f668,plain,
    ( spl4_54
    | ~ spl4_6
    | ~ spl4_38 ),
    inference(avatar_split_clause,[],[f415,f401,f197,f666]) ).

fof(f666,plain,
    ( spl4_54
  <=> ! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) != X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).

fof(f197,plain,
    ( spl4_6
  <=> ! [X0,X1] : vplus(X0,X1) != X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f401,plain,
    ( spl4_38
  <=> ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).

fof(f415,plain,
    ( ! [X2,X0,X1] : vplus(X0,vplus(X1,X2)) != X2
    | ~ spl4_6
    | ~ spl4_38 ),
    inference(superposition,[],[f198,f402]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2))
    | ~ spl4_38 ),
    inference(avatar_component_clause,[],[f401]) ).

fof(f198,plain,
    ( ! [X0,X1] : vplus(X0,X1) != X1
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f664,plain,
    ( spl4_53
    | ~ spl4_6
    | ~ spl4_29 ),
    inference(avatar_split_clause,[],[f326,f311,f197,f662]) ).

fof(f662,plain,
    ( spl4_53
  <=> ! [X0] :
        ( vskolem2(X0) != X0
        | v1 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).

fof(f311,plain,
    ( spl4_29
  <=> ! [X0] :
        ( vplus(v1,vskolem2(X0)) = X0
        | v1 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).

fof(f326,plain,
    ( ! [X0] :
        ( vskolem2(X0) != X0
        | v1 = X0 )
    | ~ spl4_6
    | ~ spl4_29 ),
    inference(superposition,[],[f198,f312]) ).

fof(f312,plain,
    ( ! [X0] :
        ( vplus(v1,vskolem2(X0)) = X0
        | v1 = X0 )
    | ~ spl4_29 ),
    inference(avatar_component_clause,[],[f311]) ).

fof(f660,plain,
    ( spl4_52
    | ~ spl4_18
    | ~ spl4_20 ),
    inference(avatar_split_clause,[],[f276,f261,f253,f658]) ).

fof(f658,plain,
    ( spl4_52
  <=> ! [X2,X0,X1] : vplus(X2,vplus(X0,X1)) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).

fof(f253,plain,
    ( spl4_18
  <=> ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f261,plain,
    ( spl4_20
  <=> ! [X2,X0,X3] : vplus(vplus(X0,X2),X3) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

fof(f276,plain,
    ( ! [X2,X0,X1] : vplus(X2,vplus(X0,X1)) != X0
    | ~ spl4_18
    | ~ spl4_20 ),
    inference(superposition,[],[f262,f254]) ).

fof(f254,plain,
    ( ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0)
    | ~ spl4_18 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f262,plain,
    ( ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0
    | ~ spl4_20 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f656,plain,
    ( spl4_51
    | ~ spl4_18
    | ~ spl4_20 ),
    inference(avatar_split_clause,[],[f274,f261,f253,f654]) ).

fof(f654,plain,
    ( spl4_51
  <=> ! [X2,X0,X1] : vplus(vplus(X1,X0),X2) != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).

fof(f274,plain,
    ( ! [X2,X0,X1] : vplus(vplus(X1,X0),X2) != X0
    | ~ spl4_18
    | ~ spl4_20 ),
    inference(superposition,[],[f262,f254]) ).

fof(f648,plain,
    ( ~ spl4_31
    | ~ spl4_36
    | spl4_43 ),
    inference(avatar_split_clause,[],[f643,f525,f358,f336]) ).

fof(f358,plain,
    ( spl4_36
  <=> ! [X2,X0,X1] :
        ( greater(vplus(X0,X2),vplus(X1,X2))
        | ~ greater(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).

fof(f643,plain,
    ( ~ greater(vd328,vd329)
    | ~ spl4_36
    | spl4_43 ),
    inference(resolution,[],[f527,f359]) ).

fof(f359,plain,
    ( ! [X2,X0,X1] :
        ( greater(vplus(X0,X2),vplus(X1,X2))
        | ~ greater(X0,X1) )
    | ~ spl4_36 ),
    inference(avatar_component_clause,[],[f358]) ).

fof(f527,plain,
    ( ~ greater(vplus(vd328,vd330),vplus(vd329,vd330))
    | spl4_43 ),
    inference(avatar_component_clause,[],[f525]) ).

fof(f642,plain,
    ( ~ spl4_2
    | ~ spl4_50 ),
    inference(avatar_contradiction_clause,[],[f637]) ).

fof(f637,plain,
    ( $false
    | ~ spl4_2
    | ~ spl4_50 ),
    inference(resolution,[],[f635,f182]) ).

fof(f182,plain,
    ( ! [X1] : ~ greater(X1,X1)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f181]) ).

fof(f181,plain,
    ( spl4_2
  <=> ! [X1] : ~ greater(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f635,plain,
    ( greater(vplus(vd328,vd330),vplus(vd328,vd330))
    | ~ spl4_50 ),
    inference(avatar_component_clause,[],[f633]) ).

fof(f633,plain,
    ( spl4_50
  <=> greater(vplus(vd328,vd330),vplus(vd328,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).

fof(f636,plain,
    ( spl4_50
    | ~ spl4_30
    | ~ spl4_49 ),
    inference(avatar_split_clause,[],[f631,f627,f332,f633]) ).

fof(f332,plain,
    ( spl4_30
  <=> vd328 = vd329 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).

fof(f627,plain,
    ( spl4_49
  <=> greater(vplus(vd329,vd330),vplus(vd328,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).

fof(f631,plain,
    ( greater(vplus(vd328,vd330),vplus(vd328,vd330))
    | ~ spl4_30
    | ~ spl4_49 ),
    inference(forward_demodulation,[],[f629,f334]) ).

fof(f334,plain,
    ( vd328 = vd329
    | ~ spl4_30 ),
    inference(avatar_component_clause,[],[f332]) ).

fof(f629,plain,
    ( greater(vplus(vd329,vd330),vplus(vd328,vd330))
    | ~ spl4_49 ),
    inference(avatar_component_clause,[],[f627]) ).

fof(f630,plain,
    ( spl4_49
    | ~ spl4_14
    | ~ spl4_17 ),
    inference(avatar_split_clause,[],[f265,f248,f229,f627]) ).

fof(f229,plain,
    ( spl4_14
  <=> ! [X0,X1] :
        ( greater(X1,X0)
        | ~ less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f265,plain,
    ( greater(vplus(vd329,vd330),vplus(vd328,vd330))
    | ~ spl4_14
    | ~ spl4_17 ),
    inference(resolution,[],[f250,f230]) ).

fof(f230,plain,
    ( ! [X0,X1] :
        ( ~ less(X0,X1)
        | greater(X1,X0) )
    | ~ spl4_14 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f250,plain,
    ( less(vplus(vd328,vd330),vplus(vd329,vd330))
    | ~ spl4_17 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f624,plain,
    ( spl4_48
    | ~ spl4_16
    | ~ spl4_17 ),
    inference(avatar_split_clause,[],[f264,f248,f237,f621]) ).

fof(f621,plain,
    ( spl4_48
  <=> leq(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).

fof(f237,plain,
    ( spl4_16
  <=> ! [X0,X1] :
        ( leq(X1,X0)
        | ~ less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).

fof(f264,plain,
    ( leq(vplus(vd328,vd330),vplus(vd329,vd330))
    | ~ spl4_16
    | ~ spl4_17 ),
    inference(resolution,[],[f250,f238]) ).

fof(f238,plain,
    ( ! [X0,X1] :
        ( ~ less(X1,X0)
        | leq(X1,X0) )
    | ~ spl4_16 ),
    inference(avatar_component_clause,[],[f237]) ).

fof(f609,plain,
    ( spl4_47
    | ~ spl4_9
    | ~ spl4_29 ),
    inference(avatar_split_clause,[],[f329,f311,f209,f607]) ).

fof(f607,plain,
    ( spl4_47
  <=> ! [X0] :
        ( less(v1,X0)
        | v1 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).

fof(f329,plain,
    ( ! [X0] :
        ( less(v1,X0)
        | v1 = X0 )
    | ~ spl4_9
    | ~ spl4_29 ),
    inference(superposition,[],[f210,f312]) ).

fof(f605,plain,
    ( spl4_46
    | ~ spl4_7
    | ~ spl4_29 ),
    inference(avatar_split_clause,[],[f327,f311,f201,f603]) ).

fof(f603,plain,
    ( spl4_46
  <=> ! [X0] :
        ( greater(X0,v1)
        | v1 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).

fof(f327,plain,
    ( ! [X0] :
        ( greater(X0,v1)
        | v1 = X0 )
    | ~ spl4_7
    | ~ spl4_29 ),
    inference(superposition,[],[f202,f312]) ).

fof(f553,plain,
    ( spl4_45
    | ~ spl4_7
    | ~ spl4_18 ),
    inference(avatar_split_clause,[],[f268,f253,f201,f551]) ).

fof(f551,plain,
    ( spl4_45
  <=> ! [X0,X1] : greater(vplus(X1,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).

fof(f268,plain,
    ( ! [X0,X1] : greater(vplus(X1,X0),X0)
    | ~ spl4_7
    | ~ spl4_18 ),
    inference(superposition,[],[f202,f254]) ).

fof(f549,plain,
    ( spl4_44
    | ~ spl4_9
    | ~ spl4_18 ),
    inference(avatar_split_clause,[],[f266,f253,f209,f547]) ).

fof(f547,plain,
    ( spl4_44
  <=> ! [X0,X1] : less(X0,vplus(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).

fof(f266,plain,
    ( ! [X0,X1] : less(X0,vplus(X1,X0))
    | ~ spl4_9
    | ~ spl4_18 ),
    inference(superposition,[],[f210,f254]) ).

fof(f534,plain,
    ( ~ spl4_30
    | spl4_32 ),
    inference(avatar_contradiction_clause,[],[f533]) ).

fof(f533,plain,
    ( $false
    | ~ spl4_30
    | spl4_32 ),
    inference(trivial_inequality_removal,[],[f530]) ).

fof(f530,plain,
    ( vplus(vd328,vd330) != vplus(vd328,vd330)
    | ~ spl4_30
    | spl4_32 ),
    inference(superposition,[],[f343,f334]) ).

fof(f343,plain,
    ( vplus(vd328,vd330) != vplus(vd329,vd330)
    | spl4_32 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f341,plain,
    ( spl4_32
  <=> vplus(vd328,vd330) = vplus(vd329,vd330) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).

fof(f528,plain,
    ( ~ spl4_43
    | spl4_31 ),
    inference(avatar_split_clause,[],[f113,f336,f525]) ).

fof(f113,plain,
    ( greater(vd328,vd329)
    | ~ greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( greater(vd328,vd329)
    | ~ greater(vplus(vd328,vd330),vplus(vd329,vd330)) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ( greater(vplus(vd328,vd330),vplus(vd329,vd330))
   => greater(vd328,vd329) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(204), 0), 0)') ).

fof(f523,plain,
    ( spl4_42
    | ~ spl4_15
    | ~ spl4_31 ),
    inference(avatar_split_clause,[],[f512,f336,f233,f520]) ).

fof(f520,plain,
    ( spl4_42
  <=> geq(vd328,vd329) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).

fof(f512,plain,
    ( geq(vd328,vd329)
    | ~ spl4_15
    | ~ spl4_31 ),
    inference(resolution,[],[f338,f234]) ).

fof(f518,plain,
    ( spl4_41
    | ~ spl4_9
    | ~ spl4_16 ),
    inference(avatar_split_clause,[],[f246,f237,f209,f516]) ).

fof(f516,plain,
    ( spl4_41
  <=> ! [X0,X1] : leq(X0,vplus(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).

fof(f246,plain,
    ( ! [X0,X1] : leq(X0,vplus(X0,X1))
    | ~ spl4_9
    | ~ spl4_16 ),
    inference(resolution,[],[f238,f210]) ).

fof(f476,plain,
    spl4_40,
    inference(avatar_split_clause,[],[f130,f474]) ).

fof(f474,plain,
    ( spl4_40
  <=> ! [X0,X1] :
        ( vplus(X0,sK0(X0,X1)) = X1
        | vplus(X1,sK1(X0,X1)) = X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( vplus(X0,sK0(X0,X1)) = X1
      | vplus(X1,sK1(X0,X1)) = X0
      | X0 = X1 ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( vplus(X0,sK0(X0,X1)) = X1
      | vplus(X1,sK1(X0,X1)) = X0
      | X0 = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f57,f96,f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
     => vplus(X0,sK0(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X1,X3) = X0
     => vplus(X1,sK1(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
      | ? [X3] : vplus(X1,X3) = X0
      | X0 = X1 ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X34,X35] :
      ( ? [X37] : vplus(X34,X37) = X35
      | ? [X36] : vplus(X35,X36) = X34
      | X34 = X35 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).

fof(f407,plain,
    spl4_39,
    inference(avatar_split_clause,[],[f162,f405]) ).

fof(f162,plain,
    ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
    inference(definition_unfolding,[],[f122,f116,f116]) ).

fof(f116,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(rectify,[],[f33]) ).

fof(f33,axiom,
    ! [X47] : vplus(v1,X47) = vsucc(X47),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

fof(f122,plain,
    ! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( vsucc(X0) = vplus(X0,v1)
      & vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X51,X52] :
      ( vplus(X51,v1) = vsucc(X51)
      & vplus(X51,vsucc(X52)) = vsucc(vplus(X51,X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

fof(f403,plain,
    spl4_38,
    inference(avatar_split_clause,[],[f149,f401]) ).

fof(f149,plain,
    ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X48,X49,X50] : vplus(vplus(X48,X49),X50) = vplus(X48,vplus(X49,X50)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof(f364,plain,
    spl4_37,
    inference(avatar_split_clause,[],[f152,f362]) ).

fof(f362,plain,
    ( spl4_37
  <=> ! [X2,X0,X1] :
        ( less(vplus(X0,X2),vplus(X1,X2))
        | ~ less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( less(vplus(X0,X2),vplus(X1,X2))
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( less(vplus(X0,X2),vplus(X1,X2))
      | ~ less(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( less(X0,X1)
     => less(vplus(X0,X2),vplus(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).

fof(f360,plain,
    spl4_36,
    inference(avatar_split_clause,[],[f151,f358]) ).

fof(f151,plain,
    ! [X2,X0,X1] :
      ( greater(vplus(X0,X2),vplus(X1,X2))
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( greater(vplus(X0,X2),vplus(X1,X2))
      | ~ greater(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( greater(X0,X1)
     => greater(vplus(X0,X2),vplus(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).

fof(f356,plain,
    spl4_35,
    inference(avatar_split_clause,[],[f147,f354]) ).

fof(f354,plain,
    ( spl4_35
  <=> ! [X0,X1] :
        ( vplus(X1,sK3(X0,X1)) = X0
        | ~ less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( vplus(X1,sK3(X0,X1)) = X0
      | ~ less(X1,X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( vplus(X1,sK3(X0,X1)) = X0
        | ~ less(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f107,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X1,X3) = X0
     => vplus(X1,sK3(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( ? [X3] : vplus(X1,X3) = X0
        | ~ less(X1,X0) ) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ( less(X1,X0)
        | ! [X2] : vplus(X1,X2) != X0 )
      & ( ? [X2] : vplus(X1,X2) = X0
        | ~ less(X1,X0) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( less(X1,X0)
    <=> ? [X2] : vplus(X1,X2) = X0 ),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X28,X29] :
      ( less(X29,X28)
    <=> ? [X30] : vplus(X29,X30) = X28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

fof(f352,plain,
    spl4_34,
    inference(avatar_split_clause,[],[f145,f350]) ).

fof(f350,plain,
    ( spl4_34
  <=> ! [X0,X1] :
        ( vplus(X0,sK2(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( vplus(X0,sK2(X0,X1)) = X1
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( vplus(X0,sK2(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f103,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X0,X3) = X1
     => vplus(X0,sK2(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X3] : vplus(X0,X3) = X1
        | ~ greater(X1,X0) ) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X2] : vplus(X0,X2) = X1
        | ~ greater(X1,X0) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
    <=> ? [X2] : vplus(X0,X2) = X1 ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X31,X32] :
      ( greater(X32,X31)
    <=> ? [X33] : vplus(X31,X33) = X32 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof(f348,plain,
    spl4_33,
    inference(avatar_split_clause,[],[f133,f346]) ).

fof(f346,plain,
    ( spl4_33
  <=> ! [X2,X0,X1] :
        ( vplus(X2,X0) != vplus(X2,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).

fof(f133,plain,
    ! [X2,X0,X1] :
      ( vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( X0 != X1
     => ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ! [X38,X39] :
      ( X38 != X39
     => ! [X40] : vplus(X40,X38) != vplus(X40,X39) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).

fof(f344,plain,
    ( ~ spl4_32
    | spl4_30 ),
    inference(avatar_split_clause,[],[f112,f332,f341]) ).

fof(f112,plain,
    ( vd328 = vd329
    | vplus(vd328,vd330) != vplus(vd329,vd330) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( vd328 = vd329
    | vplus(vd328,vd330) != vplus(vd329,vd330) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ( vplus(vd328,vd330) = vplus(vd329,vd330)
   => vd328 = vd329 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(204)), 0), 0)') ).

fof(f339,plain,
    ( spl4_30
    | spl4_31
    | spl4_1
    | ~ spl4_21 ),
    inference(avatar_split_clause,[],[f314,f279,f176,f336,f332]) ).

fof(f176,plain,
    ( spl4_1
  <=> less(vd328,vd329) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f279,plain,
    ( spl4_21
  <=> ! [X0,X1] :
        ( less(X0,X1)
        | greater(X0,X1)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).

fof(f314,plain,
    ( greater(vd328,vd329)
    | vd328 = vd329
    | spl4_1
    | ~ spl4_21 ),
    inference(resolution,[],[f280,f178]) ).

fof(f178,plain,
    ( ~ less(vd328,vd329)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f176]) ).

fof(f280,plain,
    ( ! [X0,X1] :
        ( less(X0,X1)
        | greater(X0,X1)
        | X0 = X1 )
    | ~ spl4_21 ),
    inference(avatar_component_clause,[],[f279]) ).

fof(f313,plain,
    spl4_29,
    inference(avatar_split_clause,[],[f159,f311]) ).

fof(f159,plain,
    ! [X0] :
      ( vplus(v1,vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(definition_unfolding,[],[f117,f116]) ).

fof(f117,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( v1 != X0
     => vsucc(vskolem2(X0)) = X0 ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X53] :
      ( v1 != X53
     => vsucc(vskolem2(X53)) = X53 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).

fof(f309,plain,
    spl4_28,
    inference(avatar_split_clause,[],[f156,f307]) ).

fof(f307,plain,
    ( spl4_28
  <=> ! [X2,X0,X1] :
        ( less(X0,X2)
        | ~ less(X0,X1)
        | ~ leq(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( less(X0,X2)
      | ~ less(X0,X1)
      | ~ leq(X1,X2) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( less(X0,X2)
      | ( ( ~ less(X0,X1)
          | ~ leq(X1,X2) )
        & ( ~ leq(X0,X1)
          | ~ less(X1,X2) ) ) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( ( ( less(X0,X1)
          & leq(X1,X2) )
        | ( leq(X0,X1)
          & less(X1,X2) ) )
     => less(X0,X2) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X8,X9,X10] :
      ( ( ( less(X8,X9)
          & leq(X9,X10) )
        | ( leq(X8,X9)
          & less(X9,X10) ) )
     => less(X8,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).

fof(f305,plain,
    ( spl4_27
    | ~ spl4_7
    | ~ spl4_15 ),
    inference(avatar_split_clause,[],[f245,f233,f201,f303]) ).

fof(f303,plain,
    ( spl4_27
  <=> ! [X0,X1] : geq(vplus(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).

fof(f245,plain,
    ( ! [X0,X1] : geq(vplus(X0,X1),X0)
    | ~ spl4_7
    | ~ spl4_15 ),
    inference(resolution,[],[f234,f202]) ).

fof(f301,plain,
    spl4_26,
    inference(avatar_split_clause,[],[f155,f299]) ).

fof(f299,plain,
    ( spl4_26
  <=> ! [X2,X0,X1] :
        ( less(X0,X2)
        | ~ leq(X0,X1)
        | ~ less(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).

fof(f155,plain,
    ! [X2,X0,X1] :
      ( less(X0,X2)
      | ~ leq(X0,X1)
      | ~ less(X1,X2) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f297,plain,
    spl4_25,
    inference(avatar_split_clause,[],[f154,f295]) ).

fof(f295,plain,
    ( spl4_25
  <=> ! [X2,X0,X1] :
        ( less(X0,X2)
        | ~ less(X0,X1)
        | ~ less(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).

fof(f154,plain,
    ! [X2,X0,X1] :
      ( less(X0,X2)
      | ~ less(X0,X1)
      | ~ less(X1,X2) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( less(X0,X2)
      | ~ less(X0,X1)
      | ~ less(X1,X2) ),
    inference(flattening,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1,X2] :
      ( less(X0,X2)
      | ~ less(X0,X1)
      | ~ less(X1,X2) ),
    inference(ennf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( ( less(X0,X1)
        & less(X1,X2) )
     => less(X0,X2) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X11,X12,X13] :
      ( ( less(X11,X12)
        & less(X12,X13) )
     => less(X11,X13) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).

fof(f293,plain,
    spl4_24,
    inference(avatar_split_clause,[],[f153,f291]) ).

fof(f291,plain,
    ( spl4_24
  <=> ! [X2,X0,X1] :
        ( leq(X0,X2)
        | ~ leq(X0,X1)
        | ~ leq(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).

fof(f153,plain,
    ! [X2,X0,X1] :
      ( leq(X0,X2)
      | ~ leq(X0,X1)
      | ~ leq(X1,X2) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( leq(X0,X2)
      | ~ leq(X0,X1)
      | ~ leq(X1,X2) ),
    inference(flattening,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( leq(X0,X2)
      | ~ leq(X0,X1)
      | ~ leq(X1,X2) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( ( leq(X0,X1)
        & leq(X1,X2) )
     => leq(X0,X2) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X5,X6,X7] :
      ( ( leq(X5,X6)
        & leq(X6,X7) )
     => leq(X5,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).

fof(f289,plain,
    spl4_23,
    inference(avatar_split_clause,[],[f142,f287]) ).

fof(f287,plain,
    ( spl4_23
  <=> ! [X0,X1] :
        ( X0 = X1
        | less(X1,X0)
        | ~ leq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( X0 = X1
      | less(X1,X0)
      | ~ leq(X1,X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( leq(X1,X0)
        | ( X0 != X1
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | ~ leq(X1,X0) ) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( leq(X1,X0)
        | ( X0 != X1
          & ~ less(X1,X0) ) )
      & ( X0 = X1
        | less(X1,X0)
        | ~ leq(X1,X0) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
    <=> ( X0 = X1
        | less(X1,X0) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X18,X19] :
      ( leq(X19,X18)
    <=> ( X18 = X19
        | less(X19,X18) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).

fof(f285,plain,
    spl4_22,
    inference(avatar_split_clause,[],[f139,f283]) ).

fof(f283,plain,
    ( spl4_22
  <=> ! [X0,X1] :
        ( X0 = X1
        | greater(X1,X0)
        | ~ geq(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( X0 = X1
      | greater(X1,X0)
      | ~ geq(X1,X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( geq(X1,X0)
        | ( X0 != X1
          & ~ greater(X1,X0) ) )
      & ( X0 = X1
        | greater(X1,X0)
        | ~ geq(X1,X0) ) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( geq(X1,X0)
        | ( X0 != X1
          & ~ greater(X1,X0) ) )
      & ( X0 = X1
        | greater(X1,X0)
        | ~ geq(X1,X0) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
    <=> ( X0 = X1
        | greater(X1,X0) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X20,X21] :
      ( geq(X21,X20)
    <=> ( X20 = X21
        | greater(X21,X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).

fof(f281,plain,
    spl4_21,
    inference(avatar_split_clause,[],[f129,f279]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( less(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( less(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(rectify,[],[f19]) ).

fof(f19,axiom,
    ! [X26,X27] :
      ( less(X26,X27)
      | greater(X26,X27)
      | X26 = X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

fof(f263,plain,
    spl4_20,
    inference(avatar_split_clause,[],[f169,f261]) ).

fof(f169,plain,
    ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
    inference(equality_resolution,[],[f131]) ).

fof(f131,plain,
    ! [X2,X3,X0,X1] :
      ( vplus(X0,X2) != X1
      | vplus(X1,X3) != X0 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | ! [X3] : vplus(X1,X3) != X0 ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | ~ ? [X3] : vplus(X1,X3) = X0 ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X34,X35] :
      ( ~ ? [X37] : vplus(X34,X37) = X35
      | ~ ? [X36] : vplus(X35,X36) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

fof(f259,plain,
    ( spl4_19
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(avatar_split_clause,[],[f240,f213,f201,f257]) ).

fof(f257,plain,
    ( spl4_19
  <=> ! [X0,X1] : ~ less(vplus(X0,X1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f240,plain,
    ( ! [X0,X1] : ~ less(vplus(X0,X1),X0)
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(resolution,[],[f214,f202]) ).

fof(f255,plain,
    spl4_18,
    inference(avatar_split_clause,[],[f120,f253]) ).

fof(f120,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(rectify,[],[f31]) ).

fof(f31,axiom,
    ! [X43,X44] : vplus(X44,X43) = vplus(X43,X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof(f251,plain,
    spl4_17,
    inference(avatar_split_clause,[],[f111,f248]) ).

fof(f111,plain,
    less(vplus(vd328,vd330),vplus(vd329,vd330)),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    less(vplus(vd328,vd330),vplus(vd329,vd330)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).

fof(f239,plain,
    spl4_16,
    inference(avatar_split_clause,[],[f143,f237]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | ~ less(X1,X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f235,plain,
    spl4_15,
    inference(avatar_split_clause,[],[f140,f233]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f231,plain,
    spl4_14,
    inference(avatar_split_clause,[],[f137,f229]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
      | ~ less(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
      | ~ less(X0,X1) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( less(X0,X1)
     => greater(X1,X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X22,X23] :
      ( less(X22,X23)
     => greater(X23,X22) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

fof(f227,plain,
    spl4_13,
    inference(avatar_split_clause,[],[f136,f225]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( less(X1,X0)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( less(X1,X0)
      | ~ greater(X0,X1) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( greater(X0,X1)
     => less(X1,X0) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X24,X25] :
      ( greater(X24,X25)
     => less(X25,X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

fof(f223,plain,
    spl4_12,
    inference(avatar_split_clause,[],[f135,f221]) ).

fof(f221,plain,
    ( spl4_12
  <=> ! [X0,X1] :
        ( geq(X1,X0)
        | ~ leq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
      | ~ leq(X0,X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
      | ~ leq(X0,X1) ),
    inference(ennf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
     => geq(X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X14,X15] :
      ( leq(X14,X15)
     => geq(X15,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).

fof(f219,plain,
    spl4_11,
    inference(avatar_split_clause,[],[f134,f217]) ).

fof(f217,plain,
    ( spl4_11
  <=> ! [X0,X1] :
        ( leq(X1,X0)
        | ~ geq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | ~ geq(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | ~ geq(X0,X1) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( geq(X0,X1)
     => leq(X1,X0) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X16,X17] :
      ( geq(X16,X17)
     => leq(X17,X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).

fof(f215,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f128,f213]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ greater(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X26,X27] :
      ( ~ less(X26,X27)
      | ~ greater(X26,X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

fof(f211,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f173,f209]) ).

fof(f173,plain,
    ! [X2,X1] : less(X1,vplus(X1,X2)),
    inference(equality_resolution,[],[f148]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( less(X1,X0)
      | vplus(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f207,plain,
    spl4_8,
    inference(avatar_split_clause,[],[f167,f205]) ).

fof(f205,plain,
    ( spl4_8
  <=> ! [X2,X1] : vplus(X1,X2) != X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f167,plain,
    ! [X2,X1] : vplus(X1,X2) != X1,
    inference(equality_resolution,[],[f126]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X1,X2) = X0
      | X0 != X1 ),
    inference(rectify,[],[f28]) ).

fof(f28,axiom,
    ! [X34,X35] :
      ( ~ ? [X36] : vplus(X35,X36) = X34
      | X34 != X35 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

fof(f203,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f119,f201]) ).

fof(f119,plain,
    ! [X0,X1] : greater(vplus(X0,X1),X0),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] : greater(vplus(X0,X1),X0),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X3,X4] : greater(vplus(X3,X4),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).

fof(f199,plain,
    spl4_6,
    inference(avatar_split_clause,[],[f118,f197]) ).

fof(f118,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(rectify,[],[f30]) ).

fof(f30,axiom,
    ! [X41,X42] : vplus(X41,X42) != X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

fof(f195,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f171,f193]) ).

fof(f193,plain,
    ( spl4_5
  <=> ! [X1] : leq(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f171,plain,
    ! [X1] : leq(X1,X1),
    inference(equality_resolution,[],[f144]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( leq(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f191,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f170,f189]) ).

fof(f189,plain,
    ( spl4_4
  <=> ! [X1] : geq(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f170,plain,
    ! [X1] : geq(X1,X1),
    inference(equality_resolution,[],[f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( geq(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f99]) ).

fof(f187,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f166,f185]) ).

fof(f185,plain,
    ( spl4_3
  <=> ! [X1] : ~ less(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f166,plain,
    ! [X1] : ~ less(X1,X1),
    inference(equality_resolution,[],[f125]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X26,X27] :
      ( ~ less(X26,X27)
      | X26 != X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

fof(f183,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f165,f181]) ).

fof(f165,plain,
    ! [X1] : ~ greater(X1,X1),
    inference(equality_resolution,[],[f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | X0 != X1 ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X26,X27] :
      ( ~ greater(X26,X27)
      | X26 != X27 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).

fof(f179,plain,
    ~ spl4_1,
    inference(avatar_split_clause,[],[f110,f176]) ).

fof(f110,plain,
    ~ less(vd328,vd329),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ~ less(vd328,vd329),
    inference(flattening,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ less(vd328,vd329),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    less(vd328,vd329),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17  % Problem    : NUM840+1 : TPTP v8.1.2. Released v4.1.0.
% 0.15/0.18  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.40  % Computer : n017.cluster.edu
% 0.15/0.40  % Model    : x86_64 x86_64
% 0.15/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40  % Memory   : 8042.1875MB
% 0.15/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.40  % CPULimit   : 300
% 0.15/0.40  % WCLimit    : 300
% 0.15/0.40  % DateTime   : Mon Apr 29 23:18:03 EDT 2024
% 0.15/0.40  % CPUTime    : 
% 0.15/0.41  % (20274)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.44  % (20280)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)
% 0.15/0.44  % (20278)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.44  % (20281)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)
% 0.15/0.44  % (20279)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)
% 0.15/0.44  TRYING [1]
% 0.15/0.44  TRYING [2]
% 0.15/0.45  TRYING [3]
% 0.15/0.46  TRYING [4]
% 0.22/0.47  % (20279)First to succeed.
% 0.22/0.48  % (20275)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.48  % (20279)Refutation found. Thanks to Tanya!
% 0.22/0.48  % SZS status Theorem for theBenchmark
% 0.22/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.49  % (20279)------------------------------
% 0.22/0.49  % (20279)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.49  % (20279)Termination reason: Refutation
% 0.22/0.49  
% 0.22/0.49  % (20279)Memory used [KB]: 1135
% 0.22/0.49  % (20279)Time elapsed: 0.043 s
% 0.22/0.49  % (20279)Instructions burned: 35 (million)
% 0.22/0.49  % (20279)------------------------------
% 0.22/0.49  % (20279)------------------------------
% 0.22/0.49  % (20274)Success in time 0.073 s
%------------------------------------------------------------------------------