TSTP Solution File: SWV384+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV384+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:18:26 EDT 2024

% Result   : Theorem 0.20s 0.39s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  126
% Syntax   : Number of formulae    :  385 (  94 unt;   0 def)
%            Number of atoms       : 1024 ( 175 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 1065 ( 426   ~; 438   |;  76   &)
%                                         (  86 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   90 (  88 usr;  80 prp; 0-3 aty)
%            Number of functors    :   31 (  31 usr;  15 con; 0-3 aty)
%            Number of variables   :  865 ( 811   !;  54   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f661,plain,
    $false,
    inference(avatar_sat_refutation,[],[f176,f181,f186,f191,f200,f204,f208,f212,f216,f220,f224,f228,f232,f236,f240,f250,f254,f258,f262,f266,f270,f274,f278,f284,f288,f292,f296,f300,f304,f315,f324,f329,f334,f338,f347,f354,f358,f362,f368,f373,f377,f382,f392,f396,f404,f408,f412,f416,f420,f424,f441,f449,f453,f461,f468,f477,f481,f485,f495,f500,f505,f512,f521,f526,f531,f535,f543,f556,f561,f570,f574,f578,f582,f589,f593,f598,f602,f636,f651,f657,f660]) ).

fof(f660,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_6
    | ~ spl13_4
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f637,f634,f188,f197,f178,f173]) ).

fof(f173,plain,
    ( spl13_1
  <=> ok(triple(sK4,sK5,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f178,plain,
    ( spl13_2
  <=> check_cpq(triple(sK4,sK5,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f197,plain,
    ( spl13_6
  <=> ok(triple(sK1,sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f188,plain,
    ( spl13_4
  <=> succ_cpq(triple(sK1,sK2,sK3),triple(sK4,sK5,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f634,plain,
    ( spl13_76
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ check_cpq(triple(X3,X4,X5))
        | ok(triple(X0,X1,X2))
        | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
        | ~ ok(triple(X3,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).

fof(f637,plain,
    ( ok(triple(sK1,sK2,sK3))
    | ~ check_cpq(triple(sK4,sK5,sK6))
    | ~ ok(triple(sK4,sK5,sK6))
    | ~ spl13_4
    | ~ spl13_76 ),
    inference(resolution,[],[f635,f190]) ).

fof(f190,plain,
    ( succ_cpq(triple(sK1,sK2,sK3),triple(sK4,sK5,sK6))
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f188]) ).

fof(f635,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
        | ok(triple(X0,X1,X2))
        | ~ check_cpq(triple(X3,X4,X5))
        | ~ ok(triple(X3,X4,X5)) )
    | ~ spl13_76 ),
    inference(avatar_component_clause,[],[f634]) ).

fof(f657,plain,
    ( spl13_78
    | ~ spl13_19
    | ~ spl13_34 ),
    inference(avatar_split_clause,[],[f330,f327,f252,f655]) ).

fof(f655,plain,
    ( spl13_78
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X2,triple(X0,create_slb,sK3))
        | ~ succ_cpq(X2,triple(X0,create_slb,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).

fof(f252,plain,
    ( spl13_19
  <=> ! [X0,X1] :
        ( succ_cpq(X0,findmin_cpq_eff(X1))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).

fof(f327,plain,
    ( spl13_34
  <=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).

fof(f330,plain,
    ( ! [X2,X0,X1] :
        ( succ_cpq(X2,triple(X0,create_slb,sK3))
        | ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
    | ~ spl13_19
    | ~ spl13_34 ),
    inference(superposition,[],[f253,f328]) ).

fof(f328,plain,
    ( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK3)
    | ~ spl13_34 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f253,plain,
    ( ! [X0,X1] :
        ( succ_cpq(X0,findmin_cpq_eff(X1))
        | ~ succ_cpq(X0,X1) )
    | ~ spl13_19 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f651,plain,
    ( spl13_77
    | ~ spl13_7
    | ~ spl13_43 ),
    inference(avatar_split_clause,[],[f622,f375,f202,f649]) ).

fof(f649,plain,
    ( spl13_77
  <=> ! [X2,X0,X1] : triple(X0,create_slb,sK3) = remove_cpq(triple(X0,create_slb,X1),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).

fof(f202,plain,
    ( spl13_7
  <=> ! [X0] : ~ contains_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f375,plain,
    ( spl13_43
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK3)
        | contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).

fof(f622,plain,
    ( ! [X2,X0,X1] : triple(X0,create_slb,sK3) = remove_cpq(triple(X0,create_slb,X1),X2)
    | ~ spl13_7
    | ~ spl13_43 ),
    inference(resolution,[],[f376,f203]) ).

fof(f203,plain,
    ( ! [X0] : ~ contains_slb(create_slb,X0)
    | ~ spl13_7 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f376,plain,
    ( ! [X2,X3,X0,X1] :
        ( contains_slb(X1,X3)
        | remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK3) )
    | ~ spl13_43 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f636,plain,
    ( spl13_17
    | spl13_76 ),
    inference(avatar_split_clause,[],[f117,f634,f243]) ).

fof(f243,plain,
    ( spl13_17
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).

fof(f117,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ check_cpq(triple(X3,X4,X5))
      | ~ ok(triple(X3,X4,X5))
      | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
      | ok(triple(X0,X1,X2))
      | sP0 ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3,X4,X5] :
            ( ~ check_cpq(triple(X3,X4,X5))
            | ~ ok(triple(X3,X4,X5))
            | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
        | ( ok(triple(X0,X1,X2))
          & check_cpq(triple(X0,X1,X2)) ) )
    | sP0 ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ( ! [X6,X7,X8] :
        ( ! [X9,X10,X11] :
            ( ~ check_cpq(triple(X9,X10,X11))
            | ~ ok(triple(X9,X10,X11))
            | ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
        | ( ok(triple(X6,X7,X8))
          & check_cpq(triple(X6,X7,X8)) ) )
    | sP0 ),
    inference(definition_folding,[],[f60,f90]) ).

fof(f90,plain,
    ( ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & check_cpq(im_succ_cpq(triple(X3,X4,X5)))
        & ( ~ ok(triple(X3,X4,X5))
          | ~ check_cpq(triple(X3,X4,X5)) )
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f60,plain,
    ( ! [X6,X7,X8] :
        ( ! [X9,X10,X11] :
            ( ~ check_cpq(triple(X9,X10,X11))
            | ~ ok(triple(X9,X10,X11))
            | ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
        | ( ok(triple(X6,X7,X8))
          & check_cpq(triple(X6,X7,X8)) ) )
    | ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & check_cpq(im_succ_cpq(triple(X3,X4,X5)))
        & ( ~ ok(triple(X3,X4,X5))
          | ~ check_cpq(triple(X3,X4,X5)) )
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ( ! [X6,X7,X8] :
        ( ! [X9,X10,X11] :
            ( ~ check_cpq(triple(X9,X10,X11))
            | ~ ok(triple(X9,X10,X11))
            | ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
        | ( ok(triple(X6,X7,X8))
          & check_cpq(triple(X6,X7,X8)) ) )
    | ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & check_cpq(im_succ_cpq(triple(X3,X4,X5)))
        & ( ~ ok(triple(X3,X4,X5))
          | ~ check_cpq(triple(X3,X4,X5)) )
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ( ! [X0,X1,X2,X3,X4,X5] :
        ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
       => ( ( ~ ok(triple(X3,X4,X5))
            | ~ check_cpq(triple(X3,X4,X5)) )
         => ( ~ ok(im_succ_cpq(triple(X3,X4,X5)))
            | ~ check_cpq(im_succ_cpq(triple(X3,X4,X5))) ) ) )
   => ! [X6,X7,X8] :
        ( ( ~ ok(triple(X6,X7,X8))
          | ~ check_cpq(triple(X6,X7,X8)) )
       => ! [X9,X10,X11] :
            ( succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11))
           => ( ~ check_cpq(triple(X9,X10,X11))
              | ~ ok(triple(X9,X10,X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l20_induction) ).

fof(f602,plain,
    ( spl13_75
    | ~ spl13_44
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f594,f586,f380,f600]) ).

fof(f600,plain,
    ( spl13_75
  <=> ! [X0] : triple(X0,create_slb,sK3) = triple(X0,create_slb,sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).

fof(f380,plain,
    ( spl13_44
  <=> ! [X0] : triple(X0,create_slb,bad) = triple(X0,create_slb,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).

fof(f586,plain,
    ( spl13_74
  <=> bad = sK12 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).

fof(f594,plain,
    ( ! [X0] : triple(X0,create_slb,sK3) = triple(X0,create_slb,sK12)
    | ~ spl13_44
    | ~ spl13_74 ),
    inference(forward_demodulation,[],[f381,f588]) ).

fof(f588,plain,
    ( bad = sK12
    | ~ spl13_74 ),
    inference(avatar_component_clause,[],[f586]) ).

fof(f381,plain,
    ( ! [X0] : triple(X0,create_slb,bad) = triple(X0,create_slb,sK3)
    | ~ spl13_44 ),
    inference(avatar_component_clause,[],[f380]) ).

fof(f598,plain,
    ( spl13_32
    | ~ spl13_24
    | ~ spl13_42 ),
    inference(avatar_split_clause,[],[f438,f371,f272,f312]) ).

fof(f312,plain,
    ( spl13_32
  <=> bad = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).

fof(f272,plain,
    ( spl13_24
  <=> ! [X2,X0,X1] :
        ( bad = X2
        | ok(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f371,plain,
    ( spl13_42
  <=> ! [X0,X1] : ~ ok(triple(X0,X1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).

fof(f438,plain,
    ( bad = sK3
    | ~ spl13_24
    | ~ spl13_42 ),
    inference(resolution,[],[f372,f273]) ).

fof(f273,plain,
    ( ! [X2,X0,X1] :
        ( ok(triple(X0,X1,X2))
        | bad = X2 )
    | ~ spl13_24 ),
    inference(avatar_component_clause,[],[f272]) ).

fof(f372,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,sK3))
    | ~ spl13_42 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f593,plain,
    ( spl13_64
    | ~ spl13_18
    | ~ spl13_48
    | ~ spl13_61 ),
    inference(avatar_split_clause,[],[f506,f497,f406,f247,f518]) ).

fof(f518,plain,
    ( spl13_64
  <=> ok(triple(sK10,sK11,sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).

fof(f247,plain,
    ( spl13_18
  <=> check_cpq(im_succ_cpq(triple(sK10,sK11,sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).

fof(f406,plain,
    ( spl13_48
  <=> ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
        | ok(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).

fof(f497,plain,
    ( spl13_61
  <=> ok(im_succ_cpq(triple(sK10,sK11,sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).

fof(f506,plain,
    ( ~ check_cpq(im_succ_cpq(triple(sK10,sK11,sK12)))
    | ok(triple(sK10,sK11,sK12))
    | ~ spl13_48
    | ~ spl13_61 ),
    inference(resolution,[],[f499,f407]) ).

fof(f407,plain,
    ( ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
        | ok(triple(X0,X1,X2)) )
    | ~ spl13_48 ),
    inference(avatar_component_clause,[],[f406]) ).

fof(f499,plain,
    ( ok(im_succ_cpq(triple(sK10,sK11,sK12)))
    | ~ spl13_61 ),
    inference(avatar_component_clause,[],[f497]) ).

fof(f589,plain,
    ( spl13_74
    | ~ spl13_24
    | spl13_64 ),
    inference(avatar_split_clause,[],[f522,f518,f272,f586]) ).

fof(f522,plain,
    ( bad = sK12
    | ~ spl13_24
    | spl13_64 ),
    inference(resolution,[],[f520,f273]) ).

fof(f520,plain,
    ( ~ ok(triple(sK10,sK11,sK12))
    | spl13_64 ),
    inference(avatar_component_clause,[],[f518]) ).

fof(f582,plain,
    ( spl13_63
    | ~ spl13_18
    | ~ spl13_47
    | ~ spl13_61 ),
    inference(avatar_split_clause,[],[f507,f497,f402,f247,f514]) ).

fof(f514,plain,
    ( spl13_63
  <=> check_cpq(triple(sK10,sK11,sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).

fof(f402,plain,
    ( spl13_47
  <=> ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
        | check_cpq(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).

fof(f507,plain,
    ( ~ check_cpq(im_succ_cpq(triple(sK10,sK11,sK12)))
    | check_cpq(triple(sK10,sK11,sK12))
    | ~ spl13_47
    | ~ spl13_61 ),
    inference(resolution,[],[f499,f403]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
        | check_cpq(triple(X0,X1,X2)) )
    | ~ spl13_47 ),
    inference(avatar_component_clause,[],[f402]) ).

fof(f578,plain,
    ( spl13_73
    | ~ spl13_24
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f432,f410,f272,f576]) ).

fof(f576,plain,
    ( spl13_73
  <=> ! [X0,X3,X2,X1] :
        ( ok(insert_cpq(triple(X0,X2,X3),X1))
        | bad = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).

fof(f410,plain,
    ( spl13_49
  <=> ! [X0,X3,X2,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).

fof(f432,plain,
    ( ! [X2,X3,X0,X1] :
        ( ok(insert_cpq(triple(X0,X2,X3),X1))
        | bad = X3 )
    | ~ spl13_24
    | ~ spl13_49 ),
    inference(superposition,[],[f273,f411]) ).

fof(f411,plain,
    ( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
    | ~ spl13_49 ),
    inference(avatar_component_clause,[],[f410]) ).

fof(f574,plain,
    ( spl13_72
    | ~ spl13_58
    | ~ spl13_68 ),
    inference(avatar_split_clause,[],[f550,f541,f479,f572]) ).

fof(f572,plain,
    ( spl13_72
  <=> ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(bottom,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).

fof(f479,plain,
    ( spl13_58
  <=> ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).

fof(f541,plain,
    ( spl13_68
  <=> ! [X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,bottom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).

fof(f550,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(bottom,X0) )
    | ~ spl13_58
    | ~ spl13_68 ),
    inference(resolution,[],[f542,f480]) ).

fof(f480,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0) )
    | ~ spl13_58 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f542,plain,
    ( ! [X0,X1] :
        ( ~ less_than(X0,bottom)
        | less_than(X0,X1) )
    | ~ spl13_68 ),
    inference(avatar_component_clause,[],[f541]) ).

fof(f570,plain,
    ( spl13_71
    | ~ spl13_38
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f425,f410,f352,f568]) ).

fof(f568,plain,
    ( spl13_71
  <=> ! [X0,X3,X2,X1] :
        ( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
        | ~ strictly_less_than(X1,bottom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).

fof(f352,plain,
    ( spl13_38
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ strictly_less_than(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).

fof(f425,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
        | ~ strictly_less_than(X1,bottom) )
    | ~ spl13_38
    | ~ spl13_49 ),
    inference(superposition,[],[f353,f411]) ).

fof(f353,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ strictly_less_than(X3,X4) )
    | ~ spl13_38 ),
    inference(avatar_component_clause,[],[f352]) ).

fof(f561,plain,
    ( spl13_70
    | ~ spl13_15
    | ~ spl13_29 ),
    inference(avatar_split_clause,[],[f318,f294,f234,f559]) ).

fof(f559,plain,
    ( spl13_70
  <=> ! [X2,X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,X2)
        | less_than(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).

fof(f234,plain,
    ( spl13_15
  <=> ! [X0,X1] :
        ( less_than(X1,X0)
        | less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).

fof(f294,plain,
    ( spl13_29
  <=> ! [X2,X0,X1] :
        ( less_than(X0,X2)
        | ~ less_than(X1,X2)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).

fof(f318,plain,
    ( ! [X2,X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,X2)
        | less_than(X1,X2) )
    | ~ spl13_15
    | ~ spl13_29 ),
    inference(resolution,[],[f295,f235]) ).

fof(f235,plain,
    ( ! [X0,X1] :
        ( less_than(X1,X0)
        | less_than(X0,X1) )
    | ~ spl13_15 ),
    inference(avatar_component_clause,[],[f234]) ).

fof(f295,plain,
    ( ! [X2,X0,X1] :
        ( ~ less_than(X1,X2)
        | less_than(X0,X2)
        | ~ less_than(X0,X1) )
    | ~ spl13_29 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f556,plain,
    ( spl13_69
    | ~ spl13_14
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f426,f410,f230,f554]) ).

fof(f554,plain,
    ( spl13_69
  <=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).

fof(f230,plain,
    ( spl13_14
  <=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).

fof(f426,plain,
    ( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
    | ~ spl13_14
    | ~ spl13_49 ),
    inference(superposition,[],[f231,f411]) ).

fof(f231,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
    | ~ spl13_14 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f543,plain,
    ( spl13_68
    | ~ spl13_9
    | ~ spl13_29 ),
    inference(avatar_split_clause,[],[f317,f294,f210,f541]) ).

fof(f210,plain,
    ( spl13_9
  <=> ! [X0] : less_than(bottom,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f317,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,bottom) )
    | ~ spl13_9
    | ~ spl13_29 ),
    inference(resolution,[],[f295,f211]) ).

fof(f211,plain,
    ( ! [X0] : less_than(bottom,X0)
    | ~ spl13_9 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f535,plain,
    ( spl13_67
    | ~ spl13_24
    | spl13_64
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f527,f524,f518,f272,f533]) ).

fof(f533,plain,
    ( spl13_67
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK12)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).

fof(f524,plain,
    ( spl13_65
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).

fof(f527,plain,
    ( ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK12)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl13_24
    | spl13_64
    | ~ spl13_65 ),
    inference(forward_demodulation,[],[f525,f522]) ).

fof(f525,plain,
    ( ! [X2,X0,X1] :
        ( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl13_65 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f531,plain,
    spl13_66,
    inference(avatar_split_clause,[],[f150,f529]) ).

fof(f529,plain,
    ( spl13_66
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
        | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

fof(f526,plain,
    spl13_65,
    inference(avatar_split_clause,[],[f149,f524]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).

fof(f521,plain,
    ( ~ spl13_17
    | ~ spl13_63
    | ~ spl13_64 ),
    inference(avatar_split_clause,[],[f113,f518,f514,f243]) ).

fof(f113,plain,
    ( ~ ok(triple(sK10,sK11,sK12))
    | ~ check_cpq(triple(sK10,sK11,sK12))
    | ~ sP0 ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ( ( ok(im_succ_cpq(triple(sK10,sK11,sK12)))
      & check_cpq(im_succ_cpq(triple(sK10,sK11,sK12)))
      & ( ~ ok(triple(sK10,sK11,sK12))
        | ~ check_cpq(triple(sK10,sK11,sK12)) )
      & succ_cpq(triple(sK7,sK8,sK9),triple(sK10,sK11,sK12)) )
    | ~ sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12])],[f95,f96]) ).

fof(f96,plain,
    ( ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & check_cpq(im_succ_cpq(triple(X3,X4,X5)))
        & ( ~ ok(triple(X3,X4,X5))
          | ~ check_cpq(triple(X3,X4,X5)) )
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
   => ( ok(im_succ_cpq(triple(sK10,sK11,sK12)))
      & check_cpq(im_succ_cpq(triple(sK10,sK11,sK12)))
      & ( ~ ok(triple(sK10,sK11,sK12))
        | ~ check_cpq(triple(sK10,sK11,sK12)) )
      & succ_cpq(triple(sK7,sK8,sK9),triple(sK10,sK11,sK12)) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ( ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & check_cpq(im_succ_cpq(triple(X3,X4,X5)))
        & ( ~ ok(triple(X3,X4,X5))
          | ~ check_cpq(triple(X3,X4,X5)) )
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f90]) ).

fof(f512,plain,
    ( ~ spl13_17
    | spl13_62 ),
    inference(avatar_split_clause,[],[f112,f509,f243]) ).

fof(f509,plain,
    ( spl13_62
  <=> succ_cpq(triple(sK7,sK8,sK9),triple(sK10,sK11,sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).

fof(f112,plain,
    ( succ_cpq(triple(sK7,sK8,sK9),triple(sK10,sK11,sK12))
    | ~ sP0 ),
    inference(cnf_transformation,[],[f97]) ).

fof(f505,plain,
    ( ~ spl13_1
    | ~ spl13_2
    | spl13_5
    | ~ spl13_4
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f501,f493,f188,f193,f178,f173]) ).

fof(f193,plain,
    ( spl13_5
  <=> check_cpq(triple(sK1,sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f493,plain,
    ( spl13_60
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ check_cpq(triple(X3,X4,X5))
        | check_cpq(triple(X0,X1,X2))
        | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
        | ~ ok(triple(X3,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).

fof(f501,plain,
    ( check_cpq(triple(sK1,sK2,sK3))
    | ~ check_cpq(triple(sK4,sK5,sK6))
    | ~ ok(triple(sK4,sK5,sK6))
    | ~ spl13_4
    | ~ spl13_60 ),
    inference(resolution,[],[f494,f190]) ).

fof(f494,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
        | check_cpq(triple(X0,X1,X2))
        | ~ check_cpq(triple(X3,X4,X5))
        | ~ ok(triple(X3,X4,X5)) )
    | ~ spl13_60 ),
    inference(avatar_component_clause,[],[f493]) ).

fof(f500,plain,
    ( ~ spl13_17
    | spl13_61 ),
    inference(avatar_split_clause,[],[f115,f497,f243]) ).

fof(f115,plain,
    ( ok(im_succ_cpq(triple(sK10,sK11,sK12)))
    | ~ sP0 ),
    inference(cnf_transformation,[],[f97]) ).

fof(f495,plain,
    ( spl13_17
    | spl13_60 ),
    inference(avatar_split_clause,[],[f116,f493,f243]) ).

fof(f116,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ check_cpq(triple(X3,X4,X5))
      | ~ ok(triple(X3,X4,X5))
      | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
      | check_cpq(triple(X0,X1,X2))
      | sP0 ),
    inference(cnf_transformation,[],[f98]) ).

fof(f485,plain,
    spl13_59,
    inference(avatar_split_clause,[],[f152,f483]) ).

fof(f483,plain,
    ( spl13_59
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
        | ~ less_than(lookup_slb(X1,X3),X3)
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).

fof(f152,plain,
    ! [X2,X3,X0,X1] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(lookup_slb(X1,X3),X3)
        & contains_slb(X1,X3) )
     => remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).

fof(f481,plain,
    ( spl13_58
    | ~ spl13_15
    | ~ spl13_26 ),
    inference(avatar_split_clause,[],[f310,f282,f234,f479]) ).

fof(f282,plain,
    ( spl13_26
  <=> ! [X0,X1] :
        ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).

fof(f310,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0) )
    | ~ spl13_15
    | ~ spl13_26 ),
    inference(duplicate_literal_removal,[],[f307]) ).

fof(f307,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0)
        | less_than(X0,X1) )
    | ~ spl13_15
    | ~ spl13_26 ),
    inference(resolution,[],[f283,f235]) ).

fof(f283,plain,
    ( ! [X0,X1] :
        ( ~ less_than(X0,X1)
        | less_than(X1,X0)
        | strictly_less_than(X0,X1) )
    | ~ spl13_26 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f477,plain,
    spl13_57,
    inference(avatar_split_clause,[],[f151,f475]) ).

fof(f475,plain,
    ( spl13_57
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
        | ~ strictly_less_than(X3,lookup_slb(X1,X3))
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).

fof(f151,plain,
    ! [X2,X3,X0,X1] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(X3,lookup_slb(X1,X3))
        & contains_slb(X1,X3) )
     => remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f468,plain,
    spl13_56,
    inference(avatar_split_clause,[],[f147,f466]) ).

fof(f466,plain,
    ( spl13_56
  <=> ! [X0,X3,X2,X1] :
        ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
        | ~ contains_slb(X0,X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).

fof(f147,plain,
    ! [X2,X3,X0,X1] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2,X3] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2,X3] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(X0,X2)
        & X1 != X2 )
     => remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f461,plain,
    spl13_55,
    inference(avatar_split_clause,[],[f148,f459]) ).

fof(f459,plain,
    ( spl13_55
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

fof(f453,plain,
    spl13_54,
    inference(avatar_split_clause,[],[f145,f451]) ).

fof(f451,plain,
    ( spl13_54
  <=> ! [X0,X3,X2,X1] :
        ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
        | ~ less_than(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1,X2,X3] :
      ( less_than(X2,X3)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

fof(f449,plain,
    spl13_53,
    inference(avatar_split_clause,[],[f144,f447]) ).

fof(f447,plain,
    ( spl13_53
  <=> ! [X0,X3,X2,X1] :
        ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
        | ~ strictly_less_than(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).

fof(f144,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1,X2,X3] :
      ( strictly_less_than(X3,X2)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

fof(f441,plain,
    ( ~ spl13_6
    | ~ spl13_42 ),
    inference(avatar_contradiction_clause,[],[f439]) ).

fof(f439,plain,
    ( $false
    | ~ spl13_6
    | ~ spl13_42 ),
    inference(resolution,[],[f372,f198]) ).

fof(f198,plain,
    ( ok(triple(sK1,sK2,sK3))
    | ~ spl13_6 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f424,plain,
    spl13_52,
    inference(avatar_split_clause,[],[f160,f422]) ).

fof(f422,plain,
    ( spl13_52
  <=> ! [X4,X0,X3,X2,X1] :
        ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ check_cpq(triple(X0,X1,X2))
        | ~ less_than(X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).

fof(f160,plain,
    ! [X2,X3,X0,X1,X4] :
      ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ check_cpq(triple(X0,X1,X2))
      | ~ less_than(X4,X3) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
          | ~ check_cpq(triple(X0,X1,X2)) )
        & ( check_cpq(triple(X0,X1,X2))
          | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
      | ~ less_than(X4,X3) ),
    inference(nnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) )
      | ~ less_than(X4,X3) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( less_than(X4,X3)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f420,plain,
    spl13_51,
    inference(avatar_split_clause,[],[f159,f418]) ).

fof(f418,plain,
    ( spl13_51
  <=> ! [X4,X0,X3,X2,X1] :
        ( check_cpq(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ less_than(X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).

fof(f159,plain,
    ! [X2,X3,X0,X1,X4] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ less_than(X4,X3) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f416,plain,
    spl13_50,
    inference(avatar_split_clause,[],[f146,f414]) ).

fof(f414,plain,
    ( spl13_50
  <=> ! [X0,X3,X2,X1] :
        ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
        | ~ contains_slb(X0,X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).

fof(f146,plain,
    ! [X2,X3,X0,X1] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(X0,X2)
        & X1 != X2 )
     => lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

fof(f412,plain,
    spl13_49,
    inference(avatar_split_clause,[],[f141,f410]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f408,plain,
    spl13_48,
    inference(avatar_split_clause,[],[f110,f406]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
      | ( ok(triple(X0,X1,X2))
        & check_cpq(triple(X0,X1,X2)) ) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
      | ( ok(triple(X0,X1,X2))
        & check_cpq(triple(X0,X1,X2)) ) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ( ( ~ ok(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,X1,X2)) )
     => ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_l13) ).

fof(f404,plain,
    spl13_47,
    inference(avatar_split_clause,[],[f109,f402]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ~ check_cpq(im_succ_cpq(triple(X0,X1,X2)))
      | check_cpq(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f396,plain,
    spl13_46,
    inference(avatar_split_clause,[],[f162,f394]) ).

fof(f394,plain,
    ( spl13_46
  <=> ! [X4,X0,X3,X2,X1] :
        ( X3 = X4
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X3 = X4
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
    <=> ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f392,plain,
    spl13_45,
    inference(avatar_split_clause,[],[f161,f390]) ).

fof(f390,plain,
    ( spl13_45
  <=> ! [X4,X0,X3,X2,X1] :
        ( X1 = X2
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).

fof(f161,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X2
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f382,plain,
    ( spl13_44
    | ~ spl13_33
    | ~ spl13_34 ),
    inference(avatar_split_clause,[],[f378,f327,f322,f380]) ).

fof(f322,plain,
    ( spl13_33
  <=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).

fof(f378,plain,
    ( ! [X0] : triple(X0,create_slb,bad) = triple(X0,create_slb,sK3)
    | ~ spl13_33
    | ~ spl13_34 ),
    inference(forward_demodulation,[],[f323,f328]) ).

fof(f323,plain,
    ( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
    | ~ spl13_33 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f377,plain,
    ( spl13_43
    | ~ spl13_32
    | ~ spl13_41 ),
    inference(avatar_split_clause,[],[f369,f366,f312,f375]) ).

fof(f366,plain,
    ( spl13_41
  <=> ! [X0,X3,X2,X1] :
        ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
        | contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).

fof(f369,plain,
    ( ! [X2,X3,X0,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK3)
        | contains_slb(X1,X3) )
    | ~ spl13_32
    | ~ spl13_41 ),
    inference(forward_demodulation,[],[f367,f314]) ).

fof(f314,plain,
    ( bad = sK3
    | ~ spl13_32 ),
    inference(avatar_component_clause,[],[f312]) ).

fof(f367,plain,
    ( ! [X2,X3,X0,X1] :
        ( contains_slb(X1,X3)
        | triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) )
    | ~ spl13_41 ),
    inference(avatar_component_clause,[],[f366]) ).

fof(f373,plain,
    ( spl13_42
    | ~ spl13_14
    | ~ spl13_32 ),
    inference(avatar_split_clause,[],[f339,f312,f230,f371]) ).

fof(f339,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,sK3))
    | ~ spl13_14
    | ~ spl13_32 ),
    inference(superposition,[],[f231,f314]) ).

fof(f368,plain,
    spl13_41,
    inference(avatar_split_clause,[],[f143,f366]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1] :
      ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3] :
      ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1,X2,X3] :
      ( ~ contains_slb(X1,X3)
     => triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).

fof(f362,plain,
    spl13_40,
    inference(avatar_split_clause,[],[f155,f360]) ).

fof(f360,plain,
    ( spl13_40
  <=> ! [X0,X3,X2,X1] :
        ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).

fof(f155,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X2
      | contains_slb(X0,X2)
      | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
    <=> ( X1 = X2
        | contains_slb(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f358,plain,
    spl13_39,
    inference(avatar_split_clause,[],[f163,f356]) ).

fof(f356,plain,
    ( spl13_39
  <=> ! [X4,X0,X3,X2,X1] :
        ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ~ pair_in_list(X0,X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).

fof(f163,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | ~ pair_in_list(X0,X2,X4) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f354,plain,
    spl13_38,
    inference(avatar_split_clause,[],[f158,f352]) ).

fof(f158,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(true_and_false_elimination,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f347,plain,
    spl13_37,
    inference(avatar_split_clause,[],[f168,f345]) ).

fof(f345,plain,
    ( spl13_37
  <=> ! [X2,X0,X1] :
        ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(definition_unfolding,[],[f142,f123]) ).

fof(f123,plain,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1,X2,X3] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f338,plain,
    spl13_36,
    inference(avatar_split_clause,[],[f167,f336]) ).

fof(f336,plain,
    ( spl13_36
  <=> ! [X0,X1] :
        ( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
      | ~ succ_cpq(X0,X1) ),
    inference(definition_unfolding,[],[f130,f165]) ).

fof(f165,plain,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
    inference(definition_unfolding,[],[f124,f123]) ).

fof(f124,plain,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f130,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,removemin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,removemin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,removemin_cpq_eff(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).

fof(f334,plain,
    spl13_35,
    inference(avatar_split_clause,[],[f156,f332]) ).

fof(f332,plain,
    ( spl13_35
  <=> ! [X0,X3,X2,X1] :
        ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ~ contains_slb(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | ~ contains_slb(X0,X2) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f329,plain,
    ( spl13_34
    | ~ spl13_32
    | ~ spl13_33 ),
    inference(avatar_split_clause,[],[f325,f322,f312,f327]) ).

fof(f325,plain,
    ( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK3)
    | ~ spl13_32
    | ~ spl13_33 ),
    inference(forward_demodulation,[],[f323,f314]) ).

fof(f324,plain,
    spl13_33,
    inference(avatar_split_clause,[],[f128,f322]) ).

fof(f128,plain,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f315,plain,
    ( spl13_32
    | spl13_6
    | ~ spl13_24 ),
    inference(avatar_split_clause,[],[f279,f272,f197,f312]) ).

fof(f279,plain,
    ( bad = sK3
    | spl13_6
    | ~ spl13_24 ),
    inference(resolution,[],[f273,f199]) ).

fof(f199,plain,
    ( ~ ok(triple(sK1,sK2,sK3))
    | spl13_6 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f304,plain,
    spl13_31,
    inference(avatar_split_clause,[],[f154,f302]) ).

fof(f302,plain,
    ( spl13_31
  <=> ! [X0,X3,X2,X1] :
        ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).

fof(f154,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) )
      & ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_slb(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f300,plain,
    spl13_30,
    inference(avatar_split_clause,[],[f153,f298]) ).

fof(f298,plain,
    ( spl13_30
  <=> ! [X2,X0,X1,X3] :
        ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).

fof(f153,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(X1,X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f296,plain,
    spl13_29,
    inference(avatar_split_clause,[],[f140,f294]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( ( less_than(X1,X2)
        & less_than(X0,X1) )
     => less_than(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

fof(f292,plain,
    spl13_28,
    inference(avatar_split_clause,[],[f136,f290]) ).

fof(f290,plain,
    ( spl13_28
  <=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).

fof(f136,plain,
    ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f288,plain,
    spl13_27,
    inference(avatar_split_clause,[],[f135,f286]) ).

fof(f286,plain,
    ( spl13_27
  <=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).

fof(f135,plain,
    ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f284,plain,
    spl13_26,
    inference(avatar_split_clause,[],[f132,f282]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( ~ less_than(X1,X0)
        & less_than(X0,X1) )
     => strictly_less_than(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
    <=> ( ~ less_than(X1,X0)
        & less_than(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f278,plain,
    spl13_25,
    inference(avatar_split_clause,[],[f171,f276]) ).

fof(f276,plain,
    ( spl13_25
  <=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).

fof(f171,plain,
    ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
    inference(equality_resolution,[],[f170]) ).

fof(f170,plain,
    ! [X2,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
      | X1 != X2 ),
    inference(equality_resolution,[],[f164]) ).

fof(f164,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | X3 != X4
      | X1 != X2 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f274,plain,
    spl13_24,
    inference(avatar_split_clause,[],[f139,f272]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( bad = X2
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( bad = X2
      | ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => bad = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

fof(f270,plain,
    spl13_23,
    inference(avatar_split_clause,[],[f138,f268]) ).

fof(f268,plain,
    ( spl13_23
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,remove_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,remove_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,remove_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,remove_cpq(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).

fof(f266,plain,
    spl13_22,
    inference(avatar_split_clause,[],[f137,f264]) ).

fof(f264,plain,
    ( spl13_22
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,insert_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,insert_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,insert_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,insert_cpq(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).

fof(f262,plain,
    spl13_21,
    inference(avatar_split_clause,[],[f169,f260]) ).

fof(f260,plain,
    ( spl13_21
  <=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).

fof(f169,plain,
    ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
    inference(equality_resolution,[],[f157]) ).

fof(f157,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f101]) ).

fof(f258,plain,
    spl13_20,
    inference(avatar_split_clause,[],[f166,f256]) ).

fof(f256,plain,
    ( spl13_20
  <=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).

fof(f166,plain,
    ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
    inference(definition_unfolding,[],[f127,f123]) ).

fof(f127,plain,
    ! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).

fof(f254,plain,
    spl13_19,
    inference(avatar_split_clause,[],[f131,f252]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,findmin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,findmin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,findmin_cpq_eff(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).

fof(f250,plain,
    ( ~ spl13_17
    | spl13_18 ),
    inference(avatar_split_clause,[],[f114,f247,f243]) ).

fof(f114,plain,
    ( check_cpq(im_succ_cpq(triple(sK10,sK11,sK12)))
    | ~ sP0 ),
    inference(cnf_transformation,[],[f97]) ).

fof(f240,plain,
    spl13_16,
    inference(avatar_split_clause,[],[f134,f238]) ).

fof(f238,plain,
    ( spl13_16
  <=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).

fof(f134,plain,
    ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).

fof(f236,plain,
    spl13_15,
    inference(avatar_split_clause,[],[f129,f234]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).

fof(f232,plain,
    spl13_14,
    inference(avatar_split_clause,[],[f133,f230]) ).

fof(f133,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(true_and_false_elimination,[],[f28]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( ok(triple(X0,X1,bad))
    <=> $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).

fof(f228,plain,
    spl13_13,
    inference(avatar_split_clause,[],[f126,f226]) ).

fof(f226,plain,
    ( spl13_13
  <=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).

fof(f126,plain,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

fof(f224,plain,
    spl13_12,
    inference(avatar_split_clause,[],[f122,f222]) ).

fof(f222,plain,
    ( spl13_12
  <=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f122,plain,
    ! [X0] : create_slb = update_slb(create_slb,X0),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] : create_slb = update_slb(create_slb,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f220,plain,
    spl13_11,
    inference(avatar_split_clause,[],[f125,f218]) ).

fof(f218,plain,
    ( spl13_11
  <=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).

fof(f125,plain,
    ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f216,plain,
    spl13_10,
    inference(avatar_split_clause,[],[f121,f214]) ).

fof(f214,plain,
    ( spl13_10
  <=> ! [X0] : succ_cpq(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f121,plain,
    ! [X0] : succ_cpq(X0,X0),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : succ_cpq(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).

fof(f212,plain,
    spl13_9,
    inference(avatar_split_clause,[],[f120,f210]) ).

fof(f120,plain,
    ! [X0] : less_than(bottom,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] : less_than(bottom,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).

fof(f208,plain,
    spl13_8,
    inference(avatar_split_clause,[],[f119,f206]) ).

fof(f206,plain,
    ( spl13_8
  <=> ! [X0] : less_than(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f119,plain,
    ! [X0] : less_than(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : less_than(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f204,plain,
    spl13_7,
    inference(avatar_split_clause,[],[f118,f202]) ).

fof(f118,plain,
    ! [X0] : ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : ~ contains_slb(create_slb,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f200,plain,
    ( ~ spl13_5
    | ~ spl13_6 ),
    inference(avatar_split_clause,[],[f105,f197,f193]) ).

fof(f105,plain,
    ( ~ ok(triple(sK1,sK2,sK3))
    | ~ check_cpq(triple(sK1,sK2,sK3)) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ( check_cpq(triple(sK4,sK5,sK6))
    & ok(triple(sK4,sK5,sK6))
    & succ_cpq(triple(sK1,sK2,sK3),triple(sK4,sK5,sK6))
    & ( ~ ok(triple(sK1,sK2,sK3))
      | ~ check_cpq(triple(sK1,sK2,sK3)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f56,f93,f92]) ).

fof(f92,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3,X4,X5] :
            ( check_cpq(triple(X3,X4,X5))
            & ok(triple(X3,X4,X5))
            & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
        & ( ~ ok(triple(X0,X1,X2))
          | ~ check_cpq(triple(X0,X1,X2)) ) )
   => ( ? [X5,X4,X3] :
          ( check_cpq(triple(X3,X4,X5))
          & ok(triple(X3,X4,X5))
          & succ_cpq(triple(sK1,sK2,sK3),triple(X3,X4,X5)) )
      & ( ~ ok(triple(sK1,sK2,sK3))
        | ~ check_cpq(triple(sK1,sK2,sK3)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ( ? [X5,X4,X3] :
        ( check_cpq(triple(X3,X4,X5))
        & ok(triple(X3,X4,X5))
        & succ_cpq(triple(sK1,sK2,sK3),triple(X3,X4,X5)) )
   => ( check_cpq(triple(sK4,sK5,sK6))
      & ok(triple(sK4,sK5,sK6))
      & succ_cpq(triple(sK1,sK2,sK3),triple(sK4,sK5,sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ? [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( check_cpq(triple(X3,X4,X5))
          & ok(triple(X3,X4,X5))
          & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
      & ( ~ ok(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,X1,X2)) ) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ? [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( check_cpq(triple(X3,X4,X5))
          & ok(triple(X3,X4,X5))
          & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
      & ( ~ ok(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,X1,X2)) ) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( ~ ok(triple(X0,X1,X2))
          | ~ check_cpq(triple(X0,X1,X2)) )
       => ! [X3,X4,X5] :
            ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
           => ( ~ check_cpq(triple(X3,X4,X5))
              | ~ ok(triple(X3,X4,X5)) ) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0,X1,X2] :
      ( ( ~ ok(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,X1,X2)) )
     => ! [X3,X4,X5] :
          ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
         => ( ~ check_cpq(triple(X3,X4,X5))
            | ~ ok(triple(X3,X4,X5)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l20_co) ).

fof(f191,plain,
    spl13_4,
    inference(avatar_split_clause,[],[f106,f188]) ).

fof(f106,plain,
    succ_cpq(triple(sK1,sK2,sK3),triple(sK4,sK5,sK6)),
    inference(cnf_transformation,[],[f94]) ).

fof(f186,plain,
    ~ spl13_3,
    inference(avatar_split_clause,[],[f111,f183]) ).

fof(f183,plain,
    ( spl13_3
  <=> isnonempty_slb(create_slb) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f111,plain,
    ~ isnonempty_slb(create_slb),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ~ isnonempty_slb(create_slb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

fof(f181,plain,
    spl13_2,
    inference(avatar_split_clause,[],[f108,f178]) ).

fof(f108,plain,
    check_cpq(triple(sK4,sK5,sK6)),
    inference(cnf_transformation,[],[f94]) ).

fof(f176,plain,
    spl13_1,
    inference(avatar_split_clause,[],[f107,f173]) ).

fof(f107,plain,
    ok(triple(sK4,sK5,sK6)),
    inference(cnf_transformation,[],[f94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWV384+1 : TPTP v8.2.0. Released v3.3.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n025.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   : Sun May 19 06:27:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (7775)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (7778)WARNING: value z3 for option sas not known
% 0.14/0.37  % (7779)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (7776)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (7778)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)
% 0.14/0.37  % (7780)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)
% 0.14/0.37  % (7782)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  % (7777)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  % (7781)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  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.20/0.39  % (7780)First to succeed.
% 0.20/0.39  % (7780)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7775"
% 0.20/0.39  % (7780)Refutation found. Thanks to Tanya!
% 0.20/0.39  % SZS status Theorem for theBenchmark
% 0.20/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40  % (7780)------------------------------
% 0.20/0.40  % (7780)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40  % (7780)Termination reason: Refutation
% 0.20/0.40  
% 0.20/0.40  % (7780)Memory used [KB]: 1112
% 0.20/0.40  % (7780)Time elapsed: 0.024 s
% 0.20/0.40  % (7780)Instructions burned: 34 (million)
% 0.20/0.40  % (7775)Success in time 0.031 s
%------------------------------------------------------------------------------