TSTP Solution File: RNG088+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 08:56:45 EDT 2024

% Result   : Theorem 0.14s 0.40s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  106
% Syntax   : Number of formulae    :  312 (  81 unt;   0 def)
%            Number of atoms       : 1056 ( 162 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives : 1181 ( 437   ~; 466   |; 145   &)
%                                         (  90 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   79 (  77 usr;  71 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;  11 con; 0-3 aty)
%            Number of variables   :  509 ( 472   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f644,plain,
    $false,
    inference(avatar_sat_refutation,[],[f161,f166,f171,f176,f181,f190,f195,f200,f205,f210,f215,f219,f226,f231,f236,f241,f245,f250,f254,f258,f262,f266,f270,f274,f278,f282,f287,f291,f325,f329,f333,f337,f341,f371,f375,f379,f396,f400,f404,f411,f415,f419,f435,f439,f446,f462,f466,f470,f482,f486,f490,f491,f499,f503,f511,f515,f520,f524,f528,f532,f536,f577,f581,f585,f598,f602,f623,f627,f631,f635,f643]) ).

fof(f643,plain,
    ( ~ spl11_2
    | ~ spl11_9
    | ~ spl11_11
    | spl11_7
    | ~ spl11_46 ),
    inference(avatar_split_clause,[],[f472,f444,f187,f207,f197,f163]) ).

fof(f163,plain,
    ( spl11_2
  <=> aIdeal0(xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).

fof(f197,plain,
    ( spl11_9
  <=> aElementOf0(xl,xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).

fof(f207,plain,
    ( spl11_11
  <=> aElementOf0(xn,xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_11])]) ).

fof(f187,plain,
    ( spl11_7
  <=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).

fof(f444,plain,
    ( spl11_46
  <=> ! [X0,X1,X3] :
        ( aElementOf0(sdtpldt0(X1,X3),X0)
        | ~ aElementOf0(X3,X0)
        | ~ aElementOf0(X1,X0)
        | ~ aIdeal0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_46])]) ).

fof(f472,plain,
    ( ~ aElementOf0(xn,xJ)
    | ~ aElementOf0(xl,xJ)
    | ~ aIdeal0(xJ)
    | spl11_7
    | ~ spl11_46 ),
    inference(resolution,[],[f445,f189]) ).

fof(f189,plain,
    ( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
    | spl11_7 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f445,plain,
    ( ! [X3,X0,X1] :
        ( aElementOf0(sdtpldt0(X1,X3),X0)
        | ~ aElementOf0(X3,X0)
        | ~ aElementOf0(X1,X0)
        | ~ aIdeal0(X0) )
    | ~ spl11_46 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f635,plain,
    spl11_70,
    inference(avatar_split_clause,[],[f140,f633]) ).

fof(f633,plain,
    ( spl11_70
  <=> ! [X4,X0,X5,X2,X1] :
        ( sP2(X0,X1,X2)
        | sdtpldt0(X4,X5) != sK6(X0,X1,X2)
        | ~ aElementOf0(X5,X0)
        | ~ aElementOf0(X4,X1)
        | ~ aElementOf0(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_70])]) ).

fof(f140,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP2(X0,X1,X2)
      | sdtpldt0(X4,X5) != sK6(X0,X1,X2)
      | ~ aElementOf0(X5,X0)
      | ~ aElementOf0(X4,X1)
      | ~ aElementOf0(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( sdtpldt0(X4,X5) != sK6(X0,X1,X2)
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(sK6(X0,X1,X2),X2) )
          & ( ( sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
              & aElementOf0(sK8(X0,X1,X2),X0)
              & aElementOf0(sK7(X0,X1,X2),X1) )
            | aElementOf0(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( aElementOf0(X8,X2)
              | ! [X9,X10] :
                  ( sdtpldt0(X9,X10) != X8
                  | ~ aElementOf0(X10,X0)
                  | ~ aElementOf0(X9,X1) ) )
            & ( ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
                & aElementOf0(sK10(X0,X1,X8),X0)
                & aElementOf0(sK9(X0,X1,X8),X1) )
              | ~ aElementOf0(X8,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f82,f85,f84,f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( sdtpldt0(X4,X5) != X3
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(X3,X2) )
          & ( ? [X6,X7] :
                ( sdtpldt0(X6,X7) = X3
                & aElementOf0(X7,X0)
                & aElementOf0(X6,X1) )
            | aElementOf0(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( sdtpldt0(X4,X5) != sK6(X0,X1,X2)
              | ~ aElementOf0(X5,X0)
              | ~ aElementOf0(X4,X1) )
          | ~ aElementOf0(sK6(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( sdtpldt0(X6,X7) = sK6(X0,X1,X2)
              & aElementOf0(X7,X0)
              & aElementOf0(X6,X1) )
          | aElementOf0(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( sdtpldt0(X6,X7) = sK6(X0,X1,X2)
          & aElementOf0(X7,X0)
          & aElementOf0(X6,X1) )
     => ( sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
        & aElementOf0(sK8(X0,X1,X2),X0)
        & aElementOf0(sK7(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( sdtpldt0(X11,X12) = X8
          & aElementOf0(X12,X0)
          & aElementOf0(X11,X1) )
     => ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
        & aElementOf0(sK10(X0,X1,X8),X0)
        & aElementOf0(sK9(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( sP2(X0,X1,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X0)
                  | ~ aElementOf0(X4,X1) )
              | ~ aElementOf0(X3,X2) )
            & ( ? [X6,X7] :
                  ( sdtpldt0(X6,X7) = X3
                  & aElementOf0(X7,X0)
                  & aElementOf0(X6,X1) )
              | aElementOf0(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( aElementOf0(X8,X2)
              | ! [X9,X10] :
                  ( sdtpldt0(X9,X10) != X8
                  | ~ aElementOf0(X10,X0)
                  | ~ aElementOf0(X9,X1) ) )
            & ( ? [X11,X12] :
                  ( sdtpldt0(X11,X12) = X8
                  & aElementOf0(X12,X0)
                  & aElementOf0(X11,X1) )
              | ~ aElementOf0(X8,X2) ) )
        | ~ sP2(X0,X1,X2) ) ),
    inference(rectify,[],[f81]) ).

fof(f81,plain,
    ! [X1,X0,X2] :
      ( ( sP2(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X1)
                  | ~ aElementOf0(X4,X0) )
              | ~ aElementOf0(X3,X2) )
            & ( ? [X4,X5] :
                  ( sdtpldt0(X4,X5) = X3
                  & aElementOf0(X5,X1)
                  & aElementOf0(X4,X0) )
              | aElementOf0(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( aElementOf0(X3,X2)
              | ! [X4,X5] :
                  ( sdtpldt0(X4,X5) != X3
                  | ~ aElementOf0(X5,X1)
                  | ~ aElementOf0(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( sdtpldt0(X4,X5) = X3
                  & aElementOf0(X5,X1)
                  & aElementOf0(X4,X0) )
              | ~ aElementOf0(X3,X2) ) )
        | ~ sP2(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X1,X0,X2] :
      ( sP2(X1,X0,X2)
    <=> ! [X3] :
          ( aElementOf0(X3,X2)
        <=> ? [X4,X5] :
              ( sdtpldt0(X4,X5) = X3
              & aElementOf0(X5,X1)
              & aElementOf0(X4,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f631,plain,
    spl11_69,
    inference(avatar_split_clause,[],[f139,f629]) ).

fof(f629,plain,
    ( spl11_69
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X1,X2)
        | sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
        | aElementOf0(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_69])]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | sK6(X0,X1,X2) = sdtpldt0(sK7(X0,X1,X2),sK8(X0,X1,X2))
      | aElementOf0(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f627,plain,
    spl11_68,
    inference(avatar_split_clause,[],[f131,f625]) ).

fof(f625,plain,
    ( spl11_68
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | ~ aElementOf0(sK5(X0,X1,X2),X0)
        | ~ aElementOf0(sK5(X0,X1,X2),X1)
        | ~ aElementOf0(sK5(X0,X1,X2),X2)
        | ~ aSet0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_68])]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | ~ aElementOf0(sK5(X0,X1,X2),X0)
      | ~ aElementOf0(sK5(X0,X1,X2),X1)
      | ~ aElementOf0(sK5(X0,X1,X2),X2)
      | ~ aSet0(X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ~ aElementOf0(sK5(X0,X1,X2),X0)
            | ~ aElementOf0(sK5(X0,X1,X2),X1)
            | ~ aElementOf0(sK5(X0,X1,X2),X2) )
          & ( ( aElementOf0(sK5(X0,X1,X2),X0)
              & aElementOf0(sK5(X0,X1,X2),X1) )
            | aElementOf0(sK5(X0,X1,X2),X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X4] :
              ( ( aElementOf0(X4,X2)
                | ~ aElementOf0(X4,X0)
                | ~ aElementOf0(X4,X1) )
              & ( ( aElementOf0(X4,X0)
                  & aElementOf0(X4,X1) )
                | ~ aElementOf0(X4,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f78,f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ aElementOf0(X3,X0)
            | ~ aElementOf0(X3,X1)
            | ~ aElementOf0(X3,X2) )
          & ( ( aElementOf0(X3,X0)
              & aElementOf0(X3,X1) )
            | aElementOf0(X3,X2) ) )
     => ( ( ~ aElementOf0(sK5(X0,X1,X2),X0)
          | ~ aElementOf0(sK5(X0,X1,X2),X1)
          | ~ aElementOf0(sK5(X0,X1,X2),X2) )
        & ( ( aElementOf0(sK5(X0,X1,X2),X0)
            & aElementOf0(sK5(X0,X1,X2),X1) )
          | aElementOf0(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ~ aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X2) )
            & ( ( aElementOf0(X3,X0)
                & aElementOf0(X3,X1) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X4] :
              ( ( aElementOf0(X4,X2)
                | ~ aElementOf0(X4,X0)
                | ~ aElementOf0(X4,X1) )
              & ( ( aElementOf0(X4,X0)
                  & aElementOf0(X4,X1) )
                | ~ aElementOf0(X4,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f77]) ).

fof(f77,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X2) )
            & ( ( aElementOf0(X3,X1)
                & aElementOf0(X3,X0) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ~ aElementOf0(X3,X1)
                | ~ aElementOf0(X3,X0) )
              & ( ( aElementOf0(X3,X1)
                  & aElementOf0(X3,X0) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ~ aElementOf0(X3,X1)
              | ~ aElementOf0(X3,X0)
              | ~ aElementOf0(X3,X2) )
            & ( ( aElementOf0(X3,X1)
                & aElementOf0(X3,X0) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ~ aElementOf0(X3,X1)
                | ~ aElementOf0(X3,X0) )
              & ( ( aElementOf0(X3,X1)
                  & aElementOf0(X3,X0) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ( ! [X3] :
            ( aElementOf0(X3,X2)
          <=> ( aElementOf0(X3,X1)
              & aElementOf0(X3,X0) ) )
        & aSet0(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f623,plain,
    ( spl11_67
    | ~ spl11_22
    | ~ spl11_57 ),
    inference(avatar_split_clause,[],[f560,f517,f260,f620]) ).

fof(f620,plain,
    ( spl11_67
  <=> sz00 = sdtasdt0(sdtpldt0(xk,xm),sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_67])]) ).

fof(f260,plain,
    ( spl11_22
  <=> ! [X0] :
        ( sz00 = sdtasdt0(X0,sz00)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_22])]) ).

fof(f517,plain,
    ( spl11_57
  <=> aElement0(sdtpldt0(xk,xm)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_57])]) ).

fof(f560,plain,
    ( sz00 = sdtasdt0(sdtpldt0(xk,xm),sz00)
    | ~ spl11_22
    | ~ spl11_57 ),
    inference(resolution,[],[f519,f261]) ).

fof(f261,plain,
    ( ! [X0] :
        ( ~ aElement0(X0)
        | sz00 = sdtasdt0(X0,sz00) )
    | ~ spl11_22 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f519,plain,
    ( aElement0(sdtpldt0(xk,xm))
    | ~ spl11_57 ),
    inference(avatar_component_clause,[],[f517]) ).

fof(f602,plain,
    spl11_66,
    inference(avatar_split_clause,[],[f152,f600]) ).

fof(f600,plain,
    ( spl11_66
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        | ~ aElement0(X2)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_66])]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).

fof(f598,plain,
    spl11_65,
    inference(avatar_split_clause,[],[f151,f596]) ).

fof(f596,plain,
    ( spl11_65
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        | ~ aElement0(X2)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_65])]) ).

fof(f151,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f585,plain,
    spl11_64,
    inference(avatar_split_clause,[],[f135,f583]) ).

fof(f583,plain,
    ( spl11_64
  <=> ! [X0,X8,X2,X1] :
        ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
        | ~ aElementOf0(X8,X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_64])]) ).

fof(f135,plain,
    ! [X2,X0,X1,X8] :
      ( sdtpldt0(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
      | ~ aElementOf0(X8,X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f581,plain,
    spl11_63,
    inference(avatar_split_clause,[],[f130,f579]) ).

fof(f579,plain,
    ( spl11_63
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | aElementOf0(sK5(X0,X1,X2),X0)
        | aElementOf0(sK5(X0,X1,X2),X2)
        | ~ aSet0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_63])]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | aElementOf0(sK5(X0,X1,X2),X0)
      | aElementOf0(sK5(X0,X1,X2),X2)
      | ~ aSet0(X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f577,plain,
    spl11_62,
    inference(avatar_split_clause,[],[f129,f575]) ).

fof(f575,plain,
    ( spl11_62
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | aElementOf0(sK5(X0,X1,X2),X1)
        | aElementOf0(sK5(X0,X1,X2),X2)
        | ~ aSet0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_62])]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | aElementOf0(sK5(X0,X1,X2),X1)
      | aElementOf0(sK5(X0,X1,X2),X2)
      | ~ aSet0(X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f536,plain,
    spl11_61,
    inference(avatar_split_clause,[],[f150,f534]) ).

fof(f534,plain,
    ( spl11_61
  <=> ! [X2,X0,X1] :
        ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
        | ~ aElement0(X2)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_61])]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

fof(f532,plain,
    spl11_60,
    inference(avatar_split_clause,[],[f149,f530]) ).

fof(f530,plain,
    ( spl11_60
  <=> ! [X2,X0,X1] :
        ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
        | ~ aElement0(X2)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_60])]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1,X2] :
      ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( ( aElement0(X2)
        & aElement0(X1)
        & aElement0(X0) )
     => sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

fof(f528,plain,
    spl11_59,
    inference(avatar_split_clause,[],[f122,f526]) ).

fof(f526,plain,
    ( spl11_59
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ aElementOf0(sK3(X0,X1),X0)
        | ~ aElementOf0(sK4(X0,X1),X1)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_59])]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ aElementOf0(sK3(X0,X1),X0)
      | ~ aElementOf0(sK4(X0,X1),X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ~ aElementOf0(sK3(X0,X1),X0)
        & aElementOf0(sK3(X0,X1),X1) )
      | ( ~ aElementOf0(sK4(X0,X1),X1)
        & aElementOf0(sK4(X0,X1),X0) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f46,f73,f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK3(X0,X1),X0)
        & aElementOf0(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ aElementOf0(X3,X1)
          & aElementOf0(X3,X0) )
     => ( ~ aElementOf0(sK4(X0,X1),X1)
        & aElementOf0(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
      | ? [X3] :
          ( ~ aElementOf0(X3,X1)
          & aElementOf0(X3,X0) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
      | ? [X3] :
          ( ~ aElementOf0(X3,X1)
          & aElementOf0(X3,X0) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( aSet0(X1)
        & aSet0(X0) )
     => ( ( ! [X2] :
              ( aElementOf0(X2,X1)
             => aElementOf0(X2,X0) )
          & ! [X3] :
              ( aElementOf0(X3,X0)
             => aElementOf0(X3,X1) ) )
       => X0 = X1 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aSet0(X1)
        & aSet0(X0) )
     => ( ( ! [X2] :
              ( aElementOf0(X2,X1)
             => aElementOf0(X2,X0) )
          & ! [X2] :
              ( aElementOf0(X2,X0)
             => aElementOf0(X2,X1) ) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetEq) ).

fof(f524,plain,
    spl11_58,
    inference(avatar_split_clause,[],[f121,f522]) ).

fof(f522,plain,
    ( spl11_58
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ aElementOf0(sK3(X0,X1),X0)
        | aElementOf0(sK4(X0,X1),X0)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_58])]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ aElementOf0(sK3(X0,X1),X0)
      | aElementOf0(sK4(X0,X1),X0)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f520,plain,
    ( ~ spl11_19
    | spl11_57
    | ~ spl11_6
    | ~ spl11_21 ),
    inference(avatar_split_clause,[],[f492,f256,f183,f517,f247]) ).

fof(f247,plain,
    ( spl11_19
  <=> aSet0(xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_19])]) ).

fof(f183,plain,
    ( spl11_6
  <=> aElementOf0(sdtpldt0(xk,xm),xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).

fof(f256,plain,
    ( spl11_21
  <=> ! [X0,X1] :
        ( aElement0(X1)
        | ~ aElementOf0(X1,X0)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_21])]) ).

fof(f492,plain,
    ( aElement0(sdtpldt0(xk,xm))
    | ~ aSet0(xI)
    | ~ spl11_6
    | ~ spl11_21 ),
    inference(resolution,[],[f184,f257]) ).

fof(f257,plain,
    ( ! [X0,X1] :
        ( ~ aElementOf0(X1,X0)
        | aElement0(X1)
        | ~ aSet0(X0) )
    | ~ spl11_21 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f184,plain,
    ( aElementOf0(sdtpldt0(xk,xm),xI)
    | ~ spl11_6 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f515,plain,
    spl11_56,
    inference(avatar_split_clause,[],[f120,f513]) ).

fof(f513,plain,
    ( spl11_56
  <=> ! [X0,X1] :
        ( X0 = X1
        | aElementOf0(sK3(X0,X1),X1)
        | ~ aElementOf0(sK4(X0,X1),X1)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_56])]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( X0 = X1
      | aElementOf0(sK3(X0,X1),X1)
      | ~ aElementOf0(sK4(X0,X1),X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f511,plain,
    spl11_55,
    inference(avatar_split_clause,[],[f119,f509]) ).

fof(f509,plain,
    ( spl11_55
  <=> ! [X0,X1] :
        ( X0 = X1
        | aElementOf0(sK3(X0,X1),X1)
        | aElementOf0(sK4(X0,X1),X0)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_55])]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( X0 = X1
      | aElementOf0(sK3(X0,X1),X1)
      | aElementOf0(sK4(X0,X1),X0)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f503,plain,
    spl11_54,
    inference(avatar_split_clause,[],[f138,f501]) ).

fof(f501,plain,
    ( spl11_54
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X1,X2)
        | aElementOf0(sK8(X0,X1,X2),X0)
        | aElementOf0(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_54])]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | aElementOf0(sK8(X0,X1,X2),X0)
      | aElementOf0(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f499,plain,
    spl11_53,
    inference(avatar_split_clause,[],[f137,f497]) ).

fof(f497,plain,
    ( spl11_53
  <=> ! [X2,X0,X1] :
        ( sP2(X0,X1,X2)
        | aElementOf0(sK7(X0,X1,X2),X1)
        | aElementOf0(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_53])]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( sP2(X0,X1,X2)
      | aElementOf0(sK7(X0,X1,X2),X1)
      | aElementOf0(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f491,plain,
    ( ~ spl11_1
    | ~ spl11_8
    | ~ spl11_10
    | spl11_6
    | ~ spl11_46 ),
    inference(avatar_split_clause,[],[f471,f444,f183,f202,f192,f158]) ).

fof(f158,plain,
    ( spl11_1
  <=> aIdeal0(xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).

fof(f192,plain,
    ( spl11_8
  <=> aElementOf0(xk,xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).

fof(f202,plain,
    ( spl11_10
  <=> aElementOf0(xm,xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).

fof(f471,plain,
    ( ~ aElementOf0(xm,xI)
    | ~ aElementOf0(xk,xI)
    | ~ aIdeal0(xI)
    | spl11_6
    | ~ spl11_46 ),
    inference(resolution,[],[f445,f185]) ).

fof(f185,plain,
    ( ~ aElementOf0(sdtpldt0(xk,xm),xI)
    | spl11_6 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f490,plain,
    spl11_52,
    inference(avatar_split_clause,[],[f154,f488]) ).

fof(f488,plain,
    ( spl11_52
  <=> ! [X10,X0,X9,X2,X1] :
        ( aElementOf0(sdtpldt0(X9,X10),X2)
        | ~ aElementOf0(X10,X0)
        | ~ aElementOf0(X9,X1)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_52])]) ).

fof(f154,plain,
    ! [X2,X10,X0,X1,X9] :
      ( aElementOf0(sdtpldt0(X9,X10),X2)
      | ~ aElementOf0(X10,X0)
      | ~ aElementOf0(X9,X1)
      | ~ sP2(X0,X1,X2) ),
    inference(equality_resolution,[],[f136]) ).

fof(f136,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( aElementOf0(X8,X2)
      | sdtpldt0(X9,X10) != X8
      | ~ aElementOf0(X10,X0)
      | ~ aElementOf0(X9,X1)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f486,plain,
    spl11_51,
    inference(avatar_split_clause,[],[f148,f484]) ).

fof(f484,plain,
    ( spl11_51
  <=> ! [X0,X1] :
        ( sz00 = X1
        | sz00 = X0
        | sz00 != sdtasdt0(X0,X1)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_51])]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( sz00 = X1
      | sz00 = X0
      | sz00 != sdtasdt0(X0,X1)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => ( sz00 = sdtasdt0(X0,X1)
       => ( sz00 = X1
          | sz00 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCancel) ).

fof(f482,plain,
    spl11_50,
    inference(avatar_split_clause,[],[f143,f480]) ).

fof(f480,plain,
    ( spl11_50
  <=> ! [X2,X0,X1] :
        ( sdtpldt1(X0,X1) = X2
        | ~ sP2(X1,X0,X2)
        | ~ aSet0(X2)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_50])]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( sdtpldt1(X0,X1) = X2
      | ~ sP2(X1,X0,X2)
      | ~ aSet0(X2)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtpldt1(X0,X1) = X2
            | ~ sP2(X1,X0,X2)
            | ~ aSet0(X2) )
          & ( ( sP2(X1,X0,X2)
              & aSet0(X2) )
            | sdtpldt1(X0,X1) != X2 ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtpldt1(X0,X1) = X2
            | ~ sP2(X1,X0,X2)
            | ~ aSet0(X2) )
          & ( ( sP2(X1,X0,X2)
              & aSet0(X2) )
            | sdtpldt1(X0,X1) != X2 ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( sP2(X1,X0,X2)
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f50,f70]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( ( aSet0(X1)
        & aSet0(X0) )
     => ! [X2] :
          ( sdtpldt1(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ? [X4,X5] :
                    ( sdtpldt0(X4,X5) = X3
                    & aElementOf0(X5,X1)
                    & aElementOf0(X4,X0) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).

fof(f470,plain,
    spl11_49,
    inference(avatar_split_clause,[],[f134,f468]) ).

fof(f468,plain,
    ( spl11_49
  <=> ! [X0,X8,X2,X1] :
        ( aElementOf0(sK10(X0,X1,X8),X0)
        | ~ aElementOf0(X8,X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_49])]) ).

fof(f134,plain,
    ! [X2,X0,X1,X8] :
      ( aElementOf0(sK10(X0,X1,X8),X0)
      | ~ aElementOf0(X8,X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f466,plain,
    spl11_48,
    inference(avatar_split_clause,[],[f133,f464]) ).

fof(f464,plain,
    ( spl11_48
  <=> ! [X0,X8,X2,X1] :
        ( aElementOf0(sK9(X0,X1,X8),X1)
        | ~ aElementOf0(X8,X2)
        | ~ sP2(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_48])]) ).

fof(f133,plain,
    ! [X2,X0,X1,X8] :
      ( aElementOf0(sK9(X0,X1,X8),X1)
      | ~ aElementOf0(X8,X2)
      | ~ sP2(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f462,plain,
    spl11_47,
    inference(avatar_split_clause,[],[f128,f460]) ).

fof(f460,plain,
    ( spl11_47
  <=> ! [X4,X0,X2,X1] :
        ( aElementOf0(X4,X2)
        | ~ aElementOf0(X4,X0)
        | ~ aElementOf0(X4,X1)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_47])]) ).

fof(f128,plain,
    ! [X2,X0,X1,X4] :
      ( aElementOf0(X4,X2)
      | ~ aElementOf0(X4,X0)
      | ~ aElementOf0(X4,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f446,plain,
    spl11_46,
    inference(avatar_split_clause,[],[f117,f444]) ).

fof(f117,plain,
    ! [X3,X0,X1] :
      ( aElementOf0(sdtpldt0(X1,X3),X0)
      | ~ aElementOf0(X3,X0)
      | ~ aElementOf0(X1,X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtasdt0(X2,X1),X0)
                  | ~ aElement0(X2) )
              & ! [X3] :
                  ( aElementOf0(sdtpldt0(X1,X3),X0)
                  | ~ aElementOf0(X3,X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) )
      | ~ aIdeal0(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( aIdeal0(X0)
     => ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                 => aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
        & aSet0(X0) ) ),
    inference(unused_predicate_definition_removal,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                 => aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
        & aSet0(X0) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

fof(f439,plain,
    spl11_45,
    inference(avatar_split_clause,[],[f124,f437]) ).

fof(f437,plain,
    ( spl11_45
  <=> ! [X2,X0,X1] :
        ( sdtasasdt0(X0,X1) = X2
        | ~ sP0(X1,X0,X2)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_45])]) ).

fof(f124,plain,
    ! [X2,X0,X1] :
      ( sdtasasdt0(X0,X1) = X2
      | ~ sP0(X1,X0,X2)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtasasdt0(X0,X1) = X2
            | ~ sP0(X1,X0,X2) )
          & ( sP0(X1,X0,X2)
            | sdtasasdt0(X0,X1) != X2 ) )
      | ~ sP1(X0,X1) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtasasdt0(X0,X1) = X2
        <=> sP0(X1,X0,X2) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f435,plain,
    spl11_44,
    inference(avatar_split_clause,[],[f118,f433]) ).

fof(f433,plain,
    ( spl11_44
  <=> ! [X2,X0,X1] :
        ( aElementOf0(sdtasdt0(X2,X1),X0)
        | ~ aElement0(X2)
        | ~ aElementOf0(X1,X0)
        | ~ aIdeal0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_44])]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( aElementOf0(sdtasdt0(X2,X1),X0)
      | ~ aElement0(X2)
      | ~ aElementOf0(X1,X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f419,plain,
    spl11_43,
    inference(avatar_split_clause,[],[f147,f417]) ).

fof(f417,plain,
    ( spl11_43
  <=> ! [X0,X1] :
        ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_43])]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(f415,plain,
    spl11_42,
    inference(avatar_split_clause,[],[f146,f413]) ).

fof(f413,plain,
    ( spl11_42
  <=> ! [X0,X1] :
        ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_42])]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

fof(f411,plain,
    ( ~ spl11_19
    | spl11_41
    | ~ spl11_8
    | ~ spl11_21 ),
    inference(avatar_split_clause,[],[f294,f256,f192,f408,f247]) ).

fof(f408,plain,
    ( spl11_41
  <=> aElement0(xk) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_41])]) ).

fof(f294,plain,
    ( aElement0(xk)
    | ~ aSet0(xI)
    | ~ spl11_8
    | ~ spl11_21 ),
    inference(resolution,[],[f257,f194]) ).

fof(f194,plain,
    ( aElementOf0(xk,xI)
    | ~ spl11_8 ),
    inference(avatar_component_clause,[],[f192]) ).

fof(f404,plain,
    spl11_40,
    inference(avatar_split_clause,[],[f155,f402]) ).

fof(f402,plain,
    ( spl11_40
  <=> ! [X0,X1] :
        ( sP2(X1,X0,sdtpldt1(X0,X1))
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_40])]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( sP2(X1,X0,sdtpldt1(X0,X1))
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f142]) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( sP2(X1,X0,X2)
      | sdtpldt1(X0,X1) != X2
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f400,plain,
    spl11_39,
    inference(avatar_split_clause,[],[f127,f398]) ).

fof(f398,plain,
    ( spl11_39
  <=> ! [X4,X0,X2,X1] :
        ( aElementOf0(X4,X0)
        | ~ aElementOf0(X4,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_39])]) ).

fof(f127,plain,
    ! [X2,X0,X1,X4] :
      ( aElementOf0(X4,X0)
      | ~ aElementOf0(X4,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f396,plain,
    spl11_38,
    inference(avatar_split_clause,[],[f126,f394]) ).

fof(f394,plain,
    ( spl11_38
  <=> ! [X4,X0,X1,X2] :
        ( aElementOf0(X4,X1)
        | ~ aElementOf0(X4,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_38])]) ).

fof(f126,plain,
    ! [X2,X0,X1,X4] :
      ( aElementOf0(X4,X1)
      | ~ aElementOf0(X4,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f379,plain,
    spl11_37,
    inference(avatar_split_clause,[],[f153,f377]) ).

fof(f377,plain,
    ( spl11_37
  <=> ! [X0,X1] :
        ( sP0(X1,X0,sdtasasdt0(X0,X1))
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_37])]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( sP0(X1,X0,sdtasasdt0(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(equality_resolution,[],[f123]) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | sdtasasdt0(X0,X1) != X2
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f375,plain,
    spl11_36,
    inference(avatar_split_clause,[],[f115,f373]) ).

fof(f373,plain,
    ( spl11_36
  <=> ! [X0] :
        ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_36])]) ).

fof(f115,plain,
    ! [X0] :
      ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).

fof(f371,plain,
    spl11_35,
    inference(avatar_split_clause,[],[f114,f369]) ).

fof(f369,plain,
    ( spl11_35
  <=> ! [X0] :
        ( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_35])]) ).

fof(f114,plain,
    ! [X0] :
      ( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f341,plain,
    spl11_34,
    inference(avatar_split_clause,[],[f156,f339]) ).

fof(f339,plain,
    ( spl11_34
  <=> ! [X0,X1] :
        ( aSet0(sdtpldt1(X0,X1))
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_34])]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( aSet0(sdtpldt1(X0,X1))
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f141]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( aSet0(X2)
      | sdtpldt1(X0,X1) != X2
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f337,plain,
    spl11_33,
    inference(avatar_split_clause,[],[f145,f335]) ).

fof(f335,plain,
    ( spl11_33
  <=> ! [X0,X1] :
        ( aElement0(sdtpldt0(X0,X1))
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_33])]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( aElement0(sdtpldt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => aElement0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f333,plain,
    spl11_32,
    inference(avatar_split_clause,[],[f144,f331]) ).

fof(f331,plain,
    ( spl11_32
  <=> ! [X0,X1] :
        ( aElement0(sdtasdt0(X0,X1))
        | ~ aElement0(X1)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_32])]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( aElement0(sdtasdt0(X0,X1))
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aElement0(X1)
        & aElement0(X0) )
     => aElement0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f329,plain,
    spl11_31,
    inference(avatar_split_clause,[],[f113,f327]) ).

fof(f327,plain,
    ( spl11_31
  <=> ! [X0] :
        ( sz00 = sdtpldt0(smndt0(X0),X0)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_31])]) ).

fof(f113,plain,
    ! [X0] :
      ( sz00 = sdtpldt0(smndt0(X0),X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).

fof(f325,plain,
    spl11_30,
    inference(avatar_split_clause,[],[f112,f323]) ).

fof(f323,plain,
    ( spl11_30
  <=> ! [X0] :
        ( sz00 = sdtpldt0(X0,smndt0(X0))
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_30])]) ).

fof(f112,plain,
    ! [X0] :
      ( sz00 = sdtpldt0(X0,smndt0(X0))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f291,plain,
    spl11_29,
    inference(avatar_split_clause,[],[f132,f289]) ).

fof(f289,plain,
    ( spl11_29
  <=> ! [X0,X1] :
        ( sP1(X0,X1)
        | ~ aSet0(X1)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_29])]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f48,f68,f67]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtasasdt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( aElementOf0(X3,X1)
                  & aElementOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtasasdt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( aElementOf0(X3,X1)
                  & aElementOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( ( aSet0(X1)
        & aSet0(X0) )
     => ! [X2] :
          ( sdtasasdt0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( aElementOf0(X3,X1)
                  & aElementOf0(X3,X0) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSInt) ).

fof(f287,plain,
    ( spl11_28
    | ~ spl11_2
    | ~ spl11_13 ),
    inference(avatar_split_clause,[],[f221,f217,f163,f284]) ).

fof(f284,plain,
    ( spl11_28
  <=> aSet0(xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_28])]) ).

fof(f217,plain,
    ( spl11_13
  <=> ! [X0] :
        ( aSet0(X0)
        | ~ aIdeal0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).

fof(f221,plain,
    ( aSet0(xJ)
    | ~ spl11_2
    | ~ spl11_13 ),
    inference(resolution,[],[f218,f165]) ).

fof(f165,plain,
    ( aIdeal0(xJ)
    | ~ spl11_2 ),
    inference(avatar_component_clause,[],[f163]) ).

fof(f218,plain,
    ( ! [X0] :
        ( ~ aIdeal0(X0)
        | aSet0(X0) )
    | ~ spl11_13 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f282,plain,
    spl11_27,
    inference(avatar_split_clause,[],[f111,f280]) ).

fof(f280,plain,
    ( spl11_27
  <=> ! [X0] :
        ( sdtpldt0(sz00,X0) = X0
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_27])]) ).

fof(f111,plain,
    ! [X0] :
      ( sdtpldt0(sz00,X0) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(f278,plain,
    spl11_26,
    inference(avatar_split_clause,[],[f110,f276]) ).

fof(f276,plain,
    ( spl11_26
  <=> ! [X0] :
        ( sdtpldt0(X0,sz00) = X0
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_26])]) ).

fof(f110,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f274,plain,
    spl11_25,
    inference(avatar_split_clause,[],[f109,f272]) ).

fof(f272,plain,
    ( spl11_25
  <=> ! [X0] :
        ( sdtasdt0(sz10,X0) = X0
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_25])]) ).

fof(f109,plain,
    ! [X0] :
      ( sdtasdt0(sz10,X0) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulUnit) ).

fof(f270,plain,
    spl11_24,
    inference(avatar_split_clause,[],[f108,f268]) ).

fof(f268,plain,
    ( spl11_24
  <=> ! [X0] :
        ( sdtasdt0(X0,sz10) = X0
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_24])]) ).

fof(f108,plain,
    ! [X0] :
      ( sdtasdt0(X0,sz10) = X0
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f266,plain,
    spl11_23,
    inference(avatar_split_clause,[],[f107,f264]) ).

fof(f264,plain,
    ( spl11_23
  <=> ! [X0] :
        ( sz00 = sdtasdt0(sz00,X0)
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_23])]) ).

fof(f107,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(sz00,X0)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

fof(f262,plain,
    spl11_22,
    inference(avatar_split_clause,[],[f106,f260]) ).

fof(f106,plain,
    ! [X0] :
      ( sz00 = sdtasdt0(X0,sz00)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f258,plain,
    spl11_21,
    inference(avatar_split_clause,[],[f104,f256]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(f254,plain,
    spl11_20,
    inference(avatar_split_clause,[],[f125,f252]) ).

fof(f252,plain,
    ( spl11_20
  <=> ! [X2,X0,X1] :
        ( aSet0(X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_20])]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( aSet0(X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f250,plain,
    ( spl11_19
    | ~ spl11_1
    | ~ spl11_13 ),
    inference(avatar_split_clause,[],[f220,f217,f158,f247]) ).

fof(f220,plain,
    ( aSet0(xI)
    | ~ spl11_1
    | ~ spl11_13 ),
    inference(resolution,[],[f218,f160]) ).

fof(f160,plain,
    ( aIdeal0(xI)
    | ~ spl11_1 ),
    inference(avatar_component_clause,[],[f158]) ).

fof(f245,plain,
    spl11_18,
    inference(avatar_split_clause,[],[f105,f243]) ).

fof(f243,plain,
    ( spl11_18
  <=> ! [X0] :
        ( aElement0(smndt0(X0))
        | ~ aElement0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).

fof(f105,plain,
    ! [X0] :
      ( aElement0(smndt0(X0))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( aElement0(smndt0(X0))
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( aElement0(X0)
     => aElement0(smndt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).

fof(f241,plain,
    spl11_17,
    inference(avatar_split_clause,[],[f99,f238]) ).

fof(f238,plain,
    ( spl11_17
  <=> aElementOf0(xy,sdtpldt1(xI,xJ)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).

fof(f99,plain,
    aElementOf0(xy,sdtpldt1(xI,xJ)),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,axiom,
    ( aElement0(xz)
    & aElementOf0(xy,sdtpldt1(xI,xJ))
    & aElementOf0(xx,sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).

fof(f236,plain,
    spl11_16,
    inference(avatar_split_clause,[],[f98,f233]) ).

fof(f233,plain,
    ( spl11_16
  <=> aElementOf0(xx,sdtpldt1(xI,xJ)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).

fof(f98,plain,
    aElementOf0(xx,sdtpldt1(xI,xJ)),
    inference(cnf_transformation,[],[f26]) ).

fof(f231,plain,
    spl11_15,
    inference(avatar_split_clause,[],[f97,f228]) ).

fof(f228,plain,
    ( spl11_15
  <=> xy = sdtpldt0(xm,xn) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).

fof(f97,plain,
    xy = sdtpldt0(xm,xn),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,axiom,
    ( xy = sdtpldt0(xm,xn)
    & aElementOf0(xn,xJ)
    & aElementOf0(xm,xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).

fof(f226,plain,
    spl11_14,
    inference(avatar_split_clause,[],[f94,f223]) ).

fof(f223,plain,
    ( spl11_14
  <=> xx = sdtpldt0(xk,xl) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).

fof(f94,plain,
    xx = sdtpldt0(xk,xl),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ( xx = sdtpldt0(xk,xl)
    & aElementOf0(xl,xJ)
    & aElementOf0(xk,xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).

fof(f219,plain,
    spl11_13,
    inference(avatar_split_clause,[],[f116,f217]) ).

fof(f116,plain,
    ! [X0] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f215,plain,
    ~ spl11_12,
    inference(avatar_split_clause,[],[f103,f212]) ).

fof(f212,plain,
    ( spl11_12
  <=> sz00 = sz10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_12])]) ).

fof(f103,plain,
    sz00 != sz10,
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    sz00 != sz10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnNeZr) ).

fof(f210,plain,
    spl11_11,
    inference(avatar_split_clause,[],[f96,f207]) ).

fof(f96,plain,
    aElementOf0(xn,xJ),
    inference(cnf_transformation,[],[f28]) ).

fof(f205,plain,
    spl11_10,
    inference(avatar_split_clause,[],[f95,f202]) ).

fof(f95,plain,
    aElementOf0(xm,xI),
    inference(cnf_transformation,[],[f28]) ).

fof(f200,plain,
    spl11_9,
    inference(avatar_split_clause,[],[f93,f197]) ).

fof(f93,plain,
    aElementOf0(xl,xJ),
    inference(cnf_transformation,[],[f27]) ).

fof(f195,plain,
    spl11_8,
    inference(avatar_split_clause,[],[f92,f192]) ).

fof(f92,plain,
    aElementOf0(xk,xI),
    inference(cnf_transformation,[],[f27]) ).

fof(f190,plain,
    ( ~ spl11_6
    | ~ spl11_7 ),
    inference(avatar_split_clause,[],[f89,f187,f183]) ).

fof(f89,plain,
    ( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
    | ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
    | ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
      & aElementOf0(sdtpldt0(xk,xm),xI) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ( aElementOf0(sdtpldt0(xl,xn),xJ)
    & aElementOf0(sdtpldt0(xk,xm),xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f181,plain,
    spl11_5,
    inference(avatar_split_clause,[],[f102,f178]) ).

fof(f178,plain,
    ( spl11_5
  <=> aElement0(sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).

fof(f102,plain,
    aElement0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aElement0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(f176,plain,
    spl11_4,
    inference(avatar_split_clause,[],[f101,f173]) ).

fof(f173,plain,
    ( spl11_4
  <=> aElement0(sz10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).

fof(f101,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).

fof(f171,plain,
    spl11_3,
    inference(avatar_split_clause,[],[f100,f168]) ).

fof(f168,plain,
    ( spl11_3
  <=> aElement0(xz) ),
    introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).

fof(f100,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f26]) ).

fof(f166,plain,
    spl11_2,
    inference(avatar_split_clause,[],[f91,f163]) ).

fof(f91,plain,
    aIdeal0(xJ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,axiom,
    ( aIdeal0(xJ)
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).

fof(f161,plain,
    spl11_1,
    inference(avatar_split_clause,[],[f90,f158]) ).

fof(f90,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 18:21:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (7665)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (7671)WARNING: value z3 for option sas not known
% 0.14/0.38  % (7670)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  % (7669)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (7673)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (7672)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (7675)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  % (7671)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38  % (7674)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 [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  % (7673)First to succeed.
% 0.14/0.40  TRYING [3]
% 0.14/0.40  % (7673)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7665"
% 0.14/0.40  % (7673)Refutation found. Thanks to Tanya!
% 0.14/0.40  % SZS status Theorem for theBenchmark
% 0.14/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (7673)------------------------------
% 0.14/0.40  % (7673)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (7673)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (7673)Memory used [KB]: 1133
% 0.14/0.40  % (7673)Time elapsed: 0.021 s
% 0.14/0.40  % (7673)Instructions burned: 30 (million)
% 0.14/0.40  % (7665)Success in time 0.035 s
%------------------------------------------------------------------------------