TSTP Solution File: NUM550+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM550+3 : 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 : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 14:33:20 EDT 2024

% Result   : Theorem 0.16s 0.34s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   42
% Syntax   : Number of formulae    :  135 (  39 unt;   0 def)
%            Number of atoms       :  663 ( 157 equ)
%            Maximal formula atoms :   43 (   4 avg)
%            Number of connectives :  784 ( 256   ~; 229   |; 225   &)
%                                         (  30 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   28 (  26 usr;  21 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   9 con; 0-2 aty)
%            Number of variables   :  188 ( 154   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f533,plain,
    $false,
    inference(avatar_sat_refutation,[],[f436,f441,f450,f455,f456,f461,f467,f472,f477,f482,f487,f492,f496,f500,f505,f510,f514,f520,f525,f531,f532]) ).

fof(f532,plain,
    ~ spl21_6,
    inference(avatar_split_clause,[],[f251,f458]) ).

fof(f458,plain,
    ( spl21_6
  <=> sz00 = xk ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).

fof(f251,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    ( sz00 != xk
    & aSet0(xT)
    & aSet0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).

fof(f531,plain,
    spl21_20,
    inference(avatar_split_clause,[],[f246,f528]) ).

fof(f528,plain,
    ( spl21_20
  <=> aSubsetOf0(xQ,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).

fof(f246,plain,
    aSubsetOf0(xQ,xS),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xQ)
    & aSubsetOf0(xQ,xS)
    & ! [X0] :
        ( aElementOf0(X0,xS)
        | ~ aElementOf0(X0,xQ) )
    & aSet0(xQ) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
    & xk = sbrdtbr0(xQ)
    & aSubsetOf0(xQ,xS)
    & ! [X0] :
        ( aElementOf0(X0,xQ)
       => aElementOf0(X0,xS) )
    & aSet0(xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).

fof(f525,plain,
    spl21_19,
    inference(avatar_split_clause,[],[f240,f522]) ).

fof(f522,plain,
    ( spl21_19
  <=> aElementOf0(xk,szNzAzT0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).

fof(f240,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,axiom,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).

fof(f520,plain,
    spl21_18,
    inference(avatar_split_clause,[],[f239,f517]) ).

fof(f517,plain,
    ( spl21_18
  <=> aElementOf0(xx,xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).

fof(f239,plain,
    aElementOf0(xx,xS),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).

fof(f514,plain,
    spl21_17,
    inference(avatar_split_clause,[],[f415,f512]) ).

fof(f512,plain,
    ( spl21_17
  <=> ! [X0] :
        ( aElementOf0(szmzazxdt0(X0),X0)
        | xQ = X0
        | ~ isFinite0(X0)
        | ~ aSubsetOf0(X0,szNzAzT0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).

fof(f415,plain,
    ! [X0] :
      ( aElementOf0(szmzazxdt0(X0),X0)
      | xQ = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(equality_resolution,[],[f402]) ).

fof(f402,plain,
    ! [X0,X1] :
      ( aElementOf0(X1,X0)
      | szmzazxdt0(X0) != X1
      | xQ = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(definition_unfolding,[],[f330,f238]) ).

fof(f238,plain,
    slcrc0 = xQ,
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ( slcrc0 = xQ
    & ! [X0] : ~ aElementOf0(X0,xQ) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f69,plain,
    ( slcrc0 = xQ
    & ~ ? [X0] : aElementOf0(X0,xQ) ),
    inference(flattening,[],[f68]) ).

fof(f68,negated_conjecture,
    ~ ~ ( slcrc0 = xQ
        & ~ ? [X0] : aElementOf0(X0,xQ) ),
    inference(negated_conjecture,[],[f67]) ).

fof(f67,conjecture,
    ~ ( slcrc0 = xQ
      & ~ ? [X0] : aElementOf0(X0,xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f330,plain,
    ! [X0,X1] :
      ( aElementOf0(X1,X0)
      | szmzazxdt0(X0) != X1
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f198,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzazxdt0(X0) = X1
            | ( ~ sdtlseqdt0(sK13(X0,X1),X1)
              & aElementOf0(sK13(X0,X1),X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X3] :
                  ( sdtlseqdt0(X3,X1)
                  | ~ aElementOf0(X3,X0) )
              & aElementOf0(X1,X0) )
            | szmzazxdt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f196,f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ sdtlseqdt0(X2,X1)
          & aElementOf0(X2,X0) )
     => ( ~ sdtlseqdt0(sK13(X0,X1),X1)
        & aElementOf0(sK13(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f196,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzazxdt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X2,X1)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X3] :
                  ( sdtlseqdt0(X3,X1)
                  | ~ aElementOf0(X3,X0) )
              & aElementOf0(X1,X0) )
            | szmzazxdt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(rectify,[],[f195]) ).

fof(f195,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzazxdt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X2,X1)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X2] :
                  ( sdtlseqdt0(X2,X1)
                  | ~ aElementOf0(X2,X0) )
              & aElementOf0(X1,X0) )
            | szmzazxdt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f194]) ).

fof(f194,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzazxdt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X2,X1)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X2] :
                  ( sdtlseqdt0(X2,X1)
                  | ~ aElementOf0(X2,X0) )
              & aElementOf0(X1,X0) )
            | szmzazxdt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(nnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ! [X1] :
          ( szmzazxdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlseqdt0(X2,X1)
                | ~ aElementOf0(X2,X0) )
            & aElementOf0(X1,X0) ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( szmzazxdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlseqdt0(X2,X1)
                | ~ aElementOf0(X2,X0) )
            & aElementOf0(X1,X0) ) )
      | slcrc0 = X0
      | ~ isFinite0(X0)
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,axiom,
    ! [X0] :
      ( ( slcrc0 != X0
        & isFinite0(X0)
        & aSubsetOf0(X0,szNzAzT0) )
     => ! [X1] :
          ( szmzazxdt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
               => sdtlseqdt0(X2,X1) )
            & aElementOf0(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).

fof(f510,plain,
    spl21_16,
    inference(avatar_split_clause,[],[f397,f508]) ).

fof(f508,plain,
    ( spl21_16
  <=> ! [X0,X1] :
        ( slbdtsldtrb0(X0,X1) != xQ
        | ~ aElementOf0(X1,szNzAzT0)
        | isFinite0(X0)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).

fof(f397,plain,
    ! [X0,X1] :
      ( slbdtsldtrb0(X0,X1) != xQ
      | ~ aElementOf0(X1,szNzAzT0)
      | isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(definition_unfolding,[],[f323,f238]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( slcrc0 != slbdtsldtrb0(X0,X1)
      | ~ aElementOf0(X1,szNzAzT0)
      | isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ! [X1] :
          ( slcrc0 != slbdtsldtrb0(X0,X1)
          | ~ aElementOf0(X1,szNzAzT0) )
      | isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ! [X1] :
          ( slcrc0 != slbdtsldtrb0(X0,X1)
          | ~ aElementOf0(X1,szNzAzT0) )
      | isFinite0(X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ( ~ isFinite0(X0)
        & aSet0(X0) )
     => ! [X1] :
          ( aElementOf0(X1,szNzAzT0)
         => slcrc0 != slbdtsldtrb0(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).

fof(f505,plain,
    spl21_15,
    inference(avatar_split_clause,[],[f417,f503]) ).

fof(f503,plain,
    ( spl21_15
  <=> ! [X0] :
        ( aElementOf0(szmzizndt0(X0),X0)
        | xQ = X0
        | ~ aSubsetOf0(X0,szNzAzT0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).

fof(f417,plain,
    ! [X0] :
      ( aElementOf0(szmzizndt0(X0),X0)
      | xQ = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(equality_resolution,[],[f406]) ).

fof(f406,plain,
    ! [X0,X1] :
      ( aElementOf0(X1,X0)
      | szmzizndt0(X0) != X1
      | xQ = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(definition_unfolding,[],[f336,f238]) ).

fof(f336,plain,
    ! [X0,X1] :
      ( aElementOf0(X1,X0)
      | szmzizndt0(X0) != X1
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f205,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzizndt0(X0) = X1
            | ( ~ sdtlseqdt0(X1,sK15(X0,X1))
              & aElementOf0(sK15(X0,X1),X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X3] :
                  ( sdtlseqdt0(X1,X3)
                  | ~ aElementOf0(X3,X0) )
              & aElementOf0(X1,X0) )
            | szmzizndt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f203,f204]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ sdtlseqdt0(X1,X2)
          & aElementOf0(X2,X0) )
     => ( ~ sdtlseqdt0(X1,sK15(X0,X1))
        & aElementOf0(sK15(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f203,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzizndt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X1,X2)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X3] :
                  ( sdtlseqdt0(X1,X3)
                  | ~ aElementOf0(X3,X0) )
              & aElementOf0(X1,X0) )
            | szmzizndt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(rectify,[],[f202]) ).

fof(f202,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzizndt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X1,X2)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X2] :
                  ( sdtlseqdt0(X1,X2)
                  | ~ aElementOf0(X2,X0) )
              & aElementOf0(X1,X0) )
            | szmzizndt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f201]) ).

fof(f201,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( szmzizndt0(X0) = X1
            | ? [X2] :
                ( ~ sdtlseqdt0(X1,X2)
                & aElementOf0(X2,X0) )
            | ~ aElementOf0(X1,X0) )
          & ( ( ! [X2] :
                  ( sdtlseqdt0(X1,X2)
                  | ~ aElementOf0(X2,X0) )
              & aElementOf0(X1,X0) )
            | szmzizndt0(X0) != X1 ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(nnf_transformation,[],[f131]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( szmzizndt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlseqdt0(X1,X2)
                | ~ aElementOf0(X2,X0) )
            & aElementOf0(X1,X0) ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(flattening,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( szmzizndt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlseqdt0(X1,X2)
                | ~ aElementOf0(X2,X0) )
            & aElementOf0(X1,X0) ) )
      | slcrc0 = X0
      | ~ aSubsetOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ! [X0] :
      ( ( slcrc0 != X0
        & aSubsetOf0(X0,szNzAzT0) )
     => ! [X1] :
          ( szmzizndt0(X0) = X1
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
               => sdtlseqdt0(X1,X2) )
            & aElementOf0(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).

fof(f500,plain,
    spl21_14,
    inference(avatar_split_clause,[],[f407,f498]) ).

fof(f498,plain,
    ( spl21_14
  <=> ! [X0] :
        ( xQ = X0
        | aElementOf0(sK16(X0),X0)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).

fof(f407,plain,
    ! [X0] :
      ( xQ = X0
      | aElementOf0(sK16(X0),X0)
      | ~ aSet0(X0) ),
    inference(definition_unfolding,[],[f342,f238]) ).

fof(f342,plain,
    ! [X0] :
      ( slcrc0 = X0
      | aElementOf0(sK16(X0),X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | aElementOf0(sK16(X0),X0)
        | ~ aSet0(X0) )
      & ( ( ! [X2] : ~ aElementOf0(X2,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f208,f209]) ).

fof(f209,plain,
    ! [X0] :
      ( ? [X1] : aElementOf0(X1,X0)
     => aElementOf0(sK16(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f208,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X2] : ~ aElementOf0(X2,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(rectify,[],[f207]) ).

fof(f207,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X1] : ~ aElementOf0(X1,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(flattening,[],[f206]) ).

fof(f206,plain,
    ! [X0] :
      ( ( slcrc0 = X0
        | ? [X1] : aElementOf0(X1,X0)
        | ~ aSet0(X0) )
      & ( ( ! [X1] : ~ aElementOf0(X1,X0)
          & aSet0(X0) )
        | slcrc0 != X0 ) ),
    inference(nnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0] :
      ( slcrc0 = X0
    <=> ( ! [X1] : ~ aElementOf0(X1,X0)
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( slcrc0 = X0
    <=> ( ~ ? [X1] : aElementOf0(X1,X0)
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(f496,plain,
    spl21_13,
    inference(avatar_split_clause,[],[f396,f494]) ).

fof(f494,plain,
    ( spl21_13
  <=> ! [X0] :
        ( xQ = X0
        | sz00 != sbrdtbr0(X0)
        | ~ aSet0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).

fof(f396,plain,
    ! [X0] :
      ( xQ = X0
      | sz00 != sbrdtbr0(X0)
      | ~ aSet0(X0) ),
    inference(definition_unfolding,[],[f290,f238]) ).

fof(f290,plain,
    ! [X0] :
      ( slcrc0 = X0
      | sz00 != sbrdtbr0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ( ( sz00 = sbrdtbr0(X0)
          | slcrc0 != X0 )
        & ( slcrc0 = X0
          | sz00 != sbrdtbr0(X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ( sz00 = sbrdtbr0(X0)
      <=> slcrc0 = X0 )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ( sz00 = sbrdtbr0(X0)
      <=> slcrc0 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

fof(f492,plain,
    ( ~ spl21_12
    | spl21_5
    | ~ spl21_6 ),
    inference(avatar_split_clause,[],[f462,f458,f452,f489]) ).

fof(f489,plain,
    ( spl21_12
  <=> xQ = slbdtsldtrb0(xS,sz00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).

fof(f452,plain,
    ( spl21_5
  <=> slbdtsldtrb0(xS,xk) = xQ ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).

fof(f462,plain,
    ( xQ != slbdtsldtrb0(xS,sz00)
    | spl21_5
    | ~ spl21_6 ),
    inference(superposition,[],[f454,f460]) ).

fof(f460,plain,
    ( sz00 = xk
    | ~ spl21_6 ),
    inference(avatar_component_clause,[],[f458]) ).

fof(f454,plain,
    ( slbdtsldtrb0(xS,xk) != xQ
    | spl21_5 ),
    inference(avatar_component_clause,[],[f452]) ).

fof(f487,plain,
    spl21_11,
    inference(avatar_split_clause,[],[f283,f484]) ).

fof(f484,plain,
    ( spl21_11
  <=> isCountable0(szNzAzT0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).

fof(f283,plain,
    isCountable0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(f482,plain,
    spl21_10,
    inference(avatar_split_clause,[],[f282,f479]) ).

fof(f479,plain,
    ( spl21_10
  <=> aSet0(szNzAzT0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).

fof(f282,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f477,plain,
    spl21_9,
    inference(avatar_split_clause,[],[f250,f474]) ).

fof(f474,plain,
    ( spl21_9
  <=> aSet0(xT) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).

fof(f250,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f62]) ).

fof(f472,plain,
    spl21_8,
    inference(avatar_split_clause,[],[f249,f469]) ).

fof(f469,plain,
    ( spl21_8
  <=> aSet0(xS) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).

fof(f249,plain,
    aSet0(xS),
    inference(cnf_transformation,[],[f62]) ).

fof(f467,plain,
    spl21_7,
    inference(avatar_split_clause,[],[f242,f464]) ).

fof(f464,plain,
    ( spl21_7
  <=> isFinite0(xQ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).

fof(f242,plain,
    isFinite0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    ( xk = sbrdtbr0(xQ)
    & isFinite0(xQ)
    & aSet0(xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).

fof(f461,plain,
    ( ~ spl21_3
    | spl21_6 ),
    inference(avatar_split_clause,[],[f430,f458,f443]) ).

fof(f443,plain,
    ( spl21_3
  <=> aSet0(xQ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).

fof(f430,plain,
    ( sz00 = xk
    | ~ aSet0(xQ) ),
    inference(forward_demodulation,[],[f411,f243]) ).

fof(f243,plain,
    xk = sbrdtbr0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f411,plain,
    ( sz00 = sbrdtbr0(xQ)
    | ~ aSet0(xQ) ),
    inference(equality_resolution,[],[f395]) ).

fof(f395,plain,
    ! [X0] :
      ( sz00 = sbrdtbr0(X0)
      | xQ != X0
      | ~ aSet0(X0) ),
    inference(definition_unfolding,[],[f291,f238]) ).

fof(f291,plain,
    ! [X0] :
      ( sz00 = sbrdtbr0(X0)
      | slcrc0 != X0
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f456,plain,
    spl21_3,
    inference(avatar_split_clause,[],[f241,f443]) ).

fof(f241,plain,
    aSet0(xQ),
    inference(cnf_transformation,[],[f66]) ).

fof(f455,plain,
    ~ spl21_5,
    inference(avatar_split_clause,[],[f392,f452]) ).

fof(f392,plain,
    slbdtsldtrb0(xS,xk) != xQ,
    inference(definition_unfolding,[],[f278,f238]) ).

fof(f278,plain,
    slcrc0 != slbdtsldtrb0(xS,xk),
    inference(cnf_transformation,[],[f178]) ).

fof(f178,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & aElementOf0(sK6,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ( ~ aElementOf0(sK7(X1),xS)
                & aElementOf0(sK7(X1),X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ( ~ aElementOf0(sK8(X5),xT)
                & aElementOf0(sK8(X5),X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ( ~ aElementOf0(sK9(X8),xS)
                & aElementOf0(sK9(X8),X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f173,f177,f176,f175,f174]) ).

fof(f174,plain,
    ( ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
   => aElementOf0(sK6,slbdtsldtrb0(xS,xk)) ),
    introduced(choice_axiom,[]) ).

fof(f175,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,xS)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK7(X1),xS)
        & aElementOf0(sK7(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f176,plain,
    ! [X5] :
      ( ? [X6] :
          ( ~ aElementOf0(X6,xT)
          & aElementOf0(X6,X5) )
     => ( ~ aElementOf0(sK8(X5),xT)
        & aElementOf0(sK8(X5),X5) ) ),
    introduced(choice_axiom,[]) ).

fof(f177,plain,
    ! [X8] :
      ( ? [X9] :
          ( ~ aElementOf0(X9,xS)
          & aElementOf0(X9,X8) )
     => ( ~ aElementOf0(sK9(X8),xS)
        & aElementOf0(sK9(X8),X8) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X1) != xk
          | ( ~ aSubsetOf0(X1,xS)
            & ( ? [X2] :
                  ( ~ aElementOf0(X2,xS)
                  & aElementOf0(X2,X1) )
              | ~ aSet0(X1) ) ) )
        & ( ( sbrdtbr0(X1) = xk
            & aSubsetOf0(X1,xS)
            & ! [X3] :
                ( aElementOf0(X3,xS)
                | ~ aElementOf0(X3,X1) )
            & aSet0(X1) )
          | ~ aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f81]) ).

fof(f81,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk))
    & ! [X0] :
        ( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
          | sbrdtbr0(X0) != xk
          | ( ~ aSubsetOf0(X0,xS)
            & ( ? [X1] :
                  ( ~ aElementOf0(X1,xS)
                  & aElementOf0(X1,X0) )
              | ~ aSet0(X0) ) ) )
        & ( ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X2] :
                ( aElementOf0(X2,xS)
                | ~ aElementOf0(X2,X0) )
            & aSet0(X0) )
          | ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xT,xk))
        | ~ aElementOf0(X4,slbdtsldtrb0(xS,xk)) )
    & ! [X5] :
        ( ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
          | xk != sbrdtbr0(X5)
          | ( ~ aSubsetOf0(X5,xT)
            & ( ? [X6] :
                  ( ~ aElementOf0(X6,xT)
                  & aElementOf0(X6,X5) )
              | ~ aSet0(X5) ) ) )
        & ( ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,xT)
                | ~ aElementOf0(X7,X5) )
            & aSet0(X5) )
          | ~ aElementOf0(X5,slbdtsldtrb0(xT,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
          | xk != sbrdtbr0(X8)
          | ( ~ aSubsetOf0(X8,xS)
            & ( ? [X9] :
                  ( ~ aElementOf0(X9,xS)
                  & aElementOf0(X9,X8) )
              | ~ aSet0(X8) ) ) )
        & ( ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,xS)
                | ~ aElementOf0(X10,X8) )
            & aSet0(X8) )
          | ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f70,plain,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X2] :
                    ( aElementOf0(X2,X0)
                   => aElementOf0(X2,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X3] : aElementOf0(X3,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X4] :
        ( aElementOf0(X4,slbdtsldtrb0(xS,xk))
       => aElementOf0(X4,slbdtsldtrb0(xT,xk)) )
    & ! [X5] :
        ( ( ( xk = sbrdtbr0(X5)
            & ( aSubsetOf0(X5,xT)
              | ( ! [X6] :
                    ( aElementOf0(X6,X5)
                   => aElementOf0(X6,xT) )
                & aSet0(X5) ) ) )
         => aElementOf0(X5,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X5,slbdtsldtrb0(xT,xk))
         => ( xk = sbrdtbr0(X5)
            & aSubsetOf0(X5,xT)
            & ! [X7] :
                ( aElementOf0(X7,X5)
               => aElementOf0(X7,xT) )
            & aSet0(X5) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X8] :
        ( ( ( xk = sbrdtbr0(X8)
            & ( aSubsetOf0(X8,xS)
              | ( ! [X9] :
                    ( aElementOf0(X9,X8)
                   => aElementOf0(X9,xS) )
                & aSet0(X8) ) ) )
         => aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
         => ( xk = sbrdtbr0(X8)
            & aSubsetOf0(X8,xS)
            & ! [X10] :
                ( aElementOf0(X10,X8)
               => aElementOf0(X10,xS) )
            & aSet0(X8) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    inference(rectify,[],[f63]) ).

fof(f63,axiom,
    ( ~ ( ! [X0] :
            ( ( ( sbrdtbr0(X0) = xk
                & ( aSubsetOf0(X0,xS)
                  | ( ! [X1] :
                        ( aElementOf0(X1,X0)
                       => aElementOf0(X1,xS) )
                    & aSet0(X0) ) ) )
             => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
            & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
             => ( sbrdtbr0(X0) = xk
                & aSubsetOf0(X0,xS)
                & ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
       => ( slcrc0 = slbdtsldtrb0(xS,xk)
          | ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
       => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xT)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xT) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xT)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xT) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X0] :
        ( ( ( sbrdtbr0(X0) = xk
            & ( aSubsetOf0(X0,xS)
              | ( ! [X1] :
                    ( aElementOf0(X1,X0)
                   => aElementOf0(X1,xS) )
                & aSet0(X0) ) ) )
         => aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
        & ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
         => ( sbrdtbr0(X0) = xk
            & aSubsetOf0(X0,xS)
            & ! [X1] :
                ( aElementOf0(X1,X0)
               => aElementOf0(X1,xS) )
            & aSet0(X0) ) ) )
    & aSet0(slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).

fof(f450,plain,
    ( ~ spl21_3
    | ~ spl21_4 ),
    inference(avatar_split_clause,[],[f413,f447,f443]) ).

fof(f447,plain,
    ( spl21_4
  <=> isCountable0(xQ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).

fof(f413,plain,
    ( ~ isCountable0(xQ)
    | ~ aSet0(xQ) ),
    inference(equality_resolution,[],[f398]) ).

fof(f398,plain,
    ! [X0] :
      ( xQ != X0
      | ~ isCountable0(X0)
      | ~ aSet0(X0) ),
    inference(definition_unfolding,[],[f325,f238]) ).

fof(f325,plain,
    ! [X0] :
      ( slcrc0 != X0
      | ~ isCountable0(X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0] :
      ( slcrc0 != X0
      | ~ isCountable0(X0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( slcrc0 != X0
      | ~ isCountable0(X0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ( isCountable0(X0)
        & aSet0(X0) )
     => slcrc0 != X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).

fof(f441,plain,
    spl21_2,
    inference(avatar_split_clause,[],[f394,f438]) ).

fof(f438,plain,
    ( spl21_2
  <=> slbdtrb0(sz00) = xQ ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).

fof(f394,plain,
    slbdtrb0(sz00) = xQ,
    inference(definition_unfolding,[],[f281,f238]) ).

fof(f281,plain,
    slcrc0 = slbdtrb0(sz00),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,axiom,
    slcrc0 = slbdtrb0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).

fof(f436,plain,
    spl21_1,
    inference(avatar_split_clause,[],[f237,f434]) ).

fof(f434,plain,
    ( spl21_1
  <=> ! [X0] : ~ aElementOf0(X0,xQ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).

fof(f237,plain,
    ! [X0] : ~ aElementOf0(X0,xQ),
    inference(cnf_transformation,[],[f78]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : NUM550+3 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31  % Computer : n016.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31  % CPULimit   : 300
% 0.16/0.31  % WCLimit    : 300
% 0.16/0.31  % DateTime   : Tue Apr 30 00:16:40 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.32  % (24482)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (24485)WARNING: value z3 for option sas not known
% 0.16/0.33  % (24486)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33  % (24487)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)
% 0.16/0.33  % (24484)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33  % (24483)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33  % (24489)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)
% 0.16/0.33  % (24488)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)
% 0.16/0.33  % (24485)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)
% 0.16/0.34  % (24487)First to succeed.
% 0.16/0.34  % (24485)Also succeeded, but the first one will report.
% 0.16/0.34  TRYING [1]
% 0.16/0.34  TRYING [1]
% 0.16/0.34  % (24488)Also succeeded, but the first one will report.
% 0.16/0.34  % (24487)Refutation found. Thanks to Tanya!
% 0.16/0.34  % SZS status Theorem for theBenchmark
% 0.16/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.35  % (24487)------------------------------
% 0.16/0.35  % (24487)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.35  % (24487)Termination reason: Refutation
% 0.16/0.35  
% 0.16/0.35  % (24487)Memory used [KB]: 1039
% 0.16/0.35  % (24487)Time elapsed: 0.010 s
% 0.16/0.35  % (24487)Instructions burned: 18 (million)
% 0.16/0.35  % (24487)------------------------------
% 0.16/0.35  % (24487)------------------------------
% 0.16/0.35  % (24482)Success in time 0.028 s
%------------------------------------------------------------------------------