TSTP Solution File: RNG095+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -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 : Wed May  1 03:41:50 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   81 (   8 unt;   1 typ;   0 def)
%            Number of atoms       :  595 (  41 equ)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  468 ( 169   ~; 162   |; 105   &)
%                                         (  18 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  216 ( 216 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   28 (  26 usr;   9 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  207 ( 154   !;  52   ?;  50   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_8,type,
    sQ12_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f285,plain,
    $false,
    inference(avatar_sat_refutation,[],[f230,f236,f263,f273,f277,f284]) ).

tff(f284,plain,
    spl13_10,
    inference(avatar_contradiction_clause,[],[f283]) ).

tff(f283,plain,
    ( $false
    | spl13_10 ),
    inference(subsumption_resolution,[],[f282,f141]) ).

tff(f141,plain,
    aElement0(sz10),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    aElement0(sz10),
    file('/export/starexec/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',mSortsC_01) ).

tff(f282,plain,
    ( ~ aElement0(sz10)
    | spl13_10 ),
    inference(resolution,[],[f272,f92]) ).

tff(f92,plain,
    ! [X0: $i] :
      ( aElementOf0(X0,sdtpldt1(xI,xJ))
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtpldt1(xI,xJ))
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f29]) ).

tff(f29,axiom,
    ! [X0] :
      ( aElement0(X0)
     => aElementOf0(X0,sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',m__1205_03) ).

tff(f272,plain,
    ( ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | spl13_10 ),
    inference(avatar_component_clause,[],[f270]) ).

tff(f270,plain,
    ( spl13_10
  <=> aElementOf0(sz10,sdtpldt1(xI,xJ)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

tff(f277,plain,
    ( ~ spl13_4
    | ~ spl13_5
    | spl13_9 ),
    inference(avatar_contradiction_clause,[],[f276]) ).

tff(f276,plain,
    ( $false
    | ~ spl13_4
    | ~ spl13_5
    | spl13_9 ),
    inference(subsumption_resolution,[],[f275,f219]) ).

tff(f219,plain,
    ( aSet0(xI)
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f218]) ).

tff(f218,plain,
    ( spl13_4
  <=> aSet0(xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

tff(f275,plain,
    ( ~ aSet0(xI)
    | ~ spl13_5
    | spl13_9 ),
    inference(subsumption_resolution,[],[f274,f223]) ).

tff(f223,plain,
    ( aSet0(xJ)
    | ~ spl13_5 ),
    inference(avatar_component_clause,[],[f222]) ).

tff(f222,plain,
    ( spl13_5
  <=> aSet0(xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

tff(f274,plain,
    ( ~ aSet0(xJ)
    | ~ aSet0(xI)
    | spl13_9 ),
    inference(resolution,[],[f268,f125]) ).

tff(f125,plain,
    ! [X0: $i,X1: $i] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f71]) ).

tff(f71,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f58,f70,f69]) ).

tff(f69,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ( ! [X3] :
            ( aElementOf0(X3,X2)
          <=> ? [X4,X5] :
                ( ( sdtpldt0(X4,X5) = X3 )
                & aElementOf0(X5,X1)
                & aElementOf0(X4,X0) ) )
        & aSet0(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f70,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtpldt1(X0,X1) = X2 )
        <=> sP0(X1,X0,X2) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f58,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,[],[f57]) ).

tff(f57,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]) ).

tff(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/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',mDefSSum) ).

tff(f268,plain,
    ( ~ sP1(xI,xJ)
    | spl13_9 ),
    inference(avatar_component_clause,[],[f266]) ).

tff(f266,plain,
    ( spl13_9
  <=> sP1(xI,xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

tff(f273,plain,
    ( ~ spl13_9
    | ~ spl13_10
    | ~ spl13_8 ),
    inference(avatar_split_clause,[],[f264,f261,f270,f266]) ).

tff(f261,plain,
    ( spl13_8
  <=> ! [X2] :
        ( ~ aElementOf0(sz10,X2)
        | ~ sP0(xJ,xI,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

tff(f264,plain,
    ( ~ aElementOf0(sz10,sdtpldt1(xI,xJ))
    | ~ sP1(xI,xJ)
    | ~ spl13_8 ),
    inference(resolution,[],[f262,f144]) ).

tff(f144,plain,
    ! [X0: $i,X1: $i] :
      ( sP0(X1,X0,sdtpldt1(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(equality_resolution,[],[f114]) ).

tff(f114,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( sP0(X1,X0,X2)
      | ( sdtpldt1(X0,X1) != X2 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

tff(f79,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( sdtpldt1(X0,X1) = X2 )
            | ~ sP0(X1,X0,X2) )
          & ( sP0(X1,X0,X2)
            | ( sdtpldt1(X0,X1) != X2 ) ) )
      | ~ sP1(X0,X1) ),
    inference(nnf_transformation,[],[f70]) ).

tff(f262,plain,
    ( ! [X2: $i] :
        ( ~ sP0(xJ,xI,X2)
        | ~ aElementOf0(sz10,X2) )
    | ~ spl13_8 ),
    inference(avatar_component_clause,[],[f261]) ).

tff(f263,plain,
    ( spl13_8
    | spl13_8
    | spl13_8 ),
    inference(avatar_split_clause,[],[f259,f261,f261,f261]) ).

tff(f259,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(sz10,X0)
      | ~ sP0(xJ,xI,X0)
      | ~ aElementOf0(sz10,X1)
      | ~ sP0(xJ,xI,X1)
      | ~ aElementOf0(sz10,X2)
      | ~ sP0(xJ,xI,X2) ),
    inference(resolution,[],[f251,f117]) ).

tff(f117,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( aElementOf0(sK8(X0,X1,X8),X1)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

tff(f86,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( ( sdtpldt0(X4,X5) != sK5(X0,X1,X2) )
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(sK5(X0,X1,X2),X2) )
          & ( ( ( sK5(X0,X1,X2) = sdtpldt0(sK6(X0,X1,X2),sK7(X0,X1,X2)) )
              & aElementOf0(sK7(X0,X1,X2),X0)
              & aElementOf0(sK6(X0,X1,X2),X1) )
            | aElementOf0(sK5(X0,X1,X2),X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X8] :
              ( ( aElementOf0(X8,X2)
                | ! [X9,X10] :
                    ( ( sdtpldt0(X9,X10) != X8 )
                    | ~ aElementOf0(X10,X0)
                    | ~ aElementOf0(X9,X1) ) )
              & ( ( ( sdtpldt0(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 )
                  & aElementOf0(sK9(X0,X1,X8),X0)
                  & aElementOf0(sK8(X0,X1,X8),X1) )
                | ~ aElementOf0(X8,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f82,f85,f84,f83]) ).

tff(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) != sK5(X0,X1,X2) )
              | ~ aElementOf0(X5,X0)
              | ~ aElementOf0(X4,X1) )
          | ~ aElementOf0(sK5(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ( sdtpldt0(X6,X7) = sK5(X0,X1,X2) )
              & aElementOf0(X7,X0)
              & aElementOf0(X6,X1) )
          | aElementOf0(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f84,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ( sdtpldt0(X6,X7) = sK5(X0,X1,X2) )
          & aElementOf0(X7,X0)
          & aElementOf0(X6,X1) )
     => ( ( sK5(X0,X1,X2) = sdtpldt0(sK6(X0,X1,X2),sK7(X0,X1,X2)) )
        & aElementOf0(sK7(X0,X1,X2),X0)
        & aElementOf0(sK6(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f85,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ( sdtpldt0(X11,X12) = X8 )
          & aElementOf0(X12,X0)
          & aElementOf0(X11,X1) )
     => ( ( sdtpldt0(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 )
        & aElementOf0(sK9(X0,X1,X8),X0)
        & aElementOf0(sK8(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f82,plain,
    ! [X0,X1,X2] :
      ( ( sP0(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) ) )
        | ~ aSet0(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) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f81]) ).

tff(f81,plain,
    ! [X1,X0,X2] :
      ( ( sP0(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) ) )
        | ~ aSet0(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) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f80]) ).

tff(f80,plain,
    ! [X1,X0,X2] :
      ( ( sP0(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) ) )
        | ~ aSet0(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) ) )
          & aSet0(X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f69]) ).

tff(f251,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(sK8(xJ,X0,sz10),xI)
      | ~ aElementOf0(sz10,X1)
      | ~ sP0(xJ,X0,X1)
      | ~ aElementOf0(sz10,X2)
      | ~ sP0(xJ,X0,X2) ),
    inference(resolution,[],[f233,f118]) ).

tff(f118,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( aElementOf0(sK9(X0,X1,X8),X0)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

tff(f233,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(sK9(X1,X2,sz10),xJ)
      | ~ sP0(X1,X2,X0)
      | ~ aElementOf0(sz10,X0)
      | ~ aElementOf0(sK8(X1,X2,sz10),xI) ),
    inference(resolution,[],[f231,f147]) ).

tff(f147,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sQ12_eqProxy($i,sz10,sdtpldt0(X0,X1))
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(equality_proxy_replacement,[],[f95,f146]) ).

tff(f146,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ12_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).

tff(f95,plain,
    ! [X0: $i,X1: $i] :
      ( ( sz10 != sdtpldt0(X0,X1) )
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(cnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0,X1] :
      ( ( sz10 != sdtpldt0(X0,X1) )
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(ennf_transformation,[],[f32]) ).

tff(f32,negated_conjecture,
    ~ ? [X0,X1] :
        ( ( sz10 = sdtpldt0(X0,X1) )
        & aElementOf0(X1,xJ)
        & aElementOf0(X0,xI) ),
    inference(negated_conjecture,[],[f31]) ).

tff(f31,conjecture,
    ? [X0,X1] :
      ( ( sz10 = sdtpldt0(X0,X1) )
      & aElementOf0(X1,xJ)
      & aElementOf0(X0,xI) ),
    file('/export/starexec/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',m__) ).

tff(f231,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( sQ12_eqProxy($i,X8,sdtpldt0(sK8(X0,X1,X8),sK9(X0,X1,X8)))
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(forward_literal_rewriting,[],[f157,f175]) ).

tff(f175,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ12_eqProxy(X0,X2,X1)
      | ~ sQ12_eqProxy(X0,X1,X2) ),
    inference(equality_proxy_axiom,[],[f146]) ).

tff(f157,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( sQ12_eqProxy($i,sdtpldt0(sK8(X0,X1,X8),sK9(X0,X1,X8)),X8)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(equality_proxy_replacement,[],[f119,f146]) ).

tff(f119,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( ( sdtpldt0(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 )
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f86]) ).

tff(f236,plain,
    spl13_5,
    inference(avatar_contradiction_clause,[],[f235]) ).

tff(f235,plain,
    ( $false
    | spl13_5 ),
    inference(subsumption_resolution,[],[f234,f91]) ).

tff(f91,plain,
    aIdeal0(xJ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,axiom,
    ( aIdeal0(xJ)
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',m__1205) ).

tff(f234,plain,
    ( ~ aIdeal0(xJ)
    | spl13_5 ),
    inference(resolution,[],[f224,f98]) ).

tff(f98,plain,
    ! [X0: $i] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f78]) ).

tff(f78,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ( ( ( ~ aElementOf0(sdtasdt0(sK3(X0),sK2(X0)),X0)
              & aElement0(sK3(X0)) )
            | ( ~ aElementOf0(sdtpldt0(sK2(X0),sK4(X0)),X0)
              & aElementOf0(sK4(X0),X0) ) )
          & aElementOf0(sK2(X0),X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f74,f77,f76,f75]) ).

tff(f75,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ? [X2] :
                ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                & aElement0(X2) )
            | ? [X3] :
                ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                & aElementOf0(X3,X0) ) )
          & aElementOf0(X1,X0) )
     => ( ( ? [X2] :
              ( ~ aElementOf0(sdtasdt0(X2,sK2(X0)),X0)
              & aElement0(X2) )
          | ? [X3] :
              ( ~ aElementOf0(sdtpldt0(sK2(X0),X3),X0)
              & aElementOf0(X3,X0) ) )
        & aElementOf0(sK2(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f76,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ aElementOf0(sdtasdt0(X2,sK2(X0)),X0)
          & aElement0(X2) )
     => ( ~ aElementOf0(sdtasdt0(sK3(X0),sK2(X0)),X0)
        & aElement0(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f77,plain,
    ! [X0] :
      ( ? [X3] :
          ( ~ aElementOf0(sdtpldt0(sK2(X0),X3),X0)
          & aElementOf0(X3,X0) )
     => ( ~ aElementOf0(sdtpldt0(sK2(X0),sK4(X0)),X0)
        & aElementOf0(sK4(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f74,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(rectify,[],[f73]) ).

tff(f73,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(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(flattening,[],[f72]) ).

tff(f72,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(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(nnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtasdt0(X2,X1),X0)
                  | ~ aElement0(X2) )
              & ! [X3] :
                  ( aElementOf0(sdtpldt0(X1,X3),X0)
                  | ~ aElementOf0(X3,X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f33]) ).

tff(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]) ).

tff(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/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432',mDefIdeal) ).

tff(f224,plain,
    ( ~ aSet0(xJ)
    | spl13_5 ),
    inference(avatar_component_clause,[],[f222]) ).

tff(f230,plain,
    spl13_4,
    inference(avatar_contradiction_clause,[],[f229]) ).

tff(f229,plain,
    ( $false
    | spl13_4 ),
    inference(subsumption_resolution,[],[f228,f90]) ).

tff(f90,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f28]) ).

tff(f228,plain,
    ( ~ aIdeal0(xI)
    | spl13_4 ),
    inference(resolution,[],[f220,f98]) ).

tff(f220,plain,
    ( ~ aSet0(xI)
    | spl13_4 ),
    inference(avatar_component_clause,[],[f218]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : RNG095+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 18:09:26 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.szQ2OGRRjX/Vampire---4.8_17432
% 0.55/0.75  % (17697)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.55/0.75  % (17698)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.55/0.75  % (17691)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.55/0.75  % (17692)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.55/0.75  % (17694)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.55/0.75  % (17693)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.75  % (17696)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.55/0.75  % (17695)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.55/0.75  % (17698)Refutation not found, incomplete strategy% (17698)------------------------------
% 0.55/0.75  % (17698)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.75  % (17698)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.75  
% 0.55/0.75  % (17698)Memory used [KB]: 1083
% 0.55/0.75  % (17698)Time elapsed: 0.005 s
% 0.55/0.75  % (17698)Instructions burned: 6 (million)
% 0.55/0.75  % (17698)------------------------------
% 0.55/0.75  % (17698)------------------------------
% 0.60/0.75  % (17695)Refutation not found, incomplete strategy% (17695)------------------------------
% 0.60/0.75  % (17695)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.75  % (17695)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.75  
% 0.60/0.75  % (17695)Memory used [KB]: 1135
% 0.60/0.75  % (17695)Time elapsed: 0.005 s
% 0.60/0.75  % (17695)Instructions burned: 7 (million)
% 0.60/0.75  % (17695)------------------------------
% 0.60/0.75  % (17695)------------------------------
% 0.60/0.75  % (17691)First to succeed.
% 0.60/0.75  % (17699)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.60/0.76  % (17691)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (17691)------------------------------
% 0.60/0.76  % (17691)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76  % (17691)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (17691)Memory used [KB]: 1177
% 0.60/0.76  % (17691)Time elapsed: 0.010 s
% 0.60/0.76  % (17691)Instructions burned: 14 (million)
% 0.60/0.76  % (17691)------------------------------
% 0.60/0.76  % (17691)------------------------------
% 0.60/0.76  % (17687)Success in time 0.387 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------