TSTP Solution File: RNG087+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : RNG087+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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 03:41:47 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   66 (   6 unt;   1 typ;   0 def)
%            Number of atoms       :  468 (  41 equ)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  367 ( 135   ~; 128   |;  75   &)
%                                         (  15 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  171 ( 171 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   25 (  23 usr;   9 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  175 ( 138   !;  36   ?;  51   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_7,type,
    sQ9_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f246,plain,
    $false,
    inference(avatar_sat_refutation,[],[f179,f194,f239,f245]) ).

tff(f245,plain,
    ( ~ spl10_4
    | ~ spl10_6
    | ~ spl10_12 ),
    inference(avatar_contradiction_clause,[],[f244]) ).

tff(f244,plain,
    ( $false
    | ~ spl10_4
    | ~ spl10_6
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f243,f161]) ).

tff(f161,plain,
    ( aSet0(xI)
    | ~ spl10_4 ),
    inference(avatar_component_clause,[],[f160]) ).

tff(f160,plain,
    ( spl10_4
  <=> aSet0(xI) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).

tff(f243,plain,
    ( ~ aSet0(xI)
    | ~ spl10_6
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f242,f170]) ).

tff(f170,plain,
    ( aSet0(xJ)
    | ~ spl10_6 ),
    inference(avatar_component_clause,[],[f169]) ).

tff(f169,plain,
    ( spl10_6
  <=> aSet0(xJ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).

tff(f242,plain,
    ( ~ aSet0(xJ)
    | ~ aSet0(xI)
    | ~ spl10_12 ),
    inference(resolution,[],[f241,f109]) ).

tff(f109,plain,
    ! [X0: $i,X1: $i] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

tff(f61,plain,
    ! [X0,X1] :
      ( sP1(X0,X1)
      | ~ aSet0(X1)
      | ~ aSet0(X0) ),
    inference(definition_folding,[],[f54,f60,f59]) ).

tff(f59,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(f60,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtpldt1(X0,X1) = X2 )
        <=> sP0(X1,X0,X2) )
      | ~ sP1(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f54,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,[],[f53]) ).

tff(f53,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/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985',mDefSSum) ).

tff(f241,plain,
    ( ~ sP1(xI,xJ)
    | ~ spl10_12 ),
    inference(subsumption_resolution,[],[f240,f76]) ).

tff(f76,plain,
    aElementOf0(xy,sdtpldt1(xI,xJ)),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,axiom,
    ( aElement0(xz)
    & aElementOf0(xy,sdtpldt1(xI,xJ))
    & aElementOf0(xx,sdtpldt1(xI,xJ)) ),
    file('/export/starexec/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985',m__901) ).

tff(f240,plain,
    ( ~ aElementOf0(xy,sdtpldt1(xI,xJ))
    | ~ sP1(xI,xJ)
    | ~ spl10_12 ),
    inference(resolution,[],[f238,f115]) ).

tff(f115,plain,
    ! [X0: $i,X1: $i] :
      ( sP0(X1,X0,sdtpldt1(X0,X1))
      | ~ sP1(X0,X1) ),
    inference(equality_resolution,[],[f98]) ).

tff(f98,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( sP0(X1,X0,X2)
      | ( sdtpldt1(X0,X1) != X2 )
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

tff(f65,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,[],[f60]) ).

tff(f238,plain,
    ( ! [X2: $i] :
        ( ~ sP0(xJ,xI,X2)
        | ~ aElementOf0(xy,X2) )
    | ~ spl10_12 ),
    inference(avatar_component_clause,[],[f237]) ).

tff(f237,plain,
    ( spl10_12
  <=> ! [X2] :
        ( ~ aElementOf0(xy,X2)
        | ~ sP0(xJ,xI,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).

tff(f239,plain,
    ( spl10_12
    | spl10_12
    | spl10_12 ),
    inference(avatar_split_clause,[],[f235,f237,f237,f237]) ).

tff(f235,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(xy,X0)
      | ~ sP0(xJ,xI,X0)
      | ~ aElementOf0(xy,X1)
      | ~ sP0(xJ,xI,X1)
      | ~ aElementOf0(xy,X2)
      | ~ sP0(xJ,xI,X2) ),
    inference(resolution,[],[f230,f101]) ).

tff(f101,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( aElementOf0(sK7(X0,X1,X8),X1)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f72]) ).

tff(f72,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( ( sdtpldt0(X4,X5) != sK4(X0,X1,X2) )
                | ~ aElementOf0(X5,X0)
                | ~ aElementOf0(X4,X1) )
            | ~ aElementOf0(sK4(X0,X1,X2),X2) )
          & ( ( ( sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)) )
              & aElementOf0(sK6(X0,X1,X2),X0)
              & aElementOf0(sK5(X0,X1,X2),X1) )
            | aElementOf0(sK4(X0,X1,X2),X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X8] :
              ( ( aElementOf0(X8,X2)
                | ! [X9,X10] :
                    ( ( sdtpldt0(X9,X10) != X8 )
                    | ~ aElementOf0(X10,X0)
                    | ~ aElementOf0(X9,X1) ) )
              & ( ( ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8 )
                  & aElementOf0(sK8(X0,X1,X8),X0)
                  & aElementOf0(sK7(X0,X1,X8),X1) )
                | ~ aElementOf0(X8,X2) ) )
          & aSet0(X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f68,f71,f70,f69]) ).

tff(f69,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) != sK4(X0,X1,X2) )
              | ~ aElementOf0(X5,X0)
              | ~ aElementOf0(X4,X1) )
          | ~ aElementOf0(sK4(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ( sdtpldt0(X6,X7) = sK4(X0,X1,X2) )
              & aElementOf0(X7,X0)
              & aElementOf0(X6,X1) )
          | aElementOf0(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f70,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ( sdtpldt0(X6,X7) = sK4(X0,X1,X2) )
          & aElementOf0(X7,X0)
          & aElementOf0(X6,X1) )
     => ( ( sK4(X0,X1,X2) = sdtpldt0(sK5(X0,X1,X2),sK6(X0,X1,X2)) )
        & aElementOf0(sK6(X0,X1,X2),X0)
        & aElementOf0(sK5(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f71,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ( sdtpldt0(X11,X12) = X8 )
          & aElementOf0(X12,X0)
          & aElementOf0(X11,X1) )
     => ( ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8 )
        & aElementOf0(sK8(X0,X1,X8),X0)
        & aElementOf0(sK7(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

tff(f68,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,[],[f67]) ).

tff(f67,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,[],[f66]) ).

tff(f66,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,[],[f59]) ).

tff(f230,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(sK7(xJ,X0,xy),xI)
      | ~ aElementOf0(xy,X1)
      | ~ sP0(xJ,X0,X1)
      | ~ aElementOf0(xy,X2)
      | ~ sP0(xJ,X0,X2) ),
    inference(resolution,[],[f229,f102]) ).

tff(f102,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( aElementOf0(sK8(X0,X1,X8),X0)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f72]) ).

tff(f229,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ~ aElementOf0(sK8(X1,X2,xy),xJ)
      | ~ sP0(X1,X2,X0)
      | ~ aElementOf0(xy,X0)
      | ~ aElementOf0(sK7(X1,X2,xy),xI) ),
    inference(resolution,[],[f228,f191]) ).

tff(f191,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sQ9_eqProxy($i,xy,sdtpldt0(X0,X1))
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(resolution,[],[f140,f119]) ).

tff(f119,plain,
    ! [X0: $i,X1: $i] :
      ( ~ sQ9_eqProxy($i,sdtpldt0(X0,X1),xy)
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(equality_proxy_replacement,[],[f81,f117]) ).

tff(f117,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ9_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ9_eqProxy])]) ).

tff(f81,plain,
    ! [X0: $i,X1: $i] :
      ( ( sdtpldt0(X0,X1) != xy )
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0,X1] :
      ( ( sdtpldt0(X0,X1) != xy )
      | ~ aElementOf0(X1,xJ)
      | ~ aElementOf0(X0,xI) ),
    inference(ennf_transformation,[],[f29]) ).

tff(f29,negated_conjecture,
    ~ ? [X0,X1] :
        ( ( sdtpldt0(X0,X1) = xy )
        & aElementOf0(X1,xJ)
        & aElementOf0(X0,xI) ),
    inference(negated_conjecture,[],[f28]) ).

tff(f28,conjecture,
    ? [X0,X1] :
      ( ( sdtpldt0(X0,X1) = xy )
      & aElementOf0(X1,xJ)
      & aElementOf0(X0,xI) ),
    file('/export/starexec/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985',m__) ).

tff(f140,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ9_eqProxy(X0,X2,X1)
      | ~ sQ9_eqProxy(X0,X1,X2) ),
    inference(equality_proxy_axiom,[],[f117]) ).

tff(f228,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( sQ9_eqProxy($i,X8,sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)))
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(forward_literal_rewriting,[],[f133,f140]) ).

tff(f133,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( sQ9_eqProxy($i,sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)),X8)
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(equality_proxy_replacement,[],[f103,f117]) ).

tff(f103,plain,
    ! [X2: $i,X0: $i,X1: $i,X8: $i] :
      ( ( sdtpldt0(sK7(X0,X1,X8),sK8(X0,X1,X8)) = X8 )
      | ~ aElementOf0(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f72]) ).

tff(f194,plain,
    spl10_6,
    inference(avatar_contradiction_clause,[],[f193]) ).

tff(f193,plain,
    ( $false
    | spl10_6 ),
    inference(subsumption_resolution,[],[f192,f74]) ).

tff(f74,plain,
    aIdeal0(xJ),
    inference(cnf_transformation,[],[f25]) ).

tff(f25,axiom,
    ( aIdeal0(xJ)
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985',m__870) ).

tff(f192,plain,
    ( ~ aIdeal0(xJ)
    | spl10_6 ),
    inference(resolution,[],[f171,f82]) ).

tff(f82,plain,
    ! [X0: $i] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,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,[],[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(unused_predicate_definition_removal,[],[f30]) ).

tff(f30,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/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985',mDefIdeal) ).

tff(f171,plain,
    ( ~ aSet0(xJ)
    | spl10_6 ),
    inference(avatar_component_clause,[],[f169]) ).

tff(f179,plain,
    spl10_4,
    inference(avatar_contradiction_clause,[],[f178]) ).

tff(f178,plain,
    ( $false
    | spl10_4 ),
    inference(subsumption_resolution,[],[f177,f73]) ).

tff(f73,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f25]) ).

tff(f177,plain,
    ( ~ aIdeal0(xI)
    | spl10_4 ),
    inference(resolution,[],[f162,f82]) ).

tff(f162,plain,
    ( ~ aSet0(xI)
    | spl10_4 ),
    inference(avatar_component_clause,[],[f160]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.36  % Computer : n005.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Tue Apr 30 17:28:56 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.DGUwH0F8ga/Vampire---4.8_26985
% 0.60/0.75  % (27202)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)
% 0.60/0.75  % (27204)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)
% 0.60/0.75  % (27197)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)
% 0.60/0.75  % (27199)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.75  % (27198)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)
% 0.60/0.75  % (27201)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)
% 0.60/0.75  % (27200)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)
% 0.60/0.75  % (27203)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)
% 0.60/0.75  % (27204)Refutation not found, incomplete strategy% (27204)------------------------------
% 0.60/0.75  % (27204)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.75  % (27204)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.75  
% 0.60/0.75  % (27204)Memory used [KB]: 1061
% 0.60/0.75  % (27204)Time elapsed: 0.003 s
% 0.60/0.75  % (27204)Instructions burned: 5 (million)
% 0.60/0.75  % (27204)------------------------------
% 0.60/0.75  % (27204)------------------------------
% 0.60/0.76  % (27205)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  % (27201)Refutation not found, incomplete strategy% (27201)------------------------------
% 0.60/0.76  % (27201)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76  % (27201)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.76  
% 0.60/0.76  % (27201)Memory used [KB]: 1150
% 0.60/0.76  % (27201)Time elapsed: 0.006 s
% 0.60/0.76  % (27201)Instructions burned: 7 (million)
% 0.60/0.76  % (27201)------------------------------
% 0.60/0.76  % (27201)------------------------------
% 0.60/0.76  % (27197)First to succeed.
% 0.60/0.76  % (27197)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  % (27197)------------------------------
% 0.60/0.76  % (27197)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76  % (27197)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (27197)Memory used [KB]: 1120
% 0.60/0.76  % (27197)Time elapsed: 0.008 s
% 0.60/0.76  % (27197)Instructions burned: 11 (million)
% 0.60/0.76  % (27197)------------------------------
% 0.60/0.76  % (27197)------------------------------
% 0.60/0.76  % (27187)Success in time 0.384 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------