TSTP Solution File: SET951+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n008.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 03:49:36 EDT 2024

% Result   : Theorem 0.73s 0.85s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   84 (  13 unt;   0 def)
%            Number of atoms       :  320 (  84 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  385 ( 149   ~; 145   |;  74   &)
%                                         (  11 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   8 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  203 ( 168   !;  35   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1011,plain,
    $false,
    inference(avatar_sat_refutation,[],[f757,f835,f852,f855,f929,f937,f946,f1010]) ).

fof(f1010,plain,
    ( ~ spl13_41
    | spl13_38 ),
    inference(avatar_split_clause,[],[f987,f832,f934]) ).

fof(f934,plain,
    ( spl13_41
  <=> in(sK8,cartesian_product2(sK11,sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).

fof(f832,plain,
    ( spl13_38
  <=> in(sK4(sK9,sK10,sK8),sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).

fof(f987,plain,
    ( in(sK4(sK9,sK10,sK8),sK12)
    | ~ in(sK8,cartesian_product2(sK11,sK12)) ),
    inference(superposition,[],[f72,f747]) ).

fof(f747,plain,
    sK4(sK11,sK12,sK8) = sK4(sK9,sK10,sK8),
    inference(trivial_inequality_removal,[],[f678]) ).

fof(f678,plain,
    ( sK8 != sK8
    | sK4(sK11,sK12,sK8) = sK4(sK9,sK10,sK8) ),
    inference(superposition,[],[f408,f403]) ).

fof(f403,plain,
    sK8 = unordered_pair(unordered_pair(sK3(sK9,sK10,sK8),sK4(sK9,sK10,sK8)),singleton(sK3(sK9,sK10,sK8))),
    inference(resolution,[],[f71,f107]) ).

fof(f107,plain,
    in(sK8,cartesian_product2(sK9,sK10)),
    inference(resolution,[],[f76,f57]) ).

fof(f57,plain,
    in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( ! [X5,X6] :
        ( ~ in(X6,set_intersection2(sK10,sK12))
        | ~ in(X5,set_intersection2(sK9,sK11))
        | ordered_pair(X5,X6) != sK8 )
    & in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f16,f33]) ).

fof(f33,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ! [X5,X6] :
            ( ~ in(X6,set_intersection2(X2,X4))
            | ~ in(X5,set_intersection2(X1,X3))
            | ordered_pair(X5,X6) != X0 )
        & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) )
   => ( ! [X6,X5] :
          ( ~ in(X6,set_intersection2(sK10,sK12))
          | ~ in(X5,set_intersection2(sK9,sK11))
          | ordered_pair(X5,X6) != sK8 )
      & in(sK8,set_intersection2(cartesian_product2(sK9,sK10),cartesian_product2(sK11,sK12))) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ! [X5,X6] :
          ( ~ in(X6,set_intersection2(X2,X4))
          | ~ in(X5,set_intersection2(X1,X3))
          | ordered_pair(X5,X6) != X0 )
      & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4] :
        ~ ( ! [X5,X6] :
              ~ ( in(X6,set_intersection2(X2,X4))
                & in(X5,set_intersection2(X1,X3))
                & ordered_pair(X5,X6) = X0 )
          & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X2,X3,X4] :
      ~ ( ! [X5,X6] :
            ~ ( in(X6,set_intersection2(X2,X4))
              & in(X5,set_intersection2(X1,X3))
              & ordered_pair(X5,X6) = X0 )
        & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    file('/export/starexec/sandbox2/tmp/tmp.85ZvUqq6Rw/Vampire---4.8_7365',t104_zfmisc_1) ).

fof(f76,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f46]) ).

fof(f46,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK5(X0,X1,X2),X1)
            | ~ in(sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( ( in(sK5(X0,X1,X2),X1)
              & in(sK5(X0,X1,X2),X0) )
            | in(sK5(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f26,f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK5(X0,X1,X2),X1)
          | ~ in(sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( ( in(sK5(X0,X1,X2),X1)
            & in(sK5(X0,X1,X2),X0) )
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.85ZvUqq6Rw/Vampire---4.8_7365',d3_xboole_0) ).

fof(f71,plain,
    ! [X0,X1,X8] :
      ( ~ in(X8,cartesian_product2(X0,X1))
      | unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
    inference(equality_resolution,[],[f64]) ).

fof(f64,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(definition_unfolding,[],[f40,f52]) ).

fof(f52,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.85ZvUqq6Rw/Vampire---4.8_7365',d5_tarski) ).

fof(f40,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(sK0(X0,X1,X2),X2) )
          & ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
              & in(sK2(X0,X1,X2),X1)
              & in(sK1(X0,X1,X2),X0) )
            | in(sK0(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
                & in(sK4(X0,X1,X8),X1)
                & in(sK3(X0,X1,X8),X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f22,f21,f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X1)
                | ~ in(X4,X0) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X1)
                & in(X6,X0) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK0(X0,X1,X2)
              | ~ in(X5,X1)
              | ~ in(X4,X0) )
          | ~ in(sK0(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
              & in(X7,X1)
              & in(X6,X0) )
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK0(X0,X1,X2)
          & in(X7,X1)
          & in(X6,X0) )
     => ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
        & in(sK2(X0,X1,X2),X1)
        & in(sK1(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X1)
          & in(X11,X0) )
     => ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
        & in(sK4(X0,X1,X8),X1)
        & in(sK3(X0,X1,X8),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X1)
                  & in(X6,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X1)
                  | ~ in(X9,X0) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X1)
                  & in(X11,X0) )
              | ~ in(X8,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.85ZvUqq6Rw/Vampire---4.8_7365',d2_zfmisc_1) ).

fof(f408,plain,
    ! [X0,X1] :
      ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK8
      | sK4(sK11,sK12,sK8) = X1 ),
    inference(superposition,[],[f67,f402]) ).

fof(f402,plain,
    sK8 = unordered_pair(unordered_pair(sK3(sK11,sK12,sK8),sK4(sK11,sK12,sK8)),singleton(sK3(sK11,sK12,sK8))),
    inference(resolution,[],[f71,f102]) ).

fof(f102,plain,
    in(sK8,cartesian_product2(sK11,sK12)),
    inference(resolution,[],[f75,f57]) ).

fof(f75,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X1) ),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f67,plain,
    ! [X2,X3,X0,X1] :
      ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
      | X1 = X3 ),
    inference(definition_unfolding,[],[f60,f52,f52]) ).

fof(f60,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
     => ( X1 = X3
        & X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.85ZvUqq6Rw/Vampire---4.8_7365',t33_zfmisc_1) ).

fof(f72,plain,
    ! [X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK4(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f946,plain,
    spl13_41,
    inference(avatar_contradiction_clause,[],[f945]) ).

fof(f945,plain,
    ( $false
    | spl13_41 ),
    inference(resolution,[],[f936,f102]) ).

fof(f936,plain,
    ( ~ in(sK8,cartesian_product2(sK11,sK12))
    | spl13_41 ),
    inference(avatar_component_clause,[],[f934]) ).

fof(f937,plain,
    ( ~ spl13_41
    | spl13_40 ),
    inference(avatar_split_clause,[],[f903,f849,f934]) ).

fof(f849,plain,
    ( spl13_40
  <=> in(sK3(sK9,sK10,sK8),sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).

fof(f903,plain,
    ( in(sK3(sK9,sK10,sK8),sK11)
    | ~ in(sK8,cartesian_product2(sK11,sK12)) ),
    inference(superposition,[],[f73,f746]) ).

fof(f746,plain,
    sK3(sK11,sK12,sK8) = sK3(sK9,sK10,sK8),
    inference(trivial_inequality_removal,[],[f679]) ).

fof(f679,plain,
    ( sK8 != sK8
    | sK3(sK11,sK12,sK8) = sK3(sK9,sK10,sK8) ),
    inference(superposition,[],[f410,f403]) ).

fof(f410,plain,
    ! [X0,X1] :
      ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK8
      | sK3(sK11,sK12,sK8) = X0 ),
    inference(superposition,[],[f68,f402]) ).

fof(f68,plain,
    ! [X2,X3,X0,X1] :
      ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != unordered_pair(unordered_pair(X2,X3),singleton(X2))
      | X0 = X2 ),
    inference(definition_unfolding,[],[f59,f52,f52]) ).

fof(f59,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f73,plain,
    ! [X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,cartesian_product2(X0,X1)) ),
    inference(equality_resolution,[],[f38]) ).

fof(f38,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK3(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f929,plain,
    spl13_39,
    inference(avatar_contradiction_clause,[],[f928]) ).

fof(f928,plain,
    ( $false
    | spl13_39 ),
    inference(resolution,[],[f927,f107]) ).

fof(f927,plain,
    ( ~ in(sK8,cartesian_product2(sK9,sK10))
    | spl13_39 ),
    inference(resolution,[],[f847,f73]) ).

fof(f847,plain,
    ( ~ in(sK3(sK9,sK10,sK8),sK9)
    | spl13_39 ),
    inference(avatar_component_clause,[],[f845]) ).

fof(f845,plain,
    ( spl13_39
  <=> in(sK3(sK9,sK10,sK8),sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).

fof(f855,plain,
    spl13_37,
    inference(avatar_contradiction_clause,[],[f854]) ).

fof(f854,plain,
    ( $false
    | spl13_37 ),
    inference(resolution,[],[f853,f107]) ).

fof(f853,plain,
    ( ~ in(sK8,cartesian_product2(sK9,sK10))
    | spl13_37 ),
    inference(resolution,[],[f830,f72]) ).

fof(f830,plain,
    ( ~ in(sK4(sK9,sK10,sK8),sK10)
    | spl13_37 ),
    inference(avatar_component_clause,[],[f828]) ).

fof(f828,plain,
    ( spl13_37
  <=> in(sK4(sK9,sK10,sK8),sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).

fof(f852,plain,
    ( ~ spl13_39
    | ~ spl13_40
    | spl13_24 ),
    inference(avatar_split_clause,[],[f843,f754,f849,f845]) ).

fof(f754,plain,
    ( spl13_24
  <=> in(sK3(sK9,sK10,sK8),set_intersection2(sK9,sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f843,plain,
    ( ~ in(sK3(sK9,sK10,sK8),sK11)
    | ~ in(sK3(sK9,sK10,sK8),sK9)
    | spl13_24 ),
    inference(resolution,[],[f756,f74]) ).

fof(f74,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f48]) ).

fof(f48,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f756,plain,
    ( ~ in(sK3(sK9,sK10,sK8),set_intersection2(sK9,sK11))
    | spl13_24 ),
    inference(avatar_component_clause,[],[f754]) ).

fof(f835,plain,
    ( ~ spl13_37
    | ~ spl13_38
    | spl13_23 ),
    inference(avatar_split_clause,[],[f826,f750,f832,f828]) ).

fof(f750,plain,
    ( spl13_23
  <=> in(sK4(sK9,sK10,sK8),set_intersection2(sK10,sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f826,plain,
    ( ~ in(sK4(sK9,sK10,sK8),sK12)
    | ~ in(sK4(sK9,sK10,sK8),sK10)
    | spl13_23 ),
    inference(resolution,[],[f752,f74]) ).

fof(f752,plain,
    ( ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK10,sK12))
    | spl13_23 ),
    inference(avatar_component_clause,[],[f750]) ).

fof(f757,plain,
    ( ~ spl13_23
    | ~ spl13_24 ),
    inference(avatar_split_clause,[],[f748,f754,f750]) ).

fof(f748,plain,
    ( ~ in(sK3(sK9,sK10,sK8),set_intersection2(sK9,sK11))
    | ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK10,sK12)) ),
    inference(trivial_inequality_removal,[],[f665]) ).

fof(f665,plain,
    ( sK8 != sK8
    | ~ in(sK3(sK9,sK10,sK8),set_intersection2(sK9,sK11))
    | ~ in(sK4(sK9,sK10,sK8),set_intersection2(sK10,sK12)) ),
    inference(superposition,[],[f66,f403]) ).

fof(f66,plain,
    ! [X6,X5] :
      ( sK8 != unordered_pair(unordered_pair(X5,X6),singleton(X5))
      | ~ in(X5,set_intersection2(sK9,sK11))
      | ~ in(X6,set_intersection2(sK10,sK12)) ),
    inference(definition_unfolding,[],[f58,f52]) ).

fof(f58,plain,
    ! [X6,X5] :
      ( ~ in(X6,set_intersection2(sK10,sK12))
      | ~ in(X5,set_intersection2(sK9,sK11))
      | ordered_pair(X5,X6) != sK8 ),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15  % 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
% 0.14/0.35  % Computer : n008.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   : Tue Apr 30 17:16:12 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  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.85ZvUqq6Rw/Vampire---4.8_7365
% 0.62/0.81  % (7573)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.62/0.81  % (7578)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 (2995ds/56Mi)
% 0.62/0.82  % (7571)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 (2995ds/34Mi)
% 0.62/0.82  % (7574)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.62/0.82  % (7572)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 (2995ds/51Mi)
% 0.62/0.82  % (7575)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 (2995ds/34Mi)
% 0.62/0.82  % (7576)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.62/0.82  % (7578)Refutation not found, incomplete strategy% (7578)------------------------------
% 0.62/0.82  % (7578)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (7578)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  % (7577)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 (2995ds/83Mi)
% 0.62/0.82  
% 0.62/0.82  % (7578)Memory used [KB]: 1046
% 0.62/0.82  % (7578)Time elapsed: 0.002 s
% 0.62/0.82  % (7578)Instructions burned: 4 (million)
% 0.62/0.82  % (7578)------------------------------
% 0.62/0.82  % (7578)------------------------------
% 0.62/0.82  % (7575)Refutation not found, incomplete strategy% (7575)------------------------------
% 0.62/0.82  % (7575)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.82  % (7575)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.82  
% 0.62/0.82  % (7575)Memory used [KB]: 1058
% 0.62/0.82  % (7575)Time elapsed: 0.004 s
% 0.62/0.82  % (7583)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 (2995ds/55Mi)
% 0.62/0.82  % (7575)Instructions burned: 5 (million)
% 0.62/0.82  % (7575)------------------------------
% 0.62/0.82  % (7575)------------------------------
% 0.62/0.82  % (7586)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.62/0.83  % (7574)Instruction limit reached!
% 0.62/0.83  % (7574)------------------------------
% 0.62/0.83  % (7574)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.83  % (7574)Termination reason: Unknown
% 0.62/0.83  % (7574)Termination phase: Saturation
% 0.62/0.83  
% 0.62/0.83  % (7574)Memory used [KB]: 1596
% 0.62/0.83  % (7574)Time elapsed: 0.020 s
% 0.62/0.83  % (7574)Instructions burned: 34 (million)
% 0.62/0.83  % (7574)------------------------------
% 0.62/0.83  % (7574)------------------------------
% 0.62/0.84  % (7571)Instruction limit reached!
% 0.62/0.84  % (7571)------------------------------
% 0.62/0.84  % (7571)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.84  % (7571)Termination reason: Unknown
% 0.62/0.84  % (7571)Termination phase: Saturation
% 0.62/0.84  
% 0.62/0.84  % (7571)Memory used [KB]: 1245
% 0.62/0.84  % (7571)Time elapsed: 0.021 s
% 0.62/0.84  % (7571)Instructions burned: 35 (million)
% 0.62/0.84  % (7571)------------------------------
% 0.62/0.84  % (7571)------------------------------
% 0.62/0.84  % (7583)Instruction limit reached!
% 0.62/0.84  % (7583)------------------------------
% 0.62/0.84  % (7583)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.84  % (7583)Termination reason: Unknown
% 0.62/0.84  % (7583)Termination phase: Saturation
% 0.62/0.84  
% 0.62/0.84  % (7583)Memory used [KB]: 1657
% 0.62/0.84  % (7583)Time elapsed: 0.019 s
% 0.62/0.84  % (7583)Instructions burned: 57 (million)
% 0.62/0.84  % (7583)------------------------------
% 0.62/0.84  % (7583)------------------------------
% 0.62/0.84  % (7573)Instruction limit reached!
% 0.62/0.84  % (7573)------------------------------
% 0.62/0.84  % (7573)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.84  % (7573)Termination reason: Unknown
% 0.62/0.84  % (7573)Termination phase: Saturation
% 0.62/0.84  
% 0.62/0.84  % (7573)Memory used [KB]: 1721
% 0.62/0.84  % (7573)Time elapsed: 0.025 s
% 0.62/0.84  % (7573)Instructions burned: 78 (million)
% 0.62/0.84  % (7573)------------------------------
% 0.62/0.84  % (7573)------------------------------
% 0.73/0.84  % (7592)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.73/0.84  % (7593)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.73/0.84  % (7594)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.73/0.84  % (7576)Instruction limit reached!
% 0.73/0.84  % (7576)------------------------------
% 0.73/0.84  % (7576)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.73/0.84  % (7576)Termination reason: Unknown
% 0.73/0.84  % (7576)Termination phase: Saturation
% 0.73/0.84  
% 0.73/0.84  % (7576)Memory used [KB]: 1344
% 0.73/0.84  % (7576)Time elapsed: 0.026 s
% 0.73/0.84  % (7576)Instructions burned: 45 (million)
% 0.73/0.84  % (7576)------------------------------
% 0.73/0.84  % (7576)------------------------------
% 0.73/0.84  % (7595)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.73/0.84  % (7594)Refutation not found, incomplete strategy% (7594)------------------------------
% 0.73/0.84  % (7594)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.73/0.84  % (7594)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.84  
% 0.73/0.84  % (7594)Memory used [KB]: 1063
% 0.73/0.84  % (7594)Time elapsed: 0.004 s
% 0.73/0.84  % (7594)Instructions burned: 10 (million)
% 0.73/0.84  % (7594)------------------------------
% 0.73/0.84  % (7594)------------------------------
% 0.73/0.84  % (7572)First to succeed.
% 0.73/0.84  % (7598)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.73/0.85  % (7600)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.73/0.85  % (7572)Refutation found. Thanks to Tanya!
% 0.73/0.85  % SZS status Theorem for Vampire---4
% 0.73/0.85  % SZS output start Proof for Vampire---4
% See solution above
% 0.73/0.85  % (7572)------------------------------
% 0.73/0.85  % (7572)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.73/0.85  % (7572)Termination reason: Refutation
% 0.73/0.85  
% 0.73/0.85  % (7572)Memory used [KB]: 1333
% 0.73/0.85  % (7572)Time elapsed: 0.031 s
% 0.73/0.85  % (7572)Instructions burned: 53 (million)
% 0.73/0.85  % (7572)------------------------------
% 0.73/0.85  % (7572)------------------------------
% 0.73/0.85  % (7532)Success in time 0.474 s
% 0.73/0.85  % Vampire---4.8 exiting
%------------------------------------------------------------------------------