TSTP Solution File: SET943+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET943+1 : TPTP v8.2.0. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.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 May 21 03:14:02 EDT 2024

% Result   : Theorem 0.61s 0.78s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  114 (  11 unt;   0 def)
%            Number of atoms       :  392 (  33 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  461 ( 183   ~; 196   |;  57   &)
%                                         (  16 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  183 ( 160   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f508,plain,
    $false,
    inference(avatar_sat_refutation,[],[f103,f108,f112,f133,f138,f150,f170,f277,f283,f504]) ).

fof(f504,plain,
    ( ~ spl8_1
    | ~ spl8_4
    | ~ spl8_6 ),
    inference(avatar_contradiction_clause,[],[f503]) ).

fof(f503,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_4
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f499,f98]) ).

fof(f98,plain,
    ( in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1)))
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f96,plain,
    ( spl8_1
  <=> in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f499,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1)))
    | ~ spl8_4
    | ~ spl8_6 ),
    inference(resolution,[],[f451,f174]) ).

fof(f174,plain,
    ( ! [X0] :
        ( in(X0,union(set_union2(sK0,sK1)))
        | ~ in(X0,set_union2(union(sK0),union(sK1))) )
    | ~ spl8_6 ),
    inference(resolution,[],[f119,f61]) ).

fof(f61,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK5(X0,X1),X1)
          & in(sK5(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f37,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK5(X0,X1),X1)
        & in(sK5(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f119,plain,
    ( subset(set_union2(union(sK0),union(sK1)),union(set_union2(sK0,sK1)))
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f118,plain,
    ( spl8_6
  <=> subset(set_union2(union(sK0),union(sK1)),union(set_union2(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f451,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),union(set_union2(sK0,sK1)))
    | ~ spl8_4 ),
    inference(duplicate_literal_removal,[],[f444]) ).

fof(f444,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),union(set_union2(sK0,sK1)))
    | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),union(set_union2(sK0,sK1)))
    | ~ spl8_4 ),
    inference(resolution,[],[f303,f75]) ).

fof(f75,plain,
    ! [X0,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X5] :
      ( in(X5,sK4(X0,X5))
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(sK2(X0,X1),X3) )
            | ~ in(sK2(X0,X1),X1) )
          & ( ( in(sK3(X0,X1),X0)
              & in(sK2(X0,X1),sK3(X0,X1)) )
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ( in(sK4(X0,X5),X0)
                & in(X5,sK4(X0,X5)) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f31,f34,f33,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ in(X3,X0)
                | ~ in(X2,X3) )
            | ~ in(X2,X1) )
          & ( ? [X4] :
                ( in(X4,X0)
                & in(X2,X4) )
            | in(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ in(X3,X0)
              | ~ in(sK2(X0,X1),X3) )
          | ~ in(sK2(X0,X1),X1) )
        & ( ? [X4] :
              ( in(X4,X0)
              & in(sK2(X0,X1),X4) )
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( in(X4,X0)
          & in(sK2(X0,X1),X4) )
     => ( in(sK3(X0,X1),X0)
        & in(sK2(X0,X1),sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( in(X7,X0)
          & in(X5,X7) )
     => ( in(sK4(X0,X5),X0)
        & in(X5,sK4(X0,X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X4] :
                  ( in(X4,X0)
                  & in(X2,X4) )
              | in(X2,X1) ) ) )
      & ( ! [X5] :
            ( ( in(X5,X1)
              | ! [X6] :
                  ( ~ in(X6,X0)
                  | ~ in(X5,X6) ) )
            & ( ? [X7] :
                  ( in(X7,X0)
                  & in(X5,X7) )
              | ~ in(X5,X1) ) )
        | union(X0) != X1 ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( union(X0) = X1
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) )
              | ~ in(X2,X1) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ! [X3] :
                  ( ~ in(X3,X0)
                  | ~ in(X2,X3) ) )
            & ( ? [X3] :
                  ( in(X3,X0)
                  & in(X2,X3) )
              | ~ in(X2,X1) ) )
        | union(X0) != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( union(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> ? [X3] :
              ( in(X3,X0)
              & in(X2,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).

fof(f303,plain,
    ( ! [X0] :
        ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK4(set_union2(sK0,sK1),X0))
        | ~ in(X0,union(set_union2(sK0,sK1))) )
    | ~ spl8_4 ),
    inference(resolution,[],[f111,f74]) ).

fof(f74,plain,
    ! [X0,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,union(X0)) ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X5] :
      ( in(sK4(X0,X5),X0)
      | ~ in(X5,X1)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f111,plain,
    ( ! [X0] :
        ( ~ in(X0,set_union2(sK0,sK1))
        | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),X0) )
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f110,plain,
    ( spl8_4
  <=> ! [X0] :
        ( ~ in(X0,set_union2(sK0,sK1))
        | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f283,plain,
    ( spl8_1
    | ~ spl8_2
    | ~ spl8_10 ),
    inference(avatar_contradiction_clause,[],[f282]) ).

fof(f282,plain,
    ( $false
    | spl8_1
    | ~ spl8_2
    | ~ spl8_10 ),
    inference(subsumption_resolution,[],[f278,f102]) ).

fof(f102,plain,
    ( in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))))
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f100]) ).

fof(f100,plain,
    ( spl8_2
  <=> in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f278,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))))
    | spl8_1
    | ~ spl8_10 ),
    inference(resolution,[],[f149,f165]) ).

fof(f165,plain,
    ( ! [X0] :
        ( ~ in(X0,sK0)
        | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),X0) )
    | spl8_1 ),
    inference(resolution,[],[f152,f73]) ).

fof(f73,plain,
    ! [X0,X6,X5] :
      ( in(X5,union(X0))
      | ~ in(X6,X0)
      | ~ in(X5,X6) ),
    inference(equality_resolution,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(X6,X0)
      | ~ in(X5,X6)
      | union(X0) != X1 ),
    inference(cnf_transformation,[],[f35]) ).

fof(f152,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),union(sK0))
    | spl8_1 ),
    inference(resolution,[],[f97,f77]) ).

fof(f77,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f65]) ).

fof(f65,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK6(X0,X1,X2),X1)
              & ~ in(sK6(X0,X1,X2),X0) )
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( in(sK6(X0,X1,X2),X1)
            | in(sK6(X0,X1,X2),X0)
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f42,f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK6(X0,X1,X2),X1)
            & ~ in(sK6(X0,X1,X2),X0) )
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( in(sK6(X0,X1,X2),X1)
          | in(sK6(X0,X1,X2),X0)
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(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_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f97,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1)))
    | spl8_1 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f149,plain,
    ( in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK0)
    | ~ spl8_10 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl8_10
  <=> in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

fof(f277,plain,
    ( spl8_1
    | ~ spl8_2
    | ~ spl8_9 ),
    inference(avatar_contradiction_clause,[],[f276]) ).

fof(f276,plain,
    ( $false
    | spl8_1
    | ~ spl8_2
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f266,f102]) ).

fof(f266,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))))
    | spl8_1
    | ~ spl8_9 ),
    inference(resolution,[],[f166,f145]) ).

fof(f145,plain,
    ( in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK1)
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl8_9
  <=> in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

fof(f166,plain,
    ( ! [X0] :
        ( ~ in(X0,sK1)
        | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),X0) )
    | spl8_1 ),
    inference(resolution,[],[f153,f73]) ).

fof(f153,plain,
    ( ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),union(sK1))
    | spl8_1 ),
    inference(resolution,[],[f97,f76]) ).

fof(f76,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f66]) ).

fof(f66,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f170,plain,
    spl8_8,
    inference(avatar_contradiction_clause,[],[f169]) ).

fof(f169,plain,
    ( $false
    | spl8_8 ),
    inference(subsumption_resolution,[],[f168,f159]) ).

fof(f159,plain,
    ( in(sK5(sK1,set_union2(sK0,sK1)),sK1)
    | spl8_8 ),
    inference(resolution,[],[f154,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK5(X0,X1),X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f154,plain,
    ( ~ subset(sK1,set_union2(sK0,sK1))
    | spl8_8 ),
    inference(resolution,[],[f132,f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subset(union(X0),union(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(union(X0),union(X1))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => subset(union(X0),union(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_zfmisc_1) ).

fof(f132,plain,
    ( ~ subset(union(sK1),union(set_union2(sK0,sK1)))
    | spl8_8 ),
    inference(avatar_component_clause,[],[f130]) ).

fof(f130,plain,
    ( spl8_8
  <=> subset(union(sK1),union(set_union2(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

fof(f168,plain,
    ( ~ in(sK5(sK1,set_union2(sK0,sK1)),sK1)
    | spl8_8 ),
    inference(resolution,[],[f160,f76]) ).

fof(f160,plain,
    ( ~ in(sK5(sK1,set_union2(sK0,sK1)),set_union2(sK0,sK1))
    | spl8_8 ),
    inference(resolution,[],[f154,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f150,plain,
    ( spl8_9
    | spl8_10
    | ~ spl8_3 ),
    inference(avatar_split_clause,[],[f139,f105,f147,f143]) ).

fof(f105,plain,
    ( spl8_3
  <=> in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f139,plain,
    ( in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK0)
    | in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK1)
    | ~ spl8_3 ),
    inference(resolution,[],[f107,f78]) ).

fof(f78,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_union2(X0,X1))
      | in(X4,X0)
      | in(X4,X1) ),
    inference(equality_resolution,[],[f64]) ).

fof(f64,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f107,plain,
    ( in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(sK0,sK1))
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f138,plain,
    spl8_7,
    inference(avatar_contradiction_clause,[],[f137]) ).

fof(f137,plain,
    ( $false
    | spl8_7 ),
    inference(subsumption_resolution,[],[f134,f59]) ).

fof(f59,plain,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] : subset(X0,set_union2(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(f134,plain,
    ( ~ subset(sK0,set_union2(sK0,sK1))
    | spl8_7 ),
    inference(resolution,[],[f128,f51]) ).

fof(f128,plain,
    ( ~ subset(union(sK0),union(set_union2(sK0,sK1)))
    | spl8_7 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f126,plain,
    ( spl8_7
  <=> subset(union(sK0),union(set_union2(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

fof(f133,plain,
    ( ~ spl8_7
    | ~ spl8_8
    | spl8_6 ),
    inference(avatar_split_clause,[],[f122,f118,f130,f126]) ).

fof(f122,plain,
    ( ~ subset(union(sK1),union(set_union2(sK0,sK1)))
    | ~ subset(union(sK0),union(set_union2(sK0,sK1)))
    | spl8_6 ),
    inference(resolution,[],[f120,f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).

fof(f120,plain,
    ( ~ subset(set_union2(union(sK0),union(sK1)),union(set_union2(sK0,sK1)))
    | spl8_6 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f112,plain,
    ( ~ spl8_1
    | spl8_4 ),
    inference(avatar_split_clause,[],[f93,f110,f96]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ in(X0,set_union2(sK0,sK1))
      | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),X0)
      | ~ in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1))) ),
    inference(resolution,[],[f80,f84]) ).

fof(f84,plain,
    ! [X3,X0,X1] :
      ( sQ7_eqProxy(union(X0),X1)
      | ~ in(X3,X0)
      | ~ in(sK2(X0,X1),X3)
      | ~ in(sK2(X0,X1),X1) ),
    inference(equality_proxy_replacement,[],[f57,f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( sQ7_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ7_eqProxy])]) ).

fof(f57,plain,
    ! [X3,X0,X1] :
      ( union(X0) = X1
      | ~ in(X3,X0)
      | ~ in(sK2(X0,X1),X3)
      | ~ in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f80,plain,
    ~ sQ7_eqProxy(union(set_union2(sK0,sK1)),set_union2(union(sK0),union(sK1))),
    inference(equality_proxy_replacement,[],[f45,f79]) ).

fof(f45,plain,
    union(set_union2(sK0,sK1)) != set_union2(union(sK0),union(sK1)),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    union(set_union2(sK0,sK1)) != set_union2(union(sK0),union(sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f20,f26]) ).

fof(f26,plain,
    ( ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1))
   => union(set_union2(sK0,sK1)) != set_union2(union(sK0),union(sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1] : union(set_union2(X0,X1)) != set_union2(union(X0),union(X1)),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,negated_conjecture,
    ~ ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    inference(negated_conjecture,[],[f16]) ).

fof(f16,conjecture,
    ! [X0,X1] : union(set_union2(X0,X1)) = set_union2(union(X0),union(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t96_zfmisc_1) ).

fof(f108,plain,
    ( spl8_1
    | spl8_3 ),
    inference(avatar_split_clause,[],[f92,f105,f96]) ).

fof(f92,plain,
    ( in(sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(sK0,sK1))
    | in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1))) ),
    inference(resolution,[],[f80,f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( sQ7_eqProxy(union(X0),X1)
      | in(sK3(X0,X1),X0)
      | in(sK2(X0,X1),X1) ),
    inference(equality_proxy_replacement,[],[f56,f79]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( union(X0) = X1
      | in(sK3(X0,X1),X0)
      | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f103,plain,
    ( spl8_1
    | spl8_2 ),
    inference(avatar_split_clause,[],[f91,f100,f96]) ).

fof(f91,plain,
    ( in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),sK3(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))))
    | in(sK2(set_union2(sK0,sK1),set_union2(union(sK0),union(sK1))),set_union2(union(sK0),union(sK1))) ),
    inference(resolution,[],[f80,f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( sQ7_eqProxy(union(X0),X1)
      | in(sK2(X0,X1),sK3(X0,X1))
      | in(sK2(X0,X1),X1) ),
    inference(equality_proxy_replacement,[],[f55,f79]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( union(X0) = X1
      | in(sK2(X0,X1),sK3(X0,X1))
      | in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET943+1 : TPTP v8.2.0. Released v3.2.0.
% 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
% 0.14/0.35  % Computer : n024.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
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 12:26:23 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.77  % (28340)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.61/0.77  % (28332)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 theBenchmark for (2995ds/34Mi)
% 0.61/0.77  % (28334)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.61/0.77  % (28335)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.61/0.77  % (28333)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 theBenchmark for (2995ds/51Mi)
% 0.61/0.77  % (28337)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 theBenchmark for (2995ds/34Mi)
% 0.61/0.77  % (28338)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.61/0.77  % (28339)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 theBenchmark for (2995ds/83Mi)
% 0.61/0.77  % (28338)Refutation not found, incomplete strategy% (28338)------------------------------
% 0.61/0.77  % (28338)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.77  % (28335)Refutation not found, incomplete strategy% (28335)------------------------------
% 0.61/0.77  % (28335)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.77  % (28335)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.77  
% 0.61/0.77  % (28335)Memory used [KB]: 1037
% 0.61/0.77  % (28335)Time elapsed: 0.003 s
% 0.61/0.77  % (28335)Instructions burned: 3 (million)
% 0.61/0.77  % (28338)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.77  
% 0.61/0.77  % (28338)Memory used [KB]: 1026
% 0.61/0.77  % (28338)Time elapsed: 0.003 s
% 0.61/0.77  % (28338)Instructions burned: 3 (million)
% 0.61/0.77  % (28335)------------------------------
% 0.61/0.77  % (28335)------------------------------
% 0.61/0.77  % (28339)Refutation not found, incomplete strategy% (28339)------------------------------
% 0.61/0.77  % (28339)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.77  % (28339)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.77  
% 0.61/0.77  % (28339)Memory used [KB]: 1024
% 0.61/0.77  % (28339)Time elapsed: 0.003 s
% 0.61/0.77  % (28339)Instructions burned: 3 (million)
% 0.61/0.77  % (28338)------------------------------
% 0.61/0.77  % (28338)------------------------------
% 0.61/0.77  % (28339)------------------------------
% 0.61/0.77  % (28339)------------------------------
% 0.61/0.78  % (28340)First to succeed.
% 0.61/0.78  % (28332)Also succeeded, but the first one will report.
% 0.61/0.78  % (28340)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28331"
% 0.61/0.78  % (28340)Refutation found. Thanks to Tanya!
% 0.61/0.78  % SZS status Theorem for theBenchmark
% 0.61/0.78  % SZS output start Proof for theBenchmark
% See solution above
% 0.61/0.78  % (28340)------------------------------
% 0.61/0.78  % (28340)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.78  % (28340)Termination reason: Refutation
% 0.61/0.78  
% 0.61/0.78  % (28340)Memory used [KB]: 1136
% 0.61/0.78  % (28340)Time elapsed: 0.008 s
% 0.61/0.78  % (28340)Instructions burned: 20 (million)
% 0.61/0.78  % (28331)Success in time 0.41 s
% 0.61/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------