TSTP Solution File: SET587+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 15:08:38 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  126 (  15 unt;   0 def)
%            Number of atoms       :  370 (  67 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  397 ( 153   ~; 186   |;  37   &)
%                                         (  13 <=>;   6  =>;   0  <=;   2 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  209 ( 194   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f217,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f80,f166,f168,f171,f173,f216]) ).

fof(f216,plain,
    ( ~ spl5_1
    | spl5_2 ),
    inference(avatar_contradiction_clause,[],[f215]) ).

fof(f215,plain,
    ( $false
    | ~ spl5_1
    | spl5_2 ),
    inference(subsumption_resolution,[],[f214,f61]) ).

fof(f61,plain,
    ( ~ subset(sK0,sK1)
    | spl5_2 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl5_2
  <=> subset(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f214,plain,
    ( subset(sK0,sK1)
    | ~ spl5_1 ),
    inference(duplicate_literal_removal,[],[f211]) ).

fof(f211,plain,
    ( subset(sK0,sK1)
    | subset(sK0,sK1)
    | ~ spl5_1 ),
    inference(resolution,[],[f186,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( member(sK4(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f186,plain,
    ( ! [X0] :
        ( ~ member(sK4(X0,sK1),sK0)
        | subset(X0,sK1) )
    | ~ spl5_1 ),
    inference(resolution,[],[f182,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f182,plain,
    ( ! [X0] :
        ( member(X0,sK1)
        | ~ member(X0,sK0) )
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f177,f34]) ).

fof(f34,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f177,plain,
    ( ! [X0] :
        ( member(X0,empty_set)
        | member(X0,sK1)
        | ~ member(X0,sK0) )
    | ~ spl5_1 ),
    inference(superposition,[],[f50,f58]) ).

fof(f58,plain,
    ( empty_set = difference(sK0,sK1)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl5_1
  <=> empty_set = difference(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f173,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f172]) ).

fof(f172,plain,
    ( $false
    | ~ spl5_1
    | ~ spl5_2 ),
    inference(global_subsumption,[],[f58,f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163,f169]) ).

fof(f169,plain,
    ( empty_set != difference(sK0,sK1)
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f33,f62]) ).

fof(f163,plain,
    ( empty_set = difference(sK0,sK1)
    | ~ spl5_2 ),
    inference(resolution,[],[f159,f71]) ).

fof(f164,plain,
    ( ! [X0] : difference(sK0,sK1) = difference(difference(sK0,sK1),X0)
    | ~ spl5_2 ),
    inference(resolution,[],[f159,f112]) ).

fof(f162,plain,
    ( ! [X0] :
        ( difference(sK0,sK1) = X0
        | ~ subset(X0,difference(sK0,sK1)) )
    | ~ spl5_2 ),
    inference(resolution,[],[f159,f40]) ).

fof(f161,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,difference(sK0,sK1))
        | member(X0,X1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f159,f45]) ).

fof(f159,plain,
    ( ! [X0] : subset(difference(sK0,sK1),X0)
    | ~ spl5_2 ),
    inference(duplicate_literal_removal,[],[f155]) ).

fof(f155,plain,
    ( ! [X0] :
        ( subset(difference(sK0,sK1),X0)
        | subset(difference(sK0,sK1),X0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f68,f120]) ).

fof(f157,plain,
    ! [X2,X3,X0,X1] :
      ( subset(difference(X0,difference(X1,X2)),X3)
      | member(sK4(difference(X0,difference(X1,X2)),X3),X2)
      | ~ member(sK4(difference(X0,difference(X1,X2)),X3),X1) ),
    inference(resolution,[],[f68,f50]) ).

fof(f156,plain,
    ( ! [X0,X1] :
        ( subset(difference(X0,sK1),X1)
        | ~ member(sK4(difference(X0,sK1),X1),sK0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f68,f84]) ).

fof(f160,plain,
    ! [X0,X1] : subset(difference(X0,X0),X1),
    inference(duplicate_literal_removal,[],[f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X0),X1)
      | subset(difference(X0,X0),X1) ),
    inference(resolution,[],[f68,f67]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK4(difference(X0,X1),X2),X1)
      | subset(difference(X0,X1),X2) ),
    inference(resolution,[],[f49,f46]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ subset(X0,difference(X0,X1))
      | difference(X0,X1) = X0 ),
    inference(resolution,[],[f98,f40]) ).

fof(f140,plain,
    ( ! [X0] :
        ( ~ member(sK2(X0,sK1),sK0)
        | ~ member(sK2(X0,sK1),X0)
        | sK1 = X0 )
    | ~ spl5_2 ),
    inference(resolution,[],[f37,f84]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( difference(X1,X2) = X0
      | ~ member(sK2(X0,difference(X1,X2)),X0)
      | member(sK2(X0,difference(X1,X2)),X2)
      | ~ member(sK2(X0,difference(X1,X2)),X1) ),
    inference(resolution,[],[f37,f50]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ member(sK2(X0,X1),X1)
      | X0 = X1
      | ~ member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ member(sK2(X0,X1),X1)
          | ~ member(sK2(X0,X1),X0) )
        & ( member(sK2(X0,X1),X1)
          | member(sK2(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK2(X0,X1),X1)
          | ~ member(sK2(X0,X1),X0) )
        & ( member(sK2(X0,X1),X1)
          | member(sK2(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( member(X2,X0)
        <~> member(X2,X1) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).

fof(f132,plain,
    ( ! [X0] :
        ( member(sK2(empty_set,difference(sK0,X0)),sK1)
        | empty_set = difference(sK0,X0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f107,f99]) ).

fof(f128,plain,
    ( ! [X0] :
        ( member(sK2(difference(sK0,X0),empty_set),sK1)
        | empty_set = difference(sK0,X0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f104,f99]) ).

fof(f120,plain,
    ( ! [X0,X1] :
        ( member(sK4(difference(sK0,X0),X1),sK1)
        | subset(difference(sK0,X0),X1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f99,f46]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
      | member(sK2(empty_set,difference(X0,X1)),X0) ),
    inference(resolution,[],[f107,f48]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
      | ~ member(sK2(empty_set,difference(X0,X1)),X1) ),
    inference(resolution,[],[f107,f49]) ).

fof(f107,plain,
    ! [X0] :
      ( member(sK2(empty_set,X0),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f36,f34]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
      | member(sK2(difference(X0,X1),empty_set),X0) ),
    inference(resolution,[],[f104,f48]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
      | ~ member(sK2(difference(X0,X1),empty_set),X1) ),
    inference(resolution,[],[f104,f49]) ).

fof(f104,plain,
    ! [X0] :
      ( member(sK2(X0,empty_set),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f36,f34]) ).

fof(f100,plain,
    ( ! [X0] :
        ( ~ subset(sK1,difference(sK0,X0))
        | sK1 = difference(sK0,X0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f97,f40]) ).

fof(f124,plain,
    ( ! [X0,X1] :
        ( member(sK2(difference(sK0,X0),X1),sK1)
        | member(sK2(difference(sK0,X0),X1),X1)
        | difference(sK0,X0) = X1 )
    | ~ spl5_2 ),
    inference(resolution,[],[f99,f36]) ).

fof(f123,plain,
    ( ! [X0,X1] :
        ( member(sK2(X0,difference(sK0,X1)),sK1)
        | member(sK2(X0,difference(sK0,X1)),X0)
        | difference(sK0,X1) = X0 )
    | ~ spl5_2 ),
    inference(resolution,[],[f99,f36]) ).

fof(f121,plain,
    ( ! [X2,X0,X1] :
        ( member(sK4(difference(difference(sK0,X0),X1),X2),sK1)
        | subset(difference(difference(sK0,X0),X1),X2) )
    | ~ spl5_2 ),
    inference(resolution,[],[f99,f67]) ).

fof(f99,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,difference(sK0,X1))
        | member(X0,sK1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f97,f45]) ).

fof(f103,plain,
    ! [X0] : empty_set = difference(empty_set,X0),
    inference(resolution,[],[f94,f71]) ).

fof(f113,plain,
    ! [X0] : empty_set = difference(empty_set,X0),
    inference(resolution,[],[f98,f71]) ).

fof(f98,plain,
    ! [X0,X1] : subset(difference(X0,X1),X0),
    inference(duplicate_literal_removal,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X1),X0)
      | subset(difference(X0,X1),X0) ),
    inference(resolution,[],[f67,f47]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( member(sK2(difference(X0,X1),X2),X2)
      | difference(X0,X1) = X2
      | member(sK2(difference(X0,X1),X2),X0) ),
    inference(resolution,[],[f36,f48]) ).

fof(f108,plain,
    ! [X2,X0,X1] :
      ( member(sK2(difference(X0,X1),X2),X2)
      | difference(X0,X1) = X2
      | ~ member(sK2(difference(X0,X1),X2),X1) ),
    inference(resolution,[],[f36,f49]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( member(sK2(X0,difference(X1,X2)),X0)
      | difference(X1,X2) = X0
      | member(sK2(X0,difference(X1,X2)),X1) ),
    inference(resolution,[],[f36,f48]) ).

fof(f105,plain,
    ! [X2,X0,X1] :
      ( member(sK2(X0,difference(X1,X2)),X0)
      | difference(X1,X2) = X0
      | ~ member(sK2(X0,difference(X1,X2)),X2) ),
    inference(resolution,[],[f36,f49]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( member(sK2(X0,X1),X1)
      | member(sK2(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( difference(empty_set,X1) = X0
      | ~ subset(X0,difference(empty_set,X1)) ),
    inference(resolution,[],[f94,f40]) ).

fof(f101,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(empty_set,X1))
      | member(X0,X2) ),
    inference(resolution,[],[f94,f45]) ).

fof(f94,plain,
    ! [X0,X1] : subset(difference(empty_set,X0),X1),
    inference(resolution,[],[f67,f34]) ).

fof(f97,plain,
    ( ! [X0] : subset(difference(sK0,X0),sK1)
    | ~ spl5_2 ),
    inference(duplicate_literal_removal,[],[f93]) ).

fof(f93,plain,
    ( ! [X0] :
        ( subset(difference(sK0,X0),sK1)
        | subset(difference(sK0,X0),sK1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f67,f86]) ).

fof(f96,plain,
    ! [X2,X3,X0,X1] :
      ( subset(difference(difference(X0,X1),X2),X3)
      | member(sK4(difference(difference(X0,X1),X2),X3),X0) ),
    inference(resolution,[],[f67,f48]) ).

fof(f95,plain,
    ! [X2,X3,X0,X1] :
      ( subset(difference(difference(X0,X1),X2),X3)
      | ~ member(sK4(difference(difference(X0,X1),X2),X3),X1) ),
    inference(resolution,[],[f67,f49]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( member(sK4(difference(X0,X1),X2),X0)
      | subset(difference(X0,X1),X2) ),
    inference(resolution,[],[f48,f46]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( member(sK4(X0,difference(X1,X2)),X2)
      | ~ member(sK4(X0,difference(X1,X2)),X1)
      | subset(X0,difference(X1,X2)) ),
    inference(resolution,[],[f50,f47]) ).

fof(f86,plain,
    ( ! [X0] :
        ( ~ member(sK4(X0,sK1),sK0)
        | subset(X0,sK1) )
    | ~ spl5_2 ),
    inference(resolution,[],[f84,f47]) ).

fof(f84,plain,
    ( ! [X0] :
        ( member(X0,sK1)
        | ~ member(X0,sK0) )
    | ~ spl5_2 ),
    inference(resolution,[],[f45,f62]) ).

fof(f45,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(resolution,[],[f40,f64]) ).

fof(f70,plain,
    ( sK0 = sK1
    | ~ subset(sK1,sK0)
    | ~ spl5_2 ),
    inference(resolution,[],[f40,f62]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f64,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f46,f34]) ).

fof(f62,plain,
    ( subset(sK0,sK1)
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f32,plain,
    ( subset(sK0,sK1)
    | empty_set = difference(sK0,sK1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ( ~ subset(sK0,sK1)
      | empty_set != difference(sK0,sK1) )
    & ( subset(sK0,sK1)
      | empty_set = difference(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f15]) ).

fof(f15,plain,
    ( ? [X0,X1] :
        ( ( ~ subset(X0,X1)
          | difference(X0,X1) != empty_set )
        & ( subset(X0,X1)
          | difference(X0,X1) = empty_set ) )
   => ( ( ~ subset(sK0,sK1)
        | empty_set != difference(sK0,sK1) )
      & ( subset(sK0,sK1)
        | empty_set = difference(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1] :
      ( ( ~ subset(X0,X1)
        | difference(X0,X1) != empty_set )
      & ( subset(X0,X1)
        | difference(X0,X1) = empty_set ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ? [X0,X1] :
      ( difference(X0,X1) = empty_set
    <~> subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] :
        ( difference(X0,X1) = empty_set
      <=> subset(X0,X1) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] :
      ( difference(X0,X1) = empty_set
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).

fof(f35,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

fof(f43,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK3(X0,X1),X1)
            | ~ member(sK3(X0,X1),X0) )
          & ( member(sK3(X0,X1),X1)
            | member(sK3(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK3(X0,X1),X1)
          | ~ member(sK3(X0,X1),X0) )
        & ( member(sK3(X0,X1),X1)
          | member(sK3(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f52,plain,
    ! [X1] : subset(X1,X1),
    inference(equality_resolution,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f51,plain,
    ! [X1] : subset(X1,X1),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f33,plain,
    ( ~ subset(sK0,sK1)
    | empty_set != difference(sK0,sK1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f171,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f170]) ).

fof(f170,plain,
    ( $false
    | ~ spl5_2 ),
    inference(global_subsumption,[],[f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163,f169]) ).

fof(f168,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f167]) ).

fof(f167,plain,
    ( $false
    | ~ spl5_2 ),
    inference(global_subsumption,[],[f33,f51,f52,f44,f43,f34,f35,f32,f62,f46,f64,f47,f48,f49,f40,f70,f71,f45,f84,f86,f50,f91,f67,f95,f96,f97,f94,f101,f102,f36,f105,f106,f108,f109,f98,f113,f103,f99,f121,f123,f124,f100,f104,f126,f127,f107,f130,f131,f120,f128,f132,f37,f141,f140,f112,f68,f160,f156,f157,f159,f161,f162,f164,f163]) ).

fof(f166,plain,
    ( spl5_1
    | ~ spl5_2 ),
    inference(avatar_contradiction_clause,[],[f165]) ).

fof(f165,plain,
    ( $false
    | spl5_1
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f163,f57]) ).

fof(f57,plain,
    ( empty_set != difference(sK0,sK1)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f80,plain,
    ( ~ spl5_3
    | spl5_4
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f70,f60,f77,f73]) ).

fof(f73,plain,
    ( spl5_3
  <=> subset(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f77,plain,
    ( spl5_4
  <=> sK0 = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f63,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f32,f60,f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 00:56:17 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (30018)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (30021)WARNING: value z3 for option sas not known
% 0.15/0.38  % (30025)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  % (30023)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (30021)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (30020)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (30022)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (30024)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  % (30021)First to succeed.
% 0.15/0.39  % (30019)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (30021)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (30021)------------------------------
% 0.15/0.39  % (30021)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (30021)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (30021)Memory used [KB]: 885
% 0.15/0.39  % (30021)Time elapsed: 0.009 s
% 0.15/0.39  % (30021)Instructions burned: 13 (million)
% 0.15/0.39  % (30021)------------------------------
% 0.15/0.39  % (30021)------------------------------
% 0.15/0.39  % (30018)Success in time 0.023 s
%------------------------------------------------------------------------------