TSTP Solution File: SET618+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n032.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 : Fri Sep  1 23:17:07 EDT 2023

% Result   : Theorem 0.13s 0.32s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  111 (  38 unt;   0 def)
%            Number of atoms       :  284 (  54 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  289 ( 116   ~; 113   |;  27   &)
%                                         (  28 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   27 (  25 usr;  23 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :  151 (; 140   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f179,plain,
    $false,
    inference(avatar_sat_refutation,[],[f56,f60,f64,f68,f72,f76,f80,f84,f91,f95,f99,f103,f110,f116,f120,f124,f131,f147,f151,f163,f169,f173,f178]) ).

fof(f178,plain,
    ( spl4_1
    | ~ spl4_22 ),
    inference(avatar_contradiction_clause,[],[f177]) ).

fof(f177,plain,
    ( $false
    | spl4_1
    | ~ spl4_22 ),
    inference(trivial_inequality_removal,[],[f176]) ).

fof(f176,plain,
    ( empty_set != empty_set
    | spl4_1
    | ~ spl4_22 ),
    inference(superposition,[],[f55,f172]) ).

fof(f172,plain,
    ( ! [X0] : empty_set = symmetric_difference(X0,X0)
    | ~ spl4_22 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f171,plain,
    ( spl4_22
  <=> ! [X0] : empty_set = symmetric_difference(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).

fof(f55,plain,
    ( empty_set != symmetric_difference(sK0,sK0)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f53,plain,
    ( spl4_1
  <=> empty_set = symmetric_difference(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f173,plain,
    ( spl4_22
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_17 ),
    inference(avatar_split_clause,[],[f140,f129,f70,f66,f171]) ).

fof(f66,plain,
    ( spl4_4
  <=> ! [X0] : difference(X0,X0) = empty_set ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f70,plain,
    ( spl4_5
  <=> ! [X0] : union(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f129,plain,
    ( spl4_17
  <=> ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).

fof(f140,plain,
    ( ! [X0] : empty_set = symmetric_difference(X0,X0)
    | ~ spl4_4
    | ~ spl4_5
    | ~ spl4_17 ),
    inference(forward_demodulation,[],[f132,f71]) ).

fof(f71,plain,
    ( ! [X0] : union(X0,X0) = X0
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f132,plain,
    ( ! [X0] : symmetric_difference(X0,X0) = union(empty_set,empty_set)
    | ~ spl4_4
    | ~ spl4_17 ),
    inference(superposition,[],[f130,f67]) ).

fof(f67,plain,
    ( ! [X0] : difference(X0,X0) = empty_set
    | ~ spl4_4 ),
    inference(avatar_component_clause,[],[f66]) ).

fof(f130,plain,
    ( ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0))
    | ~ spl4_17 ),
    inference(avatar_component_clause,[],[f129]) ).

fof(f169,plain,
    ( spl4_21
    | ~ spl4_6
    | ~ spl4_11 ),
    inference(avatar_split_clause,[],[f105,f97,f74,f167]) ).

fof(f167,plain,
    ( spl4_21
  <=> ! [X2,X1] :
        ( subset(X1,X2)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).

fof(f74,plain,
    ( spl4_6
  <=> ! [X2,X0] :
        ( ~ member(X2,X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f97,plain,
    ( spl4_11
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | member(sK3(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f105,plain,
    ( ! [X2,X1] :
        ( subset(X1,X2)
        | ~ empty(X1) )
    | ~ spl4_6
    | ~ spl4_11 ),
    inference(resolution,[],[f98,f75]) ).

fof(f75,plain,
    ( ! [X2,X0] :
        ( ~ member(X2,X0)
        | ~ empty(X0) )
    | ~ spl4_6 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f98,plain,
    ( ! [X0,X1] :
        ( member(sK3(X0,X1),X0)
        | subset(X0,X1) )
    | ~ spl4_11 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f163,plain,
    ( spl4_20
    | ~ spl4_2
    | ~ spl4_11 ),
    inference(avatar_split_clause,[],[f104,f97,f58,f161]) ).

fof(f161,plain,
    ( spl4_20
  <=> ! [X0] : subset(empty_set,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

fof(f58,plain,
    ( spl4_2
  <=> ! [X0] : ~ member(X0,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f104,plain,
    ( ! [X0] : subset(empty_set,X0)
    | ~ spl4_2
    | ~ spl4_11 ),
    inference(resolution,[],[f98,f59]) ).

fof(f59,plain,
    ( ! [X0] : ~ member(X0,empty_set)
    | ~ spl4_2 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f151,plain,
    spl4_19,
    inference(avatar_split_clause,[],[f48,f149]) ).

fof(f149,plain,
    ( spl4_19
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ member(sK2(X0,X1),X1)
        | ~ member(sK2(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK2(X0,X1),X1)
      | ~ member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,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) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f25,f26]) ).

fof(f26,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(f25,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,[],[f24]) ).

fof(f24,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,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',equal_member_defn) ).

fof(f147,plain,
    spl4_18,
    inference(avatar_split_clause,[],[f47,f145]) ).

fof(f145,plain,
    ( spl4_18
  <=> ! [X0,X1] :
        ( X0 = X1
        | member(sK2(X0,X1),X1)
        | member(sK2(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK2(X0,X1),X1)
      | member(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f131,plain,
    spl4_17,
    inference(avatar_split_clause,[],[f41,f129]) ).

fof(f41,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',symmetric_difference_defn) ).

fof(f124,plain,
    spl4_16,
    inference(avatar_split_clause,[],[f49,f122]) ).

fof(f122,plain,
    ( spl4_16
  <=> ! [X0,X1,X3] :
        ( member(X3,X1)
        | ~ member(X3,X0)
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,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,[],[f28]) ).

fof(f28,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,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',subset_defn) ).

fof(f120,plain,
    spl4_15,
    inference(avatar_split_clause,[],[f46,f118]) ).

fof(f118,plain,
    ( spl4_15
  <=> ! [X0,X1,X3] :
        ( member(X3,X0)
        | ~ member(X3,X1)
        | X0 != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).

fof(f46,plain,
    ! [X3,X0,X1] :
      ( member(X3,X0)
      | ~ member(X3,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f116,plain,
    spl4_14,
    inference(avatar_split_clause,[],[f44,f114]) ).

fof(f114,plain,
    ( spl4_14
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

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

fof(f22,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/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',equal_defn) ).

fof(f110,plain,
    ( spl4_13
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f85,f78,f58,f107]) ).

fof(f107,plain,
    ( spl4_13
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f78,plain,
    ( spl4_7
  <=> ! [X0] :
        ( empty(X0)
        | member(sK1(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f85,plain,
    ( empty(empty_set)
    | ~ spl4_2
    | ~ spl4_7 ),
    inference(resolution,[],[f79,f59]) ).

fof(f79,plain,
    ( ! [X0] :
        ( member(sK1(X0),X0)
        | empty(X0) )
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f78]) ).

fof(f103,plain,
    spl4_12,
    inference(avatar_split_clause,[],[f51,f101]) ).

fof(f101,plain,
    ( spl4_12
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ member(sK3(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK3(X0,X1),X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f99,plain,
    spl4_11,
    inference(avatar_split_clause,[],[f50,f97]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f95,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f40,f93]) ).

fof(f93,plain,
    ( spl4_10
  <=> ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f40,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] : symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',commutativity_of_symmetric_difference) ).

fof(f91,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f39,f89]) ).

fof(f89,plain,
    ( spl4_9
  <=> ! [X0,X1] : union(X0,X1) = union(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f39,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',commutativity_of_union) ).

fof(f84,plain,
    spl4_8,
    inference(avatar_split_clause,[],[f43,f82]) ).

fof(f82,plain,
    ( spl4_8
  <=> ! [X0,X1] :
        ( subset(X1,X0)
        | X0 != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f80,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f38,f78]) ).

fof(f38,plain,
    ! [X0] :
      ( empty(X0)
      | member(sK1(X0),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0] :
      ( ( empty(X0)
        | member(sK1(X0),X0) )
      & ( ! [X2] : ~ member(X2,X0)
        | ~ empty(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ? [X1] : member(X1,X0)
     => member(sK1(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0] :
      ( ( empty(X0)
        | ? [X1] : member(X1,X0) )
      & ( ! [X2] : ~ member(X2,X0)
        | ~ empty(X0) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( ( empty(X0)
        | ? [X1] : member(X1,X0) )
      & ( ! [X1] : ~ member(X1,X0)
        | ~ empty(X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( empty(X0)
    <=> ! [X1] : ~ member(X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',empty_defn) ).

fof(f76,plain,
    spl4_6,
    inference(avatar_split_clause,[],[f37,f74]) ).

fof(f37,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f72,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f36,f70]) ).

fof(f36,plain,
    ! [X0] : union(X0,X0) = X0,
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : union(X0,X0) = X0,
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',idempotency_of_union) ).

fof(f68,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f35,f66]) ).

fof(f35,plain,
    ! [X0] : difference(X0,X0) = empty_set,
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : difference(X0,X0) = empty_set,
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',self_difference_is_empty_set) ).

fof(f64,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f34,f62]) ).

fof(f62,plain,
    ( spl4_3
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f34,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : subset(X0,X0),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',reflexivity_of_subset) ).

fof(f60,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f33,f58]) ).

fof(f33,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',empty_set_defn) ).

fof(f56,plain,
    ~ spl4_1,
    inference(avatar_split_clause,[],[f32,f53]) ).

fof(f32,plain,
    empty_set != symmetric_difference(sK0,sK0),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    empty_set != symmetric_difference(sK0,sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f16]) ).

fof(f16,plain,
    ( ? [X0] : empty_set != symmetric_difference(X0,X0)
   => empty_set != symmetric_difference(sK0,sK0) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0] : empty_set != symmetric_difference(X0,X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : empty_set = symmetric_difference(X0,X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : empty_set = symmetric_difference(X0,X0),
    file('/export/starexec/sandbox/tmp/tmp.SyeJaVRJiY/Vampire---4.8_4368',prove_th93) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.08  % Problem    : SET618+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.10  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit   : 300
% 0.09/0.28  % WCLimit    : 300
% 0.09/0.28  % DateTime   : Wed Aug 30 15:45:17 EDT 2023
% 0.09/0.28  % CPUTime    : 
% 0.13/0.32  % (4478)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.32  % (4479)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.13/0.32  % (4480)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.13/0.32  % (4483)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 Vampire---4 for (531ds/0Mi)
% 0.13/0.32  % (4482)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.13/0.32  % (4484)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 Vampire---4 for (522ds/0Mi)
% 0.13/0.32  TRYING [1]
% 0.13/0.32  % (4481)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 Vampire---4 for (569ds/0Mi)
% 0.13/0.32  TRYING [2]
% 0.13/0.32  TRYING [3]
% 0.13/0.32  TRYING [1]
% 0.13/0.32  % (4485)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 Vampire---4 for (497ds/0Mi)
% 0.13/0.32  % (4483)First to succeed.
% 0.13/0.32  TRYING [1]
% 0.13/0.32  TRYING [2]
% 0.13/0.32  TRYING [4]
% 0.13/0.32  TRYING [2]
% 0.13/0.32  TRYING [3]
% 0.13/0.32  % (4484)Also succeeded, but the first one will report.
% 0.13/0.32  TRYING [4]
% 0.13/0.32  % (4482)Also succeeded, but the first one will report.
% 0.13/0.32  % (4483)Refutation found. Thanks to Tanya!
% 0.13/0.32  % SZS status Theorem for Vampire---4
% 0.13/0.32  % SZS output start Proof for Vampire---4
% See solution above
% 0.13/0.32  % (4483)------------------------------
% 0.13/0.32  % (4483)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.13/0.32  % (4483)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.13/0.32  % (4483)Termination reason: Refutation
% 0.13/0.32  
% 0.13/0.32  % (4483)Memory used [KB]: 5500
% 0.13/0.32  % (4483)Time elapsed: 0.003 s
% 0.13/0.32  % (4483)------------------------------
% 0.13/0.32  % (4483)------------------------------
% 0.13/0.32  % (4478)Success in time 0.037 s
% 0.13/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------