TSTP Solution File: SET980+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Sun May  5 09:19:51 EDT 2024

% Result   : Theorem 0.18s 0.38s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  163 (  12 unt;   0 def)
%            Number of atoms       :  448 ( 122 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  519 ( 234   ~; 225   |;  33   &)
%                                         (  19 <=>;   7  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   18 (  16 usr;  16 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  133 ( 115   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f437,plain,
    $false,
    inference(avatar_sat_refutation,[],[f67,f114,f155,f162,f164,f166,f182,f197,f204,f212,f214,f216,f235,f272,f337,f366,f369,f371,f392,f394,f396,f411,f418,f420,f422,f426,f436]) ).

fof(f436,plain,
    ( ~ spl8_2
    | ~ spl8_3 ),
    inference(avatar_contradiction_clause,[],[f435]) ).

fof(f435,plain,
    ( $false
    | ~ spl8_2
    | ~ spl8_3 ),
    inference(subsumption_resolution,[],[f434,f37]) ).

fof(f37,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( ( sK1 != sK3
      | sK0 != sK2 )
    & empty_set != sK1
    & empty_set != sK0
    & cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f18]) ).

fof(f18,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( X1 != X3
          | X0 != X2 )
        & empty_set != X1
        & empty_set != X0
        & cartesian_product2(X2,X3) = cartesian_product2(X0,X1) )
   => ( ( sK1 != sK3
        | sK0 != sK2 )
      & empty_set != sK1
      & empty_set != sK0
      & cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1,X2,X3] :
      ( ( X1 != X3
        | X0 != X2 )
      & empty_set != X1
      & empty_set != X0
      & cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ? [X0,X1,X2,X3] :
      ( ( X1 != X3
        | X0 != X2 )
      & empty_set != X1
      & empty_set != X0
      & cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
       => ( ( X1 = X3
            & X0 = X2 )
          | empty_set = X1
          | empty_set = X0 ) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X2,X3] :
      ( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
     => ( ( X1 = X3
          & X0 = X2 )
        | empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

fof(f434,plain,
    ( empty_set = sK1
    | ~ spl8_2
    | ~ spl8_3 ),
    inference(forward_demodulation,[],[f65,f105]) ).

fof(f105,plain,
    ( empty_set = sK3
    | ~ spl8_3 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f103,plain,
    ( spl8_3
  <=> empty_set = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).

fof(f65,plain,
    ( sK1 = sK3
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl8_2
  <=> sK1 = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f426,plain,
    ( ~ spl8_3
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(avatar_contradiction_clause,[],[f425]) ).

fof(f425,plain,
    ( $false
    | ~ spl8_3
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f424,f37]) ).

fof(f424,plain,
    ( empty_set = sK1
    | ~ spl8_3
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(forward_demodulation,[],[f273,f105]) ).

fof(f273,plain,
    ( sK1 = sK3
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f262,f168]) ).

fof(f168,plain,
    ( ! [X0] :
        ( ~ in(sK5(X0,sK3),sK1)
        | sK3 = X0
        | ~ in(sK5(X0,sK3),X0) )
    | ~ spl8_7 ),
    inference(resolution,[],[f154,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ in(sK5(X0,X1),X1)
      | X0 = X1
      | ~ in(sK5(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK5(X0,X1),X1)
          | ~ in(sK5(X0,X1),X0) )
        & ( in(sK5(X0,X1),X1)
          | in(sK5(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK5(X0,X1),X1)
          | ~ in(sK5(X0,X1),X0) )
        & ( in(sK5(X0,X1),X1)
          | in(sK5(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

fof(f154,plain,
    ( ! [X0] :
        ( in(X0,sK3)
        | ~ in(X0,sK1) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f153]) ).

fof(f153,plain,
    ( spl8_7
  <=> ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

fof(f262,plain,
    ( in(sK5(sK1,sK3),sK1)
    | sK1 = sK3
    | ~ spl8_13 ),
    inference(factoring,[],[f219]) ).

fof(f219,plain,
    ( ! [X0] :
        ( in(sK5(X0,sK3),sK1)
        | in(sK5(X0,sK3),X0)
        | sK3 = X0 )
    | ~ spl8_13 ),
    inference(resolution,[],[f203,f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( in(sK5(X0,X1),X1)
      | in(sK5(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f203,plain,
    ( ! [X0] :
        ( ~ in(X0,sK3)
        | in(X0,sK1) )
    | ~ spl8_13 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f202,plain,
    ( spl8_13
  <=> ! [X0] :
        ( ~ in(X0,sK3)
        | in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).

fof(f422,plain,
    ~ spl8_9,
    inference(avatar_contradiction_clause,[],[f421]) ).

fof(f421,plain,
    ( $false
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f416,f37]) ).

fof(f416,plain,
    ( empty_set = sK1
    | ~ spl8_9 ),
    inference(resolution,[],[f181,f126]) ).

fof(f126,plain,
    ! [X0] :
      ( in(sK5(empty_set,X0),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f46,f56]) ).

fof(f56,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK4(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f181,plain,
    ( ! [X0] : ~ in(X0,sK1)
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f180]) ).

fof(f180,plain,
    ( spl8_9
  <=> ! [X0] : ~ in(X0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

fof(f420,plain,
    ~ spl8_9,
    inference(avatar_contradiction_clause,[],[f419]) ).

fof(f419,plain,
    ( $false
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f415,f37]) ).

fof(f415,plain,
    ( empty_set = sK1
    | ~ spl8_9 ),
    inference(resolution,[],[f181,f124]) ).

fof(f124,plain,
    ! [X0] :
      ( in(sK5(X0,empty_set),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f46,f56]) ).

fof(f418,plain,
    ~ spl8_9,
    inference(avatar_contradiction_clause,[],[f417]) ).

fof(f417,plain,
    ( $false
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f412,f37]) ).

fof(f412,plain,
    ( empty_set = sK1
    | ~ spl8_9 ),
    inference(resolution,[],[f181,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( in(sK4(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f411,plain,
    ( spl8_6
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(avatar_split_clause,[],[f205,f199,f177,f150]) ).

fof(f150,plain,
    ( spl8_6
  <=> ! [X1] : ~ in(X1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f177,plain,
    ( spl8_8
  <=> ! [X1] :
        ( ~ in(X1,sK0)
        | in(X1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

fof(f199,plain,
    ( spl8_12
  <=> ! [X1] : ~ in(X1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

fof(f205,plain,
    ( ! [X0] : ~ in(X0,sK0)
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(resolution,[],[f200,f178]) ).

fof(f178,plain,
    ( ! [X1] :
        ( in(X1,sK2)
        | ~ in(X1,sK0) )
    | ~ spl8_8 ),
    inference(avatar_component_clause,[],[f177]) ).

fof(f200,plain,
    ( ! [X1] : ~ in(X1,sK2)
    | ~ spl8_12 ),
    inference(avatar_component_clause,[],[f199]) ).

fof(f396,plain,
    ( spl8_3
    | ~ spl8_15 ),
    inference(avatar_contradiction_clause,[],[f395]) ).

fof(f395,plain,
    ( $false
    | spl8_3
    | ~ spl8_15 ),
    inference(subsumption_resolution,[],[f390,f104]) ).

fof(f104,plain,
    ( empty_set != sK3
    | spl8_3 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f390,plain,
    ( empty_set = sK3
    | ~ spl8_15 ),
    inference(resolution,[],[f234,f126]) ).

fof(f234,plain,
    ( ! [X0] : ~ in(X0,sK3)
    | ~ spl8_15 ),
    inference(avatar_component_clause,[],[f233]) ).

fof(f233,plain,
    ( spl8_15
  <=> ! [X0] : ~ in(X0,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).

fof(f394,plain,
    ( spl8_3
    | ~ spl8_15 ),
    inference(avatar_contradiction_clause,[],[f393]) ).

fof(f393,plain,
    ( $false
    | spl8_3
    | ~ spl8_15 ),
    inference(subsumption_resolution,[],[f389,f104]) ).

fof(f389,plain,
    ( empty_set = sK3
    | ~ spl8_15 ),
    inference(resolution,[],[f234,f124]) ).

fof(f392,plain,
    ( spl8_3
    | ~ spl8_15 ),
    inference(avatar_contradiction_clause,[],[f391]) ).

fof(f391,plain,
    ( $false
    | spl8_3
    | ~ spl8_15 ),
    inference(subsumption_resolution,[],[f386,f104]) ).

fof(f386,plain,
    ( empty_set = sK3
    | ~ spl8_15 ),
    inference(resolution,[],[f234,f41]) ).

fof(f371,plain,
    ( ~ spl8_1
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[],[f370]) ).

fof(f370,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(subsumption_resolution,[],[f356,f36]) ).

fof(f36,plain,
    empty_set != sK0,
    inference(cnf_transformation,[],[f19]) ).

fof(f356,plain,
    ( empty_set = sK0
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(superposition,[],[f61,f109]) ).

fof(f109,plain,
    ( empty_set = sK2
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f107]) ).

fof(f107,plain,
    ( spl8_4
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f61,plain,
    ( sK0 = sK2
    | ~ spl8_1 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl8_1
  <=> sK0 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f369,plain,
    ( ~ spl8_4
    | spl8_5 ),
    inference(avatar_contradiction_clause,[],[f368]) ).

fof(f368,plain,
    ( $false
    | ~ spl8_4
    | spl8_5 ),
    inference(subsumption_resolution,[],[f367,f113]) ).

fof(f113,plain,
    ( empty_set != cartesian_product2(sK0,sK1)
    | spl8_5 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f111,plain,
    ( spl8_5
  <=> empty_set = cartesian_product2(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

fof(f367,plain,
    ( empty_set = cartesian_product2(sK0,sK1)
    | ~ spl8_4 ),
    inference(forward_demodulation,[],[f355,f58]) ).

fof(f58,plain,
    ! [X1] : empty_set = cartesian_product2(empty_set,X1),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
    <=> ( empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(f355,plain,
    ( cartesian_product2(sK0,sK1) = cartesian_product2(empty_set,sK3)
    | ~ spl8_4 ),
    inference(superposition,[],[f35,f109]) ).

fof(f35,plain,
    cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f366,plain,
    ( ~ spl8_1
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[],[f365]) ).

fof(f365,plain,
    ( $false
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(subsumption_resolution,[],[f354,f36]) ).

fof(f354,plain,
    ( empty_set = sK0
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(superposition,[],[f109,f61]) ).

fof(f337,plain,
    ( spl8_1
    | ~ spl8_8
    | ~ spl8_14 ),
    inference(avatar_contradiction_clause,[],[f336]) ).

fof(f336,plain,
    ( $false
    | spl8_1
    | ~ spl8_8
    | ~ spl8_14 ),
    inference(subsumption_resolution,[],[f335,f332]) ).

fof(f332,plain,
    ( in(sK5(sK0,sK2),sK0)
    | spl8_1
    | ~ spl8_14 ),
    inference(subsumption_resolution,[],[f324,f62]) ).

fof(f62,plain,
    ( sK0 != sK2
    | spl8_1 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f324,plain,
    ( in(sK5(sK0,sK2),sK0)
    | sK0 = sK2
    | ~ spl8_14 ),
    inference(factoring,[],[f238]) ).

fof(f238,plain,
    ( ! [X0] :
        ( in(sK5(X0,sK2),sK0)
        | in(sK5(X0,sK2),X0)
        | sK2 = X0 )
    | ~ spl8_14 ),
    inference(resolution,[],[f231,f46]) ).

fof(f231,plain,
    ( ! [X1] :
        ( ~ in(X1,sK2)
        | in(X1,sK0) )
    | ~ spl8_14 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f230,plain,
    ( spl8_14
  <=> ! [X1] :
        ( ~ in(X1,sK2)
        | in(X1,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).

fof(f335,plain,
    ( ~ in(sK5(sK0,sK2),sK0)
    | spl8_1
    | ~ spl8_8
    | ~ spl8_14 ),
    inference(subsumption_resolution,[],[f333,f62]) ).

fof(f333,plain,
    ( sK0 = sK2
    | ~ in(sK5(sK0,sK2),sK0)
    | spl8_1
    | ~ spl8_8
    | ~ spl8_14 ),
    inference(resolution,[],[f332,f185]) ).

fof(f185,plain,
    ( ! [X0] :
        ( ~ in(sK5(X0,sK2),sK0)
        | sK2 = X0
        | ~ in(sK5(X0,sK2),X0) )
    | ~ spl8_8 ),
    inference(resolution,[],[f178,f47]) ).

fof(f272,plain,
    ( spl8_2
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(avatar_contradiction_clause,[],[f271]) ).

fof(f271,plain,
    ( $false
    | spl8_2
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f270,f267]) ).

fof(f267,plain,
    ( in(sK5(sK1,sK3),sK1)
    | spl8_2
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f262,f66]) ).

fof(f66,plain,
    ( sK1 != sK3
    | spl8_2 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f270,plain,
    ( ~ in(sK5(sK1,sK3),sK1)
    | spl8_2
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(subsumption_resolution,[],[f268,f66]) ).

fof(f268,plain,
    ( sK1 = sK3
    | ~ in(sK5(sK1,sK3),sK1)
    | spl8_2
    | ~ spl8_7
    | ~ spl8_13 ),
    inference(resolution,[],[f267,f168]) ).

fof(f235,plain,
    ( spl8_14
    | spl8_15 ),
    inference(avatar_split_clause,[],[f172,f233,f230]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK3)
      | ~ in(X1,sK2)
      | in(X1,sK0) ),
    inference(resolution,[],[f148,f51]) ).

fof(f51,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f148,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
      | ~ in(X1,sK3)
      | ~ in(X0,sK2) ),
    inference(superposition,[],[f53,f35]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f216,plain,
    ( spl8_4
    | ~ spl8_12 ),
    inference(avatar_contradiction_clause,[],[f215]) ).

fof(f215,plain,
    ( $false
    | spl8_4
    | ~ spl8_12 ),
    inference(subsumption_resolution,[],[f210,f108]) ).

fof(f108,plain,
    ( empty_set != sK2
    | spl8_4 ),
    inference(avatar_component_clause,[],[f107]) ).

fof(f210,plain,
    ( empty_set = sK2
    | ~ spl8_12 ),
    inference(resolution,[],[f200,f126]) ).

fof(f214,plain,
    ( spl8_4
    | ~ spl8_12 ),
    inference(avatar_contradiction_clause,[],[f213]) ).

fof(f213,plain,
    ( $false
    | spl8_4
    | ~ spl8_12 ),
    inference(subsumption_resolution,[],[f209,f108]) ).

fof(f209,plain,
    ( empty_set = sK2
    | ~ spl8_12 ),
    inference(resolution,[],[f200,f124]) ).

fof(f212,plain,
    ( spl8_4
    | ~ spl8_12 ),
    inference(avatar_contradiction_clause,[],[f211]) ).

fof(f211,plain,
    ( $false
    | spl8_4
    | ~ spl8_12 ),
    inference(subsumption_resolution,[],[f206,f108]) ).

fof(f206,plain,
    ( empty_set = sK2
    | ~ spl8_12 ),
    inference(resolution,[],[f200,f41]) ).

fof(f204,plain,
    ( spl8_12
    | spl8_13 ),
    inference(avatar_split_clause,[],[f171,f202,f199]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK3)
      | ~ in(X1,sK2)
      | in(X0,sK1) ),
    inference(resolution,[],[f148,f52]) ).

fof(f52,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f197,plain,
    ( ~ spl8_10
    | ~ spl8_11
    | ~ spl8_7
    | ~ spl8_8 ),
    inference(avatar_split_clause,[],[f184,f177,f153,f194,f190]) ).

fof(f190,plain,
    ( spl8_10
  <=> in(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

fof(f194,plain,
    ( spl8_11
  <=> in(sK3,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).

fof(f184,plain,
    ( ~ in(sK3,sK0)
    | ~ in(sK2,sK1)
    | ~ spl8_7
    | ~ spl8_8 ),
    inference(resolution,[],[f178,f167]) ).

fof(f167,plain,
    ( ! [X0] :
        ( ~ in(sK3,X0)
        | ~ in(X0,sK1) )
    | ~ spl8_7 ),
    inference(resolution,[],[f154,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f182,plain,
    ( spl8_8
    | spl8_9 ),
    inference(avatar_split_clause,[],[f144,f180,f177]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK1)
      | ~ in(X1,sK0)
      | in(X1,sK2) ),
    inference(resolution,[],[f53,f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
      | in(X0,sK2) ),
    inference(superposition,[],[f51,f35]) ).

fof(f166,plain,
    ~ spl8_6,
    inference(avatar_contradiction_clause,[],[f165]) ).

fof(f165,plain,
    ( $false
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f160,f36]) ).

fof(f160,plain,
    ( empty_set = sK0
    | ~ spl8_6 ),
    inference(resolution,[],[f151,f126]) ).

fof(f151,plain,
    ( ! [X1] : ~ in(X1,sK0)
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f164,plain,
    ~ spl8_6,
    inference(avatar_contradiction_clause,[],[f163]) ).

fof(f163,plain,
    ( $false
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f159,f36]) ).

fof(f159,plain,
    ( empty_set = sK0
    | ~ spl8_6 ),
    inference(resolution,[],[f151,f124]) ).

fof(f162,plain,
    ~ spl8_6,
    inference(avatar_contradiction_clause,[],[f161]) ).

fof(f161,plain,
    ( $false
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f156,f36]) ).

fof(f156,plain,
    ( empty_set = sK0
    | ~ spl8_6 ),
    inference(resolution,[],[f151,f41]) ).

fof(f155,plain,
    ( spl8_6
    | spl8_7 ),
    inference(avatar_split_clause,[],[f143,f153,f150]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK1)
      | ~ in(X1,sK0)
      | in(X0,sK3) ),
    inference(resolution,[],[f53,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
      | in(X1,sK3) ),
    inference(superposition,[],[f52,f35]) ).

fof(f114,plain,
    ( spl8_3
    | spl8_4
    | ~ spl8_5 ),
    inference(avatar_split_clause,[],[f101,f111,f107,f103]) ).

fof(f101,plain,
    ( empty_set != cartesian_product2(sK0,sK1)
    | empty_set = sK2
    | empty_set = sK3 ),
    inference(superposition,[],[f48,f35]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( empty_set != cartesian_product2(X0,X1)
      | empty_set = X0
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f67,plain,
    ( ~ spl8_1
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f38,f64,f60]) ).

fof(f38,plain,
    ( sK1 != sK3
    | sK0 != sK2 ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.12/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri May  3 16:50:23 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (13011)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35  % (13013)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35  % (13012)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.36  TRYING [1]
% 0.18/0.36  TRYING [2]
% 0.18/0.36  % (13014)WARNING: value z3 for option sas not known
% 0.18/0.36  % (13015)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36  % (13014)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)
% 0.18/0.36  % (13016)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)
% 0.18/0.36  % (13018)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)
% 0.18/0.36  TRYING [3]
% 0.18/0.36  TRYING [1]
% 0.18/0.36  TRYING [2]
% 0.18/0.36  % (13017)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)
% 0.18/0.36  TRYING [3]
% 0.18/0.37  TRYING [4]
% 0.18/0.37  TRYING [4]
% 0.18/0.38  % (13014)First to succeed.
% 0.18/0.38  % (13014)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13011"
% 0.18/0.38  % (13014)Refutation found. Thanks to Tanya!
% 0.18/0.38  % SZS status Theorem for theBenchmark
% 0.18/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.38  % (13014)------------------------------
% 0.18/0.38  % (13014)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.38  % (13014)Termination reason: Refutation
% 0.18/0.38  
% 0.18/0.38  % (13014)Memory used [KB]: 930
% 0.18/0.38  % (13014)Time elapsed: 0.021 s
% 0.18/0.38  % (13014)Instructions burned: 24 (million)
% 0.18/0.38  % (13011)Success in time 0.037 s
%------------------------------------------------------------------------------