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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 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 : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:09:15 EDT 2024

% Result   : Theorem 0.59s 0.78s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  119 (  14 unt;   0 def)
%            Number of atoms       :  336 ( 107 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  382 ( 165   ~; 161   |;  33   &)
%                                         (  16 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  13 usr;  13 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  133 ( 115   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f337,plain,
    $false,
    inference(avatar_sat_refutation,[],[f59,f115,f122,f129,f140,f152,f163,f196,f227,f257,f258,f300,f336]) ).

fof(f336,plain,
    ( spl8_2
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(avatar_contradiction_clause,[],[f335]) ).

fof(f335,plain,
    ( $false
    | spl8_2
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(subsumption_resolution,[],[f334,f226]) ).

fof(f226,plain,
    ( in(sK4(sK3,sK1),sK3)
    | ~ spl8_16 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f224,plain,
    ( spl8_16
  <=> in(sK4(sK3,sK1),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).

fof(f334,plain,
    ( ~ in(sK4(sK3,sK1),sK3)
    | spl8_2
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(subsumption_resolution,[],[f332,f58]) ).

fof(f58,plain,
    ( sK1 != sK3
    | spl8_2 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl8_2
  <=> sK1 = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).

fof(f332,plain,
    ( sK1 = sK3
    | ~ in(sK4(sK3,sK1),sK3)
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(resolution,[],[f307,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | X0 = X1
      | ~ in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK4(X0,X1),X1)
          | ~ in(sK4(X0,X1),X0) )
        & ( in(sK4(X0,X1),X1)
          | in(sK4(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,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/sandbox/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801',t2_tarski) ).

fof(f307,plain,
    ( in(sK4(sK3,sK1),sK1)
    | ~ spl8_11
    | ~ spl8_16 ),
    inference(resolution,[],[f226,f139]) ).

fof(f139,plain,
    ( ! [X0] :
        ( ~ in(X0,sK3)
        | in(X0,sK1) )
    | ~ spl8_11 ),
    inference(avatar_component_clause,[],[f138]) ).

fof(f138,plain,
    ( spl8_11
  <=> ! [X0] :
        ( ~ in(X0,sK3)
        | in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).

fof(f300,plain,
    ~ spl8_9,
    inference(avatar_contradiction_clause,[],[f299]) ).

fof(f299,plain,
    ( $false
    | ~ spl8_9 ),
    inference(subsumption_resolution,[],[f287,f33]) ).

fof(f33,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])],[f16,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(f16,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,[],[f15]) ).

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(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/sandbox/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801',t134_zfmisc_1) ).

fof(f287,plain,
    ( empty_set = sK1
    | ~ spl8_9 ),
    inference(resolution,[],[f121,f91]) ).

fof(f91,plain,
    ! [X0] :
      ( in(sK4(X0,empty_set),X0)
      | empty_set = X0 ),
    inference(resolution,[],[f35,f47]) ).

fof(f47,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f28]) ).

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

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

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

fof(f25,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/sandbox/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801',d1_xboole_0) ).

fof(f35,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X1)
      | X0 = X1
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f121,plain,
    ( ! [X0] : ~ in(X0,sK1)
    | ~ spl8_9 ),
    inference(avatar_component_clause,[],[f120]) ).

fof(f120,plain,
    ( spl8_9
  <=> ! [X0] : ~ in(X0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).

fof(f258,plain,
    ( spl8_12
    | spl8_9
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f245,f56,f120,f142]) ).

fof(f142,plain,
    ( spl8_12
  <=> ! [X1] :
        ( ~ in(X1,sK2)
        | in(X1,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).

fof(f245,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK1)
        | ~ in(X1,sK2)
        | in(X1,sK0) )
    | ~ spl8_2 ),
    inference(resolution,[],[f238,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF6)
      | in(X0,sK0) ),
    inference(forward_demodulation,[],[f63,f50]) ).

fof(f50,plain,
    sF6 = sF7,
    inference(definition_folding,[],[f31,f49,f48]) ).

fof(f48,plain,
    cartesian_product2(sK2,sK3) = sF6,
    introduced(function_definition,[new_symbols(definition,[sF6])]) ).

fof(f49,plain,
    cartesian_product2(sK0,sK1) = sF7,
    introduced(function_definition,[new_symbols(definition,[sF7])]) ).

fof(f31,plain,
    cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF7)
      | in(X0,sK0) ),
    inference(superposition,[],[f42,f49]) ).

fof(f42,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/sandbox/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801',l55_zfmisc_1) ).

fof(f238,plain,
    ( ! [X0,X1] :
        ( in(ordered_pair(X0,X1),sF6)
        | ~ in(X1,sK1)
        | ~ in(X0,sK2) )
    | ~ spl8_2 ),
    inference(superposition,[],[f44,f228]) ).

fof(f228,plain,
    ( sF6 = cartesian_product2(sK2,sK1)
    | ~ spl8_2 ),
    inference(superposition,[],[f48,f57]) ).

fof(f57,plain,
    ( sK1 = sK3
    | ~ spl8_2 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f44,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(f257,plain,
    ( spl8_1
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(avatar_contradiction_clause,[],[f256]) ).

fof(f256,plain,
    ( $false
    | spl8_1
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(subsumption_resolution,[],[f255,f248]) ).

fof(f248,plain,
    ( in(sK4(sK2,sK0),sK2)
    | spl8_1
    | ~ spl8_8 ),
    inference(subsumption_resolution,[],[f247,f54]) ).

fof(f54,plain,
    ( sK0 != sK2
    | spl8_1 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f52,plain,
    ( spl8_1
  <=> sK0 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).

fof(f247,plain,
    ( in(sK4(sK2,sK0),sK2)
    | sK0 = sK2
    | ~ spl8_8 ),
    inference(factoring,[],[f165]) ).

fof(f165,plain,
    ( ! [X0] :
        ( in(sK4(X0,sK0),sK2)
        | sK0 = X0
        | in(sK4(X0,sK0),X0) )
    | ~ spl8_8 ),
    inference(resolution,[],[f118,f35]) ).

fof(f118,plain,
    ( ! [X1] :
        ( ~ in(X1,sK0)
        | in(X1,sK2) )
    | ~ spl8_8 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f117,plain,
    ( spl8_8
  <=> ! [X1] :
        ( ~ in(X1,sK0)
        | in(X1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).

fof(f255,plain,
    ( ~ in(sK4(sK2,sK0),sK2)
    | spl8_1
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(subsumption_resolution,[],[f253,f54]) ).

fof(f253,plain,
    ( sK0 = sK2
    | ~ in(sK4(sK2,sK0),sK2)
    | spl8_1
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(resolution,[],[f249,f36]) ).

fof(f249,plain,
    ( in(sK4(sK2,sK0),sK0)
    | spl8_1
    | ~ spl8_8
    | ~ spl8_12 ),
    inference(resolution,[],[f248,f143]) ).

fof(f143,plain,
    ( ! [X1] :
        ( ~ in(X1,sK2)
        | in(X1,sK0) )
    | ~ spl8_12 ),
    inference(avatar_component_clause,[],[f142]) ).

fof(f227,plain,
    ( spl8_2
    | spl8_16
    | ~ spl8_7 ),
    inference(avatar_split_clause,[],[f222,f113,f224,f56]) ).

fof(f113,plain,
    ( spl8_7
  <=> ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).

fof(f222,plain,
    ( in(sK4(sK3,sK1),sK3)
    | sK1 = sK3
    | ~ spl8_7 ),
    inference(factoring,[],[f154]) ).

fof(f154,plain,
    ( ! [X0] :
        ( in(sK4(X0,sK1),sK3)
        | sK1 = X0
        | in(sK4(X0,sK1),X0) )
    | ~ spl8_7 ),
    inference(resolution,[],[f114,f35]) ).

fof(f114,plain,
    ( ! [X0] :
        ( ~ in(X0,sK1)
        | in(X0,sK3) )
    | ~ spl8_7 ),
    inference(avatar_component_clause,[],[f113]) ).

fof(f196,plain,
    ~ spl8_5,
    inference(avatar_split_clause,[],[f90,f86]) ).

fof(f86,plain,
    ( spl8_5
  <=> empty_set = sF6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).

fof(f90,plain,
    empty_set != sF6,
    inference(superposition,[],[f76,f50]) ).

fof(f76,plain,
    empty_set != sF7,
    inference(subsumption_resolution,[],[f75,f33]) ).

fof(f75,plain,
    ( empty_set != sF7
    | empty_set = sK1 ),
    inference(subsumption_resolution,[],[f73,f32]) ).

fof(f32,plain,
    empty_set != sK0,
    inference(cnf_transformation,[],[f19]) ).

fof(f73,plain,
    ( empty_set != sF7
    | empty_set = sK0
    | empty_set = sK1 ),
    inference(superposition,[],[f37,f49]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( empty_set != cartesian_product2(X0,X1)
      | empty_set = X0
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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/sandbox/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801',t113_zfmisc_1) ).

fof(f163,plain,
    ( ~ spl8_4
    | spl8_5 ),
    inference(avatar_contradiction_clause,[],[f162]) ).

fof(f162,plain,
    ( $false
    | ~ spl8_4
    | spl8_5 ),
    inference(subsumption_resolution,[],[f161,f88]) ).

fof(f88,plain,
    ( empty_set != sF6
    | spl8_5 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f161,plain,
    ( empty_set = sF6
    | ~ spl8_4 ),
    inference(forward_demodulation,[],[f159,f46]) ).

fof(f46,plain,
    ! [X1] : empty_set = cartesian_product2(empty_set,X1),
    inference(equality_resolution,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f159,plain,
    ( sF6 = cartesian_product2(empty_set,sK3)
    | ~ spl8_4 ),
    inference(superposition,[],[f48,f84]) ).

fof(f84,plain,
    ( empty_set = sK2
    | ~ spl8_4 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f82,plain,
    ( spl8_4
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).

fof(f152,plain,
    ( spl8_4
    | ~ spl8_10 ),
    inference(avatar_split_clause,[],[f150,f135,f82]) ).

fof(f135,plain,
    ( spl8_10
  <=> ! [X1] : ~ in(X1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).

fof(f150,plain,
    ( empty_set = sK2
    | ~ spl8_10 ),
    inference(resolution,[],[f136,f91]) ).

fof(f136,plain,
    ( ! [X1] : ~ in(X1,sK2)
    | ~ spl8_10 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f140,plain,
    ( spl8_10
    | spl8_11 ),
    inference(avatar_split_clause,[],[f131,f138,f135]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK3)
      | ~ in(X1,sK2)
      | in(X0,sK1) ),
    inference(resolution,[],[f103,f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF6)
      | in(X1,sK1) ),
    inference(forward_demodulation,[],[f68,f50]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF7)
      | in(X1,sK1) ),
    inference(superposition,[],[f43,f49]) ).

fof(f43,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),sF6)
      | ~ in(X1,sK3)
      | ~ in(X0,sK2) ),
    inference(superposition,[],[f44,f48]) ).

fof(f129,plain,
    ~ spl8_6,
    inference(avatar_contradiction_clause,[],[f128]) ).

fof(f128,plain,
    ( $false
    | ~ spl8_6 ),
    inference(subsumption_resolution,[],[f125,f32]) ).

fof(f125,plain,
    ( empty_set = sK0
    | ~ spl8_6 ),
    inference(resolution,[],[f111,f91]) ).

fof(f111,plain,
    ( ! [X1] : ~ in(X1,sK0)
    | ~ spl8_6 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f110,plain,
    ( spl8_6
  <=> ! [X1] : ~ in(X1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).

fof(f122,plain,
    ( spl8_8
    | spl8_9 ),
    inference(avatar_split_clause,[],[f107,f120,f117]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK1)
      | ~ in(X1,sK0)
      | in(X1,sK2) ),
    inference(resolution,[],[f104,f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF6)
      | in(X0,sK2) ),
    inference(superposition,[],[f42,f48]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),sF6)
      | ~ in(X1,sK1)
      | ~ in(X0,sK0) ),
    inference(forward_demodulation,[],[f102,f50]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X1),sF7)
      | ~ in(X1,sK1)
      | ~ in(X0,sK0) ),
    inference(superposition,[],[f44,f49]) ).

fof(f115,plain,
    ( spl8_6
    | spl8_7 ),
    inference(avatar_split_clause,[],[f105,f113,f110]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ in(X0,sK1)
      | ~ in(X1,sK0)
      | in(X0,sK3) ),
    inference(resolution,[],[f104,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sF6)
      | in(X1,sK3) ),
    inference(superposition,[],[f43,f48]) ).

fof(f59,plain,
    ( ~ spl8_1
    | ~ spl8_2 ),
    inference(avatar_split_clause,[],[f34,f56,f52]) ).

fof(f34,plain,
    ( sK1 != sK3
    | sK0 != sK2 ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.14/0.15  % 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
% 0.15/0.36  % Computer : n008.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   : Fri May  3 16:50:23 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  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/tmp/tmp.B8cDioJwj9/Vampire---4.8_30801
% 0.59/0.76  % (31070)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.76  % (31073)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.59/0.76  % (31072)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.59/0.76  % (31074)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.59/0.76  % (31075)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.59/0.76  % (31071)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.59/0.76  % (31077)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.59/0.76  % (31076)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.59/0.76  % (31070)Refutation not found, incomplete strategy% (31070)------------------------------
% 0.59/0.76  % (31070)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.76  % (31070)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.76  
% 0.59/0.76  % (31070)Memory used [KB]: 976
% 0.59/0.76  % (31070)Time elapsed: 0.003 s
% 0.59/0.76  % (31070)Instructions burned: 3 (million)
% 0.59/0.76  % (31070)------------------------------
% 0.59/0.76  % (31070)------------------------------
% 0.59/0.76  % (31077)Refutation not found, incomplete strategy% (31077)------------------------------
% 0.59/0.76  % (31077)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.76  % (31077)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.76  
% 0.59/0.76  % (31077)Memory used [KB]: 1050
% 0.59/0.76  % (31077)Time elapsed: 0.004 s
% 0.59/0.76  % (31074)Refutation not found, incomplete strategy% (31074)------------------------------
% 0.59/0.76  % (31074)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.76  % (31077)Instructions burned: 3 (million)
% 0.59/0.76  % (31074)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.76  
% 0.59/0.76  % (31074)Memory used [KB]: 1055
% 0.59/0.76  % (31074)Time elapsed: 0.004 s
% 0.59/0.76  % (31074)Instructions burned: 4 (million)
% 0.59/0.76  % (31077)------------------------------
% 0.59/0.76  % (31077)------------------------------
% 0.59/0.76  % (31074)------------------------------
% 0.59/0.76  % (31074)------------------------------
% 0.59/0.77  % (31075)Refutation not found, incomplete strategy% (31075)------------------------------
% 0.59/0.77  % (31075)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.77  % (31075)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.77  
% 0.59/0.77  % (31075)Memory used [KB]: 1073
% 0.59/0.77  % (31075)Time elapsed: 0.005 s
% 0.59/0.77  % (31075)Instructions burned: 5 (million)
% 0.59/0.77  % (31078)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.59/0.77  % (31075)------------------------------
% 0.59/0.77  % (31075)------------------------------
% 0.59/0.77  % (31079)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.59/0.77  % (31079)Refutation not found, incomplete strategy% (31079)------------------------------
% 0.59/0.77  % (31079)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.77  % (31079)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.77  
% 0.59/0.77  % (31079)Memory used [KB]: 962
% 0.59/0.77  % (31079)Time elapsed: 0.003 s
% 0.59/0.77  % (31079)Instructions burned: 3 (million)
% 0.59/0.77  % (31079)------------------------------
% 0.59/0.77  % (31079)------------------------------
% 0.59/0.77  % (31080)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.59/0.77  % (31081)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.59/0.78  % (31080)First to succeed.
% 0.59/0.78  % (31082)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.59/0.78  % (31073)Instruction limit reached!
% 0.59/0.78  % (31073)------------------------------
% 0.59/0.78  % (31073)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.78  % (31073)Termination reason: Unknown
% 0.59/0.78  % (31073)Termination phase: Saturation
% 0.59/0.78  
% 0.59/0.78  % (31073)Memory used [KB]: 1443
% 0.59/0.78  % (31073)Time elapsed: 0.018 s
% 0.59/0.78  % (31073)Instructions burned: 33 (million)
% 0.59/0.78  % (31073)------------------------------
% 0.59/0.78  % (31073)------------------------------
% 0.59/0.78  % (31080)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31060"
% 0.59/0.78  % (31080)Refutation found. Thanks to Tanya!
% 0.59/0.78  % SZS status Theorem for Vampire---4
% 0.59/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.59/0.78  % (31080)------------------------------
% 0.59/0.78  % (31080)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.78  % (31080)Termination reason: Refutation
% 0.59/0.78  
% 0.59/0.78  % (31080)Memory used [KB]: 1104
% 0.59/0.78  % (31080)Time elapsed: 0.010 s
% 0.59/0.78  % (31080)Instructions burned: 12 (million)
% 0.59/0.78  % (31060)Success in time 0.403 s
% 0.59/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------