TSTP Solution File: SEU239+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 15:25:32 EDT 2024

% Result   : Theorem 0.20s 0.37s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  127 (  16 unt;   0 def)
%            Number of atoms       :  359 (  12 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  375 ( 143   ~; 142   |;  49   &)
%                                         (  22 <=>;  18  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   26 (  24 usr;  17 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :  107 (  84   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f321,plain,
    $false,
    inference(avatar_sat_refutation,[],[f126,f171,f188,f199,f214,f232,f294,f303,f311,f320]) ).

fof(f320,plain,
    ( ~ spl9_1
    | ~ spl9_2 ),
    inference(avatar_contradiction_clause,[],[f319]) ).

fof(f319,plain,
    ( $false
    | ~ spl9_1
    | ~ spl9_2 ),
    inference(subsumption_resolution,[],[f318,f120]) ).

fof(f120,plain,
    ( reflexive(sK0)
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f119,plain,
    ( spl9_1
  <=> reflexive(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f318,plain,
    ( ~ reflexive(sK0)
    | ~ spl9_1
    | ~ spl9_2 ),
    inference(subsumption_resolution,[],[f317,f80]) ).

fof(f80,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ( ( ( ~ in(ordered_pair(sK1,sK1),sK0)
        & in(sK1,relation_field(sK0)) )
      | ~ reflexive(sK0) )
    & ( ! [X2] :
          ( in(ordered_pair(X2,X2),sK0)
          | ~ in(X2,relation_field(sK0)) )
      | reflexive(sK0) )
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f59,f61,f60]) ).

fof(f60,plain,
    ( ? [X0] :
        ( ( ? [X1] :
              ( ~ in(ordered_pair(X1,X1),X0)
              & in(X1,relation_field(X0)) )
          | ~ reflexive(X0) )
        & ( ! [X2] :
              ( in(ordered_pair(X2,X2),X0)
              | ~ in(X2,relation_field(X0)) )
          | reflexive(X0) )
        & relation(X0) )
   => ( ( ? [X1] :
            ( ~ in(ordered_pair(X1,X1),sK0)
            & in(X1,relation_field(sK0)) )
        | ~ reflexive(sK0) )
      & ( ! [X2] :
            ( in(ordered_pair(X2,X2),sK0)
            | ~ in(X2,relation_field(sK0)) )
        | reflexive(sK0) )
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ( ? [X1] :
        ( ~ in(ordered_pair(X1,X1),sK0)
        & in(X1,relation_field(sK0)) )
   => ( ~ in(ordered_pair(sK1,sK1),sK0)
      & in(sK1,relation_field(sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ? [X0] :
      ( ( ? [X1] :
            ( ~ in(ordered_pair(X1,X1),X0)
            & in(X1,relation_field(X0)) )
        | ~ reflexive(X0) )
      & ( ! [X2] :
            ( in(ordered_pair(X2,X2),X0)
            | ~ in(X2,relation_field(X0)) )
        | reflexive(X0) )
      & relation(X0) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ? [X0] :
      ( ( ? [X1] :
            ( ~ in(ordered_pair(X1,X1),X0)
            & in(X1,relation_field(X0)) )
        | ~ reflexive(X0) )
      & ( ! [X1] :
            ( in(ordered_pair(X1,X1),X0)
            | ~ in(X1,relation_field(X0)) )
        | reflexive(X0) )
      & relation(X0) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ? [X0] :
      ( ( ? [X1] :
            ( ~ in(ordered_pair(X1,X1),X0)
            & in(X1,relation_field(X0)) )
        | ~ reflexive(X0) )
      & ( ! [X1] :
            ( in(ordered_pair(X1,X1),X0)
            | ~ in(X1,relation_field(X0)) )
        | reflexive(X0) )
      & relation(X0) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ? [X0] :
      ( ( reflexive(X0)
      <~> ! [X1] :
            ( in(ordered_pair(X1,X1),X0)
            | ~ in(X1,relation_field(X0)) ) )
      & relation(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ( reflexive(X0)
        <=> ! [X1] :
              ( in(X1,relation_field(X0))
             => in(ordered_pair(X1,X1),X0) ) ) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f25,conjecture,
    ! [X0] :
      ( relation(X0)
     => ( reflexive(X0)
      <=> ! [X1] :
            ( in(X1,relation_field(X0))
           => in(ordered_pair(X1,X1),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).

fof(f317,plain,
    ( ~ relation(sK0)
    | ~ reflexive(sK0)
    | ~ spl9_1
    | ~ spl9_2 ),
    inference(subsumption_resolution,[],[f316,f125]) ).

fof(f125,plain,
    ( in(sK1,relation_field(sK0))
    | ~ spl9_2 ),
    inference(avatar_component_clause,[],[f123]) ).

fof(f123,plain,
    ( spl9_2
  <=> in(sK1,relation_field(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f316,plain,
    ( ~ in(sK1,relation_field(sK0))
    | ~ relation(sK0)
    | ~ reflexive(sK0)
    | ~ spl9_1 ),
    inference(resolution,[],[f315,f252]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( in(ordered_pair(X0,X0),X1)
      | ~ in(X0,relation_field(X1))
      | ~ relation(X1)
      | ~ reflexive(X1) ),
    inference(duplicate_literal_removal,[],[f249]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_field(X1))
      | in(ordered_pair(X0,X0),X1)
      | ~ relation(X1)
      | ~ reflexive(X1)
      | ~ relation(X1) ),
    inference(resolution,[],[f89,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( is_reflexive_in(X0,relation_field(X0))
      | ~ reflexive(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( ( reflexive(X0)
          | ~ is_reflexive_in(X0,relation_field(X0)) )
        & ( is_reflexive_in(X0,relation_field(X0))
          | ~ reflexive(X0) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( reflexive(X0)
      <=> is_reflexive_in(X0,relation_field(X0)) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( relation(X0)
     => ( reflexive(X0)
      <=> is_reflexive_in(X0,relation_field(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).

fof(f89,plain,
    ! [X3,X0,X1] :
      ( ~ is_reflexive_in(X0,X1)
      | ~ in(X3,X1)
      | in(ordered_pair(X3,X3),X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_reflexive_in(X0,X1)
            | ( ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
              & in(sK2(X0,X1),X1) ) )
          & ( ! [X3] :
                ( in(ordered_pair(X3,X3),X0)
                | ~ in(X3,X1) )
            | ~ is_reflexive_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f65,f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(ordered_pair(X2,X2),X0)
          & in(X2,X1) )
     => ( ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
        & in(sK2(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_reflexive_in(X0,X1)
            | ? [X2] :
                ( ~ in(ordered_pair(X2,X2),X0)
                & in(X2,X1) ) )
          & ( ! [X3] :
                ( in(ordered_pair(X3,X3),X0)
                | ~ in(X3,X1) )
            | ~ is_reflexive_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( is_reflexive_in(X0,X1)
            | ? [X2] :
                ( ~ in(ordered_pair(X2,X2),X0)
                & in(X2,X1) ) )
          & ( ! [X2] :
                ( in(ordered_pair(X2,X2),X0)
                | ~ in(X2,X1) )
            | ~ is_reflexive_in(X0,X1) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( is_reflexive_in(X0,X1)
        <=> ! [X2] :
              ( in(ordered_pair(X2,X2),X0)
              | ~ in(X2,X1) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( is_reflexive_in(X0,X1)
        <=> ! [X2] :
              ( in(X2,X1)
             => in(ordered_pair(X2,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).

fof(f315,plain,
    ( ~ in(ordered_pair(sK1,sK1),sK0)
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f83,f120]) ).

fof(f83,plain,
    ( ~ in(ordered_pair(sK1,sK1),sK0)
    | ~ reflexive(sK0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f311,plain,
    spl9_1,
    inference(avatar_contradiction_clause,[],[f310]) ).

fof(f310,plain,
    ( $false
    | spl9_1 ),
    inference(subsumption_resolution,[],[f309,f80]) ).

fof(f309,plain,
    ( ~ relation(sK0)
    | spl9_1 ),
    inference(subsumption_resolution,[],[f307,f121]) ).

fof(f121,plain,
    ( ~ reflexive(sK0)
    | spl9_1 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f307,plain,
    ( reflexive(sK0)
    | ~ relation(sK0)
    | spl9_1 ),
    inference(resolution,[],[f306,f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ is_reflexive_in(X0,relation_field(X0))
      | reflexive(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f306,plain,
    ( is_reflexive_in(sK0,relation_field(sK0))
    | spl9_1 ),
    inference(subsumption_resolution,[],[f305,f80]) ).

fof(f305,plain,
    ( is_reflexive_in(sK0,relation_field(sK0))
    | ~ relation(sK0)
    | spl9_1 ),
    inference(duplicate_literal_removal,[],[f304]) ).

fof(f304,plain,
    ( is_reflexive_in(sK0,relation_field(sK0))
    | is_reflexive_in(sK0,relation_field(sK0))
    | ~ relation(sK0)
    | spl9_1 ),
    inference(resolution,[],[f285,f90]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( in(sK2(X0,X1),X1)
      | is_reflexive_in(X0,X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f285,plain,
    ( ! [X0] :
        ( ~ in(sK2(sK0,X0),relation_field(sK0))
        | is_reflexive_in(sK0,X0) )
    | spl9_1 ),
    inference(subsumption_resolution,[],[f282,f80]) ).

fof(f282,plain,
    ( ! [X0] :
        ( is_reflexive_in(sK0,X0)
        | ~ relation(sK0)
        | ~ in(sK2(sK0,X0),relation_field(sK0)) )
    | spl9_1 ),
    inference(resolution,[],[f91,f161]) ).

fof(f161,plain,
    ( ! [X2] :
        ( in(ordered_pair(X2,X2),sK0)
        | ~ in(X2,relation_field(sK0)) )
    | spl9_1 ),
    inference(subsumption_resolution,[],[f81,f121]) ).

fof(f81,plain,
    ! [X2] :
      ( in(ordered_pair(X2,X2),sK0)
      | ~ in(X2,relation_field(sK0))
      | reflexive(sK0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
      | is_reflexive_in(X0,X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f303,plain,
    ( ~ spl9_15
    | ~ spl9_16
    | spl9_10 ),
    inference(avatar_split_clause,[],[f281,f211,f300,f296]) ).

fof(f296,plain,
    ( spl9_15
  <=> empty(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).

fof(f300,plain,
    ( spl9_16
  <=> reflexive(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).

fof(f211,plain,
    ( spl9_10
  <=> empty(relation_field(sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).

fof(f281,plain,
    ( ~ reflexive(sK7)
    | ~ empty(sK7)
    | spl9_10 ),
    inference(subsumption_resolution,[],[f274,f113]) ).

fof(f113,plain,
    relation(sK7),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ( function(sK7)
    & relation(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f39,f76]) ).

fof(f76,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK7)
      & relation(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f31]) ).

fof(f31,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

fof(f274,plain,
    ( ~ reflexive(sK7)
    | ~ empty(sK7)
    | ~ relation(sK7)
    | spl9_10 ),
    inference(resolution,[],[f267,f213]) ).

fof(f213,plain,
    ( ~ empty(relation_field(sK7))
    | spl9_10 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f267,plain,
    ! [X0] :
      ( empty(relation_field(X0))
      | ~ reflexive(X0)
      | ~ empty(X0)
      | ~ relation(X0) ),
    inference(resolution,[],[f263,f158]) ).

fof(f158,plain,
    ! [X0] :
      ( in(sK3(X0),X0)
      | empty(X0) ),
    inference(resolution,[],[f106,f96]) ).

fof(f96,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] : element(sK3(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK3(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f19,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f263,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_field(X1))
      | ~ relation(X1)
      | ~ reflexive(X1)
      | ~ empty(X1) ),
    inference(resolution,[],[f252,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f294,plain,
    ( ~ spl9_13
    | ~ spl9_14
    | spl9_8 ),
    inference(avatar_split_clause,[],[f280,f196,f291,f287]) ).

fof(f287,plain,
    ( spl9_13
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).

fof(f291,plain,
    ( spl9_14
  <=> reflexive(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).

fof(f196,plain,
    ( spl9_8
  <=> empty(relation_field(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).

fof(f280,plain,
    ( ~ reflexive(sK6)
    | ~ empty(sK6)
    | spl9_8 ),
    inference(subsumption_resolution,[],[f273,f111]) ).

fof(f111,plain,
    relation(sK6),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( function(sK6)
    & relation(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f74]) ).

fof(f74,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK6)
      & relation(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(f273,plain,
    ( ~ reflexive(sK6)
    | ~ empty(sK6)
    | ~ relation(sK6)
    | spl9_8 ),
    inference(resolution,[],[f267,f198]) ).

fof(f198,plain,
    ( ~ empty(relation_field(sK6))
    | spl9_8 ),
    inference(avatar_component_clause,[],[f196]) ).

fof(f232,plain,
    ( spl9_11
    | ~ spl9_12 ),
    inference(avatar_split_clause,[],[f215,f229,f225]) ).

fof(f225,plain,
    ( spl9_11
  <=> empty(relation_rng(empty_set)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).

fof(f229,plain,
    ( spl9_12
  <=> empty(relation_field(empty_set)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).

fof(f215,plain,
    ( ~ empty(relation_field(empty_set))
    | empty(relation_rng(empty_set)) ),
    inference(superposition,[],[f103,f177]) ).

fof(f177,plain,
    relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
    inference(forward_demodulation,[],[f176,f129]) ).

fof(f129,plain,
    empty_set = sK8,
    inference(resolution,[],[f93,f116]) ).

fof(f116,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ( function(sK8)
    & empty(sK8)
    & relation(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f29,f78]) ).

fof(f78,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK8)
      & empty(sK8)
      & relation(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(f93,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f176,plain,
    relation_field(sK8) = set_union2(relation_dom(sK8),relation_rng(sK8)),
    inference(resolution,[],[f86,f115]) ).

fof(f115,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f79]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( relation(X0)
     => relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X1,X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X1,X0))
      | empty(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( ~ empty(X0)
     => ~ empty(set_union2(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).

fof(f214,plain,
    ( spl9_9
    | ~ spl9_10 ),
    inference(avatar_split_clause,[],[f204,f211,f207]) ).

fof(f207,plain,
    ( spl9_9
  <=> empty(relation_rng(sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).

fof(f204,plain,
    ( ~ empty(relation_field(sK7))
    | empty(relation_rng(sK7)) ),
    inference(superposition,[],[f103,f175]) ).

fof(f175,plain,
    relation_field(sK7) = set_union2(relation_dom(sK7),relation_rng(sK7)),
    inference(resolution,[],[f86,f113]) ).

fof(f199,plain,
    ( spl9_7
    | ~ spl9_8 ),
    inference(avatar_split_clause,[],[f189,f196,f192]) ).

fof(f192,plain,
    ( spl9_7
  <=> empty(relation_rng(sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).

fof(f189,plain,
    ( ~ empty(relation_field(sK6))
    | empty(relation_rng(sK6)) ),
    inference(superposition,[],[f103,f174]) ).

fof(f174,plain,
    relation_field(sK6) = set_union2(relation_dom(sK6),relation_rng(sK6)),
    inference(resolution,[],[f86,f111]) ).

fof(f188,plain,
    ( spl9_5
    | ~ spl9_6 ),
    inference(avatar_split_clause,[],[f178,f185,f181]) ).

fof(f181,plain,
    ( spl9_5
  <=> empty(relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).

fof(f185,plain,
    ( spl9_6
  <=> empty(relation_field(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).

fof(f178,plain,
    ( ~ empty(relation_field(sK0))
    | empty(relation_rng(sK0)) ),
    inference(superposition,[],[f103,f173]) ).

fof(f173,plain,
    relation_field(sK0) = set_union2(relation_dom(sK0),relation_rng(sK0)),
    inference(resolution,[],[f86,f80]) ).

fof(f171,plain,
    ( ~ spl9_3
    | spl9_4
    | spl9_1 ),
    inference(avatar_split_clause,[],[f163,f119,f169,f165]) ).

fof(f165,plain,
    ( spl9_3
  <=> empty(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).

fof(f169,plain,
    ( spl9_4
  <=> ! [X0] : ~ in(X0,relation_field(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).

fof(f163,plain,
    ( ! [X0] :
        ( ~ in(X0,relation_field(sK0))
        | ~ empty(sK0) )
    | spl9_1 ),
    inference(resolution,[],[f161,f108]) ).

fof(f126,plain,
    ( ~ spl9_1
    | spl9_2 ),
    inference(avatar_split_clause,[],[f82,f123,f119]) ).

fof(f82,plain,
    ( in(sK1,relation_field(sK0))
    | ~ reflexive(sK0) ),
    inference(cnf_transformation,[],[f62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Apr 29 20:42:41 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (1522)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.35  % (1526)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.36  TRYING [1]
% 0.20/0.36  TRYING [2]
% 0.20/0.36  % (1525)WARNING: value z3 for option sas not known
% 0.20/0.36  TRYING [3]
% 0.20/0.36  % (1523)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.36  % (1525)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)
% 0.20/0.36  % (1524)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.36  % (1527)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)
% 0.20/0.36  % (1528)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)
% 0.20/0.36  % (1529)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)
% 0.20/0.36  TRYING [1]
% 0.20/0.37  TRYING [4]
% 0.20/0.37  TRYING [2]
% 0.20/0.37  TRYING [1]
% 0.20/0.37  TRYING [2]
% 0.20/0.37  % (1525)First to succeed.
% 0.20/0.37  TRYING [3]
% 0.20/0.37  % (1527)Also succeeded, but the first one will report.
% 0.20/0.37  % (1525)Refutation found. Thanks to Tanya!
% 0.20/0.37  % SZS status Theorem for theBenchmark
% 0.20/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.37  % (1525)------------------------------
% 0.20/0.37  % (1525)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.37  % (1525)Termination reason: Refutation
% 0.20/0.37  
% 0.20/0.37  % (1525)Memory used [KB]: 900
% 0.20/0.37  % (1525)Time elapsed: 0.013 s
% 0.20/0.37  % (1525)Instructions burned: 15 (million)
% 0.20/0.37  % (1525)------------------------------
% 0.20/0.37  % (1525)------------------------------
% 0.20/0.37  % (1522)Success in time 0.029 s
%------------------------------------------------------------------------------