TSTP Solution File: SEU186+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU186+2 : 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 : n028.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 15:23:27 EDT 2024

% Result   : Theorem 7.83s 1.49s
% Output   : Refutation 7.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   75 (  18 unt;   0 def)
%            Number of atoms       :  306 (  75 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  369 ( 138   ~; 123   |;  75   &)
%                                         (  14 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;   2 con; 0-3 aty)
%            Number of variables   :  235 ( 180   !;  55   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f41203,plain,
    $false,
    inference(trivial_inequality_removal,[],[f41202]) ).

fof(f41202,plain,
    empty_set != empty_set,
    inference(superposition,[],[f469,f32911]) ).

fof(f32911,plain,
    empty_set = sK12,
    inference(forward_demodulation,[],[f30861,f572]) ).

fof(f572,plain,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,axiom,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).

fof(f30861,plain,
    sK12 = set_intersection2(sK12,empty_set),
    inference(backward_demodulation,[],[f20569,f30491]) ).

fof(f30491,plain,
    ! [X0] : empty_set = cartesian_product2(empty_set,X0),
    inference(resolution,[],[f30442,f609]) ).

fof(f609,plain,
    ! [X0] :
      ( in(sK33(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f376]) ).

fof(f376,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK33(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f374,f375]) ).

fof(f375,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK33(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f374,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f373]) ).

fof(f373,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f30442,plain,
    ! [X0,X1] : ~ in(X0,cartesian_product2(empty_set,X1)),
    inference(resolution,[],[f13893,f779]) ).

fof(f779,plain,
    ! [X0,X1] : sP7(X1,X0,cartesian_product2(X0,X1)),
    inference(equality_resolution,[],[f711]) ).

fof(f711,plain,
    ! [X2,X0,X1] :
      ( sP7(X1,X0,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f434]) ).

fof(f434,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ~ sP7(X1,X0,X2) )
      & ( sP7(X1,X0,X2)
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f305]) ).

fof(f305,plain,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> sP7(X1,X0,X2) ),
    inference(definition_folding,[],[f16,f304]) ).

fof(f304,plain,
    ! [X1,X0,X2] :
      ( sP7(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(f13893,plain,
    ! [X2,X0,X1] :
      ( ~ sP7(X2,empty_set,X1)
      | ~ in(X0,X1) ),
    inference(resolution,[],[f703,f763]) ).

fof(f763,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f608]) ).

fof(f608,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f376]) ).

fof(f703,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK52(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f433]) ).

fof(f433,plain,
    ! [X0,X1,X2] :
      ( ( sP7(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK49(X0,X1,X2)
                | ~ in(X5,X0)
                | ~ in(X4,X1) )
            | ~ in(sK49(X0,X1,X2),X2) )
          & ( ( sK49(X0,X1,X2) = ordered_pair(sK50(X0,X1,X2),sK51(X0,X1,X2))
              & in(sK51(X0,X1,X2),X0)
              & in(sK50(X0,X1,X2),X1) )
            | in(sK49(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X0)
                  | ~ in(X9,X1) ) )
            & ( ( ordered_pair(sK52(X0,X1,X8),sK53(X0,X1,X8)) = X8
                & in(sK53(X0,X1,X8),X0)
                & in(sK52(X0,X1,X8),X1) )
              | ~ in(X8,X2) ) )
        | ~ sP7(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52,sK53])],[f429,f432,f431,f430]) ).

fof(f430,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X0)
                | ~ in(X4,X1) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X0)
                & in(X6,X1) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK49(X0,X1,X2)
              | ~ in(X5,X0)
              | ~ in(X4,X1) )
          | ~ in(sK49(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK49(X0,X1,X2)
              & in(X7,X0)
              & in(X6,X1) )
          | in(sK49(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f431,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK49(X0,X1,X2)
          & in(X7,X0)
          & in(X6,X1) )
     => ( sK49(X0,X1,X2) = ordered_pair(sK50(X0,X1,X2),sK51(X0,X1,X2))
        & in(sK51(X0,X1,X2),X0)
        & in(sK50(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f432,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X0)
          & in(X11,X1) )
     => ( ordered_pair(sK52(X0,X1,X8),sK53(X0,X1,X8)) = X8
        & in(sK53(X0,X1,X8),X0)
        & in(sK52(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f429,plain,
    ! [X0,X1,X2] :
      ( ( sP7(X0,X1,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X0)
                  | ~ in(X4,X1) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X0)
                  & in(X6,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X0)
                  | ~ in(X9,X1) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X0)
                  & in(X11,X1) )
              | ~ in(X8,X2) ) )
        | ~ sP7(X0,X1,X2) ) ),
    inference(rectify,[],[f428]) ).

fof(f428,plain,
    ! [X1,X0,X2] :
      ( ( sP7(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP7(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f304]) ).

fof(f20569,plain,
    sK12 = set_intersection2(sK12,cartesian_product2(empty_set,empty_set)),
    inference(resolution,[],[f20123,f467]) ).

fof(f467,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f315]) ).

fof(f315,plain,
    ( empty_set != sK12
    & ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f178,f314]) ).

fof(f314,plain,
    ( ? [X0] :
        ( empty_set != X0
        & ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
        & relation(X0) )
   => ( empty_set != sK12
      & ! [X2,X1] : ~ in(ordered_pair(X1,X2),sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f178,plain,
    ? [X0] :
      ( empty_set != X0
      & ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
      & relation(X0) ),
    inference(flattening,[],[f177]) ).

fof(f177,plain,
    ? [X0] :
      ( empty_set != X0
      & ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f148]) ).

fof(f148,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
         => empty_set = X0 ) ),
    inference(negated_conjecture,[],[f147]) ).

fof(f147,conjecture,
    ! [X0] :
      ( relation(X0)
     => ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
       => empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

fof(f20123,plain,
    ( ~ relation(sK12)
    | sK12 = set_intersection2(sK12,cartesian_product2(empty_set,empty_set)) ),
    inference(resolution,[],[f19938,f501]) ).

fof(f501,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f111]) ).

fof(f111,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f19938,plain,
    ( subset(sK12,cartesian_product2(empty_set,empty_set))
    | ~ relation(sK12) ),
    inference(backward_demodulation,[],[f19285,f19374]) ).

fof(f19374,plain,
    empty_set = relation_rng(sK12),
    inference(resolution,[],[f19358,f609]) ).

fof(f19358,plain,
    ! [X0] : ~ in(X0,relation_rng(sK12)),
    inference(resolution,[],[f19339,f467]) ).

fof(f19339,plain,
    ! [X0] :
      ( ~ relation(sK12)
      | ~ in(X0,relation_rng(sK12)) ),
    inference(resolution,[],[f762,f468]) ).

fof(f468,plain,
    ! [X2,X1] : ~ in(ordered_pair(X1,X2),sK12),
    inference(cnf_transformation,[],[f315]) ).

fof(f762,plain,
    ! [X0,X5] :
      ( in(ordered_pair(sK29(X0,X5),X5),X0)
      | ~ in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f599]) ).

fof(f599,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK29(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f367]) ).

fof(f367,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK27(X0,X1)),X0)
                | ~ in(sK27(X0,X1),X1) )
              & ( in(ordered_pair(sK28(X0,X1),sK27(X0,X1)),X0)
                | in(sK27(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK29(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29])],[f363,f366,f365,f364]) ).

fof(f364,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK27(X0,X1)),X0)
          | ~ in(sK27(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK27(X0,X1)),X0)
          | in(sK27(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK27(X0,X1)),X0)
     => in(ordered_pair(sK28(X0,X1),sK27(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f366,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK29(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f363,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f362]) ).

fof(f362,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f248]) ).

fof(f248,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f19285,plain,
    ( subset(sK12,cartesian_product2(empty_set,relation_rng(sK12)))
    | ~ relation(sK12) ),
    inference(superposition,[],[f475,f15192]) ).

fof(f15192,plain,
    empty_set = relation_dom(sK12),
    inference(resolution,[],[f15177,f609]) ).

fof(f15177,plain,
    ! [X0] : ~ in(X0,relation_dom(sK12)),
    inference(resolution,[],[f15146,f467]) ).

fof(f15146,plain,
    ! [X0] :
      ( ~ relation(sK12)
      | ~ in(X0,relation_dom(sK12)) ),
    inference(resolution,[],[f760,f468]) ).

fof(f760,plain,
    ! [X0,X5] :
      ( in(ordered_pair(X5,sK26(X0,X5)),X0)
      | ~ in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f595]) ).

fof(f595,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(X5,sK26(X0,X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f361]) ).

fof(f361,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK24(X0,X1),X3),X0)
                | ~ in(sK24(X0,X1),X1) )
              & ( in(ordered_pair(sK24(X0,X1),sK25(X0,X1)),X0)
                | in(sK24(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK26(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f357,f360,f359,f358]) ).

fof(f358,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X2,X4),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(sK24(X0,X1),X3),X0)
          | ~ in(sK24(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK24(X0,X1),X4),X0)
          | in(sK24(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f359,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK24(X0,X1),X4),X0)
     => in(ordered_pair(sK24(X0,X1),sK25(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f360,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK26(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f357,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f356]) ).

fof(f356,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f247]) ).

fof(f247,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f475,plain,
    ! [X0] :
      ( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f108]) ).

fof(f108,axiom,
    ! [X0] :
      ( relation(X0)
     => subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).

fof(f469,plain,
    empty_set != sK12,
    inference(cnf_transformation,[],[f315]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU186+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Apr 29 21:12:29 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (18425)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38  % (18428)WARNING: value z3 for option sas not known
% 0.20/0.38  % (18427)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38  % (18429)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38  % (18426)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38  % (18431)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)
% 0.20/0.38  % (18430)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)
% 0.20/0.38  % (18432)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)
% 0.20/0.38  % (18428)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)
% 0.20/0.41  TRYING [1]
% 0.20/0.41  TRYING [2]
% 0.20/0.44  TRYING [3]
% 0.20/0.50  TRYING [1]
% 0.20/0.50  TRYING [1]
% 0.20/0.51  TRYING [2]
% 0.20/0.51  TRYING [2]
% 0.20/0.52  TRYING [3]
% 1.43/0.56  TRYING [4]
% 1.43/0.60  TRYING [3]
% 1.43/0.61  TRYING [4]
% 2.28/0.72  TRYING [5]
% 4.88/1.07  TRYING [4]
% 5.73/1.21  TRYING [5]
% 6.86/1.34  TRYING [6]
% 7.83/1.48  % (18431)First to succeed.
% 7.83/1.49  % (18431)Refutation found. Thanks to Tanya!
% 7.83/1.49  % SZS status Theorem for theBenchmark
% 7.83/1.49  % SZS output start Proof for theBenchmark
% See solution above
% 7.83/1.49  % (18431)------------------------------
% 7.83/1.49  % (18431)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 7.83/1.49  % (18431)Termination reason: Refutation
% 7.83/1.49  
% 7.83/1.49  % (18431)Memory used [KB]: 11060
% 7.83/1.49  % (18431)Time elapsed: 1.104 s
% 7.83/1.49  % (18431)Instructions burned: 2941 (million)
% 7.83/1.49  % (18431)------------------------------
% 7.83/1.49  % (18431)------------------------------
% 7.83/1.49  % (18425)Success in time 1.122 s
%------------------------------------------------------------------------------