TSTP Solution File: SEU224+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU224+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n029.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 : Wed Aug 31 18:32:38 EDT 2022

% Result   : Theorem 1.49s 0.55s
% Output   : Refutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   65 (   7 unt;   0 def)
%            Number of atoms       :  334 (  58 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  418 ( 149   ~; 149   |;  91   &)
%                                         (  11 <=>;  16  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  156 ( 130   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f380,plain,
    $false,
    inference(subsumption_resolution,[],[f379,f359]) ).

fof(f359,plain,
    in(sK7,relation_dom(sK9)),
    inference(duplicate_literal_removal,[],[f351]) ).

fof(f351,plain,
    ( in(sK7,relation_dom(sK9))
    | in(sK7,relation_dom(sK9)) ),
    inference(resolution,[],[f299,f156]) ).

fof(f156,plain,
    ( in(sK7,relation_dom(relation_dom_restriction(sK9,sK8)))
    | in(sK7,relation_dom(sK9)) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ( ( ~ in(sK7,sK8)
      | ~ in(sK7,relation_dom(sK9))
      | ~ in(sK7,relation_dom(relation_dom_restriction(sK9,sK8))) )
    & ( ( in(sK7,sK8)
        & in(sK7,relation_dom(sK9)) )
      | in(sK7,relation_dom(relation_dom_restriction(sK9,sK8))) )
    & function(sK9)
    & relation(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f100,f101]) ).

fof(f101,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ in(X0,X1)
          | ~ in(X0,relation_dom(X2))
          | ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) )
        & ( ( in(X0,X1)
            & in(X0,relation_dom(X2)) )
          | in(X0,relation_dom(relation_dom_restriction(X2,X1))) )
        & function(X2)
        & relation(X2) )
   => ( ( ~ in(sK7,sK8)
        | ~ in(sK7,relation_dom(sK9))
        | ~ in(sK7,relation_dom(relation_dom_restriction(sK9,sK8))) )
      & ( ( in(sK7,sK8)
          & in(sK7,relation_dom(sK9)) )
        | in(sK7,relation_dom(relation_dom_restriction(sK9,sK8))) )
      & function(sK9)
      & relation(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X0,X1)
        | ~ in(X0,relation_dom(X2))
        | ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) )
      & ( ( in(X0,X1)
          & in(X0,relation_dom(X2)) )
        | in(X0,relation_dom(relation_dom_restriction(X2,X1))) )
      & function(X2)
      & relation(X2) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ? [X2,X0,X1] :
      ( ( ~ in(X2,X0)
        | ~ in(X2,relation_dom(X1))
        | ~ in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      & ( ( in(X2,X0)
          & in(X2,relation_dom(X1)) )
        | in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X2,X0,X1] :
      ( ( ~ in(X2,X0)
        | ~ in(X2,relation_dom(X1))
        | ~ in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      & ( ( in(X2,X0)
          & in(X2,relation_dom(X1)) )
        | in(X2,relation_dom(relation_dom_restriction(X1,X0))) )
      & function(X1)
      & relation(X1) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ? [X2,X0,X1] :
      ( ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
      <~> ( in(X2,X0)
          & in(X2,relation_dom(X1)) ) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ? [X2,X0,X1] :
      ( ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
      <~> ( in(X2,X0)
          & in(X2,relation_dom(X1)) ) )
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ~ ! [X2,X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ( in(X2,relation_dom(relation_dom_restriction(X1,X0)))
        <=> ( in(X2,X0)
            & in(X2,relation_dom(X1)) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( ( function(X2)
          & relation(X2) )
       => ( ( in(X1,relation_dom(X2))
            & in(X1,X0) )
        <=> in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ! [X0,X2,X1] :
      ( ( function(X2)
        & relation(X2) )
     => ( ( in(X1,relation_dom(X2))
          & in(X1,X0) )
      <=> in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).

fof(f299,plain,
    ! [X2,X3] :
      ( ~ in(X3,relation_dom(relation_dom_restriction(sK9,X2)))
      | in(X3,relation_dom(sK9)) ),
    inference(superposition,[],[f174,f289]) ).

fof(f289,plain,
    ! [X7] : relation_dom(relation_dom_restriction(sK9,X7)) = set_intersection2(relation_dom(sK9),X7),
    inference(subsumption_resolution,[],[f284,f154]) ).

fof(f154,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f102]) ).

fof(f284,plain,
    ! [X7] :
      ( relation_dom(relation_dom_restriction(sK9,X7)) = set_intersection2(relation_dom(sK9),X7)
      | ~ relation(sK9) ),
    inference(resolution,[],[f279,f155]) ).

fof(f155,plain,
    function(sK9),
    inference(cnf_transformation,[],[f102]) ).

fof(f279,plain,
    ! [X2,X0] :
      ( ~ function(X2)
      | relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0)
      | ~ relation(X2) ),
    inference(subsumption_resolution,[],[f278,f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_dom_restriction(X0,X1)) ),
    inference(rectify,[],[f73]) ).

fof(f73,plain,
    ! [X1,X0] :
      ( ~ relation(X1)
      | relation(relation_dom_restriction(X1,X0)) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( relation(X1)
     => relation(relation_dom_restriction(X1,X0)) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f278,plain,
    ! [X2,X0] :
      ( ~ function(X2)
      | relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0)
      | ~ relation(X2)
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(subsumption_resolution,[],[f176,f149]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X1,X0] :
      ( ~ relation(X1)
      | ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) )
      | ~ function(X1) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X1,X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( relation(relation_dom_restriction(X0,X1))
        & function(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f176,plain,
    ! [X2,X0] :
      ( ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(X2)
      | ~ relation(relation_dom_restriction(X2,X0))
      | relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0)
      | ~ function(X2) ),
    inference(equality_resolution,[],[f138]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( ~ function(X2)
      | ~ relation(X2)
      | relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 )
            & ( relation_dom_restriction(X2,X0) = X1
              | ( apply(X2,sK5(X1,X2)) != apply(X1,sK5(X1,X2))
                & in(sK5(X1,X2),relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) ) ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f90,f91]) ).

fof(f91,plain,
    ! [X1,X2] :
      ( ? [X4] :
          ( apply(X1,X4) != apply(X2,X4)
          & in(X4,relation_dom(X1)) )
     => ( apply(X2,sK5(X1,X2)) != apply(X1,sK5(X1,X2))
        & in(sK5(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 )
            & ( relation_dom_restriction(X2,X0) = X1
              | ? [X4] :
                  ( apply(X1,X4) != apply(X2,X4)
                  & in(X4,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) ) ) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ( ! [X3] :
                    ( apply(X2,X3) = apply(X0,X3)
                    | ~ in(X3,relation_dom(X0)) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ? [X3] :
                  ( apply(X2,X3) != apply(X0,X3)
                  & in(X3,relation_dom(X0)) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ( ! [X3] :
                    ( apply(X2,X3) = apply(X0,X3)
                    | ~ in(X3,relation_dom(X0)) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ? [X3] :
                  ( apply(X2,X3) != apply(X0,X3)
                  & in(X3,relation_dom(X0)) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ function(X2)
          | ~ relation(X2)
          | ( ( ! [X3] :
                  ( apply(X2,X3) = apply(X0,X3)
                  | ~ in(X3,relation_dom(X0)) )
              & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
          <=> relation_dom_restriction(X2,X1) = X0 ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( ! [X3] :
                  ( apply(X2,X3) = apply(X0,X3)
                  | ~ in(X3,relation_dom(X0)) )
              & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
          <=> relation_dom_restriction(X2,X1) = X0 )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
              & ! [X3] :
                  ( in(X3,relation_dom(X0))
                 => apply(X2,X3) = apply(X0,X3) ) )
          <=> relation_dom_restriction(X2,X1) = X0 ) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
          <=> relation_dom_restriction(X2,X0) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

fof(f174,plain,
    ! [X2,X1,X4] :
      ( ~ in(X4,set_intersection2(X2,X1))
      | in(X4,X2) ),
    inference(equality_resolution,[],[f121]) ).

fof(f121,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_intersection2(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X2,X1) = X0
        | ( ( ~ in(sK2(X0,X1,X2),X1)
            | ~ in(sK2(X0,X1,X2),X2)
            | ~ in(sK2(X0,X1,X2),X0) )
          & ( ( in(sK2(X0,X1,X2),X1)
              & in(sK2(X0,X1,X2),X2) )
            | in(sK2(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( ( in(X4,X1)
                & in(X4,X2) )
              | ~ in(X4,X0) ) )
        | set_intersection2(X2,X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X2)
            | ~ in(X3,X0) )
          & ( ( in(X3,X1)
              & in(X3,X2) )
            | in(X3,X0) ) )
     => ( ( ~ in(sK2(X0,X1,X2),X1)
          | ~ in(sK2(X0,X1,X2),X2)
          | ~ in(sK2(X0,X1,X2),X0) )
        & ( ( in(sK2(X0,X1,X2),X1)
            & in(sK2(X0,X1,X2),X2) )
          | in(sK2(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X2)
              | ~ in(X3,X0) )
            & ( ( in(X3,X1)
                & in(X3,X2) )
              | in(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( ( in(X4,X1)
                & in(X4,X2) )
              | ~ in(X4,X0) ) )
        | set_intersection2(X2,X1) != X0 ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X1,X0,X2] :
      ( ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) ) )
        | set_intersection2(X2,X0) != X1 ) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X1,X0,X2] :
      ( ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X2)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) ) )
        | set_intersection2(X2,X0) != X1 ) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X1,X0,X2] :
      ( set_intersection2(X2,X0) = X1
    <=> ! [X3] :
          ( in(X3,X1)
        <=> ( in(X3,X0)
            & in(X3,X2) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X2,X0] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) )
    <=> set_intersection2(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f379,plain,
    ~ in(sK7,relation_dom(sK9)),
    inference(subsumption_resolution,[],[f377,f335]) ).

fof(f335,plain,
    in(sK7,sK8),
    inference(duplicate_literal_removal,[],[f328]) ).

fof(f328,plain,
    ( in(sK7,sK8)
    | in(sK7,sK8) ),
    inference(resolution,[],[f300,f157]) ).

fof(f157,plain,
    ( in(sK7,relation_dom(relation_dom_restriction(sK9,sK8)))
    | in(sK7,sK8) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f300,plain,
    ! [X4,X5] :
      ( ~ in(X5,relation_dom(relation_dom_restriction(sK9,X4)))
      | in(X5,X4) ),
    inference(superposition,[],[f173,f289]) ).

fof(f173,plain,
    ! [X2,X1,X4] :
      ( ~ in(X4,set_intersection2(X2,X1))
      | in(X4,X1) ),
    inference(equality_resolution,[],[f122]) ).

fof(f122,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f377,plain,
    ( ~ in(sK7,sK8)
    | ~ in(sK7,relation_dom(sK9)) ),
    inference(duplicate_literal_removal,[],[f374]) ).

fof(f374,plain,
    ( ~ in(sK7,relation_dom(sK9))
    | ~ in(sK7,relation_dom(sK9))
    | ~ in(sK7,sK8)
    | ~ in(sK7,sK8) ),
    inference(resolution,[],[f298,f158]) ).

fof(f158,plain,
    ( ~ in(sK7,relation_dom(relation_dom_restriction(sK9,sK8)))
    | ~ in(sK7,relation_dom(sK9))
    | ~ in(sK7,sK8) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f298,plain,
    ! [X0,X1] :
      ( in(X1,relation_dom(relation_dom_restriction(sK9,X0)))
      | ~ in(X1,X0)
      | ~ in(X1,relation_dom(sK9)) ),
    inference(superposition,[],[f172,f289]) ).

fof(f172,plain,
    ! [X2,X1,X4] :
      ( in(X4,set_intersection2(X2,X1))
      | ~ in(X4,X2)
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f123]) ).

fof(f123,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X1)
      | ~ in(X4,X2)
      | set_intersection2(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU224+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 15:02:27 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (30636)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (30654)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.50  % (30642)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (30650)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51  TRYING [1]
% 0.19/0.51  % (30639)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (30645)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51  % (30658)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52  TRYING [2]
% 0.19/0.52  % (30633)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52  % (30661)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.52  % (30633)Refutation not found, incomplete strategy% (30633)------------------------------
% 0.19/0.52  % (30633)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (30633)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (30633)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (30633)Memory used [KB]: 5628
% 0.19/0.52  % (30633)Time elapsed: 0.116 s
% 0.19/0.52  % (30633)Instructions burned: 7 (million)
% 0.19/0.52  % (30633)------------------------------
% 0.19/0.52  % (30633)------------------------------
% 0.19/0.52  % (30634)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52  % (30655)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52  TRYING [3]
% 0.19/0.52  % (30637)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52  % (30632)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52  % (30647)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53  % (30635)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (30662)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.53  TRYING [1]
% 0.19/0.53  % (30649)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.53  % (30653)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.53  % (30652)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (30638)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (30651)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (30641)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (30640)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54  % (30640)Instruction limit reached!
% 0.19/0.54  % (30640)------------------------------
% 0.19/0.54  % (30640)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (30640)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (30640)Termination reason: Unknown
% 0.19/0.54  % (30640)Termination phase: Preprocessing 3
% 0.19/0.54  
% 0.19/0.54  % (30640)Memory used [KB]: 895
% 0.19/0.54  % (30640)Time elapsed: 0.002 s
% 0.19/0.54  % (30640)Instructions burned: 2 (million)
% 0.19/0.54  % (30640)------------------------------
% 0.19/0.54  % (30640)------------------------------
% 0.19/0.54  TRYING [1]
% 0.19/0.54  TRYING [2]
% 0.19/0.54  % (30646)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.54  % (30644)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.54  TRYING [3]
% 1.49/0.54  % (30639)Instruction limit reached!
% 1.49/0.54  % (30639)------------------------------
% 1.49/0.54  % (30639)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.54  % (30639)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.54  % (30639)Termination reason: Unknown
% 1.49/0.54  % (30639)Termination phase: Saturation
% 1.49/0.54  
% 1.49/0.54  % (30639)Memory used [KB]: 5500
% 1.49/0.54  % (30639)Time elapsed: 0.116 s
% 1.49/0.54  % (30639)Instructions burned: 7 (million)
% 1.49/0.54  % (30639)------------------------------
% 1.49/0.54  % (30639)------------------------------
% 1.49/0.54  % (30660)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.49/0.54  TRYING [2]
% 1.49/0.54  % (30659)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.49/0.54  % (30648)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.49/0.55  TRYING [3]
% 1.49/0.55  % (30656)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.49/0.55  % (30655)First to succeed.
% 1.49/0.55  % (30655)Refutation found. Thanks to Tanya!
% 1.49/0.55  % SZS status Theorem for theBenchmark
% 1.49/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.55  % (30655)------------------------------
% 1.49/0.55  % (30655)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.55  % (30655)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.55  % (30655)Termination reason: Refutation
% 1.49/0.55  
% 1.49/0.55  % (30655)Memory used [KB]: 1151
% 1.49/0.55  % (30655)Time elapsed: 0.095 s
% 1.49/0.55  % (30655)Instructions burned: 11 (million)
% 1.49/0.55  % (30655)------------------------------
% 1.49/0.55  % (30655)------------------------------
% 1.49/0.55  % (30631)Success in time 0.203 s
%------------------------------------------------------------------------------