TSTP Solution File: SEU058+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU058+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n002.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 18:26:30 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  103 (   8 unt;   0 def)
%            Number of atoms       :  436 (  40 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  557 ( 224   ~; 238   |;  67   &)
%                                         (  21 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  11 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  146 ( 129   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f551,plain,
    $false,
    inference(avatar_sat_refutation,[],[f219,f268,f271,f325,f332,f356,f362,f382,f387,f400,f401,f508,f513,f532,f533,f536,f550]) ).

fof(f550,plain,
    ( ~ spl13_8
    | ~ spl13_7
    | ~ spl13_33
    | ~ spl13_5
    | spl13_23 ),
    inference(avatar_split_clause,[],[f539,f296,f200,f384,f208,f212]) ).

fof(f212,plain,
    ( spl13_8
  <=> relation(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f208,plain,
    ( spl13_7
  <=> function(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f384,plain,
    ( spl13_33
  <=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).

fof(f200,plain,
    ( spl13_5
  <=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f296,plain,
    ( spl13_23
  <=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f539,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
    | ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
    | ~ function(sK9)
    | ~ relation(sK9)
    | spl13_23 ),
    inference(resolution,[],[f298,f159]) ).

fof(f159,plain,
    ! [X0,X1,X4] :
      ( in(X4,relation_inverse_image(X0,X1))
      | ~ in(X4,relation_dom(X0))
      | ~ in(apply(X0,X4),X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f132]) ).

fof(f132,plain,
    ! [X2,X0,X1,X4] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X4,X2)
      | ~ in(X4,relation_dom(X0))
      | ~ in(apply(X0,X4),X1)
      | relation_inverse_image(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ( ( ~ in(sK5(X0,X1,X2),X2)
                | ~ in(sK5(X0,X1,X2),relation_dom(X0))
                | ~ in(apply(X0,sK5(X0,X1,X2)),X1) )
              & ( in(sK5(X0,X1,X2),X2)
                | ( in(sK5(X0,X1,X2),relation_dom(X0))
                  & in(apply(X0,sK5(X0,X1,X2)),X1) ) ) ) )
          & ( ! [X4] :
                ( ( ( in(X4,relation_dom(X0))
                    & in(apply(X0,X4),X1) )
                  | ~ in(X4,X2) )
                & ( in(X4,X2)
                  | ~ in(X4,relation_dom(X0))
                  | ~ in(apply(X0,X4),X1) ) )
            | relation_inverse_image(X0,X1) != X2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f90,f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X2)
            | ~ in(X3,relation_dom(X0))
            | ~ in(apply(X0,X3),X1) )
          & ( in(X3,X2)
            | ( in(X3,relation_dom(X0))
              & in(apply(X0,X3),X1) ) ) )
     => ( ( ~ in(sK5(X0,X1,X2),X2)
          | ~ in(sK5(X0,X1,X2),relation_dom(X0))
          | ~ in(apply(X0,sK5(X0,X1,X2)),X1) )
        & ( in(sK5(X0,X1,X2),X2)
          | ( in(sK5(X0,X1,X2),relation_dom(X0))
            & in(apply(X0,sK5(X0,X1,X2)),X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f88,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,X2)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1) )
                & ( in(X3,X2)
                  | ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) ) ) ) )
          & ( ! [X3] :
                ( ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) )
                  | ~ in(X3,X2) )
                & ( in(X3,X2)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1) ) )
            | relation_inverse_image(X0,X1) != X2 ) ) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) )
            <=> in(X3,X2) ) ) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) )
            <=> in(X3,X2) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) )
            <=> in(X3,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).

fof(f298,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
    | spl13_23 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f536,plain,
    ( ~ spl13_23
    | ~ spl13_24
    | spl13_9 ),
    inference(avatar_split_clause,[],[f534,f216,f300,f296]) ).

fof(f300,plain,
    ( spl13_24
  <=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f216,plain,
    ( spl13_9
  <=> in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f534,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
    | ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
    | spl13_9 ),
    inference(resolution,[],[f218,f156]) ).

fof(f156,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_intersection2(X0,X1))
      | ~ in(X4,X0)
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f119]) ).

fof(f119,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ( ( ~ in(sK3(X0,X1,X2),X2)
            | ~ in(sK3(X0,X1,X2),X1)
            | ~ in(sK3(X0,X1,X2),X0) )
          & ( in(sK3(X0,X1,X2),X2)
            | ( in(sK3(X0,X1,X2),X1)
              & in(sK3(X0,X1,X2),X0) ) ) ) )
      & ( ! [X4] :
            ( ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) )
            & ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X2)
            | ~ in(X3,X1)
            | ~ in(X3,X0) )
          & ( in(X3,X2)
            | ( in(X3,X1)
              & in(X3,X0) ) ) )
     => ( ( ~ in(sK3(X0,X1,X2),X2)
          | ~ in(sK3(X0,X1,X2),X1)
          | ~ in(sK3(X0,X1,X2),X0) )
        & ( in(sK3(X0,X1,X2),X2)
          | ( in(sK3(X0,X1,X2),X1)
            & in(sK3(X0,X1,X2),X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ( set_intersection2(X2,X0) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | ( in(X3,X0)
                & in(X3,X2) ) ) ) )
      & ( ! [X3] :
            ( ( ( in(X3,X0)
                & in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_intersection2(X2,X0) != X1 ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( set_intersection2(X2,X0) = X1
    <=> ! [X3] :
          ( ( in(X3,X0)
            & in(X3,X2) )
        <=> in(X3,X1) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,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(f218,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | spl13_9 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f533,plain,
    ( spl13_33
    | ~ spl13_6 ),
    inference(avatar_split_clause,[],[f525,f204,f384]) ).

fof(f204,plain,
    ( spl13_6
  <=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f525,plain,
    ( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
    | ~ spl13_6 ),
    inference(resolution,[],[f205,f154]) ).

fof(f154,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X1) ),
    inference(equality_resolution,[],[f121]) ).

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

fof(f205,plain,
    ( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
    | ~ spl13_6 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f532,plain,
    ( spl13_28
    | ~ spl13_6 ),
    inference(avatar_split_clause,[],[f526,f204,f322]) ).

fof(f322,plain,
    ( spl13_28
  <=> in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).

fof(f526,plain,
    ( in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
    | ~ spl13_6 ),
    inference(resolution,[],[f205,f155]) ).

fof(f155,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_intersection2(X0,X1))
      | in(X4,X0) ),
    inference(equality_resolution,[],[f120]) ).

fof(f120,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f83]) ).

fof(f513,plain,
    ( ~ spl13_23
    | ~ spl13_8
    | ~ spl13_7
    | spl13_33 ),
    inference(avatar_split_clause,[],[f511,f384,f208,f212,f296]) ).

fof(f511,plain,
    ( ~ function(sK9)
    | ~ relation(sK9)
    | ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
    | spl13_33 ),
    inference(resolution,[],[f386,f158]) ).

fof(f158,plain,
    ! [X0,X1,X4] :
      ( in(apply(X0,X4),X1)
      | ~ function(X0)
      | ~ relation(X0)
      | ~ in(X4,relation_inverse_image(X0,X1)) ),
    inference(equality_resolution,[],[f133]) ).

fof(f133,plain,
    ! [X2,X0,X1,X4] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(apply(X0,X4),X1)
      | ~ in(X4,X2)
      | relation_inverse_image(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f92]) ).

fof(f386,plain,
    ( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
    | spl13_33 ),
    inference(avatar_component_clause,[],[f384]) ).

fof(f508,plain,
    ( ~ spl13_7
    | ~ spl13_8
    | ~ spl13_24
    | spl13_28 ),
    inference(avatar_split_clause,[],[f501,f322,f300,f212,f208]) ).

fof(f501,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
    | ~ relation(sK9)
    | ~ function(sK9)
    | spl13_28 ),
    inference(resolution,[],[f324,f158]) ).

fof(f324,plain,
    ( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
    | spl13_28 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f401,plain,
    ( spl13_23
    | ~ spl13_9 ),
    inference(avatar_split_clause,[],[f394,f216,f296]) ).

fof(f394,plain,
    ( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
    | ~ spl13_9 ),
    inference(resolution,[],[f217,f154]) ).

fof(f217,plain,
    ( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | ~ spl13_9 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f400,plain,
    ( spl13_24
    | ~ spl13_9 ),
    inference(avatar_split_clause,[],[f395,f216,f300]) ).

fof(f395,plain,
    ( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
    | ~ spl13_9 ),
    inference(resolution,[],[f217,f155]) ).

fof(f387,plain,
    ( ~ spl13_33
    | ~ spl13_28
    | spl13_6 ),
    inference(avatar_split_clause,[],[f371,f204,f322,f384]) ).

fof(f371,plain,
    ( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
    | ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK10)
    | spl13_6 ),
    inference(resolution,[],[f206,f156]) ).

fof(f206,plain,
    ( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
    | spl13_6 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f382,plain,
    ( spl13_29
    | ~ spl13_7
    | spl13_9
    | ~ spl13_8
    | spl13_6 ),
    inference(avatar_split_clause,[],[f370,f204,f212,f216,f208,f329]) ).

fof(f329,plain,
    ( spl13_29
  <=> sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).

fof(f370,plain,
    ( ~ relation(sK9)
    | in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | ~ function(sK9)
    | sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | spl13_6 ),
    inference(resolution,[],[f206,f169]) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( in(apply(X0,sK5(X0,X1,X2)),X1)
      | sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
      | ~ function(X0)
      | ~ relation(X0)
      | in(sK5(X0,X1,X2),X2) ),
    inference(equality_proxy_replacement,[],[f135,f160]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( sQ12_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).

fof(f135,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | relation_inverse_image(X0,X1) = X2
      | in(sK5(X0,X1,X2),X2)
      | in(apply(X0,sK5(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f362,plain,
    ~ spl13_29,
    inference(avatar_contradiction_clause,[],[f361]) ).

fof(f361,plain,
    ( $false
    | ~ spl13_29 ),
    inference(resolution,[],[f331,f171]) ).

fof(f171,plain,
    ~ sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),
    inference(equality_proxy_replacement,[],[f148,f160]) ).

fof(f148,plain,
    relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ( relation(sK9)
    & function(sK9)
    & relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f53,f98]) ).

fof(f98,plain,
    ( ? [X0,X1,X2] :
        ( relation(X1)
        & function(X1)
        & relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) )
   => ( relation(sK9)
      & function(sK9)
      & relation_inverse_image(sK9,set_intersection2(sK8,sK10)) != set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( relation(X1)
      & function(X1)
      & relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ? [X1,X2,X0] :
      ( relation_inverse_image(X1,set_intersection2(X0,X2)) != set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2))
      & relation(X1)
      & function(X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ~ ! [X1,X2,X0] :
        ( ( relation(X1)
          & function(X1) )
       => relation_inverse_image(X1,set_intersection2(X0,X2)) = set_intersection2(relation_inverse_image(X1,X0),relation_inverse_image(X1,X2)) ),
    inference(rectify,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( ( relation(X2)
          & function(X2) )
       => relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0,X2,X1] :
      ( ( relation(X2)
        & function(X2) )
     => relation_inverse_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_funct_1) ).

fof(f331,plain,
    ( sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | ~ spl13_29 ),
    inference(avatar_component_clause,[],[f329]) ).

fof(f356,plain,
    ( spl13_5
    | ~ spl13_8
    | ~ spl13_7
    | ~ spl13_23 ),
    inference(avatar_split_clause,[],[f351,f296,f208,f212,f200]) ).

fof(f351,plain,
    ( ~ function(sK9)
    | ~ relation(sK9)
    | in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
    | ~ spl13_23 ),
    inference(resolution,[],[f297,f157]) ).

fof(f157,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,relation_inverse_image(X0,X1))
      | in(X4,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f134]) ).

fof(f134,plain,
    ! [X2,X0,X1,X4] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(X4,relation_dom(X0))
      | ~ in(X4,X2)
      | relation_inverse_image(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f92]) ).

fof(f297,plain,
    ( in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK10))
    | ~ spl13_23 ),
    inference(avatar_component_clause,[],[f296]) ).

fof(f332,plain,
    ( spl13_9
    | ~ spl13_8
    | ~ spl13_7
    | spl13_29
    | spl13_5 ),
    inference(avatar_split_clause,[],[f326,f200,f329,f208,f212,f216]) ).

fof(f326,plain,
    ( sQ12_eqProxy(relation_inverse_image(sK9,set_intersection2(sK8,sK10)),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | ~ function(sK9)
    | ~ relation(sK9)
    | in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | spl13_5 ),
    inference(resolution,[],[f202,f168]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( in(sK5(X0,X1,X2),relation_dom(X0))
      | in(sK5(X0,X1,X2),X2)
      | ~ function(X0)
      | sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
      | ~ relation(X0) ),
    inference(equality_proxy_replacement,[],[f136,f160]) ).

fof(f136,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | relation_inverse_image(X0,X1) = X2
      | in(sK5(X0,X1,X2),X2)
      | in(sK5(X0,X1,X2),relation_dom(X0)) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f202,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
    | spl13_5 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f325,plain,
    ( ~ spl13_7
    | ~ spl13_5
    | ~ spl13_8
    | ~ spl13_28
    | spl13_24 ),
    inference(avatar_split_clause,[],[f314,f300,f322,f212,f200,f208]) ).

fof(f314,plain,
    ( ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),sK8)
    | ~ relation(sK9)
    | ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9))
    | ~ function(sK9)
    | spl13_24 ),
    inference(resolution,[],[f302,f159]) ).

fof(f302,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_inverse_image(sK9,sK8))
    | spl13_24 ),
    inference(avatar_component_clause,[],[f300]) ).

fof(f271,plain,
    spl13_8,
    inference(avatar_contradiction_clause,[],[f269]) ).

fof(f269,plain,
    ( $false
    | spl13_8 ),
    inference(resolution,[],[f214,f150]) ).

fof(f150,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f99]) ).

fof(f214,plain,
    ( ~ relation(sK9)
    | spl13_8 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f268,plain,
    spl13_7,
    inference(avatar_contradiction_clause,[],[f266]) ).

fof(f266,plain,
    ( $false
    | spl13_7 ),
    inference(resolution,[],[f210,f149]) ).

fof(f149,plain,
    function(sK9),
    inference(cnf_transformation,[],[f99]) ).

fof(f210,plain,
    ( ~ function(sK9)
    | spl13_7 ),
    inference(avatar_component_clause,[],[f208]) ).

fof(f219,plain,
    ( ~ spl13_5
    | ~ spl13_6
    | ~ spl13_7
    | ~ spl13_8
    | ~ spl13_9 ),
    inference(avatar_split_clause,[],[f177,f216,f212,f208,f204,f200]) ).

fof(f177,plain,
    ( ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))
    | ~ relation(sK9)
    | ~ function(sK9)
    | ~ in(apply(sK9,sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10)))),set_intersection2(sK8,sK10))
    | ~ in(sK5(sK9,set_intersection2(sK8,sK10),set_intersection2(relation_inverse_image(sK9,sK8),relation_inverse_image(sK9,sK10))),relation_dom(sK9)) ),
    inference(resolution,[],[f171,f167]) ).

fof(f167,plain,
    ! [X2,X0,X1] :
      ( sQ12_eqProxy(relation_inverse_image(X0,X1),X2)
      | ~ relation(X0)
      | ~ in(sK5(X0,X1,X2),relation_dom(X0))
      | ~ in(sK5(X0,X1,X2),X2)
      | ~ in(apply(X0,sK5(X0,X1,X2)),X1)
      | ~ function(X0) ),
    inference(equality_proxy_replacement,[],[f137,f160]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | relation_inverse_image(X0,X1) = X2
      | ~ in(sK5(X0,X1,X2),X2)
      | ~ in(sK5(X0,X1,X2),relation_dom(X0))
      | ~ in(apply(X0,sK5(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU058+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:47:59 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (872)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50  % (891)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.50  % (867)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50  % (869)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50  % (893)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.51  % (883)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.51  % (891)Instruction limit reached!
% 0.19/0.51  % (891)------------------------------
% 0.19/0.51  % (891)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (887)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (882)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.52  % (888)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.52  % (882)First to succeed.
% 0.19/0.52  % (891)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (891)Termination reason: Unknown
% 0.19/0.52  % (891)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (891)Memory used [KB]: 6140
% 0.19/0.52  % (891)Time elapsed: 0.100 s
% 0.19/0.52  % (891)Instructions burned: 9 (million)
% 0.19/0.52  % (891)------------------------------
% 0.19/0.52  % (891)------------------------------
% 0.19/0.52  % (873)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.52  % (864)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.52  % (866)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (864)Refutation not found, incomplete strategy% (864)------------------------------
% 0.19/0.52  % (864)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (864)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (864)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (864)Memory used [KB]: 6012
% 0.19/0.52  % (864)Time elapsed: 0.114 s
% 0.19/0.52  % (864)Instructions burned: 3 (million)
% 0.19/0.52  % (864)------------------------------
% 0.19/0.52  % (864)------------------------------
% 0.19/0.52  % (878)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53  % (871)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.53  % (882)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53  % (882)------------------------------
% 0.19/0.53  % (882)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (882)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (882)Termination reason: Refutation
% 0.19/0.53  
% 0.19/0.53  % (882)Memory used [KB]: 6268
% 0.19/0.53  % (882)Time elapsed: 0.125 s
% 0.19/0.53  % (882)Instructions burned: 8 (million)
% 0.19/0.53  % (882)------------------------------
% 0.19/0.53  % (882)------------------------------
% 0.19/0.53  % (862)Success in time 0.177 s
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