TSTP Solution File: SET685+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET685+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n012.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 18:21:53 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   83 (   9 unt;   0 def)
%            Number of atoms       :  515 (   4 equ)
%            Maximal formula atoms :   32 (   6 avg)
%            Number of connectives :  664 ( 232   ~; 197   |; 180   &)
%                                         (  13 <=>;  40  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   8 con; 0-4 aty)
%            Number of variables   :  202 ( 129   !;  73   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f331,plain,
    $false,
    inference(avatar_sat_refutation,[],[f193,f197,f202,f314,f330]) ).

fof(f330,plain,
    ( spl17_2
    | ~ spl17_3
    | ~ spl17_5 ),
    inference(avatar_contradiction_clause,[],[f329]) ).

fof(f329,plain,
    ( $false
    | spl17_2
    | ~ spl17_3
    | ~ spl17_5 ),
    inference(subsumption_resolution,[],[f322,f315]) ).

fof(f315,plain,
    ( ~ member(sK4,image(sK3,sK1))
    | spl17_2 ),
    inference(forward_demodulation,[],[f186,f215]) ).

fof(f215,plain,
    ! [X0] : image(sK3,X0) = image4(sK2,sK0,sK3,X0),
    inference(unit_resulting_resolution,[],[f130,f130,f130,f112,f149]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type)
      | image4(X0,X1,X2,X3) = image(X2,X3)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ~ ilf_type(X3,set_type)
                  | image4(X0,X1,X2,X3) = image(X2,X3) )
              | ~ ilf_type(X2,relation_type(X0,X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).

fof(f112,plain,
    ilf_type(sK3,relation_type(sK2,sK0)),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ( ilf_type(sK0,set_type)
    & ~ empty(sK0)
    & ilf_type(sK1,set_type)
    & ~ empty(sK1)
    & ilf_type(sK2,set_type)
    & ilf_type(sK4,member_type(sK0))
    & ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
      | ! [X5] :
          ( ~ ilf_type(X5,member_type(sK2))
          | ~ member(ordered_pair(X5,sK4),sK3)
          | ~ member(X5,sK1) ) )
    & ( member(sK4,image4(sK2,sK0,sK3,sK1))
      | ( ilf_type(sK5,member_type(sK2))
        & member(ordered_pair(sK5,sK4),sK3)
        & member(sK5,sK1) ) )
    & ilf_type(sK3,relation_type(sK2,sK0))
    & ~ empty(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f65,f71,f70,f69,f68,f67,f66]) ).

fof(f66,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ~ empty(X0)
        & ? [X1] :
            ( ilf_type(X1,set_type)
            & ~ empty(X1)
            & ? [X2] :
                ( ilf_type(X2,set_type)
                & ? [X3] :
                    ( ? [X4] :
                        ( ilf_type(X4,member_type(X0))
                        & ( ~ member(X4,image4(X2,X0,X3,X1))
                          | ! [X5] :
                              ( ~ ilf_type(X5,member_type(X2))
                              | ~ member(ordered_pair(X5,X4),X3)
                              | ~ member(X5,X1) ) )
                        & ( member(X4,image4(X2,X0,X3,X1))
                          | ? [X6] :
                              ( ilf_type(X6,member_type(X2))
                              & member(ordered_pair(X6,X4),X3)
                              & member(X6,X1) ) ) )
                    & ilf_type(X3,relation_type(X2,X0)) )
                & ~ empty(X2) ) ) )
   => ( ilf_type(sK0,set_type)
      & ~ empty(sK0)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ~ empty(X1)
          & ? [X2] :
              ( ilf_type(X2,set_type)
              & ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(sK0))
                      & ( ~ member(X4,image4(X2,sK0,X3,X1))
                        | ! [X5] :
                            ( ~ ilf_type(X5,member_type(X2))
                            | ~ member(ordered_pair(X5,X4),X3)
                            | ~ member(X5,X1) ) )
                      & ( member(X4,image4(X2,sK0,X3,X1))
                        | ? [X6] :
                            ( ilf_type(X6,member_type(X2))
                            & member(ordered_pair(X6,X4),X3)
                            & member(X6,X1) ) ) )
                  & ilf_type(X3,relation_type(X2,sK0)) )
              & ~ empty(X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ( ? [X1] :
        ( ilf_type(X1,set_type)
        & ~ empty(X1)
        & ? [X2] :
            ( ilf_type(X2,set_type)
            & ? [X3] :
                ( ? [X4] :
                    ( ilf_type(X4,member_type(sK0))
                    & ( ~ member(X4,image4(X2,sK0,X3,X1))
                      | ! [X5] :
                          ( ~ ilf_type(X5,member_type(X2))
                          | ~ member(ordered_pair(X5,X4),X3)
                          | ~ member(X5,X1) ) )
                    & ( member(X4,image4(X2,sK0,X3,X1))
                      | ? [X6] :
                          ( ilf_type(X6,member_type(X2))
                          & member(ordered_pair(X6,X4),X3)
                          & member(X6,X1) ) ) )
                & ilf_type(X3,relation_type(X2,sK0)) )
            & ~ empty(X2) ) )
   => ( ilf_type(sK1,set_type)
      & ~ empty(sK1)
      & ? [X2] :
          ( ilf_type(X2,set_type)
          & ? [X3] :
              ( ? [X4] :
                  ( ilf_type(X4,member_type(sK0))
                  & ( ~ member(X4,image4(X2,sK0,X3,sK1))
                    | ! [X5] :
                        ( ~ ilf_type(X5,member_type(X2))
                        | ~ member(ordered_pair(X5,X4),X3)
                        | ~ member(X5,sK1) ) )
                  & ( member(X4,image4(X2,sK0,X3,sK1))
                    | ? [X6] :
                        ( ilf_type(X6,member_type(X2))
                        & member(ordered_pair(X6,X4),X3)
                        & member(X6,sK1) ) ) )
              & ilf_type(X3,relation_type(X2,sK0)) )
          & ~ empty(X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ( ? [X2] :
        ( ilf_type(X2,set_type)
        & ? [X3] :
            ( ? [X4] :
                ( ilf_type(X4,member_type(sK0))
                & ( ~ member(X4,image4(X2,sK0,X3,sK1))
                  | ! [X5] :
                      ( ~ ilf_type(X5,member_type(X2))
                      | ~ member(ordered_pair(X5,X4),X3)
                      | ~ member(X5,sK1) ) )
                & ( member(X4,image4(X2,sK0,X3,sK1))
                  | ? [X6] :
                      ( ilf_type(X6,member_type(X2))
                      & member(ordered_pair(X6,X4),X3)
                      & member(X6,sK1) ) ) )
            & ilf_type(X3,relation_type(X2,sK0)) )
        & ~ empty(X2) )
   => ( ilf_type(sK2,set_type)
      & ? [X3] :
          ( ? [X4] :
              ( ilf_type(X4,member_type(sK0))
              & ( ~ member(X4,image4(sK2,sK0,X3,sK1))
                | ! [X5] :
                    ( ~ ilf_type(X5,member_type(sK2))
                    | ~ member(ordered_pair(X5,X4),X3)
                    | ~ member(X5,sK1) ) )
              & ( member(X4,image4(sK2,sK0,X3,sK1))
                | ? [X6] :
                    ( ilf_type(X6,member_type(sK2))
                    & member(ordered_pair(X6,X4),X3)
                    & member(X6,sK1) ) ) )
          & ilf_type(X3,relation_type(sK2,sK0)) )
      & ~ empty(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ilf_type(X4,member_type(sK0))
            & ( ~ member(X4,image4(sK2,sK0,X3,sK1))
              | ! [X5] :
                  ( ~ ilf_type(X5,member_type(sK2))
                  | ~ member(ordered_pair(X5,X4),X3)
                  | ~ member(X5,sK1) ) )
            & ( member(X4,image4(sK2,sK0,X3,sK1))
              | ? [X6] :
                  ( ilf_type(X6,member_type(sK2))
                  & member(ordered_pair(X6,X4),X3)
                  & member(X6,sK1) ) ) )
        & ilf_type(X3,relation_type(sK2,sK0)) )
   => ( ? [X4] :
          ( ilf_type(X4,member_type(sK0))
          & ( ~ member(X4,image4(sK2,sK0,sK3,sK1))
            | ! [X5] :
                ( ~ ilf_type(X5,member_type(sK2))
                | ~ member(ordered_pair(X5,X4),sK3)
                | ~ member(X5,sK1) ) )
          & ( member(X4,image4(sK2,sK0,sK3,sK1))
            | ? [X6] :
                ( ilf_type(X6,member_type(sK2))
                & member(ordered_pair(X6,X4),sK3)
                & member(X6,sK1) ) ) )
      & ilf_type(sK3,relation_type(sK2,sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ( ? [X4] :
        ( ilf_type(X4,member_type(sK0))
        & ( ~ member(X4,image4(sK2,sK0,sK3,sK1))
          | ! [X5] :
              ( ~ ilf_type(X5,member_type(sK2))
              | ~ member(ordered_pair(X5,X4),sK3)
              | ~ member(X5,sK1) ) )
        & ( member(X4,image4(sK2,sK0,sK3,sK1))
          | ? [X6] :
              ( ilf_type(X6,member_type(sK2))
              & member(ordered_pair(X6,X4),sK3)
              & member(X6,sK1) ) ) )
   => ( ilf_type(sK4,member_type(sK0))
      & ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
        | ! [X5] :
            ( ~ ilf_type(X5,member_type(sK2))
            | ~ member(ordered_pair(X5,sK4),sK3)
            | ~ member(X5,sK1) ) )
      & ( member(sK4,image4(sK2,sK0,sK3,sK1))
        | ? [X6] :
            ( ilf_type(X6,member_type(sK2))
            & member(ordered_pair(X6,sK4),sK3)
            & member(X6,sK1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ( ? [X6] :
        ( ilf_type(X6,member_type(sK2))
        & member(ordered_pair(X6,sK4),sK3)
        & member(X6,sK1) )
   => ( ilf_type(sK5,member_type(sK2))
      & member(ordered_pair(sK5,sK4),sK3)
      & member(sK5,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ~ empty(X0)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ~ empty(X1)
          & ? [X2] :
              ( ilf_type(X2,set_type)
              & ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(X0))
                      & ( ~ member(X4,image4(X2,X0,X3,X1))
                        | ! [X5] :
                            ( ~ ilf_type(X5,member_type(X2))
                            | ~ member(ordered_pair(X5,X4),X3)
                            | ~ member(X5,X1) ) )
                      & ( member(X4,image4(X2,X0,X3,X1))
                        | ? [X6] :
                            ( ilf_type(X6,member_type(X2))
                            & member(ordered_pair(X6,X4),X3)
                            & member(X6,X1) ) ) )
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ~ empty(X2) ) ) ),
    inference(rectify,[],[f64]) ).

fof(f64,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ~ empty(X0)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ~ empty(X1)
          & ? [X2] :
              ( ilf_type(X2,set_type)
              & ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(X0))
                      & ( ~ member(X4,image4(X2,X0,X3,X1))
                        | ! [X5] :
                            ( ~ ilf_type(X5,member_type(X2))
                            | ~ member(ordered_pair(X5,X4),X3)
                            | ~ member(X5,X1) ) )
                      & ( member(X4,image4(X2,X0,X3,X1))
                        | ? [X5] :
                            ( ilf_type(X5,member_type(X2))
                            & member(ordered_pair(X5,X4),X3)
                            & member(X5,X1) ) ) )
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ~ empty(X2) ) ) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ~ empty(X0)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ~ empty(X1)
          & ? [X2] :
              ( ilf_type(X2,set_type)
              & ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(X0))
                      & ( ~ member(X4,image4(X2,X0,X3,X1))
                        | ! [X5] :
                            ( ~ ilf_type(X5,member_type(X2))
                            | ~ member(ordered_pair(X5,X4),X3)
                            | ~ member(X5,X1) ) )
                      & ( member(X4,image4(X2,X0,X3,X1))
                        | ? [X5] :
                            ( ilf_type(X5,member_type(X2))
                            & member(ordered_pair(X5,X4),X3)
                            & member(X5,X1) ) ) )
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ~ empty(X2) ) ) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ~ empty(X0)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ~ empty(X1)
          & ? [X2] :
              ( ilf_type(X2,set_type)
              & ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(X0))
                      & ( ? [X5] :
                            ( ilf_type(X5,member_type(X2))
                            & member(ordered_pair(X5,X4),X3)
                            & member(X5,X1) )
                      <~> member(X4,image4(X2,X0,X3,X1)) ) )
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ~ empty(X2) ) ) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ilf_type(X4,member_type(X0))
                      & ( ? [X5] :
                            ( ilf_type(X5,member_type(X2))
                            & member(ordered_pair(X5,X4),X3)
                            & member(X5,X1) )
                      <~> member(X4,image4(X2,X0,X3,X1)) ) )
                  & ilf_type(X3,relation_type(X2,X0)) )
              & ~ empty(X2)
              & ilf_type(X2,set_type) )
          & ~ empty(X1)
          & ilf_type(X1,set_type) )
      & ~ empty(X0)
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0] :
        ( ( ~ empty(X0)
          & ilf_type(X0,set_type) )
       => ! [X1] :
            ( ( ~ empty(X1)
              & ilf_type(X1,set_type) )
           => ! [X2] :
                ( ( ~ empty(X2)
                  & ilf_type(X2,set_type) )
               => ! [X3] :
                    ( ilf_type(X3,relation_type(X2,X0))
                   => ! [X4] :
                        ( ilf_type(X4,member_type(X0))
                       => ( ? [X5] :
                              ( ilf_type(X5,member_type(X2))
                              & member(ordered_pair(X5,X4),X3)
                              & member(X5,X1) )
                        <=> member(X4,image4(X2,X0,X3,X1)) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0] :
      ( ( ~ empty(X0)
        & ilf_type(X0,set_type) )
     => ! [X1] :
          ( ( ~ empty(X1)
            & ilf_type(X1,set_type) )
         => ! [X2] :
              ( ( ~ empty(X2)
                & ilf_type(X2,set_type) )
             => ! [X3] :
                  ( ilf_type(X3,relation_type(X2,X0))
                 => ! [X4] :
                      ( ilf_type(X4,member_type(X0))
                     => ( ? [X5] :
                            ( ilf_type(X5,member_type(X2))
                            & member(ordered_pair(X5,X4),X3)
                            & member(X5,X1) )
                      <=> member(X4,image4(X2,X0,X3,X1)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_52) ).

fof(f130,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).

fof(f186,plain,
    ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
    | spl17_2 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f185,plain,
    ( spl17_2
  <=> member(sK4,image4(sK2,sK0,sK3,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).

fof(f322,plain,
    ( member(sK4,image(sK3,sK1))
    | ~ spl17_3
    | ~ spl17_5 ),
    inference(unit_resulting_resolution,[],[f192,f130,f130,f130,f246,f201,f160]) ).

fof(f160,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X3,X1),X2)
      | ~ member(X3,X0)
      | ~ ilf_type(X2,binary_relation_type)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | member(X1,image(X2,X0)) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( member(X1,image(X2,X0))
                  | ! [X3] :
                      ( ~ ilf_type(X3,set_type)
                      | ~ member(ordered_pair(X3,X1),X2)
                      | ~ member(X3,X0) ) )
                & ( ( ilf_type(sK11(X0,X1,X2),set_type)
                    & member(ordered_pair(sK11(X0,X1,X2),X1),X2)
                    & member(sK11(X0,X1,X2),X0) )
                  | ~ member(X1,image(X2,X0)) ) )
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f94,f95]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ilf_type(X4,set_type)
          & member(ordered_pair(X4,X1),X2)
          & member(X4,X0) )
     => ( ilf_type(sK11(X0,X1,X2),set_type)
        & member(ordered_pair(sK11(X0,X1,X2),X1),X2)
        & member(sK11(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( member(X1,image(X2,X0))
                  | ! [X3] :
                      ( ~ ilf_type(X3,set_type)
                      | ~ member(ordered_pair(X3,X1),X2)
                      | ~ member(X3,X0) ) )
                & ( ? [X4] :
                      ( ilf_type(X4,set_type)
                      & member(ordered_pair(X4,X1),X2)
                      & member(X4,X0) )
                  | ~ member(X1,image(X2,X0)) ) )
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(rectify,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ( ( member(X1,image(X2,X0))
                  | ! [X3] :
                      ( ~ ilf_type(X3,set_type)
                      | ~ member(ordered_pair(X3,X1),X2)
                      | ~ member(X3,X0) ) )
                & ( ? [X3] :
                      ( ilf_type(X3,set_type)
                      & member(ordered_pair(X3,X1),X2)
                      & member(X3,X0) )
                  | ~ member(X1,image(X2,X0)) ) )
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ( member(X1,image(X2,X0))
              <=> ? [X3] :
                    ( ilf_type(X3,set_type)
                    & member(ordered_pair(X3,X1),X2)
                    & member(X3,X0) ) )
              | ~ ilf_type(X2,binary_relation_type) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,binary_relation_type)
             => ( member(X1,image(X2,X0))
              <=> ? [X3] :
                    ( ilf_type(X3,set_type)
                    & member(ordered_pair(X3,X1),X2)
                    & member(X3,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f201,plain,
    ( member(ordered_pair(sK5,sK4),sK3)
    | ~ spl17_5 ),
    inference(avatar_component_clause,[],[f199]) ).

fof(f199,plain,
    ( spl17_5
  <=> member(ordered_pair(sK5,sK4),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).

fof(f246,plain,
    ilf_type(sK3,binary_relation_type),
    inference(unit_resulting_resolution,[],[f130,f242,f177]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ilf_type(X0,binary_relation_type)
      | ~ relation_like(X0) ),
    inference(duplicate_literal_removal,[],[f172]) ).

fof(f172,plain,
    ! [X0] :
      ( ilf_type(X0,binary_relation_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ relation_like(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( ( ( ilf_type(X0,binary_relation_type)
          | ~ ilf_type(X0,set_type)
          | ~ relation_like(X0) )
        & ( ( ilf_type(X0,set_type)
            & relation_like(X0) )
          | ~ ilf_type(X0,binary_relation_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( ( ( ilf_type(X0,binary_relation_type)
          | ~ ilf_type(X0,set_type)
          | ~ relation_like(X0) )
        & ( ( ilf_type(X0,set_type)
            & relation_like(X0) )
          | ~ ilf_type(X0,binary_relation_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ( ilf_type(X0,binary_relation_type)
      <=> ( ilf_type(X0,set_type)
          & relation_like(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(X0,binary_relation_type)
      <=> ( ilf_type(X0,set_type)
          & relation_like(X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).

fof(f242,plain,
    relation_like(sK3),
    inference(unit_resulting_resolution,[],[f130,f130,f214,f109]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type)
      | relation_like(X2)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
              | relation_like(X2) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,subset_type(cross_product(X0,X1)))
             => relation_like(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).

fof(f214,plain,
    ilf_type(sK3,subset_type(cross_product(sK2,sK0))),
    inference(unit_resulting_resolution,[],[f130,f130,f112,f155]) ).

fof(f155,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
                | ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ~ ilf_type(X3,relation_type(X0,X1))
                | ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) )
            & ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).

fof(f192,plain,
    ( member(sK5,sK1)
    | ~ spl17_3 ),
    inference(avatar_component_clause,[],[f190]) ).

fof(f190,plain,
    ( spl17_3
  <=> member(sK5,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).

fof(f314,plain,
    ( ~ spl17_2
    | ~ spl17_4 ),
    inference(avatar_contradiction_clause,[],[f313]) ).

fof(f313,plain,
    ( $false
    | ~ spl17_2
    | ~ spl17_4 ),
    inference(subsumption_resolution,[],[f310,f271]) ).

fof(f271,plain,
    ( ~ ilf_type(sK11(sK1,sK4,sK3),member_type(sK2))
    | ~ spl17_2
    | ~ spl17_4 ),
    inference(unit_resulting_resolution,[],[f250,f252,f196]) ).

fof(f196,plain,
    ( ! [X5] :
        ( ~ member(ordered_pair(X5,sK4),sK3)
        | ~ ilf_type(X5,member_type(sK2))
        | ~ member(X5,sK1) )
    | ~ spl17_4 ),
    inference(avatar_component_clause,[],[f195]) ).

fof(f195,plain,
    ( spl17_4
  <=> ! [X5] :
        ( ~ member(X5,sK1)
        | ~ member(ordered_pair(X5,sK4),sK3)
        | ~ ilf_type(X5,member_type(sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f252,plain,
    ( member(ordered_pair(sK11(sK1,sK4,sK3),sK4),sK3)
    | ~ spl17_2 ),
    inference(unit_resulting_resolution,[],[f130,f130,f216,f246,f158]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( member(ordered_pair(sK11(X0,X1,X2),X1),X2)
      | ~ ilf_type(X2,binary_relation_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ member(X1,image(X2,X0)) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f216,plain,
    ( member(sK4,image(sK3,sK1))
    | ~ spl17_2 ),
    inference(backward_demodulation,[],[f187,f215]) ).

fof(f187,plain,
    ( member(sK4,image4(sK2,sK0,sK3,sK1))
    | ~ spl17_2 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f250,plain,
    ( member(sK11(sK1,sK4,sK3),sK1)
    | ~ spl17_2 ),
    inference(unit_resulting_resolution,[],[f130,f130,f216,f246,f157]) ).

fof(f157,plain,
    ! [X2,X0,X1] :
      ( member(sK11(X0,X1,X2),X0)
      | ~ ilf_type(X2,binary_relation_type)
      | ~ ilf_type(X1,set_type)
      | ~ member(X1,image(X2,X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f310,plain,
    ( ilf_type(sK11(sK1,sK4,sK3),member_type(sK2))
    | ~ spl17_2 ),
    inference(unit_resulting_resolution,[],[f111,f130,f130,f273,f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | empty(X1)
      | ~ member(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ( ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) )
            & ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ( member(X0,X1)
          <=> ilf_type(X0,member_type(X1)) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,X1)
          <=> ilf_type(X0,member_type(X1)) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( member(X0,X1)
          <=> ilf_type(X0,member_type(X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).

fof(f273,plain,
    ( member(sK11(sK1,sK4,sK3),sK2)
    | ~ spl17_2 ),
    inference(unit_resulting_resolution,[],[f130,f130,f112,f130,f130,f252,f150]) ).

fof(f150,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ member(ordered_pair(X2,X3),X4)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X4,relation_type(X0,X1))
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ! [X2] :
              ( ~ ilf_type(X2,set_type)
              | ! [X3] :
                  ( ! [X4] :
                      ( ( member(X3,X1)
                        & member(X2,X0) )
                      | ~ member(ordered_pair(X2,X3),X4)
                      | ~ ilf_type(X4,relation_type(X0,X1)) )
                  | ~ ilf_type(X3,set_type) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ( member(X3,X1)
                        & member(X2,X0) )
                      | ~ member(ordered_pair(X2,X3),X4)
                      | ~ ilf_type(X4,relation_type(X0,X1)) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => ! [X4] :
                      ( ilf_type(X4,relation_type(X0,X1))
                     => ( member(ordered_pair(X2,X3),X4)
                       => ( member(X3,X1)
                          & member(X2,X0) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

fof(f111,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f72]) ).

fof(f202,plain,
    ( spl17_2
    | spl17_5 ),
    inference(avatar_split_clause,[],[f114,f199,f185]) ).

fof(f114,plain,
    ( member(ordered_pair(sK5,sK4),sK3)
    | member(sK4,image4(sK2,sK0,sK3,sK1)) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f197,plain,
    ( spl17_4
    | ~ spl17_2 ),
    inference(avatar_split_clause,[],[f116,f185,f195]) ).

fof(f116,plain,
    ! [X5] :
      ( ~ member(sK4,image4(sK2,sK0,sK3,sK1))
      | ~ member(X5,sK1)
      | ~ ilf_type(X5,member_type(sK2))
      | ~ member(ordered_pair(X5,sK4),sK3) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f193,plain,
    ( spl17_3
    | spl17_2 ),
    inference(avatar_split_clause,[],[f113,f185,f190]) ).

fof(f113,plain,
    ( member(sK4,image4(sK2,sK0,sK3,sK1))
    | member(sK5,sK1) ),
    inference(cnf_transformation,[],[f72]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET685+3 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.14/0.34  % Computer : n012.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   : Tue Aug 30 14:13:05 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.49  % (8801)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)
% 0.21/0.50  % (8793)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)
% 0.21/0.50  % (8809)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.50  % (8817)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)
% 0.21/0.51  % (8814)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.51  % (8809)Instruction limit reached!
% 0.21/0.51  % (8809)------------------------------
% 0.21/0.51  % (8809)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (8800)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)
% 0.21/0.51  % (8809)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (8809)Termination reason: Unknown
% 0.21/0.51  % (8809)Termination phase: Property scanning
% 0.21/0.51  
% 0.21/0.51  % (8809)Memory used [KB]: 1535
% 0.21/0.51  % (8809)Time elapsed: 0.004 s
% 0.21/0.51  % (8809)Instructions burned: 4 (million)
% 0.21/0.51  % (8809)------------------------------
% 0.21/0.51  % (8809)------------------------------
% 0.21/0.51  % (8801)First to succeed.
% 0.21/0.51  % (8805)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (8793)Refutation not found, incomplete strategy% (8793)------------------------------
% 0.21/0.51  % (8793)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (8793)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (8793)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51  
% 0.21/0.51  % (8793)Memory used [KB]: 6140
% 0.21/0.51  % (8793)Time elapsed: 0.098 s
% 0.21/0.51  % (8793)Instructions burned: 7 (million)
% 0.21/0.51  % (8793)------------------------------
% 0.21/0.51  % (8793)------------------------------
% 0.21/0.51  % (8816)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)
% 0.21/0.52  % (8798)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)
% 0.21/0.52  % (8801)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (8801)------------------------------
% 0.21/0.52  % (8801)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (8801)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (8801)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (8801)Memory used [KB]: 6268
% 0.21/0.52  % (8801)Time elapsed: 0.109 s
% 0.21/0.52  % (8801)Instructions burned: 16 (million)
% 0.21/0.52  % (8801)------------------------------
% 0.21/0.52  % (8801)------------------------------
% 0.21/0.52  % (8791)Success in time 0.17 s
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