TSTP Solution File: SET645+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET645+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_sat --cores 0 -t %d %s

% Computer : n006.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 18:25:12 EDT 2022

% Result   : Theorem 1.44s 0.56s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   87 (  16 unt;   3 typ;   0 def)
%            Number of atoms       :  395 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  503 ( 192   ~; 175   |;  87   &)
%                                         (  10 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :  210 ( 172   !;  38   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_6,type,
    sQ15_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_7,type,
    sQ16_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_8,type,
    sQ17_eqProxy: ( $real * $real ) > $o ).

fof(f404,plain,
    $false,
    inference(subsumption_resolution,[],[f396,f399]) ).

fof(f399,plain,
    ~ member(sK7,sK5),
    inference(subsumption_resolution,[],[f150,f395]) ).

fof(f395,plain,
    member(sK8,sK6),
    inference(resolution,[],[f380,f346]) ).

fof(f346,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,X3) ),
    inference(subsumption_resolution,[],[f345,f158]) ).

fof(f158,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(literal_reordering,[],[f127]) ).

fof(f127,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).

fof(f345,plain,
    ! [X2,X3,X0,X1] :
      ( member(X1,X3)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f344,f158]) ).

fof(f344,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X0,set_type)
      | member(X1,X3) ),
    inference(subsumption_resolution,[],[f343,f158]) ).

fof(f343,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X1,X3)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f175,f158]) ).

fof(f175,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X3,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,set_type)
      | member(X1,X3)
      | ~ ilf_type(X1,set_type) ),
    inference(literal_reordering,[],[f133]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X2,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X3,set_type)
      | member(X1,X3)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ! [X3] :
                  ( ( ( ( member(X0,X2)
                        & member(X1,X3) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
                    & ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X0,X2)
                      | ~ member(X1,X3) ) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ! [X3] :
                  ( ( ( ( member(X0,X2)
                        & member(X1,X3) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
                    & ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X0,X2)
                      | ~ member(X1,X3) ) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ! [X2] :
              ( ! [X3] :
                  ( ( ( member(X0,X2)
                      & member(X1,X3) )
                  <=> member(ordered_pair(X0,X1),cross_product(X2,X3)) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) ) )
      | ~ ilf_type(X0,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,set_type)
             => ! [X3] :
                  ( ilf_type(X3,set_type)
                 => ( ( member(X0,X2)
                      & member(X1,X3) )
                  <=> member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f380,plain,
    member(ordered_pair(sK7,sK8),cross_product(sK5,sK6)),
    inference(resolution,[],[f320,f152]) ).

fof(f152,plain,
    member(ordered_pair(sK7,sK8),sK9),
    inference(literal_reordering,[],[f120]) ).

fof(f120,plain,
    member(ordered_pair(sK7,sK8),sK9),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ( member(ordered_pair(sK7,sK8),sK9)
    & ( ~ member(sK7,sK5)
      | ~ member(sK8,sK6) )
    & ilf_type(sK9,relation_type(sK5,sK6))
    & ilf_type(sK8,set_type)
    & ilf_type(sK7,set_type)
    & ilf_type(sK6,set_type)
    & ilf_type(sK5,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f35,f76,f75,f74,f73,f72]) ).

fof(f72,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( member(ordered_pair(X2,X3),X4)
                        & ( ~ member(X2,X0)
                          | ~ member(X3,X1) )
                        & 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) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( member(ordered_pair(X2,X3),X4)
                      & ( ~ member(X2,sK5)
                        | ~ member(X3,X1) )
                      & ilf_type(X4,relation_type(sK5,X1)) )
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK5,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( member(ordered_pair(X2,X3),X4)
                    & ( ~ member(X2,sK5)
                      | ~ member(X3,X1) )
                    & ilf_type(X4,relation_type(sK5,X1)) )
                & ilf_type(X3,set_type) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( member(ordered_pair(X2,X3),X4)
                  & ( ~ member(X2,sK5)
                    | ~ member(X3,sK6) )
                  & ilf_type(X4,relation_type(sK5,sK6)) )
              & ilf_type(X3,set_type) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK6,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( member(ordered_pair(X2,X3),X4)
                & ( ~ member(X2,sK5)
                  | ~ member(X3,sK6) )
                & ilf_type(X4,relation_type(sK5,sK6)) )
            & ilf_type(X3,set_type) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ? [X4] :
              ( member(ordered_pair(sK7,X3),X4)
              & ( ~ member(sK7,sK5)
                | ~ member(X3,sK6) )
              & ilf_type(X4,relation_type(sK5,sK6)) )
          & ilf_type(X3,set_type) )
      & ilf_type(sK7,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( member(ordered_pair(sK7,X3),X4)
            & ( ~ member(sK7,sK5)
              | ~ member(X3,sK6) )
            & ilf_type(X4,relation_type(sK5,sK6)) )
        & ilf_type(X3,set_type) )
   => ( ? [X4] :
          ( member(ordered_pair(sK7,sK8),X4)
          & ( ~ member(sK7,sK5)
            | ~ member(sK8,sK6) )
          & ilf_type(X4,relation_type(sK5,sK6)) )
      & ilf_type(sK8,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ( ? [X4] :
        ( member(ordered_pair(sK7,sK8),X4)
        & ( ~ member(sK7,sK5)
          | ~ member(sK8,sK6) )
        & ilf_type(X4,relation_type(sK5,sK6)) )
   => ( member(ordered_pair(sK7,sK8),sK9)
      & ( ~ member(sK7,sK5)
        | ~ member(sK8,sK6) )
      & ilf_type(sK9,relation_type(sK5,sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( member(ordered_pair(X2,X3),X4)
                      & ( ~ member(X2,X0)
                        | ~ member(X3,X1) )
                      & 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(flattening,[],[f34]) ).

fof(f34,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ( ~ member(X2,X0)
                        | ~ member(X3,X1) )
                      & 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,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [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(X2,X0)
                            & member(X3,X1) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [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(X2,X0)
                          & member(X3,X1) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_7) ).

fof(f320,plain,
    ! [X0] :
      ( ~ member(X0,sK9)
      | member(X0,cross_product(sK5,sK6)) ),
    inference(resolution,[],[f318,f309]) ).

fof(f309,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(subsumption_resolution,[],[f308,f158]) ).

fof(f308,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | member(X2,X1)
      | ~ member(X0,power_set(X1))
      | ~ member(X2,X0) ),
    inference(subsumption_resolution,[],[f307,f158]) ).

fof(f307,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X0,set_type)
      | member(X2,X1)
      | ~ ilf_type(X1,set_type)
      | ~ member(X2,X0) ),
    inference(subsumption_resolution,[],[f171,f158]) ).

fof(f171,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | member(X2,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(literal_reordering,[],[f91]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ( ~ member(sK0(X0,X1),X1)
                & member(sK0(X0,X1),X0)
                & ilf_type(sK0(X0,X1),set_type) ) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f53,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X1)
          & member(X3,X0)
          & ilf_type(X3,set_type) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0)
        & ilf_type(sK0(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X3] :
                  ( ~ member(X3,X1)
                  & member(X3,X0)
                  & ilf_type(X3,set_type) ) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) ) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ( ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) )
          <=> member(X0,power_set(X1)) )
          | ~ ilf_type(X1,set_type) ) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( member(X2,X1)
                | ~ member(X2,X0)
                | ~ ilf_type(X2,set_type) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( member(X0,power_set(X1))
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).

fof(f318,plain,
    member(sK9,power_set(cross_product(sK5,sK6))),
    inference(subsumption_resolution,[],[f317,f242]) ).

fof(f242,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f184,f158]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(literal_reordering,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ~ empty(power_set(X0)) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).

fof(f317,plain,
    ( empty(power_set(cross_product(sK5,sK6)))
    | member(sK9,power_set(cross_product(sK5,sK6))) ),
    inference(resolution,[],[f296,f265]) ).

fof(f265,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | empty(X1)
      | member(X0,X1) ),
    inference(subsumption_resolution,[],[f264,f158]) ).

fof(f264,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | empty(X1) ),
    inference(subsumption_resolution,[],[f161,f158]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | member(X0,X1)
      | empty(X1)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X0,member_type(X1)) ),
    inference(literal_reordering,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X0,set_type)
      | empty(X1)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ~ ilf_type(X1,set_type)
          | ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) ) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( empty(X1)
          | ~ ilf_type(X1,set_type)
          | ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | empty(X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ~ empty(X1)
            & ilf_type(X1,set_type) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).

fof(f296,plain,
    ilf_type(sK9,member_type(power_set(cross_product(sK5,sK6)))),
    inference(resolution,[],[f290,f277]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,subset_type(X0))
      | ilf_type(X1,member_type(power_set(X0))) ),
    inference(subsumption_resolution,[],[f276,f158]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X1,subset_type(X0))
      | ilf_type(X1,member_type(power_set(X0))) ),
    inference(subsumption_resolution,[],[f182,f158]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X0,set_type)
      | ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type) ),
    inference(literal_reordering,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ilf_type(X1,member_type(power_set(X0))) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) )
            & ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).

fof(f290,plain,
    ilf_type(sK9,subset_type(cross_product(sK5,sK6))),
    inference(resolution,[],[f289,f159]) ).

fof(f159,plain,
    ilf_type(sK9,relation_type(sK5,sK6)),
    inference(literal_reordering,[],[f118]) ).

fof(f118,plain,
    ilf_type(sK9,relation_type(sK5,sK6)),
    inference(cnf_transformation,[],[f77]) ).

fof(f289,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1))) ),
    inference(subsumption_resolution,[],[f288,f158]) ).

fof(f288,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1))) ),
    inference(subsumption_resolution,[],[f143,f158]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type) ),
    inference(literal_reordering,[],[f93]) ).

fof(f93,plain,
    ! [X2,X0,X1] :
      ( ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [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))) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => ilf_type(X2,subset_type(cross_product(X0,X1))) )
            & ! [X3] :
                ( ilf_type(X3,subset_type(cross_product(X0,X1)))
               => ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ! [X3] :
                ( ilf_type(X3,relation_type(X0,X1))
               => ilf_type(X3,subset_type(cross_product(X0,X1))) )
            & ! [X2] :
                ( ilf_type(X2,subset_type(cross_product(X0,X1)))
               => ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

fof(f150,plain,
    ( ~ member(sK8,sK6)
    | ~ member(sK7,sK5) ),
    inference(literal_reordering,[],[f119]) ).

fof(f119,plain,
    ( ~ member(sK7,sK5)
    | ~ member(sK8,sK6) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f396,plain,
    member(sK7,sK5),
    inference(resolution,[],[f380,f342]) ).

fof(f342,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(subsumption_resolution,[],[f341,f158]) ).

fof(f341,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X2,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(subsumption_resolution,[],[f340,f158]) ).

fof(f340,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | member(X0,X2)
      | ~ ilf_type(X2,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
    inference(subsumption_resolution,[],[f339,f158]) ).

fof(f339,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X3,set_type)
      | member(X0,X2)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
    inference(subsumption_resolution,[],[f145,f158]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X2,set_type)
      | member(X0,X2) ),
    inference(literal_reordering,[],[f134]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1] :
      ( ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X3,set_type)
      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2)
      | ~ ilf_type(X2,set_type) ),
    inference(cnf_transformation,[],[f87]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % 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 : n006.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 14:08:40 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (32227)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.49  % (32227)Instruction limit reached!
% 0.19/0.49  % (32227)------------------------------
% 0.19/0.49  % (32227)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (32243)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)
% 0.19/0.50  % (32229)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)
% 0.19/0.50  % (32235)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)
% 0.19/0.50  % (32245)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51  % (32230)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.31/0.52  % (32227)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.52  % (32227)Termination reason: Unknown
% 1.31/0.52  % (32227)Termination phase: Saturation
% 1.31/0.52  
% 1.31/0.52  % (32227)Memory used [KB]: 5628
% 1.31/0.52  % (32227)Time elapsed: 0.099 s
% 1.31/0.52  % (32227)Instructions burned: 8 (million)
% 1.31/0.52  % (32227)------------------------------
% 1.31/0.52  % (32227)------------------------------
% 1.31/0.52  % (32221)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)
% 1.31/0.52  % (32242)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)
% 1.31/0.53  % (32222)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)
% 1.31/0.53  % (32220)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)
% 1.31/0.53  % (32247)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)
% 1.31/0.53  % (32248)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.31/0.53  % (32228)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.31/0.53  % (32234)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)
% 1.31/0.53  % (32224)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.31/0.53  % (32223)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)
% 1.31/0.53  % (32228)Instruction limit reached!
% 1.31/0.53  % (32228)------------------------------
% 1.31/0.53  % (32228)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.53  % (32228)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.53  % (32228)Termination reason: Unknown
% 1.31/0.53  % (32228)Termination phase: Blocked clause elimination
% 1.31/0.53  
% 1.31/0.53  % (32228)Memory used [KB]: 1023
% 1.31/0.53  % (32228)Time elapsed: 0.004 s
% 1.31/0.53  % (32228)Instructions burned: 4 (million)
% 1.31/0.53  % (32228)------------------------------
% 1.31/0.53  % (32228)------------------------------
% 1.31/0.53  % (32225)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)
% 1.31/0.53  % (32231)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)
% 1.31/0.54  % (32236)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)
% 1.44/0.54  % (32226)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)
% 1.44/0.54  % (32249)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)
% 1.44/0.54  % (32239)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)
% 1.44/0.54  % (32240)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)
% 1.44/0.54  % (32244)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.44/0.54  % (32238)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.44/0.54  % (32241)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.44/0.55  % (32237)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.44/0.55  % (32233)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.44/0.55  % (32232)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.44/0.55  TRYING [1]
% 1.44/0.55  TRYING [2]
% 1.44/0.55  % (32246)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)
% 1.44/0.56  % (32234)First to succeed.
% 1.44/0.56  % (32234)Refutation found. Thanks to Tanya!
% 1.44/0.56  % SZS status Theorem for theBenchmark
% 1.44/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.56  % (32234)------------------------------
% 1.44/0.56  % (32234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.56  % (32234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.56  % (32234)Termination reason: Refutation
% 1.44/0.56  
% 1.44/0.56  % (32234)Memory used [KB]: 6012
% 1.44/0.56  % (32234)Time elapsed: 0.010 s
% 1.44/0.56  % (32234)Instructions burned: 11 (million)
% 1.44/0.56  % (32234)------------------------------
% 1.44/0.56  % (32234)------------------------------
% 1.44/0.56  % (32219)Success in time 0.208 s
%------------------------------------------------------------------------------