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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---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_uns --cores 0 -t %d %s

% Computer : n019.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 18:21:44 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   64 (   9 unt;   0 def)
%            Number of atoms       :  316 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  385 ( 133   ~; 119   |;  86   &)
%                                         (  12 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :  135 (  97   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f460,plain,
    $false,
    inference(avatar_sat_refutation,[],[f150,f237,f459]) ).

fof(f459,plain,
    spl14_2,
    inference(avatar_contradiction_clause,[],[f458]) ).

fof(f458,plain,
    ( $false
    | spl14_2 ),
    inference(subsumption_resolution,[],[f453,f111]) ).

fof(f111,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(f453,plain,
    ( ~ ilf_type(cross_product(sK5,sK6),set_type)
    | spl14_2 ),
    inference(unit_resulting_resolution,[],[f378,f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,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(f378,plain,
    ( empty(power_set(cross_product(sK5,sK6)))
    | spl14_2 ),
    inference(unit_resulting_resolution,[],[f111,f111,f163,f288,f132]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X0,member_type(X1))
      | empty(X1)
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | empty(X1)
          | ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) ) ) ),
    inference(nnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ~ ilf_type(X0,set_type)
      | ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | empty(X1)
          | ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    inference(flattening,[],[f42]) ).

fof(f42,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(f288,plain,
    ( ! [X0] : ~ member(sK9,power_set(cross_product(X0,sK6)))
    | spl14_2 ),
    inference(unit_resulting_resolution,[],[f111,f114,f111,f111,f249,f105]) ).

fof(f105,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,power_set(X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ member(X2,X0)
      | ~ ilf_type(X1,set_type)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ( member(sK3(X0,X1),X0)
                & ~ member(sK3(X0,X1),X1)
                & ilf_type(sK3(X0,X1),set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f65,f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1)
          & ilf_type(X3,set_type) )
     => ( member(sK3(X0,X1),X0)
        & ~ member(sK3(X0,X1),X1)
        & ilf_type(sK3(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f65,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X3] :
                  ( member(X3,X0)
                  & ~ member(X3,X1)
                  & ilf_type(X3,set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X2] :
                  ( ~ member(X2,X0)
                  | member(X2,X1)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) )
            & ( member(X0,power_set(X1))
              | ? [X2] :
                  ( member(X2,X0)
                  & ~ member(X2,X1)
                  & ilf_type(X2,set_type) ) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ~ member(X2,X0)
                | member(X2,X1)
                | ~ ilf_type(X2,set_type) )
          <=> member(X0,power_set(X1)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f38]) ).

fof(f38,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(f249,plain,
    ( ! [X0,X1] : ~ member(ordered_pair(X0,sK8),cross_product(X1,sK6))
    | spl14_2 ),
    inference(unit_resulting_resolution,[],[f111,f111,f111,f111,f149,f123]) ).

fof(f123,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type)
      | member(X1,X3) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [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(X1,X3)
                        & member(X0,X2) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
                    & ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X1,X3)
                      | ~ member(X0,X2) ) ) ) ) ) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [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(X1,X3)
                        & member(X0,X2) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) )
                    & ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X1,X3)
                      | ~ member(X0,X2) ) ) ) ) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [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(X1,X3)
                      & member(X0,X2) )
                  <=> member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ),
    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(X1,X3)
                      & member(X0,X2) )
                  <=> member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

fof(f149,plain,
    ( ~ member(sK8,sK6)
    | spl14_2 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl14_2
  <=> member(sK8,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).

fof(f114,plain,
    member(ordered_pair(sK7,sK8),sK9),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ( ilf_type(sK5,set_type)
    & ilf_type(sK6,set_type)
    & ilf_type(sK8,set_type)
    & ilf_type(sK9,relation_type(sK5,sK6))
    & member(ordered_pair(sK7,sK8),sK9)
    & ( ~ member(sK7,sK5)
      | ~ member(sK8,sK6) )
    & ilf_type(sK7,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f49,f74,f73,f72,f71,f70]) ).

fof(f70,plain,
    ( ? [X0] :
        ( ilf_type(X0,set_type)
        & ? [X1] :
            ( ilf_type(X1,set_type)
            & ? [X2] :
                ( ? [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) ) ) )
                & ilf_type(X2,set_type) ) ) )
   => ( ilf_type(sK5,set_type)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ? [X2] :
              ( ? [X3] :
                  ( ilf_type(X3,set_type)
                  & ? [X4] :
                      ( ilf_type(X4,relation_type(sK5,X1))
                      & member(ordered_pair(X2,X3),X4)
                      & ( ~ member(X2,sK5)
                        | ~ member(X3,X1) ) ) )
              & ilf_type(X2,set_type) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ( ? [X1] :
        ( ilf_type(X1,set_type)
        & ? [X2] :
            ( ? [X3] :
                ( ilf_type(X3,set_type)
                & ? [X4] :
                    ( ilf_type(X4,relation_type(sK5,X1))
                    & member(ordered_pair(X2,X3),X4)
                    & ( ~ member(X2,sK5)
                      | ~ member(X3,X1) ) ) )
            & ilf_type(X2,set_type) ) )
   => ( ilf_type(sK6,set_type)
      & ? [X2] :
          ( ? [X3] :
              ( ilf_type(X3,set_type)
              & ? [X4] :
                  ( ilf_type(X4,relation_type(sK5,sK6))
                  & member(ordered_pair(X2,X3),X4)
                  & ( ~ member(X2,sK5)
                    | ~ member(X3,sK6) ) ) )
          & ilf_type(X2,set_type) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ilf_type(X3,set_type)
            & ? [X4] :
                ( ilf_type(X4,relation_type(sK5,sK6))
                & member(ordered_pair(X2,X3),X4)
                & ( ~ member(X2,sK5)
                  | ~ member(X3,sK6) ) ) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ilf_type(X3,set_type)
          & ? [X4] :
              ( ilf_type(X4,relation_type(sK5,sK6))
              & member(ordered_pair(sK7,X3),X4)
              & ( ~ member(sK7,sK5)
                | ~ member(X3,sK6) ) ) )
      & ilf_type(sK7,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ( ? [X3] :
        ( ilf_type(X3,set_type)
        & ? [X4] :
            ( ilf_type(X4,relation_type(sK5,sK6))
            & member(ordered_pair(sK7,X3),X4)
            & ( ~ member(sK7,sK5)
              | ~ member(X3,sK6) ) ) )
   => ( ilf_type(sK8,set_type)
      & ? [X4] :
          ( ilf_type(X4,relation_type(sK5,sK6))
          & member(ordered_pair(sK7,sK8),X4)
          & ( ~ member(sK7,sK5)
            | ~ member(sK8,sK6) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ( ? [X4] :
        ( ilf_type(X4,relation_type(sK5,sK6))
        & member(ordered_pair(sK7,sK8),X4)
        & ( ~ member(sK7,sK5)
          | ~ member(sK8,sK6) ) )
   => ( ilf_type(sK9,relation_type(sK5,sK6))
      & member(ordered_pair(sK7,sK8),sK9)
      & ( ~ member(sK7,sK5)
        | ~ member(sK8,sK6) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ? [X0] :
      ( ilf_type(X0,set_type)
      & ? [X1] :
          ( ilf_type(X1,set_type)
          & ? [X2] :
              ( ? [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) ) ) )
              & ilf_type(X2,set_type) ) ) ),
    inference(flattening,[],[f48]) ).

fof(f48,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(X3,X1)
                            & member(X2,X0) ) ) ) ) ) ) ),
    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(X3,X1)
                          & member(X2,X0) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_7) ).

fof(f163,plain,
    ilf_type(sK9,member_type(power_set(cross_product(sK5,sK6)))),
    inference(unit_resulting_resolution,[],[f111,f111,f156,f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ( ilf_type(X1,member_type(power_set(X0)))
              | ~ ilf_type(X1,subset_type(X0)) )
            & ( ilf_type(X1,subset_type(X0))
              | ~ ilf_type(X1,member_type(power_set(X0))) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ ilf_type(X1,set_type)
          | ( ilf_type(X1,member_type(power_set(X0)))
          <=> ilf_type(X1,subset_type(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,member_type(power_set(X0)))
          <=> ilf_type(X1,subset_type(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).

fof(f156,plain,
    ilf_type(sK9,subset_type(cross_product(sK5,sK6))),
    inference(unit_resulting_resolution,[],[f111,f111,f115,f109]) ).

fof(f109,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type)
      | ~ ilf_type(X1,set_type) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ! [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)) ) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[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(f115,plain,
    ilf_type(sK9,relation_type(sK5,sK6)),
    inference(cnf_transformation,[],[f75]) ).

fof(f237,plain,
    spl14_1,
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | spl14_1 ),
    inference(subsumption_resolution,[],[f231,f111]) ).

fof(f231,plain,
    ( ~ ilf_type(cross_product(sK5,sK6),set_type)
    | spl14_1 ),
    inference(unit_resulting_resolution,[],[f208,f134]) ).

fof(f208,plain,
    ( empty(power_set(cross_product(sK5,sK6)))
    | spl14_1 ),
    inference(unit_resulting_resolution,[],[f111,f169,f111,f163,f132]) ).

fof(f169,plain,
    ( ! [X0] : ~ member(sK9,power_set(cross_product(sK5,X0)))
    | spl14_1 ),
    inference(unit_resulting_resolution,[],[f111,f114,f111,f111,f152,f105]) ).

fof(f152,plain,
    ( ! [X0,X1] : ~ member(ordered_pair(sK7,X0),cross_product(sK5,X1))
    | spl14_1 ),
    inference(unit_resulting_resolution,[],[f111,f111,f111,f111,f145,f122]) ).

fof(f122,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f145,plain,
    ( ~ member(sK7,sK5)
    | spl14_1 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl14_1
  <=> member(sK7,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).

fof(f150,plain,
    ( ~ spl14_1
    | ~ spl14_2 ),
    inference(avatar_split_clause,[],[f113,f147,f143]) ).

fof(f113,plain,
    ( ~ member(sK8,sK6)
    | ~ member(sK7,sK5) ),
    inference(cnf_transformation,[],[f75]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % 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 : n019.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 14:12:50 EDT 2022
% 0.12/0.35  % CPUTime    : 
% 0.20/0.46  % (9811)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)
% 0.20/0.47  % (9819)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.48  % (9819)Instruction limit reached!
% 0.20/0.48  % (9819)------------------------------
% 0.20/0.48  % (9819)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (9819)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (9819)Termination reason: Unknown
% 0.20/0.48  % (9819)Termination phase: Finite model building preprocessing
% 0.20/0.48  
% 0.20/0.48  % (9819)Memory used [KB]: 1535
% 0.20/0.48  % (9819)Time elapsed: 0.005 s
% 0.20/0.48  % (9819)Instructions burned: 4 (million)
% 0.20/0.48  % (9819)------------------------------
% 0.20/0.48  % (9819)------------------------------
% 0.20/0.48  % (9811)First to succeed.
% 0.20/0.49  % (9811)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (9811)------------------------------
% 0.20/0.49  % (9811)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (9811)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (9811)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (9811)Memory used [KB]: 6396
% 0.20/0.49  % (9811)Time elapsed: 0.086 s
% 0.20/0.49  % (9811)Instructions burned: 27 (million)
% 0.20/0.49  % (9811)------------------------------
% 0.20/0.49  % (9811)------------------------------
% 0.20/0.49  % (9801)Success in time 0.133 s
%------------------------------------------------------------------------------