TSTP Solution File: SET646+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -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 May  1 03:48:28 EDT 2024

% Result   : Theorem 0.57s 0.76s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   88 (  14 unt;   0 def)
%            Number of atoms       :  465 (  40 equ)
%            Maximal formula atoms :   15 (   5 avg)
%            Number of connectives :  601 ( 224   ~; 209   |; 109   &)
%                                         (  16 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  222 ( 188   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f370,plain,
    $false,
    inference(subsumption_resolution,[],[f369,f110]) ).

fof(f110,plain,
    member(sK2,sK0),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ( ~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1))
    & member(sK3,sK1)
    & member(sK2,sK0)
    & ilf_type(sK3,set_type)
    & ilf_type(sK2,set_type)
    & ilf_type(sK1,set_type)
    & ilf_type(sK0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f64,f63,f62,f61]) ).

fof(f61,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
                    & member(X3,X1)
                    & member(X2,X0)
                    & ilf_type(X3,set_type) )
                & ilf_type(X2,set_type) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,X1))
                  & member(X3,X1)
                  & member(X2,sK0)
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK0,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,X1))
                & member(X3,X1)
                & member(X2,sK0)
                & ilf_type(X3,set_type) )
            & ilf_type(X2,set_type) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,sK1))
              & member(X3,sK1)
              & member(X2,sK0)
              & ilf_type(X3,set_type) )
          & ilf_type(X2,set_type) )
      & ilf_type(sK1,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f63,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,sK1))
            & member(X3,sK1)
            & member(X2,sK0)
            & ilf_type(X3,set_type) )
        & ilf_type(X2,set_type) )
   => ( ? [X3] :
          ( ~ ilf_type(singleton(ordered_pair(sK2,X3)),relation_type(sK0,sK1))
          & member(X3,sK1)
          & member(sK2,sK0)
          & ilf_type(X3,set_type) )
      & ilf_type(sK2,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ( ? [X3] :
        ( ~ ilf_type(singleton(ordered_pair(sK2,X3)),relation_type(sK0,sK1))
        & member(X3,sK1)
        & member(sK2,sK0)
        & ilf_type(X3,set_type) )
   => ( ~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1))
      & member(sK3,sK1)
      & member(sK2,sK0)
      & ilf_type(sK3,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
                  & member(X3,X1)
                  & member(X2,X0)
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
                  & member(X3,X1)
                  & member(X2,X0)
                  & ilf_type(X3,set_type) )
              & ilf_type(X2,set_type) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,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)
                   => ( ( member(X3,X1)
                        & member(X2,X0) )
                     => ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,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)
                 => ( ( member(X3,X1)
                      & member(X2,X0) )
                   => ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',prove_relset_1_8) ).

fof(f369,plain,
    ~ member(sK2,sK0),
    inference(subsumption_resolution,[],[f362,f111]) ).

fof(f111,plain,
    member(sK3,sK1),
    inference(cnf_transformation,[],[f65]) ).

fof(f362,plain,
    ( ~ member(sK3,sK1)
    | ~ member(sK2,sK0) ),
    inference(resolution,[],[f348,f208]) ).

fof(f208,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,X3)
      | ~ member(X0,X2) ),
    inference(subsumption_resolution,[],[f207,f113]) ).

fof(f113,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p25) ).

fof(f207,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,X3)
      | ~ member(X0,X2)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f206,f113]) ).

fof(f206,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,X3)
      | ~ member(X0,X2)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f205,f113]) ).

fof(f205,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,X3)
      | ~ member(X0,X2)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f133,f113]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( member(ordered_pair(X0,X1),cross_product(X2,X3))
      | ~ member(X1,X3)
      | ~ member(X0,X2)
      | ~ ilf_type(X3,set_type)
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X1,X3)
                      | ~ member(X0,X2) )
                    & ( ( member(X1,X3)
                        & member(X0,X2) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                      | ~ member(X1,X3)
                      | ~ member(X0,X2) )
                    & ( ( member(X1,X3)
                        & member(X0,X2) )
                      | ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
                  | ~ ilf_type(X3,set_type) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                  <=> ( member(X1,X3)
                      & member(X0,X2) ) )
                  | ~ 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)
                 => ( member(ordered_pair(X0,X1),cross_product(X2,X3))
                  <=> ( member(X1,X3)
                      & member(X0,X2) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p2) ).

fof(f348,plain,
    ~ member(ordered_pair(sK2,sK3),cross_product(sK0,sK1)),
    inference(backward_demodulation,[],[f304,f346]) ).

fof(f346,plain,
    ordered_pair(sK2,sK3) = sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),
    inference(resolution,[],[f303,f194]) ).

fof(f194,plain,
    ! [X1,X4] :
      ( ~ member(X4,singleton(X1))
      | X1 = X4 ),
    inference(subsumption_resolution,[],[f193,f113]) ).

fof(f193,plain,
    ! [X0,X1,X4] :
      ( X1 = X4
      | ~ member(X4,singleton(X1))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f192,f113]) ).

fof(f192,plain,
    ! [X0,X1,X4] :
      ( X1 = X4
      | ~ member(X4,singleton(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f191,f113]) ).

fof(f191,plain,
    ! [X0,X1,X4] :
      ( X1 = X4
      | ~ member(X4,singleton(X1))
      | ~ ilf_type(singleton(X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f171,f113]) ).

fof(f171,plain,
    ! [X0,X1,X4] :
      ( X1 = X4
      | ~ member(X4,singleton(X1))
      | ~ ilf_type(X4,set_type)
      | ~ ilf_type(singleton(X1),set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(equality_resolution,[],[f117]) ).

fof(f117,plain,
    ! [X2,X0,X1,X4] :
      ( X1 = X4
      | ~ member(X4,X2)
      | ~ ilf_type(X4,set_type)
      | singleton(X1) != X2
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( singleton(X1) = X2
                  | ( ( sK4(X1,X2) != X1
                      | ~ member(sK4(X1,X2),X2) )
                    & ( sK4(X1,X2) = X1
                      | member(sK4(X1,X2),X2) )
                    & ilf_type(sK4(X1,X2),set_type) ) )
                & ( ! [X4] :
                      ( ( ( member(X4,X2)
                          | X1 != X4 )
                        & ( X1 = X4
                          | ~ member(X4,X2) ) )
                      | ~ ilf_type(X4,set_type) )
                  | singleton(X1) != X2 ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f69,f70]) ).

fof(f70,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( ( X1 != X3
            | ~ member(X3,X2) )
          & ( X1 = X3
            | member(X3,X2) )
          & ilf_type(X3,set_type) )
     => ( ( sK4(X1,X2) != X1
          | ~ member(sK4(X1,X2),X2) )
        & ( sK4(X1,X2) = X1
          | member(sK4(X1,X2),X2) )
        & ilf_type(sK4(X1,X2),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( singleton(X1) = X2
                  | ? [X3] :
                      ( ( X1 != X3
                        | ~ member(X3,X2) )
                      & ( X1 = X3
                        | member(X3,X2) )
                      & ilf_type(X3,set_type) ) )
                & ( ! [X4] :
                      ( ( ( member(X4,X2)
                          | X1 != X4 )
                        & ( X1 = X4
                          | ~ member(X4,X2) ) )
                      | ~ ilf_type(X4,set_type) )
                  | singleton(X1) != X2 ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( singleton(X1) = X2
                  | ? [X3] :
                      ( ( X1 != X3
                        | ~ member(X3,X2) )
                      & ( X1 = X3
                        | member(X3,X2) )
                      & ilf_type(X3,set_type) ) )
                & ( ! [X3] :
                      ( ( ( member(X3,X2)
                          | X1 != X3 )
                        & ( X1 = X3
                          | ~ member(X3,X2) ) )
                      | ~ ilf_type(X3,set_type) )
                  | singleton(X1) != X2 ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( singleton(X1) = X2
                  | ? [X3] :
                      ( ( X1 != X3
                        | ~ member(X3,X2) )
                      & ( X1 = X3
                        | member(X3,X2) )
                      & ilf_type(X3,set_type) ) )
                & ( ! [X3] :
                      ( ( ( member(X3,X2)
                          | X1 != X3 )
                        & ( X1 = X3
                          | ~ member(X3,X2) ) )
                      | ~ ilf_type(X3,set_type) )
                  | singleton(X1) != X2 ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( singleton(X1) = X2
              <=> ! [X3] :
                    ( ( member(X3,X2)
                    <=> X1 = X3 )
                    | ~ ilf_type(X3,set_type) ) )
              | ~ ilf_type(X2,set_type) )
          | ~ 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,set_type)
             => ( singleton(X1) = X2
              <=> ! [X3] :
                    ( ilf_type(X3,set_type)
                   => ( member(X3,X2)
                    <=> X1 = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p5) ).

fof(f303,plain,
    member(sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),singleton(ordered_pair(sK2,sK3))),
    inference(resolution,[],[f301,f258]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK14(X0,X1),X0) ),
    inference(subsumption_resolution,[],[f257,f113]) ).

fof(f257,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK14(X0,X1),X0)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f165,f113]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | member(sK14(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK14(X0,X1),X1)
                & member(sK14(X0,X1),X0)
                & ilf_type(sK14(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f103,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK14(X0,X1),X1)
        & member(sK14(X0,X1),X0)
        & ilf_type(sK14(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ? [X2] :
                  ( ~ member(X2,X1)
                  & member(X2,X0)
                  & ilf_type(X2,set_type) ) )
            & ( ! [X2] :
                  ( member(X2,X1)
                  | ~ member(X2,X0)
                  | ~ ilf_type(X2,set_type) )
              | ~ member(X0,power_set(X1)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,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(flattening,[],[f59]) ).

fof(f59,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,[],[f17]) ).

fof(f17,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/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p17) ).

fof(f301,plain,
    ~ member(singleton(ordered_pair(sK2,sK3)),power_set(cross_product(sK0,sK1))),
    inference(resolution,[],[f298,f251]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1) ),
    inference(subsumption_resolution,[],[f250,f247]) ).

fof(f247,plain,
    ! [X2,X0] :
      ( ~ empty(X0)
      | ~ member(X2,X0) ),
    inference(subsumption_resolution,[],[f246,f113]) ).

fof(f246,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ empty(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f155,f113]) ).

fof(f155,plain,
    ! [X2,X0] :
      ( ~ member(X2,X0)
      | ~ ilf_type(X2,set_type)
      | ~ empty(X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ( member(sK12(X0),X0)
            & ilf_type(sK12(X0),set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f96,f97]) ).

fof(f97,plain,
    ! [X0] :
      ( ? [X1] :
          ( member(X1,X0)
          & ilf_type(X1,set_type) )
     => ( member(sK12(X0),X0)
        & ilf_type(sK12(X0),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X2] :
              ( ~ member(X2,X0)
              | ~ ilf_type(X2,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f95]) ).

fof(f95,plain,
    ! [X0] :
      ( ( ( empty(X0)
          | ? [X1] :
              ( member(X1,X0)
              & ilf_type(X1,set_type) ) )
        & ( ! [X1] :
              ( ~ member(X1,X0)
              | ~ ilf_type(X1,set_type) )
          | ~ empty(X0) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ( empty(X0)
      <=> ! [X1] :
            ( ~ member(X1,X0)
            | ~ ilf_type(X1,set_type) ) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( empty(X0)
      <=> ! [X1] :
            ( ilf_type(X1,set_type)
           => ~ member(X1,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p21) ).

fof(f250,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | empty(X1) ),
    inference(subsumption_resolution,[],[f249,f113]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f160,f113]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X0,member_type(X1))
              | ~ member(X0,X1) )
            & ( member(X0,X1)
              | ~ ilf_type(X0,member_type(X1)) ) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) )
          | ~ ilf_type(X1,set_type)
          | empty(X1) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ( ilf_type(X1,set_type)
            & ~ empty(X1) )
         => ( ilf_type(X0,member_type(X1))
          <=> member(X0,X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p19) ).

fof(f298,plain,
    ~ ilf_type(singleton(ordered_pair(sK2,sK3)),member_type(power_set(cross_product(sK0,sK1)))),
    inference(resolution,[],[f296,f242]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,member_type(power_set(X0))) ),
    inference(subsumption_resolution,[],[f241,f113]) ).

fof(f241,plain,
    ! [X0,X1] :
      ( ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f154,f113]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( 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(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,subset_type(X0))
          <=> ilf_type(X1,member_type(power_set(X0))) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,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/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p12) ).

fof(f296,plain,
    ~ ilf_type(singleton(ordered_pair(sK2,sK3)),subset_type(cross_product(sK0,sK1))),
    inference(resolution,[],[f222,f112]) ).

fof(f112,plain,
    ~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1)),
    inference(cnf_transformation,[],[f65]) ).

fof(f222,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ),
    inference(subsumption_resolution,[],[f221,f113]) ).

fof(f221,plain,
    ! [X3,X0,X1] :
      ( ilf_type(X3,relation_type(X0,X1))
      | ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f135,f113]) ).

fof(f135,plain,
    ! [X3,X0,X1] :
      ( 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(cnf_transformation,[],[f40]) ).

fof(f40,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,[],[f28]) ).

fof(f28,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,[],[f3]) ).

fof(f3,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/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p3) ).

fof(f304,plain,
    ~ member(sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),cross_product(sK0,sK1)),
    inference(resolution,[],[f301,f256]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK14(X0,X1),X1) ),
    inference(subsumption_resolution,[],[f255,f113]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK14(X0,X1),X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f166,f113]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ member(sK14(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f105]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Apr 30 17:12:11 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530
% 0.57/0.75  % (29755)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (29761)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.75  % (29757)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75  % (29756)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.75  % (29758)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.75  % (29759)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (29760)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75  % (29755)Refutation not found, incomplete strategy% (29755)------------------------------
% 0.57/0.75  % (29755)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (29755)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (29755)Memory used [KB]: 1098
% 0.57/0.75  % (29755)Time elapsed: 0.004 s
% 0.57/0.75  % (29755)Instructions burned: 8 (million)
% 0.57/0.75  % (29755)------------------------------
% 0.57/0.75  % (29755)------------------------------
% 0.57/0.75  % (29760)Refutation not found, incomplete strategy% (29760)------------------------------
% 0.57/0.75  % (29760)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (29760)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (29760)Memory used [KB]: 1030
% 0.57/0.75  % (29760)Time elapsed: 0.003 s
% 0.57/0.75  % (29760)Instructions burned: 3 (million)
% 0.57/0.75  % (29760)------------------------------
% 0.57/0.75  % (29760)------------------------------
% 0.57/0.75  % (29758)Refutation not found, incomplete strategy% (29758)------------------------------
% 0.57/0.75  % (29758)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (29758)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (29758)Memory used [KB]: 1032
% 0.57/0.75  % (29762)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.75  % (29758)Time elapsed: 0.003 s
% 0.57/0.75  % (29758)Instructions burned: 3 (million)
% 0.57/0.75  % (29758)------------------------------
% 0.57/0.75  % (29758)------------------------------
% 0.57/0.75  % (29759)Refutation not found, incomplete strategy% (29759)------------------------------
% 0.57/0.75  % (29759)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (29759)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (29759)Memory used [KB]: 1113
% 0.57/0.75  % (29759)Time elapsed: 0.004 s
% 0.57/0.75  % (29759)Instructions burned: 6 (million)
% 0.57/0.75  % (29759)------------------------------
% 0.57/0.75  % (29759)------------------------------
% 0.57/0.75  % (29762)Refutation not found, incomplete strategy% (29762)------------------------------
% 0.57/0.75  % (29762)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (29762)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (29762)Memory used [KB]: 1032
% 0.57/0.75  % (29762)Time elapsed: 0.003 s
% 0.57/0.75  % (29763)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.57/0.75  % (29762)Instructions burned: 4 (million)
% 0.57/0.75  % (29762)------------------------------
% 0.57/0.75  % (29762)------------------------------
% 0.57/0.76  % (29764)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.57/0.76  % (29765)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.57/0.76  % (29766)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.57/0.76  % (29767)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.57/0.76  % (29757)First to succeed.
% 0.57/0.76  % (29757)Refutation found. Thanks to Tanya!
% 0.57/0.76  % SZS status Theorem for Vampire---4
% 0.57/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76  % (29757)------------------------------
% 0.57/0.76  % (29757)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.76  % (29757)Termination reason: Refutation
% 0.57/0.76  
% 0.57/0.76  % (29757)Memory used [KB]: 1171
% 0.57/0.76  % (29757)Time elapsed: 0.012 s
% 0.57/0.76  % (29757)Instructions burned: 18 (million)
% 0.57/0.76  % (29757)------------------------------
% 0.57/0.76  % (29757)------------------------------
% 0.57/0.76  % (29725)Success in time 0.393 s
% 0.57/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------