TSTP Solution File: SET656+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET656+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 : Sun May  5 09:07:51 EDT 2024

% Result   : Theorem 0.56s 0.75s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  102 (  13 unt;   0 def)
%            Number of atoms       :  396 (  22 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  486 ( 192   ~; 181   |;  58   &)
%                                         (  16 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :  190 ( 172   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f467,plain,
    $false,
    inference(avatar_sat_refutation,[],[f341,f425,f459,f466]) ).

fof(f466,plain,
    ~ spl18_6,
    inference(avatar_contradiction_clause,[],[f465]) ).

fof(f465,plain,
    ( $false
    | ~ spl18_6 ),
    inference(subsumption_resolution,[],[f464,f126]) ).

fof(f126,plain,
    sK2 != intersection(sK2,cross_product(sK0,sK1)),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ( sK2 != intersection(sK2,cross_product(sK0,sK1))
    & ilf_type(sK2,relation_type(sK0,sK1))
    & ilf_type(sK1,set_type)
    & ilf_type(sK0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f73,f72,f71]) ).

fof(f71,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( intersection(X2,cross_product(X0,X1)) != X2
                & ilf_type(X2,relation_type(X0,X1)) )
            & ilf_type(X1,set_type) )
        & ilf_type(X0,set_type) )
   => ( ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(sK0,X1)) != X2
              & ilf_type(X2,relation_type(sK0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(sK0,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( intersection(X2,cross_product(sK0,X1)) != X2
            & ilf_type(X2,relation_type(sK0,X1)) )
        & ilf_type(X1,set_type) )
   => ( ? [X2] :
          ( intersection(X2,cross_product(sK0,sK1)) != X2
          & ilf_type(X2,relation_type(sK0,sK1)) )
      & ilf_type(sK1,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ( ? [X2] :
        ( intersection(X2,cross_product(sK0,sK1)) != X2
        & ilf_type(X2,relation_type(sK0,sK1)) )
   => ( sK2 != intersection(sK2,cross_product(sK0,sK1))
      & ilf_type(sK2,relation_type(sK0,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( intersection(X2,cross_product(X0,X1)) != X2
              & ilf_type(X2,relation_type(X0,X1)) )
          & ilf_type(X1,set_type) )
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ! [X1] :
            ( ilf_type(X1,set_type)
           => ! [X2] :
                ( ilf_type(X2,relation_type(X0,X1))
               => intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f31,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,relation_type(X0,X1))
             => intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',prove_relset_1_18) ).

fof(f464,plain,
    ( sK2 = intersection(sK2,cross_product(sK0,sK1))
    | ~ spl18_6 ),
    inference(resolution,[],[f420,f218]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | intersection(X0,X1) = X0 ),
    inference(subsumption_resolution,[],[f217,f127]) ).

fof(f127,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p30) ).

fof(f217,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f134,f127]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ subset(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1] :
          ( intersection(X0,X1) = X0
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ! [X1] :
          ( intersection(X0,X1) = X0
          | ~ subset(X0,X1)
          | ~ ilf_type(X1,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)
         => ( subset(X0,X1)
           => intersection(X0,X1) = X0 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p1) ).

fof(f420,plain,
    ( subset(sK2,cross_product(sK0,sK1))
    | ~ spl18_6 ),
    inference(avatar_component_clause,[],[f418]) ).

fof(f418,plain,
    ( spl18_6
  <=> subset(sK2,cross_product(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

fof(f459,plain,
    spl18_7,
    inference(avatar_contradiction_clause,[],[f458]) ).

fof(f458,plain,
    ( $false
    | spl18_7 ),
    inference(subsumption_resolution,[],[f456,f125]) ).

fof(f125,plain,
    ilf_type(sK2,relation_type(sK0,sK1)),
    inference(cnf_transformation,[],[f74]) ).

fof(f456,plain,
    ( ~ ilf_type(sK2,relation_type(sK0,sK1))
    | spl18_7 ),
    inference(resolution,[],[f451,f222]) ).

fof(f222,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1)) ),
    inference(subsumption_resolution,[],[f221,f127]) ).

fof(f221,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f137,f127]) ).

fof(f137,plain,
    ! [X2,X0,X1] :
      ( ilf_type(X2,subset_type(cross_product(X0,X1)))
      | ~ ilf_type(X2,relation_type(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,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,[],[f33]) ).

fof(f33,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,[],[f6]) ).

fof(f6,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.dd5uJ1ntxE/Vampire---4.8_24657',p6) ).

fof(f451,plain,
    ( ~ ilf_type(sK2,subset_type(cross_product(sK0,sK1)))
    | spl18_7 ),
    inference(resolution,[],[f441,f268]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f267,f127]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ilf_type(X1,member_type(power_set(X0)))
      | ~ ilf_type(X1,subset_type(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f168,f127]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( 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(cnf_transformation,[],[f103]) ).

fof(f103,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,[],[f57]) ).

fof(f57,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,[],[f13]) ).

fof(f13,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.dd5uJ1ntxE/Vampire---4.8_24657',p13) ).

fof(f441,plain,
    ( ~ ilf_type(sK2,member_type(power_set(cross_product(sK0,sK1))))
    | spl18_7 ),
    inference(subsumption_resolution,[],[f437,f278]) ).

fof(f278,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f183,f127]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p20) ).

fof(f437,plain,
    ( ~ ilf_type(sK2,member_type(power_set(cross_product(sK0,sK1))))
    | empty(power_set(cross_product(sK0,sK1)))
    | spl18_7 ),
    inference(resolution,[],[f424,f277]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | empty(X1) ),
    inference(subsumption_resolution,[],[f276,f127]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f181,f127]) ).

fof(f181,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ ilf_type(X0,member_type(X1))
      | ~ ilf_type(X1,set_type)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,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,[],[f64]) ).

fof(f64,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,[],[f63]) ).

fof(f63,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,[],[f21]) ).

fof(f21,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.dd5uJ1ntxE/Vampire---4.8_24657',p21) ).

fof(f424,plain,
    ( ~ member(sK2,power_set(cross_product(sK0,sK1)))
    | spl18_7 ),
    inference(avatar_component_clause,[],[f422]) ).

fof(f422,plain,
    ( spl18_7
  <=> member(sK2,power_set(cross_product(sK0,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).

fof(f425,plain,
    ( spl18_6
    | ~ spl18_7
    | spl18_1 ),
    inference(avatar_split_clause,[],[f409,f330,f422,f418]) ).

fof(f330,plain,
    ( spl18_1
  <=> member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

fof(f409,plain,
    ( ~ member(sK2,power_set(cross_product(sK0,sK1)))
    | subset(sK2,cross_product(sK0,sK1))
    | spl18_1 ),
    inference(resolution,[],[f345,f251]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( member(sK7(X0,X1),X0)
      | subset(X0,X1) ),
    inference(subsumption_resolution,[],[f250,f127]) ).

fof(f250,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK7(X0,X1),X0)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f155,f127]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK7(X0,X1),X0)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,X1)
              | ( ~ member(sK7(X0,X1),X1)
                & member(sK7(X0,X1),X0)
                & ilf_type(sK7(X0,X1),set_type) ) )
            & ( ! [X3] :
                  ( member(X3,X1)
                  | ~ member(X3,X0)
                  | ~ ilf_type(X3,set_type) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f90,f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK7(X0,X1),X1)
        & member(sK7(X0,X1),X0)
        & ilf_type(sK7(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,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) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( subset(X0,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) )
              | ~ subset(X0,X1) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( subset(X0,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)
         => ( subset(X0,X1)
          <=> ! [X2] :
                ( ilf_type(X2,set_type)
               => ( member(X2,X0)
                 => member(X2,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p17) ).

fof(f345,plain,
    ( ! [X0] :
        ( ~ member(sK7(sK2,cross_product(sK0,sK1)),X0)
        | ~ member(X0,power_set(cross_product(sK0,sK1))) )
    | spl18_1 ),
    inference(resolution,[],[f332,f285]) ).

fof(f285,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ member(X0,power_set(X1)) ),
    inference(subsumption_resolution,[],[f284,f127]) ).

fof(f284,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f283,f127]) ).

fof(f283,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ member(X0,power_set(X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f188,f127]) ).

fof(f188,plain,
    ! [X3,X0,X1] :
      ( 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(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( member(X0,power_set(X1))
              | ( ~ member(sK17(X0,X1),X1)
                & member(sK17(X0,X1),X0)
                & ilf_type(sK17(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,[sK17])],[f120,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK17(X0,X1),X1)
        & member(sK17(X0,X1),X0)
        & ilf_type(sK17(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,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,[],[f119]) ).

fof(f119,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,[],[f70]) ).

fof(f70,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,[],[f69]) ).

fof(f69,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,[],[f19]) ).

fof(f19,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.dd5uJ1ntxE/Vampire---4.8_24657',p19) ).

fof(f332,plain,
    ( ~ member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1))
    | spl18_1 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f341,plain,
    ~ spl18_1,
    inference(avatar_split_clause,[],[f328,f330]) ).

fof(f328,plain,
    ~ member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1)),
    inference(superposition,[],[f311,f287]) ).

fof(f287,plain,
    ! [X0] : intersection(X0,X0) = X0,
    inference(resolution,[],[f218,f247]) ).

fof(f247,plain,
    ! [X0] : subset(X0,X0),
    inference(subsumption_resolution,[],[f152,f127]) ).

fof(f152,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( subset(X0,X0)
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => subset(X0,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p18) ).

fof(f311,plain,
    ! [X0] : ~ member(sK7(sK2,cross_product(sK0,sK1)),intersection(cross_product(sK0,sK1),X0)),
    inference(trivial_inequality_removal,[],[f307]) ).

fof(f307,plain,
    ! [X0] :
      ( sK2 != sK2
      | ~ member(sK7(sK2,cross_product(sK0,sK1)),intersection(cross_product(sK0,sK1),X0)) ),
    inference(superposition,[],[f126,f298]) ).

fof(f298,plain,
    ! [X2,X0,X1] :
      ( intersection(X0,X1) = X0
      | ~ member(sK7(X0,X1),intersection(X1,X2)) ),
    inference(resolution,[],[f289,f216]) ).

fof(f216,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(subsumption_resolution,[],[f215,f127]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f214,f127]) ).

fof(f214,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f131,f127]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1))
      | ~ ilf_type(X2,set_type)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( member(X2,intersection(X0,X1))
                  | ~ member(X2,X1)
                  | ~ member(X2,X0) )
                & ( ( member(X2,X1)
                    & member(X2,X0) )
                  | ~ member(X2,intersection(X0,X1)) ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( member(X2,intersection(X0,X1))
                  | ~ member(X2,X1)
                  | ~ member(X2,X0) )
                & ( ( member(X2,X1)
                    & member(X2,X0) )
                  | ~ member(X2,intersection(X0,X1)) ) )
              | ~ 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] :
              ( ( member(X2,intersection(X0,X1))
              <=> ( member(X2,X1)
                  & member(X2,X0) ) )
              | ~ ilf_type(X2,set_type) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ! [X2] :
              ( ilf_type(X2,set_type)
             => ( member(X2,intersection(X0,X1))
              <=> ( member(X2,X1)
                  & member(X2,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p4) ).

fof(f289,plain,
    ! [X0,X1] :
      ( ~ member(sK7(X0,X1),X1)
      | intersection(X0,X1) = X0 ),
    inference(resolution,[],[f249,f218]) ).

fof(f249,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK7(X0,X1),X1) ),
    inference(subsumption_resolution,[],[f248,f127]) ).

fof(f248,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK7(X0,X1),X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f156,f127]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK7(X0,X1),X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14  % 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
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 16:50:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35  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.dd5uJ1ntxE/Vampire---4.8_24657
% 0.56/0.73  % (24907)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)
% 0.56/0.73  % (24901)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)
% 0.56/0.73  % (24903)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.73  % (24902)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)
% 0.56/0.73  % (24906)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)
% 0.56/0.73  % (24904)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)
% 0.56/0.73  % (24905)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)
% 0.56/0.73  % (24906)Refutation not found, incomplete strategy% (24906)------------------------------
% 0.56/0.73  % (24906)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.73  % (24904)Refutation not found, incomplete strategy% (24904)------------------------------
% 0.56/0.73  % (24904)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.73  % (24904)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.73  
% 0.56/0.73  % (24904)Memory used [KB]: 1041
% 0.56/0.73  % (24904)Time elapsed: 0.003 s
% 0.56/0.73  % (24904)Instructions burned: 3 (million)
% 0.56/0.73  % (24906)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.73  
% 0.56/0.73  % (24906)Memory used [KB]: 1026
% 0.56/0.73  % (24906)Time elapsed: 0.003 s
% 0.56/0.73  % (24906)Instructions burned: 3 (million)
% 0.56/0.73  % (24904)------------------------------
% 0.56/0.73  % (24904)------------------------------
% 0.56/0.73  % (24906)------------------------------
% 0.56/0.73  % (24906)------------------------------
% 0.56/0.74  % (24908)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)
% 0.56/0.74  % (24909)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)
% 0.56/0.74  % (24908)Refutation not found, incomplete strategy% (24908)------------------------------
% 0.56/0.74  % (24908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (24908)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (24908)Memory used [KB]: 1040
% 0.56/0.74  % (24908)Time elapsed: 0.004 s
% 0.56/0.74  % (24908)Instructions burned: 3 (million)
% 0.56/0.74  % (24908)------------------------------
% 0.56/0.74  % (24908)------------------------------
% 0.56/0.74  % (24903)First to succeed.
% 0.56/0.75  % (24911)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)
% 0.56/0.75  % (24903)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24820"
% 0.56/0.75  % (24903)Refutation found. Thanks to Tanya!
% 0.56/0.75  % SZS status Theorem for Vampire---4
% 0.56/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.75  % (24903)------------------------------
% 0.56/0.75  % (24903)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (24903)Termination reason: Refutation
% 0.56/0.75  
% 0.56/0.75  % (24903)Memory used [KB]: 1184
% 0.56/0.75  % (24903)Time elapsed: 0.015 s
% 0.56/0.75  % (24903)Instructions burned: 23 (million)
% 0.56/0.75  % (24820)Success in time 0.387 s
% 0.56/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------