TSTP Solution File: SET666+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Tue Apr 30 15:10:06 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   85 (  17 unt;   0 def)
%            Number of atoms       :  303 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  363 ( 145   ~; 131   |;  41   &)
%                                         (  17 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :  164 ( 156   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1246,plain,
    $false,
    inference(subsumption_resolution,[],[f1237,f1179]) ).

fof(f1179,plain,
    ~ member(sK19(cross_product(sK13,sK13),identity_relation_of(sK13)),cross_product(sK13,sK13)),
    inference(unit_resulting_resolution,[],[f1167,f170]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( ~ member(sK19(X0,X1),X0)
      | sP9(X0,X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ( sP9(X0,X1)
        | ( ~ member(sK19(X0,X1),X0)
          & member(sK19(X0,X1),X1)
          & ilf_type(sK19(X0,X1),set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP9(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f103,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK19(X0,X1),X0)
        & member(sK19(X0,X1),X1)
        & ilf_type(sK19(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( sP9(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1)
            & ilf_type(X2,set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP9(X0,X1) ) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X1,X0] :
      ( ( sP9(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0)
            & ilf_type(X2,set_type) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0)
            | ~ ilf_type(X2,set_type) )
        | ~ sP9(X1,X0) ) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X1,X0] :
      ( sP9(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0)
          | ~ ilf_type(X2,set_type) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f1167,plain,
    ~ sP9(cross_product(sK13,sK13),identity_relation_of(sK13)),
    inference(unit_resulting_resolution,[],[f214,f1165,f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ sP10(X0,X1)
      | ~ sP9(X1,X0)
      | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ( ( member(X0,power_set(X1))
          | ~ sP9(X1,X0) )
        & ( sP9(X1,X0)
          | ~ member(X0,power_set(X1)) ) )
      | ~ sP10(X0,X1) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
      <=> sP9(X1,X0) )
      | ~ sP10(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f1165,plain,
    ~ member(identity_relation_of(sK13),power_set(cross_product(sK13,sK13))),
    inference(unit_resulting_resolution,[],[f196,f1163,f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | ilf_type(X0,member_type(X1))
      | empty(X1) ),
    inference(subsumption_resolution,[],[f230,f125]) ).

fof(f125,plain,
    ! [X0] : ilf_type(X0,set_type),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] : ilf_type(X0,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ilf_type(X0,member_type(X1))
      | ~ member(X0,X1)
      | empty(X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f185,f125]) ).

fof(f185,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,[],[f114]) ).

fof(f114,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,[],[f50]) ).

fof(f50,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,[],[f49]) ).

fof(f49,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,[],[f18]) ).

fof(f18,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/sandbox/benchmark/theBenchmark.p',p18) ).

fof(f1163,plain,
    ~ ilf_type(identity_relation_of(sK13),member_type(power_set(cross_product(sK13,sK13)))),
    inference(unit_resulting_resolution,[],[f1150,f220]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,member_type(power_set(X0)))
      | ilf_type(X1,subset_type(X0)) ),
    inference(subsumption_resolution,[],[f219,f125]) ).

fof(f219,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,[],[f175,f125]) ).

fof(f175,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,[],[f107]) ).

fof(f107,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,[],[f45]) ).

fof(f45,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/sandbox/benchmark/theBenchmark.p',p12) ).

fof(f1150,plain,
    ~ ilf_type(identity_relation_of(sK13),subset_type(cross_product(sK13,sK13))),
    inference(unit_resulting_resolution,[],[f335,f208]) ).

fof(f208,plain,
    ! [X3,X0,X1] :
      ( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
      | ilf_type(X3,relation_type(X0,X1)) ),
    inference(subsumption_resolution,[],[f207,f125]) ).

fof(f207,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,[],[f156,f125]) ).

fof(f156,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,[],[f39]) ).

fof(f39,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,[],[f27]) ).

fof(f27,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,[],[f1]) ).

fof(f1,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/sandbox/benchmark/theBenchmark.p',p1) ).

fof(f335,plain,
    ~ ilf_type(identity_relation_of(sK13),relation_type(sK13,sK13)),
    inference(unit_resulting_resolution,[],[f124,f216]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ~ ilf_type(X1,relation_type(X0,X0))
      | ilf_type(X1,identity_relation_of_type(X0)) ),
    inference(subsumption_resolution,[],[f215,f125]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( ilf_type(X1,identity_relation_of_type(X0))
      | ~ ilf_type(X1,relation_type(X0,X0))
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f173,f125]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ilf_type(X1,identity_relation_of_type(X0))
      | ~ ilf_type(X1,relation_type(X0,X0))
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ilf_type(X1,identity_relation_of_type(X0))
              | ~ ilf_type(X1,relation_type(X0,X0)) )
            & ( ilf_type(X1,relation_type(X0,X0))
              | ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(nnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ilf_type(X1,identity_relation_of_type(X0))
          <=> ilf_type(X1,relation_type(X0,X0)) )
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ! [X1] :
          ( ilf_type(X1,set_type)
         => ( ilf_type(X1,identity_relation_of_type(X0))
          <=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).

fof(f124,plain,
    ~ ilf_type(identity_relation_of(sK13),identity_relation_of_type(sK13)),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ( ~ ilf_type(identity_relation_of(sK13),identity_relation_of_type(sK13))
    & ilf_type(sK13,set_type) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f28,f76]) ).

fof(f76,plain,
    ( ? [X0] :
        ( ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
        & ilf_type(X0,set_type) )
   => ( ~ ilf_type(identity_relation_of(sK13),identity_relation_of_type(sK13))
      & ilf_type(sK13,set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ? [X0] :
      ( ~ ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
      & ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,negated_conjecture,
    ~ ! [X0] :
        ( ilf_type(X0,set_type)
       => ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
    inference(negated_conjecture,[],[f25]) ).

fof(f25,conjecture,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_29) ).

fof(f196,plain,
    ! [X0] : ~ empty(power_set(X0)),
    inference(subsumption_resolution,[],[f129,f125]) ).

fof(f129,plain,
    ! [X0] :
      ( ~ empty(power_set(X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) )
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => ( ilf_type(power_set(X0),set_type)
        & ~ empty(power_set(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).

fof(f214,plain,
    ! [X0,X1] : sP10(X0,X1),
    inference(subsumption_resolution,[],[f213,f125]) ).

fof(f213,plain,
    ! [X0,X1] :
      ( sP10(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f171,f125]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( sP10(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP10(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(definition_folding,[],[f43,f71,f70]) ).

fof(f43,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,[],[f42]) ).

fof(f42,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,[],[f16]) ).

fof(f16,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/sandbox/benchmark/theBenchmark.p',p16) ).

fof(f1237,plain,
    member(sK19(cross_product(sK13,sK13),identity_relation_of(sK13)),cross_product(sK13,sK13)),
    inference(unit_resulting_resolution,[],[f324,f1180,f209]) ).

fof(f209,plain,
    ! [X3,X0,X1] :
      ( ~ sP7(X0,X1)
      | ~ member(X3,X1)
      | member(X3,X0) ),
    inference(subsumption_resolution,[],[f160,f125]) ).

fof(f160,plain,
    ! [X3,X0,X1] :
      ( member(X3,X0)
      | ~ member(X3,X1)
      | ~ ilf_type(X3,set_type)
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( sP7(X0,X1)
        | ( ~ member(sK18(X0,X1),X0)
          & member(sK18(X0,X1),X1)
          & ilf_type(sK18(X0,X1),set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP7(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X0)
          & member(X2,X1)
          & ilf_type(X2,set_type) )
     => ( ~ member(sK18(X0,X1),X0)
        & member(sK18(X0,X1),X1)
        & ilf_type(sK18(X0,X1),set_type) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( sP7(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1)
            & ilf_type(X2,set_type) ) )
      & ( ! [X3] :
            ( member(X3,X0)
            | ~ member(X3,X1)
            | ~ ilf_type(X3,set_type) )
        | ~ sP7(X0,X1) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,plain,
    ! [X1,X0] :
      ( ( sP7(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0)
            & ilf_type(X2,set_type) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0)
            | ~ ilf_type(X2,set_type) )
        | ~ sP7(X1,X0) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X1,X0] :
      ( sP7(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0)
          | ~ ilf_type(X2,set_type) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f1180,plain,
    member(sK19(cross_product(sK13,sK13),identity_relation_of(sK13)),identity_relation_of(sK13)),
    inference(unit_resulting_resolution,[],[f1167,f169]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( sP9(X0,X1)
      | member(sK19(X0,X1),X1) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f324,plain,
    ! [X0] : sP7(cross_product(X0,X0),identity_relation_of(X0)),
    inference(unit_resulting_resolution,[],[f195,f211,f158]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ~ sP8(X0,X1)
      | ~ subset(X0,X1)
      | sP7(X1,X0) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( ( subset(X0,X1)
          | ~ sP7(X1,X0) )
        & ( sP7(X1,X0)
          | ~ subset(X0,X1) ) )
      | ~ sP8(X0,X1) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
      <=> sP7(X1,X0) )
      | ~ sP8(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f211,plain,
    ! [X0,X1] : sP8(X0,X1),
    inference(subsumption_resolution,[],[f210,f125]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( sP8(X0,X1)
      | ~ ilf_type(X0,set_type) ),
    inference(subsumption_resolution,[],[f164,f125]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( sP8(X0,X1)
      | ~ ilf_type(X1,set_type)
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( sP8(X0,X1)
          | ~ ilf_type(X1,set_type) )
      | ~ ilf_type(X0,set_type) ),
    inference(definition_folding,[],[f41,f68,f67]) ).

fof(f41,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,[],[f40]) ).

fof(f40,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,[],[f14]) ).

fof(f14,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/sandbox/benchmark/theBenchmark.p',p14) ).

fof(f195,plain,
    ! [X0] : subset(identity_relation_of(X0),cross_product(X0,X0)),
    inference(subsumption_resolution,[],[f128,f125]) ).

fof(f128,plain,
    ! [X0] :
      ( subset(identity_relation_of(X0),cross_product(X0,X0))
      | ~ ilf_type(X0,set_type) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( subset(identity_relation_of(X0),cross_product(X0,X0))
      | ~ ilf_type(X0,set_type) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ilf_type(X0,set_type)
     => subset(identity_relation_of(X0),cross_product(X0,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n020.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 Apr 30 01:24:17 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (13796)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35  % (13800)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.36  % (13799)WARNING: value z3 for option sas not known
% 0.13/0.36  TRYING [3]
% 0.13/0.36  % (13798)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (13799)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36  % (13801)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36  % (13802)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36  % (13797)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (13803)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37  TRYING [4]
% 0.13/0.37  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.13/0.38  % (13803)First to succeed.
% 0.13/0.38  % (13799)Also succeeded, but the first one will report.
% 0.13/0.38  % (13803)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (13803)------------------------------
% 0.13/0.38  % (13803)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (13803)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (13803)Memory used [KB]: 1143
% 0.13/0.38  % (13803)Time elapsed: 0.024 s
% 0.13/0.38  % (13803)Instructions burned: 38 (million)
% 0.13/0.38  % (13803)------------------------------
% 0.13/0.38  % (13803)------------------------------
% 0.13/0.38  % (13796)Success in time 0.04 s
%------------------------------------------------------------------------------