TSTP Solution File: SET685+3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET685+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.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 : Fri May 19 11:54:04 EDT 2023

% Result   : Theorem 6.71s 2.50s
% Output   : Refutation 6.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  129 (  14 unt;  25 typ;   0 def)
%            Number of atoms       :  446 (  39 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives : 1419 ( 101   ~;  87   |;  56   &; 992   @)
%                                         (  12 <=>; 171  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   28 (  25 usr;  12 con; 0-4 aty)
%            Number of variables   :  192 (   0   ^; 171   !;  21   ?; 192   :)

% Comments : 
%------------------------------------------------------------------------------
thf(empty_type,type,
    empty: $i > $o ).

thf(ilf_type_type,type,
    ilf_type: $i > $i > $o ).

thf(set_type_type,type,
    set_type: $i ).

thf(relation_type_type,type,
    relation_type: $i > $i > $i ).

thf(member_type_type,type,
    member_type: $i > $i ).

thf(member_type,type,
    member: $i > $i > $o ).

thf(image4_type,type,
    image4: $i > $i > $i > $i > $i ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

thf(subset_type_type,type,
    subset_type: $i > $i ).

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(cross_product_type,type,
    cross_product: $i > $i > $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(binary_relation_type_type,type,
    binary_relation_type: $i ).

thf(relation_like_type,type,
    relation_like: $i > $o ).

thf(image_type,type,
    image: $i > $i > $i ).

thf(power_set_type,type,
    power_set: $i > $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $o ).

thf(sk7_type,type,
    sk7: $i ).

thf(sk9_type,type,
    sk9: $i > $i ).

thf(sk11_type,type,
    sk11: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ! [B: $i] :
          ( ( ~ ( empty @ B )
            & ( ilf_type @ B @ set_type ) )
         => ! [C: $i] :
              ( ( ~ ( empty @ C )
                & ( ilf_type @ C @ set_type ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ ( relation_type @ C @ A ) )
                 => ! [E: $i] :
                      ( ( ilf_type @ E @ ( member_type @ A ) )
                     => ( ( member @ E @ ( image4 @ C @ A @ D @ B ) )
                      <=> ? [F: $i] :
                            ( ( ilf_type @ F @ ( member_type @ C ) )
                            & ( member @ ( ordered_pair @ F @ E ) @ D )
                            & ( member @ F @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_52) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( empty @ A )
          & ( ilf_type @ A @ set_type ) )
       => ! [B: $i] :
            ( ( ~ ( empty @ B )
              & ( ilf_type @ B @ set_type ) )
           => ! [C: $i] :
                ( ( ~ ( empty @ C )
                  & ( ilf_type @ C @ set_type ) )
               => ! [D: $i] :
                    ( ( ilf_type @ D @ ( relation_type @ C @ A ) )
                   => ! [E: $i] :
                        ( ( ilf_type @ E @ ( member_type @ A ) )
                       => ( ( member @ E @ ( image4 @ C @ A @ D @ B ) )
                        <=> ? [F: $i] :
                              ( ( ilf_type @ F @ ( member_type @ C ) )
                              & ( member @ ( ordered_pair @ F @ E ) @ D )
                              & ( member @ F @ B ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(30,plain,
    ~ ! [A: $i] :
        ( ( ~ ( empty @ A )
          & ( ilf_type @ A @ set_type ) )
       => ! [B: $i] :
            ( ( ~ ( empty @ B )
              & ( ilf_type @ B @ set_type ) )
           => ! [C: $i] :
                ( ( ~ ( empty @ C )
                  & ( ilf_type @ C @ set_type ) )
               => ! [D: $i] :
                    ( ( ilf_type @ D @ ( relation_type @ C @ A ) )
                   => ! [E: $i] :
                        ( ( ilf_type @ E @ ( member_type @ A ) )
                       => ( ( ( member @ E @ ( image4 @ C @ A @ D @ B ) )
                           => ? [F: $i] :
                                ( ( ilf_type @ F @ ( member_type @ C ) )
                                & ( member @ ( ordered_pair @ F @ E ) @ D )
                                & ( member @ F @ B ) ) )
                          & ( ? [F: $i] :
                                ( ( ilf_type @ F @ ( member_type @ C ) )
                                & ( member @ ( ordered_pair @ F @ E ) @ D )
                                & ( member @ F @ B ) )
                           => ( member @ E @ ( image4 @ C @ A @ D @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(39,plain,
    ( sk6
    | ( member @ sk7 @ sk2 ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(36,plain,
    ( sk6
    | ~ ( member @ sk5 @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(167,plain,
    ( sk6
    | ( ( member @ sk7 @ sk2 )
     != ( member @ sk5 @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[39,36]) ).

thf(169,plain,
    ( sk6
    | ( sk7 != sk5 )
    | ( ( image4 @ sk3 @ sk1 @ sk4 @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[167]) ).

thf(41,plain,
    ilf_type @ sk4 @ ( relation_type @ sk3 @ sk1 ),
    inference(cnf,[status(esa)],[30]) ).

thf(44,plain,
    ( sk6
    | ( ilf_type @ sk7 @ ( member_type @ sk3 ) ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( empty @ A )
      <=> ! [B: $i] :
            ( ( ilf_type @ B @ set_type )
           => ~ ( member @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).

thf(108,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( ( empty @ A )
         => ! [B: $i] :
              ( ( ilf_type @ B @ set_type )
             => ~ ( member @ B @ A ) ) )
        & ( ! [B: $i] :
              ( ( ilf_type @ B @ set_type )
             => ~ ( member @ B @ A ) )
         => ( empty @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).

thf(48,plain,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(43,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ ( member_type @ sk3 ) )
      | ~ ( member @ ( ordered_pair @ A @ sk5 ) @ sk4 )
      | ~ ( member @ A @ sk2 )
      | ~ sk6 ),
    inference(cnf,[status(esa)],[30]) ).

thf(33,plain,
    ilf_type @ sk5 @ ( member_type @ sk1 ),
    inference(cnf,[status(esa)],[30]) ).

thf(191,plain,
    ! [A: $i] :
      ( ~ ( member @ ( ordered_pair @ A @ sk5 ) @ sk4 )
      | ~ ( member @ A @ sk2 )
      | ~ sk6
      | ( ( ilf_type @ sk5 @ ( member_type @ sk1 ) )
       != ( ilf_type @ A @ ( member_type @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[33,43]) ).

thf(200,plain,
    ! [A: $i] :
      ( ~ ( member @ ( ordered_pair @ A @ sk5 ) @ sk4 )
      | ~ ( member @ A @ sk2 )
      | ~ sk6
      | ( sk5 != A )
      | ( ( member_type @ sk3 )
       != ( member_type @ sk1 ) ) ),
    inference(simp,[status(thm)],[191]) ).

thf(205,plain,
    ( ~ ( member @ ( ordered_pair @ sk5 @ sk5 ) @ sk4 )
    | ~ ( member @ sk5 @ sk2 )
    | ~ sk6
    | ( ( member_type @ sk3 )
     != ( member_type @ sk1 ) ) ),
    inference(simp,[status(thm)],[200]) ).

thf(239,plain,
    ( ~ ( member @ ( ordered_pair @ sk5 @ sk5 ) @ sk4 )
    | ~ ( member @ sk5 @ sk2 )
    | ~ sk6
    | ( sk3 != sk1 ) ),
    inference(simp,[status(thm)],[205]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ binary_relation_type )
             => ( ( member @ B @ ( image @ C @ A ) )
              <=> ? [D: $i] :
                    ( ( ilf_type @ D @ set_type )
                    & ( member @ ( ordered_pair @ D @ B ) @ C )
                    & ( member @ D @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

thf(101,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ binary_relation_type )
             => ( ( ( member @ B @ ( image @ C @ A ) )
                 => ? [D: $i] :
                      ( ( ilf_type @ D @ set_type )
                      & ( member @ ( ordered_pair @ D @ B ) @ C )
                      & ( member @ D @ A ) ) )
                & ( ? [D: $i] :
                      ( ( ilf_type @ D @ set_type )
                      & ( member @ ( ordered_pair @ D @ B ) @ C )
                      & ( member @ D @ A ) )
                 => ( member @ B @ ( image @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(13,axiom,
    ? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).

thf(87,plain,
    ? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(88,plain,
    ilf_type @ sk11 @ binary_relation_type,
    inference(cnf,[status(esa)],[87]) ).

thf(35,plain,
    ( sk6
    | ( member @ ( ordered_pair @ sk7 @ sk5 ) @ sk4 ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(168,plain,
    ( sk6
    | ( ( member @ ( ordered_pair @ sk7 @ sk5 ) @ sk4 )
     != ( member @ sk5 @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[35,36]) ).

thf(170,plain,
    ( sk6
    | ( ( ordered_pair @ sk7 @ sk5 )
     != sk5 )
    | ( ( image4 @ sk3 @ sk1 @ sk4 @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[168]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).

thf(115,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(179,plain,
    ! [A: $i] :
      ( ~ ( member @ ( ordered_pair @ A @ sk5 ) @ sk4 )
      | ~ ( member @ A @ sk2 )
      | ~ sk6
      | ( ( ilf_type @ sk11 @ binary_relation_type )
       != ( ilf_type @ A @ ( member_type @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[88,43]) ).

thf(195,plain,
    ! [A: $i] :
      ( ~ ( member @ ( ordered_pair @ A @ sk5 ) @ sk4 )
      | ~ ( member @ A @ sk2 )
      | ~ sk6
      | ( sk11 != A )
      | ( ( member_type @ sk3 )
       != binary_relation_type ) ),
    inference(simp,[status(thm)],[179]) ).

thf(202,plain,
    ( ~ ( member @ ( ordered_pair @ sk11 @ sk5 ) @ sk4 )
    | ~ ( member @ sk11 @ sk2 )
    | ~ sk6
    | ( ( member_type @ sk3 )
     != binary_relation_type ) ),
    inference(simp,[status(thm)],[195]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ! [C: $i] :
                ( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
               => ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
            & ! [C: $i] :
                ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
               => ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).

thf(56,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ! [C: $i] :
                ( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
               => ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
            & ! [C: $i] :
                ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
               => ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(28,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ( ( image4 @ A @ B @ C @ D )
                    = ( image @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).

thf(142,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ( ( image4 @ A @ B @ C @ D )
                    = ( image @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(42,plain,
    ( ( member @ sk5 @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) )
    | ~ sk6 ),
    inference(cnf,[status(esa)],[30]) ).

thf(37,plain,
    ~ ( empty @ sk1 ),
    inference(cnf,[status(esa)],[30]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( unordered_pair @ A @ B ) @ set_type ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).

thf(52,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( unordered_pair @ A @ B ) @ set_type ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).

thf(125,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ( relation_like @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).

thf(106,plain,
    ! [A: $i] :
      ( ( ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ( relation_like @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ set_type )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ! [E: $i] :
                      ( ( ilf_type @ E @ ( relation_type @ A @ B ) )
                     => ( ( member @ ( ordered_pair @ C @ D ) @ E )
                       => ( ( member @ C @ A )
                          & ( member @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

thf(84,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ set_type )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ! [E: $i] :
                      ( ( ilf_type @ E @ ( relation_type @ A @ B ) )
                     => ( ( member @ ( ordered_pair @ C @ D ) @ E )
                       => ( ( member @ C @ A )
                          & ( member @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ~ ( empty @ B )
            & ( ilf_type @ B @ set_type ) )
         => ( ( ilf_type @ A @ ( member_type @ B ) )
          <=> ( member @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).

thf(45,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ~ ( empty @ B )
            & ( ilf_type @ B @ set_type ) )
         => ( ( ( ilf_type @ A @ ( member_type @ B ) )
             => ( member @ A @ B ) )
            & ( ( member @ A @ B )
             => ( ilf_type @ A @ ( member_type @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ( empty @ B )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( ilf_type @ A @ ( member_type @ B ) )
      | ( member @ A @ B ) ),
    inference(cnf,[status(esa)],[45]) ).

thf(29,axiom,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).

thf(145,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(146,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(cnf,[status(esa)],[145]) ).

thf(279,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ( empty @ B )
      | ~ $true
      | ~ ( ilf_type @ A @ ( member_type @ B ) )
      | ( member @ A @ B ) ),
    inference(rewrite,[status(thm)],[47,146]) ).

thf(280,plain,
    ! [B: $i,A: $i] :
      ( ( empty @ B )
      | ~ ( ilf_type @ A @ ( member_type @ B ) )
      | ( member @ A @ B ) ),
    inference(simp,[status(thm)],[279]) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ( empty @ B )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( member @ A @ B )
      | ( ilf_type @ A @ ( member_type @ B ) ) ),
    inference(cnf,[status(esa)],[45]) ).

thf(220,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ( empty @ B )
      | ~ $true
      | ~ ( member @ A @ B )
      | ( ilf_type @ A @ ( member_type @ B ) ) ),
    inference(rewrite,[status(thm)],[46,146]) ).

thf(221,plain,
    ! [B: $i,A: $i] :
      ( ( empty @ B )
      | ~ ( member @ A @ B )
      | ( ilf_type @ A @ ( member_type @ B ) ) ),
    inference(simp,[status(thm)],[220]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( image @ A @ B ) @ set_type ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).

thf(132,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( image @ A @ B ) @ set_type ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( relation_like @ A )
      <=> ! [B: $i] :
            ( ( ilf_type @ B @ set_type )
           => ( ( member @ B @ A )
             => ? [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                  & ? [D: $i] :
                      ( ( ilf_type @ D @ set_type )
                      & ( B
                        = ( ordered_pair @ C @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).

thf(89,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( ( relation_like @ A )
         => ! [B: $i] :
              ( ( ilf_type @ B @ set_type )
             => ( ( member @ B @ A )
               => ? [C: $i] :
                    ( ( ilf_type @ C @ set_type )
                    & ? [D: $i] :
                        ( ( ilf_type @ D @ set_type )
                        & ( B
                          = ( ordered_pair @ C @ D ) ) ) ) ) ) )
        & ( ! [B: $i] :
              ( ( ilf_type @ B @ set_type )
             => ( ( member @ B @ A )
               => ? [C: $i] :
                    ( ( ilf_type @ C @ set_type )
                    & ? [D: $i] :
                        ( ( ilf_type @ D @ set_type )
                        & ( B
                          = ( ordered_pair @ C @ D ) ) ) ) ) )
         => ( relation_like @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ilf_type @ ( singleton @ A ) @ set_type ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).

thf(60,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ilf_type @ ( singleton @ A ) @ set_type ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( member @ A @ ( power_set @ B ) )
          <=> ! [C: $i] :
                ( ( ilf_type @ C @ set_type )
               => ( ( member @ C @ A )
                 => ( member @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).

thf(117,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( ( member @ A @ ( power_set @ B ) )
             => ! [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                 => ( ( member @ C @ A )
                   => ( member @ C @ B ) ) ) )
            & ( ! [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                 => ( ( member @ C @ A )
                   => ( member @ C @ B ) ) )
             => ( member @ A @ ( power_set @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(38,plain,
    ~ ( empty @ sk3 ),
    inference(cnf,[status(esa)],[30]) ).

thf(246,plain,
    ( ~ ( member @ sk5 @ sk2 )
    | ~ sk6
    | ( ( member_type @ sk3 )
     != ( member_type @ sk1 ) )
    | ( ( member @ ( ordered_pair @ sk5 @ sk5 ) @ sk4 )
     != ( member @ sk5 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[205]) ).

thf(256,plain,
    ( ~ ( member @ sk5 @ sk2 )
    | ~ sk6
    | ( sk3 != sk1 )
    | ( ( ordered_pair @ sk5 @ sk5 )
     != sk5 )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[246]) ).

thf(224,plain,
    ! [B: $i,A: $i] :
      ( sk6
      | ( empty @ B )
      | ( ilf_type @ A @ ( member_type @ B ) )
      | ( ( member @ ( ordered_pair @ sk7 @ sk5 ) @ sk4 )
       != ( member @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[35,221]) ).

thf(225,plain,
    ( sk6
    | ( empty @ sk4 )
    | ( ilf_type @ ( ordered_pair @ sk7 @ sk5 ) @ ( member_type @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( ordered_pair @ sk7 @ sk5 )),bind(B,$thf( sk4 ))]]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ set_type )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ! [E: $i] :
                      ( ( ilf_type @ E @ set_type )
                     => ( ( E
                          = ( ordered_pair @ C @ D ) )
                      <=> ( E
                          = ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

thf(134,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ set_type )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ! [E: $i] :
                      ( ( ilf_type @ E @ set_type )
                     => ( ( ( E
                            = ( ordered_pair @ C @ D ) )
                         => ( E
                            = ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) )
                        & ( ( E
                            = ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) )
                         => ( E
                            = ( ordered_pair @ C @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(32,plain,
    ~ ( empty @ sk2 ),
    inference(cnf,[status(esa)],[30]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

thf(54,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(222,plain,
    ! [B: $i,A: $i] :
      ( sk6
      | ( empty @ B )
      | ( ilf_type @ A @ ( member_type @ B ) )
      | ( ( member @ sk7 @ sk2 )
       != ( member @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[39,221]) ).

thf(223,plain,
    ( sk6
    | ( empty @ sk2 )
    | ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).

thf(235,plain,
    ( sk6
    | $false
    | ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
    inference(rewrite,[status(thm)],[223,32]) ).

thf(236,plain,
    ( sk6
    | ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
    inference(simp,[status(thm)],[235]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ( ilf_type @ ( image4 @ A @ B @ C @ D ) @ ( subset_type @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).

thf(130,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ set_type )
                 => ( ilf_type @ ( image4 @ A @ B @ C @ D ) @ ( subset_type @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( ilf_type @ B @ ( subset_type @ A ) )
          <=> ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).

thf(112,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( ( ilf_type @ B @ ( subset_type @ A ) )
             => ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) )
            & ( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
             => ( ilf_type @ B @ ( subset_type @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).

thf(50,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( A = B )
          <=> ! [C: $i] :
                ( ( ilf_type @ C @ set_type )
               => ( ( member @ C @ A )
                <=> ( member @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

thf(67,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( ( A = B )
             => ! [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                 => ( ( ( member @ C @ A )
                     => ( member @ C @ B ) )
                    & ( ( member @ C @ B )
                     => ( member @ C @ A ) ) ) ) )
            & ( ! [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                 => ( ( ( member @ C @ A )
                     => ( member @ C @ B ) )
                    & ( ( member @ C @ B )
                     => ( member @ C @ A ) ) ) )
             => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ~ ( empty @ ( power_set @ A ) )
        & ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).

thf(127,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ~ ( empty @ ( power_set @ A ) )
        & ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(51,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ) ),
    inference(cnf,[status(esa)],[50]) ).

thf(230,plain,
    ! [A: $i] :
      ( ~ $true
      | ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ) ),
    inference(rewrite,[status(thm)],[51,146]) ).

thf(231,plain,
    ! [A: $i] : ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ),
    inference(simp,[status(thm)],[230]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
             => ( relation_like @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).

thf(99,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
             => ( relation_like @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(128,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( empty @ ( power_set @ A ) ) ),
    inference(cnf,[status(esa)],[127]) ).

thf(162,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( empty @ ( power_set @ A ) ) ),
    inference(rewrite,[status(thm)],[128,146]) ).

thf(163,plain,
    ! [A: $i] :
      ~ ( empty @ ( power_set @ A ) ),
    inference(simp,[status(thm)],[162]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( ilf_type @ A @ binary_relation_type )
      <=> ( ( relation_like @ A )
          & ( ilf_type @ A @ set_type ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).

thf(62,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( ( ilf_type @ A @ binary_relation_type )
         => ( ( relation_like @ A )
            & ( ilf_type @ A @ set_type ) ) )
        & ( ( ( relation_like @ A )
            & ( ilf_type @ A @ set_type ) )
         => ( ilf_type @ A @ binary_relation_type ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(226,plain,
    ! [B: $i,A: $i] :
      ( ~ sk6
      | ( empty @ B )
      | ( ilf_type @ A @ ( member_type @ B ) )
      | ( ( member @ sk5 @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) )
       != ( member @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[42,221]) ).

thf(227,plain,
    ( ~ sk6
    | ( empty @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) )
    | ( ilf_type @ sk5 @ ( member_type @ ( image4 @ sk3 @ sk1 @ sk4 @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( sk5 )),bind(B,$thf( image4 @ sk3 @ sk1 @ sk4 @ sk2 ))]]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( unordered_pair @ A @ B )
            = ( unordered_pair @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).

thf(122,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( unordered_pair @ A @ B )
            = ( unordered_pair @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(440,plain,
    $false,
    inference(e,[status(thm)],[169,41,44,39,108,48,43,239,101,88,170,115,202,56,142,42,37,52,125,106,84,280,221,132,89,60,117,38,33,256,225,134,205,32,45,54,236,130,35,112,145,50,67,127,231,99,87,36,146,30,163,62,227,122]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET685+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n014.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 18:50:43 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.84/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/0.97  % [INFO] 	 Parsing done (131ms). 
% 1.30/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.94/1.25  % [INFO] 	 Found a conjecture and 27 axioms. Running axiom selection ... 
% 1.94/1.30  % [INFO] 	 Axiom selection finished. Selected 27 axioms (removed 0 axioms). 
% 2.14/1.34  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.14/1.35  % [INFO] 	 Type checking passed. 
% 2.14/1.35  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 6.71/2.49  % External prover 'e' found a proof!
% 6.71/2.49  % [INFO] 	 Killing All external provers ... 
% 6.71/2.50  % Time passed: 1982ms (effective reasoning time: 1517ms)
% 6.71/2.50  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.71/2.50  % Axioms used in derivation (27): p27, p12, p18, p15, p26, p3, p22, p11, p2, p17, p9, p1, p24, p13, p16, p20, p10, p19, p4, p7, p5, p23, p21, p25, p14, p6, p8
% 6.71/2.50  % No. of inferences in proof: 104
% 6.71/2.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1982 ms resp. 1517 ms w/o parsing
% 6.71/2.54  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.71/2.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------