TSTP Solution File: SET681+3 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 May 21 03:03:32 EDT 2024

% Result   : Theorem 4.38s 2.07s
% Output   : Refutation 4.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   84 (   5 unt;  18 typ;   0 def)
%            Number of atoms       :  308 (  18 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 1022 (  17   ~;   0   |;  48   &; 763   @)
%                                         (  12 <=>; 182  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  18 usr;   3 con; 0-3 aty)
%            Number of variables   :  171 (   0   ^ 150   !;  21   ?; 171   :)

% 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(range_type,type,
    range: $i > $i > $i > $i ).

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

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

thf(range_of_type,type,
    range_of: $i > $i ).

thf(domain_of_type,type,
    domain_of: $i > $i ).

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

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

thf(domain_type,type,
    domain: $i > $i > $i > $i ).

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

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

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

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

thf(21,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/sandbox/benchmark/theBenchmark.p',p3) ).

thf(115,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)],[21]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ( domain @ A @ B @ C )
                = ( domain_of @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).

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 ) )
             => ( ( domain @ A @ B @ C )
                = ( domain_of @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',p5) ).

thf(137,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)],[29]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).

thf(53,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ilf_type @ ( singleton @ A ) @ set_type ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).

thf(96,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ilf_type @ ( singleton @ A ) @ set_type ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(25,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/sandbox/benchmark/theBenchmark.p',p7) ).

thf(128,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)],[25]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ! [B: $i] :
          ( ( ~ ( empty @ B )
            & ( ilf_type @ B @ set_type ) )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ B @ A ) )
             => ! [D: $i] :
                  ( ( ilf_type @ D @ ( member_type @ A ) )
                 => ( ( member @ D @ ( range @ B @ A @ C ) )
                  <=> ? [E: $i] :
                        ( ( ilf_type @ E @ ( member_type @ B ) )
                        & ( member @ ( ordered_pair @ E @ D ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_48) ).

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

thf(34,plain,
    ~ ! [A: $i] :
        ( ( ~ ( empty @ A )
          & ( ilf_type @ A @ set_type ) )
       => ! [B: $i] :
            ( ( ~ ( empty @ B )
              & ( ilf_type @ B @ set_type ) )
           => ! [C: $i] :
                ( ( ilf_type @ C @ ( relation_type @ B @ A ) )
               => ! [D: $i] :
                    ( ( ilf_type @ D @ ( member_type @ A ) )
                   => ( ( ( member @ D @ ( range @ B @ A @ C ) )
                       => ? [E: $i] :
                            ( ( ilf_type @ E @ ( member_type @ B ) )
                            & ( member @ ( ordered_pair @ E @ D ) @ C ) ) )
                      & ( ? [E: $i] :
                            ( ( ilf_type @ E @ ( member_type @ B ) )
                            & ( member @ ( ordered_pair @ E @ D ) @ C ) )
                       => ( member @ D @ ( range @ B @ A @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,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/sandbox/benchmark/theBenchmark.p',p4) ).

thf(98,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)],[17]) ).

thf(10,axiom,
    ? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).

thf(63,plain,
    ? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(14,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/sandbox/benchmark/theBenchmark.p',p22) ).

thf(87,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)],[14]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ( relation_like @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).

thf(110,plain,
    ! [A: $i] :
      ( ( ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ( relation_like @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(24,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/sandbox/benchmark/theBenchmark.p',p8) ).

thf(125,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)],[24]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ binary_relation_type )
         => ( ( member @ A @ ( range_of @ B ) )
          <=> ? [C: $i] :
                ( ( ilf_type @ C @ set_type )
                & ( member @ ( ordered_pair @ C @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

thf(46,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ binary_relation_type )
         => ( ( ( member @ A @ ( range_of @ B ) )
             => ? [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                  & ( member @ ( ordered_pair @ C @ A ) @ B ) ) )
            & ( ? [C: $i] :
                  ( ( ilf_type @ C @ set_type )
                  & ( member @ ( ordered_pair @ C @ A ) @ B ) )
             => ( member @ A @ ( range_of @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).

thf(57,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(18,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/sandbox/benchmark/theBenchmark.p',p6) ).

thf(106,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)],[18]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ~ ( empty @ ( power_set @ A ) )
        & ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).

thf(84,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)],[13]) ).

thf(33,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/sandbox/benchmark/theBenchmark.p',p24) ).

thf(147,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)],[33]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( ilf_type @ A @ set_type ) )
     => ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).

thf(61,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)],[9]) ).

thf(27,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/sandbox/benchmark/theBenchmark.p',p15) ).

thf(133,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)],[27]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( empty @ A )
      <=> ! [B: $i] :
            ( ( ilf_type @ B @ set_type )
           => ~ ( member @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).

thf(92,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)],[15]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).

thf(65,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,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/sandbox/benchmark/theBenchmark.p',p13) ).

thf(59,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)],[8]) ).

thf(22,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/sandbox/benchmark/theBenchmark.p',p17) ).

thf(118,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)],[22]) ).

thf(26,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/sandbox/benchmark/theBenchmark.p',p19) ).

thf(130,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)],[26]) ).

thf(28,axiom,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).

thf(135,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(20,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/sandbox/benchmark/theBenchmark.p',p16) ).

thf(112,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)],[20]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ilf_type @ ( range_of @ A ) @ set_type ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).

thf(123,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ilf_type @ ( range_of @ A ) @ set_type ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(32,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/sandbox/benchmark/theBenchmark.p',p26) ).

thf(145,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)],[32]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ binary_relation_type )
             => ( ( member @ ( ordered_pair @ A @ B ) @ C )
               => ( ( member @ A @ ( domain_of @ C ) )
                  & ( member @ B @ ( range_of @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

thf(50,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ binary_relation_type )
             => ( ( member @ ( ordered_pair @ A @ B ) @ C )
               => ( ( member @ A @ ( domain_of @ C ) )
                  & ( member @ B @ ( range_of @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,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/sandbox/benchmark/theBenchmark.p',p21) ).

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)],[12]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).

thf(55,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ( range @ A @ B @ C )
                = ( range_of @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).

thf(139,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
             => ( ( range @ A @ B @ C )
                = ( range_of @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(161,plain,
    $false,
    inference(e,[status(thm)],[115,142,137,53,96,128,34,98,63,87,110,125,46,57,106,84,147,61,133,92,65,59,118,130,135,112,123,145,50,67,55,139]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SET681+3 : TPTP v8.2.0. Released v2.2.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n009.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 12:39:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.97/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.13/0.99  % [INFO] 	 Parsing done (113ms). 
% 1.13/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.76/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.76/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.76/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.27  % [INFO] 	 Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ... 
% 2.17/1.32  % [INFO] 	 Axiom selection finished. Selected 31 axioms (removed 0 axioms). 
% 2.17/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.17/1.37  % [INFO] 	 Type checking passed. 
% 2.17/1.38  % [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 ... 
% 4.38/2.07  % External prover 'e' found a proof!
% 4.38/2.07  % [INFO] 	 Killing All external provers ... 
% 4.38/2.07  % Time passed: 1531ms (effective reasoning time: 1067ms)
% 4.38/2.07  % 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)>
% 4.38/2.07  % Axioms used in derivation (31): p27, p12, p18, p26, p3, p22, p11, p2, p17, p9, p24, p16, p20, p10, p19, p4, p7, p5, p23, p21, p29, p15, p25, p14, p28, p1, p31, p30, p13, p6, p8
% 4.38/2.07  % No. of inferences in proof: 66
% 4.38/2.07  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1531 ms resp. 1067 ms w/o parsing
% 4.69/2.12  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.69/2.12  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------