TSTP Solution File: SET664+3 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 11:54:00 EDT 2023

% Result   : Theorem 37.84s 7.80s
% Output   : Refutation 37.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   94 (  16 unt;  16 typ;   0 def)
%            Number of atoms       :  249 (  39 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  748 (  91   ~;  84   |;   9   &; 504   @)
%                                         (   2 <=>;  58  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   8 con; 0-2 aty)
%            Number of variables   :  137 (   0   ^; 137   !;   0   ?; 137   :)

% Comments : 
%------------------------------------------------------------------------------
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(empty_set_type,type,
    empty_set: $i ).

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

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

thf(subset_type,type,
    subset: $i > $i > $o ).

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

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

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

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

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

thf(1,conjecture,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ! [C: $i] :
              ( ( ilf_type @ C @ ( relation_type @ B @ A ) )
             => ( ( ilf_type @ C @ ( relation_type @ B @ empty_set ) )
               => ( C = empty_set ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ilf_type @ A @ set_type )
       => ! [B: $i] :
            ( ( ilf_type @ B @ set_type )
           => ! [C: $i] :
                ( ( ilf_type @ C @ ( relation_type @ B @ A ) )
               => ( ( ilf_type @ C @ ( relation_type @ B @ empty_set ) )
                 => ( C = empty_set ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(37,plain,
    ~ ! [A: $i] :
        ( ( ilf_type @ A @ set_type )
       => ! [B: $i] :
            ( ( ilf_type @ B @ set_type )
           => ! [C: $i] :
                ( ( ilf_type @ C @ ( relation_type @ B @ A ) )
               => ( ( ilf_type @ C @ ( relation_type @ B @ empty_set ) )
                 => ( C = empty_set ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(38,plain,
    ilf_type @ sk3 @ ( relation_type @ sk2 @ sk1 ),
    inference(cnf,[status(esa)],[37]) ).

thf(20,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',p6) ).

thf(107,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)],[20]) ).

thf(108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
    inference(cnf,[status(esa)],[107]) ).

thf(110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[108]) ).

thf(18,axiom,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).

thf(103,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(104,plain,
    ! [A: $i] : ( ilf_type @ A @ set_type ),
    inference(cnf,[status(esa)],[103]) ).

thf(12815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
    inference(rewrite,[status(thm)],[110,104]) ).

thf(12816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[12815]) ).

thf(12843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
      | ( ( ilf_type @ sk3 @ ( relation_type @ sk2 @ sk1 ) )
       != ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[38,12816]) ).

thf(12844,plain,
    ilf_type @ sk3 @ ( subset_type @ ( cross_product @ sk2 @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[12843:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 ))]]) ).

thf(19,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',p28) ).

thf(105,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)],[19]) ).

thf(106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
      | ( relation_like @ C ) ),
    inference(cnf,[status(esa)],[105]) ).

thf(11795,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
      | ( relation_like @ C ) ),
    inference(rewrite,[status(thm)],[106,104]) ).

thf(11796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
      | ( relation_like @ C ) ),
    inference(simp,[status(thm)],[11795]) ).

thf(13076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( relation_like @ C )
      | ( ( ilf_type @ sk3 @ ( subset_type @ ( cross_product @ sk2 @ sk1 ) ) )
       != ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12844,11796]) ).

thf(13077,plain,
    relation_like @ sk3,
    inference(pattern_uni,[status(thm)],[13076:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 ))]]) ).

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',p13) ).

thf(60,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(63,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( relation_like @ A )
      | ~ ( ilf_type @ A @ set_type )
      | ( ilf_type @ A @ binary_relation_type ) ),
    inference(cnf,[status(esa)],[60]) ).

thf(64,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( relation_like @ A )
      | ( ilf_type @ A @ binary_relation_type ) ),
    inference(simp,[status(thm)],[63]) ).

thf(997,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( relation_like @ A )
      | ( ilf_type @ A @ binary_relation_type ) ),
    inference(rewrite,[status(thm)],[64,104]) ).

thf(998,plain,
    ! [A: $i] :
      ( ~ ( relation_like @ A )
      | ( ilf_type @ A @ binary_relation_type ) ),
    inference(simp,[status(thm)],[997]) ).

thf(13129,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
      | ( ( relation_like @ sk3 )
       != ( relation_like @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13077,998]) ).

thf(13130,plain,
    ilf_type @ sk3 @ binary_relation_type,
    inference(pattern_uni,[status(thm)],[13129:[bind(A,$thf( sk3 ))]]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ( ( ( domain_of @ A )
            = empty_set )
          | ( ( range_of @ A )
            = empty_set ) )
       => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

thf(122,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ binary_relation_type )
     => ( ( ( ( domain_of @ A )
            = empty_set )
          | ( ( range_of @ A )
            = empty_set ) )
       => ( A = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(123,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ binary_relation_type )
      | ( ( range_of @ A )
       != empty_set )
      | ( A = empty_set ) ),
    inference(cnf,[status(esa)],[122]) ).

thf(125,plain,
    ! [A: $i] :
      ( ( ( range_of @ A )
       != empty_set )
      | ( A = empty_set )
      | ~ ( ilf_type @ A @ binary_relation_type ) ),
    inference(lifteq,[status(thm)],[123]) ).

thf(14890,plain,
    ! [A: $i] :
      ( ( ( range_of @ A )
       != empty_set )
      | ( A = empty_set )
      | ( ( ilf_type @ sk3 @ binary_relation_type )
       != ( ilf_type @ A @ binary_relation_type ) ) ),
    inference(paramod_ordered,[status(thm)],[13130,125]) ).

thf(14891,plain,
    ( ( ( range_of @ sk3 )
     != empty_set )
    | ( sk3 = empty_set ) ),
    inference(pattern_uni,[status(thm)],[14890:[bind(A,$thf( sk3 ))]]) ).

thf(40,plain,
    ilf_type @ sk3 @ ( relation_type @ sk2 @ empty_set ),
    inference(cnf,[status(esa)],[37]) ).

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 ) )
             => ( ( subset @ ( domain_of @ C ) @ A )
                & ( subset @ ( range_of @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

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 ) )
             => ( ( subset @ ( domain_of @ C ) @ A )
                & ( subset @ ( range_of @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(67,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( subset @ ( range_of @ C ) @ B ) ),
    inference(cnf,[status(esa)],[65]) ).

thf(1370,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( subset @ ( range_of @ C ) @ B ) ),
    inference(rewrite,[status(thm)],[67,104]) ).

thf(1371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ C @ ( relation_type @ A @ B ) )
      | ( subset @ ( range_of @ C ) @ B ) ),
    inference(simp,[status(thm)],[1370]) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset @ ( range_of @ C ) @ B )
      | ( ( ilf_type @ sk3 @ ( relation_type @ sk2 @ empty_set ) )
       != ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[40,1371]) ).

thf(1428,plain,
    subset @ ( range_of @ sk3 ) @ empty_set,
    inference(pattern_uni,[status(thm)],[1427:[bind(A,$thf( sk2 )),bind(B,$thf( empty_set )),bind(C,$thf( sk3 ))]]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( subset @ A @ B )
          <=> ! [C: $i] :
                ( ( ilf_type @ C @ set_type )
               => ( ( member @ C @ A )
                 => ( member @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

thf(52,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ! [B: $i] :
          ( ( ilf_type @ B @ set_type )
         => ( ( ( subset @ A @ 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 ) ) )
             => ( subset @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ( member @ ( sk4 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(549,plain,
    ! [B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ( member @ ( sk4 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(rewrite,[status(thm)],[54,104]) ).

thf(550,plain,
    ! [B: $i,A: $i] :
      ( ( member @ ( sk4 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[549]) ).

thf(56,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( ilf_type @ B @ set_type )
      | ~ ( subset @ A @ B )
      | ~ ( ilf_type @ C @ set_type )
      | ~ ( member @ C @ A )
      | ( member @ C @ B ) ),
    inference(cnf,[status(esa)],[52]) ).

thf(264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ ( subset @ A @ B )
      | ~ $true
      | ~ ( member @ C @ A )
      | ( member @ C @ B ) ),
    inference(rewrite,[status(thm)],[56,104]) ).

thf(265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( member @ C @ A )
      | ( member @ C @ B ) ),
    inference(simp,[status(thm)],[264]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ~ ( member @ A @ empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).

thf(150,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ~ ( member @ A @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(151,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( member @ A @ empty_set ) ),
    inference(cnf,[status(esa)],[150]) ).

thf(252,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( member @ A @ empty_set ) ),
    inference(rewrite,[status(thm)],[151,104]) ).

thf(253,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(simp,[status(thm)],[252]) ).

thf(268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( member @ C @ A )
      | ( ( member @ C @ B )
       != ( member @ D @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[265,253]) ).

thf(269,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( member @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(273,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ empty_set )
      | ~ ( member @ B @ A ) ),
    inference(simp,[status(thm)],[269]) ).

thf(565,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ~ ( subset @ C @ empty_set )
      | ( ( member @ ( sk4 @ B @ A ) @ A )
       != ( member @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[550,273]) ).

thf(566,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ B @ A )
      | ~ ( subset @ B @ empty_set ) ),
    inference(pattern_uni,[status(thm)],[565:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( sk4 @ E @ F ))]]) ).

thf(570,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ B @ A )
      | ~ ( subset @ B @ empty_set ) ),
    inference(simp,[status(thm)],[566]) ).

thf(1567,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ B @ A )
      | ( ( subset @ ( range_of @ sk3 ) @ empty_set )
       != ( subset @ B @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[1428,570]) ).

thf(1568,plain,
    ! [A: $i] : ( subset @ ( range_of @ sk3 ) @ A ),
    inference(pattern_uni,[status(thm)],[1567:[bind(A,$thf( A )),bind(B,$thf( range_of @ sk3 ))]]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( subset @ A @ empty_set )
       => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

thf(100,plain,
    ! [A: $i] :
      ( ( ilf_type @ A @ set_type )
     => ( ( subset @ A @ empty_set )
       => ( A = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(101,plain,
    ! [A: $i] :
      ( ~ ( ilf_type @ A @ set_type )
      | ~ ( subset @ A @ empty_set )
      | ( A = empty_set ) ),
    inference(cnf,[status(esa)],[100]) ).

thf(102,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ ( ilf_type @ A @ set_type )
      | ~ ( subset @ A @ empty_set ) ),
    inference(lifteq,[status(thm)],[101]) ).

thf(10411,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ $true
      | ~ ( subset @ A @ empty_set ) ),
    inference(rewrite,[status(thm)],[102,104]) ).

thf(10412,plain,
    ! [A: $i] :
      ( ( A = empty_set )
      | ~ ( subset @ A @ empty_set ) ),
    inference(simp,[status(thm)],[10411]) ).

thf(10544,plain,
    ! [B: $i,A: $i] :
      ( ( B = empty_set )
      | ( ( subset @ ( range_of @ sk3 ) @ A )
       != ( subset @ B @ empty_set ) ) ),
    inference(paramod_ordered,[status(thm)],[1568,10412]) ).

thf(10545,plain,
    ( ( range_of @ sk3 )
    = empty_set ),
    inference(pattern_uni,[status(thm)],[10544:[bind(A,$thf( empty_set )),bind(B,$thf( range_of @ sk3 ))]]) ).

thf(15804,plain,
    ( ( empty_set != empty_set )
    | ( sk3 = empty_set ) ),
    inference(rewrite,[status(thm)],[14891,10545]) ).

thf(15805,plain,
    sk3 = empty_set,
    inference(simp,[status(thm)],[15804]) ).

thf(41,plain,
    sk3 != empty_set,
    inference(cnf,[status(esa)],[37]) ).

thf(43,plain,
    sk3 != empty_set,
    inference(lifteq,[status(thm)],[41]) ).

thf(15806,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[15805,43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May 18 19:30:27 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.92/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.35/0.98  % [INFO] 	 Parsing done (138ms). 
% 1.35/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.74/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.74/1.20  % [INFO] 	 Scanning for conjecture ... 
% 2.00/1.27  % [INFO] 	 Found a conjecture and 34 axioms. Running axiom selection ... 
% 2.00/1.31  % [INFO] 	 Axiom selection finished. Selected 34 axioms (removed 0 axioms). 
% 2.27/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.37/1.37  % [INFO] 	 Type checking passed. 
% 2.37/1.37  % [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 ... 
% 37.84/7.79  % [INFO] 	 Killing All external provers ... 
% 37.84/7.79  % Time passed: 7287ms (effective reasoning time: 6800ms)
% 37.84/7.79  % 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)>
% 37.84/7.80  % Axioms used in derivation (9): p19, p4, p2, p28, p1, p13, p6, p3, p33
% 37.84/7.80  % No. of inferences in proof: 78
% 37.84/7.80  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7287 ms resp. 6800 ms w/o parsing
% 37.84/7.83  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.84/7.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------