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