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