TSTP Solution File: SET686+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:54:05 EDT 2023
% Result : Theorem 7.12s 2.41s
% Output : Refutation 7.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 53
% Syntax : Number of formulae : 127 ( 14 unt; 25 typ; 0 def)
% Number of atoms : 435 ( 36 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1377 ( 98 ~; 82 |; 56 &; 960 @)
% ( 12 <=>; 169 =>; 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 : 190 ( 0 ^; 169 !; 21 ?; 190 :)
% 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(inverse4_type,type,
inverse4: $i > $i > $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(subset_type_type,type,
subset_type: $i > $i ).
thf(binary_relation_type_type,type,
binary_relation_type: $i ).
thf(inverse2_type,type,
inverse2: $i > $i > $i ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(relation_like_type,type,
relation_like: $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $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 ).
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(sk12_type,type,
sk12: $i ).
thf(21,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',p9) ).
thf(120,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)],[21]) ).
thf(8,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 @ ( inverse2 @ C @ A ) )
<=> ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( member @ ( ordered_pair @ B @ D ) @ C )
& ( member @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(56,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 @ ( inverse2 @ C @ A ) )
=> ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( member @ ( ordered_pair @ B @ D ) @ C )
& ( member @ D @ A ) ) )
& ( ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( member @ ( ordered_pair @ B @ D ) @ C )
& ( member @ D @ A ) )
=> ( member @ B @ ( inverse2 @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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 @ A @ C ) )
=> ! [E: $i] :
( ( ilf_type @ E @ ( member_type @ A ) )
=> ( ( member @ E @ ( inverse4 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( ilf_type @ F @ ( member_type @ C ) )
& ( member @ ( ordered_pair @ E @ F ) @ D )
& ( member @ F @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_53) ).
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 @ A @ C ) )
=> ! [E: $i] :
( ( ilf_type @ E @ ( member_type @ A ) )
=> ( ( member @ E @ ( inverse4 @ A @ C @ D @ B ) )
<=> ? [F: $i] :
( ( ilf_type @ F @ ( member_type @ C ) )
& ( member @ ( ordered_pair @ E @ F ) @ 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 @ A @ C ) )
=> ! [E: $i] :
( ( ilf_type @ E @ ( member_type @ A ) )
=> ( ( ( member @ E @ ( inverse4 @ A @ C @ D @ B ) )
=> ? [F: $i] :
( ( ilf_type @ F @ ( member_type @ C ) )
& ( member @ ( ordered_pair @ E @ F ) @ D )
& ( member @ F @ B ) ) )
& ( ? [F: $i] :
( ( ilf_type @ F @ ( member_type @ C ) )
& ( member @ ( ordered_pair @ E @ F ) @ D )
& ( member @ F @ B ) )
=> ( member @ E @ ( inverse4 @ A @ C @ D @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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 @ ( subset_type @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
thf(52,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(36,plain,
( sk6
| ( member @ ( ordered_pair @ sk5 @ sk7 ) @ sk4 ) ),
inference(cnf,[status(esa)],[30]) ).
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/sandbox/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(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(20,axiom,
! [A: $i] : ( ilf_type @ A @ set_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
thf(118,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(119,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(cnf,[status(esa)],[118]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ $true
| ( empty @ B )
| ~ $true
| ~ ( member @ A @ B )
| ( ilf_type @ A @ ( member_type @ B ) ) ),
inference(rewrite,[status(thm)],[46,119]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( member @ A @ B )
| ( ilf_type @ A @ ( member_type @ B ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(227,plain,
! [B: $i,A: $i] :
( sk6
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ ( ordered_pair @ sk5 @ sk7 ) @ sk4 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36,222]) ).
thf(228,plain,
( sk6
| ( empty @ sk4 )
| ( ilf_type @ ( ordered_pair @ sk5 @ sk7 ) @ ( member_type @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( ordered_pair @ sk5 @ sk7 )),bind(B,$thf( sk4 ))]]) ).
thf(28,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',p5) ).
thf(141,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)],[28]) ).
thf(22,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',p17) ).
thf(124,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)],[22]) ).
thf(39,plain,
( sk6
| ( member @ sk7 @ sk2 ) ),
inference(cnf,[status(esa)],[30]) ).
thf(29,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
thf(145,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(43,plain,
ilf_type @ sk4 @ ( relation_type @ sk1 @ sk3 ),
inference(cnf,[status(esa)],[30]) ).
thf(15,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',p12) ).
thf(99,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)],[15]) ).
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/sandbox/benchmark/theBenchmark.p',p19) ).
thf(69,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(16,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',p22) ).
thf(101,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)],[16]) ).
thf(9,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',p21) ).
thf(61,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)],[9]) ).
thf(13,axiom,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
thf(89,plain,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( inverse2 @ A @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(116,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( inverse2 @ A @ B ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,plain,
~ ( empty @ sk3 ),
inference(cnf,[status(esa)],[30]) ).
thf(26,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',p13) ).
thf(137,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)],[26]) ).
thf(33,plain,
~ ( empty @ sk2 ),
inference(cnf,[status(esa)],[30]) ).
thf(24,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',p20) ).
thf(129,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)],[24]) ).
thf(41,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ ( member_type @ sk3 ) )
| ~ ( member @ ( ordered_pair @ sk5 @ A ) @ sk4 )
| ~ ( member @ A @ sk2 )
| ~ sk6 ),
inference(cnf,[status(esa)],[30]) ).
thf(25,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] : ( ilf_type @ B @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(134,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] : ( ilf_type @ B @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,plain,
ilf_type @ sk12 @ binary_relation_type,
inference(cnf,[status(esa)],[89]) ).
thf(191,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ sk5 @ A ) @ sk4 )
| ~ ( member @ A @ sk2 )
| ~ sk6
| ( ( ilf_type @ sk12 @ binary_relation_type )
!= ( ilf_type @ A @ ( member_type @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[90,41]) ).
thf(198,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ sk5 @ A ) @ sk4 )
| ~ ( member @ A @ sk2 )
| ~ sk6
| ( sk12 != A )
| ( ( member_type @ sk3 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[191]) ).
thf(205,plain,
( ~ ( member @ ( ordered_pair @ sk5 @ sk12 ) @ sk4 )
| ~ ( member @ sk12 @ sk2 )
| ~ sk6
| ( ( member_type @ sk3 )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[198]) ).
thf(34,plain,
ilf_type @ sk5 @ ( member_type @ sk1 ),
inference(cnf,[status(esa)],[30]) ).
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/sandbox/benchmark/theBenchmark.p',p15) ).
thf(64,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(180,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ sk5 @ A ) @ sk4 )
| ~ ( member @ A @ sk2 )
| ~ sk6
| ( ( ilf_type @ sk5 @ ( member_type @ sk1 ) )
!= ( ilf_type @ A @ ( member_type @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,41]) ).
thf(197,plain,
! [A: $i] :
( ~ ( member @ ( ordered_pair @ sk5 @ A ) @ sk4 )
| ~ ( member @ A @ sk2 )
| ~ sk6
| ( sk5 != A )
| ( ( member_type @ sk3 )
!= ( member_type @ sk1 ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(204,plain,
( ~ ( member @ ( ordered_pair @ sk5 @ sk5 ) @ sk4 )
| ~ ( member @ sk5 @ sk2 )
| ~ sk6
| ( ( member_type @ sk3 )
!= ( member_type @ sk1 ) ) ),
inference(simp,[status(thm)],[197]) ).
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/sandbox/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(53,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(235,plain,
! [A: $i] :
( ~ $true
| ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[53,119]) ).
thf(236,plain,
! [A: $i] : ( ilf_type @ ( sk9 @ A ) @ ( subset_type @ A ) ),
inference(simp,[status(thm)],[235]) ).
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/sandbox/benchmark/theBenchmark.p',p2) ).
thf(86,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(14,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',p3) ).
thf(91,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)],[14]) ).
thf(240,plain,
( ~ ( member @ ( ordered_pair @ sk5 @ sk5 ) @ sk4 )
| ~ ( member @ sk5 @ sk2 )
| ~ sk6
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[204]) ).
thf(247,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)],[204]) ).
thf(251,plain,
( ~ ( member @ sk5 @ sk2 )
| ~ sk6
| ( sk3 != sk1 )
| ( ( ordered_pair @ sk5 @ sk5 )
!= sk5 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[247]) ).
thf(35,plain,
( sk6
| ~ ( member @ sk5 @ ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(165,plain,
( sk6
| ( ( member @ sk7 @ sk2 )
!= ( member @ sk5 @ ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,35]) ).
thf(167,plain,
( sk6
| ( sk7 != sk5 )
| ( ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[165]) ).
thf(4,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',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(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(281,plain,
! [B: $i,A: $i] :
( ~ $true
| ( empty @ B )
| ~ $true
| ~ ( ilf_type @ A @ ( member_type @ B ) )
| ( member @ A @ B ) ),
inference(rewrite,[status(thm)],[47,119]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ~ ( ilf_type @ A @ ( member_type @ B ) )
| ( member @ A @ B ) ),
inference(simp,[status(thm)],[281]) ).
thf(5,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(50,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,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 @ ( inverse4 @ A @ B @ C @ D ) @ ( subset_type @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
thf(127,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 @ ( inverse4 @ A @ B @ C @ D ) @ ( subset_type @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,plain,
( sk6
| ( ilf_type @ sk7 @ ( member_type @ sk3 ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(40,plain,
( ( member @ sk5 @ ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 ) )
| ~ sk6 ),
inference(cnf,[status(esa)],[30]) ).
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 ) ) )
=> ( relation_like @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
thf(114,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)],[18]) ).
thf(62,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ ( power_set @ A ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(170,plain,
! [A: $i] :
( ~ $true
| ~ ( empty @ ( power_set @ A ) ) ),
inference(rewrite,[status(thm)],[62,119]) ).
thf(171,plain,
! [A: $i] :
~ ( empty @ ( power_set @ A ) ),
inference(simp,[status(thm)],[170]) ).
thf(27,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',p6) ).
thf(139,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)],[27]) ).
thf(166,plain,
( sk6
| ( ( member @ ( ordered_pair @ sk5 @ sk7 ) @ sk4 )
!= ( member @ sk5 @ ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,35]) ).
thf(168,plain,
( sk6
| ( ( ordered_pair @ sk5 @ sk7 )
!= sk5 )
| ( ( inverse4 @ sk1 @ sk3 @ sk4 @ sk2 )
!= sk4 ) ),
inference(simp,[status(thm)],[166]) ).
thf(223,plain,
! [B: $i,A: $i] :
( sk6
| ( empty @ B )
| ( ilf_type @ A @ ( member_type @ B ) )
| ( ( member @ sk7 @ sk2 )
!= ( member @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39,222]) ).
thf(224,plain,
( sk6
| ( empty @ sk2 )
| ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( sk7 )),bind(B,$thf( sk2 ))]]) ).
thf(272,plain,
( sk6
| $false
| ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
inference(rewrite,[status(thm)],[224,33]) ).
thf(273,plain,
( sk6
| ( ilf_type @ sk7 @ ( member_type @ sk2 ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(17,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 )
=> ( ( inverse4 @ A @ B @ C @ D )
= ( inverse2 @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
thf(111,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 )
=> ( ( inverse4 @ A @ B @ C @ D )
= ( inverse2 @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(439,plain,
$false,
inference(e,[status(thm)],[120,56,37,52,228,141,124,39,145,43,99,119,69,101,61,89,116,38,137,33,129,41,134,205,34,45,64,118,204,54,236,86,91,240,251,167,35,48,282,50,127,31,40,114,171,139,36,168,30,273,222,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET686+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 19:15:30 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/0.99 % [INFO] Parsing done (140ms).
% 1.39/1.00 % [INFO] Running in sequential loop mode.
% 1.74/1.19 % [INFO] eprover registered as external prover.
% 1.74/1.19 % [INFO] cvc4 registered as external prover.
% 1.74/1.19 % [INFO] Scanning for conjecture ...
% 1.92/1.26 % [INFO] Found a conjecture and 27 axioms. Running axiom selection ...
% 2.05/1.31 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 2.31/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.31/1.36 % [INFO] Type checking passed.
% 2.31/1.36 % [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 ...
% 7.12/2.41 % External prover 'e' found a proof!
% 7.12/2.41 % [INFO] Killing All external provers ...
% 7.12/2.41 % Time passed: 1884ms (effective reasoning time: 1409ms)
% 7.12/2.41 % 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)>
% 7.12/2.41 % 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
% 7.12/2.41 % No. of inferences in proof: 102
% 7.12/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1884 ms resp. 1409 ms w/o parsing
% 7.12/2.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.12/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------