TSTP Solution File: SET660+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET660+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 8.07s 2.67s
% Output : Refutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 62
% Syntax : Number of formulae : 171 ( 14 unt; 27 typ; 0 def)
% Number of atoms : 558 ( 58 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1777 ( 143 ~; 122 |; 46 &;1246 @)
% ( 15 <=>; 205 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 10 con; 0-3 aty)
% Number of variables : 315 ( 0 ^; 294 !; 21 ?; 315 :)
% 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(member_type,type,
member: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(subset_type_type,type,
subset_type: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(binary_relation_type_type,type,
binary_relation_type: $i ).
thf(relation_like_type,type,
relation_like: $i > $o ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(member_type_type,type,
member_type: $i > $i ).
thf(domain_of_type,type,
domain_of: $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: $o ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk19_type,type,
sk19: $i > $i ).
thf(22,axiom,
! [A: $i] : ( ilf_type @ A @ set_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
thf(137,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(138,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(cnf,[status(esa)],[137]) ).
thf(36,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
thf(184,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(17,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',p26) ).
thf(117,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)],[17]) ).
thf(10,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ A @ ( power_set @ B ) )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
thf(77,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)],[10]) ).
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/sandbox/benchmark/theBenchmark.p',p27) ).
thf(129,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(6,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',p8) ).
thf(59,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)],[6]) ).
thf(1,conjecture,
! [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 )
=> ( ( member @ D @ B )
=> ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( member @ ( ordered_pair @ E @ D ) @ C ) ) ) )
<=> ( ( range @ A @ B @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_23) ).
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 @ A @ B ) )
=> ( ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( member @ ( ordered_pair @ E @ D ) @ C ) ) ) )
<=> ( ( range @ A @ B @ C )
= B ) ) ) ) ),
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 @ A @ B ) )
=> ( ( ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( member @ ( ordered_pair @ E @ D ) @ C ) ) ) )
=> ( ( range @ A @ B @ C )
= B ) )
& ( ( ( range @ A @ B @ C )
= B )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ B )
=> ? [E: $i] :
( ( ilf_type @ E @ set_type )
& ( member @ ( ordered_pair @ E @ D ) @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
ilf_type @ sk3 @ ( relation_type @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[37]) ).
thf(47,plain,
( sk4
| ( member @ sk6 @ sk2 ) ),
inference(cnf,[status(esa)],[37]) ).
thf(25,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',p28) ).
thf(144,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)],[25]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ A )
| ~ ( ilf_type @ B @ set_type )
| ~ ( member @ B @ A ) ),
inference(cnf,[status(esa)],[144]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( empty @ A )
| ~ $true
| ~ ( member @ B @ A ) ),
inference(rewrite,[status(thm)],[145,138]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( member @ B @ A ) ),
inference(simp,[status(thm)],[236]) ).
thf(240,plain,
! [B: $i,A: $i] :
( sk4
| ~ ( empty @ A )
| ( ( member @ sk6 @ sk2 )
!= ( member @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,237]) ).
thf(241,plain,
( sk4
| ~ ( empty @ sk2 ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( sk2 )),bind(B,$thf( sk6 ))]]) ).
thf(11,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(82,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)],[11]) ).
thf(3,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',p7) ).
thf(51,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)],[3]) ).
thf(52,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)],[51]) ).
thf(54,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)],[52]) ).
thf(347,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)],[54,138]) ).
thf(348,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)],[347]) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( ilf_type @ sk3 @ ( relation_type @ sk1 @ sk2 ) )
!= ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,348]) ).
thf(354,plain,
ilf_type @ sk3 @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
thf(139,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(140,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( subset @ A @ A ) ),
inference(cnf,[status(esa)],[139]) ).
thf(256,plain,
! [A: $i] :
( ~ $true
| ( subset @ A @ A ) ),
inference(rewrite,[status(thm)],[140,138]) ).
thf(257,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[256]) ).
thf(28,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',p5) ).
thf(152,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)],[28]) ).
thf(5,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(57,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)],[5]) ).
thf(31,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(164,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)],[31]) ).
thf(14,axiom,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
thf(106,plain,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
<=> ( member @ C @ B ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
thf(61,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [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)],[7]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',p20) ).
thf(112,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)],[16]) ).
thf(116,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)],[112]) ).
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)],[116,138]) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(simp,[status(thm)],[264]) ).
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',p23) ).
thf(74,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(53,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 ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(rewrite,[status(thm)],[53,138]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(29,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
thf(160,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( empty @ D )
| ( ( member @ C @ B )
!= ( member @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[265,237]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ ( empty @ B ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(43,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( member @ A @ sk2 )
| ( member @ ( ordered_pair @ ( sk5 @ A ) @ A ) @ sk3 )
| ~ sk4 ),
inference(cnf,[status(esa)],[37]) ).
thf(223,plain,
! [A: $i] :
( ~ $true
| ~ ( member @ A @ sk2 )
| ( member @ ( ordered_pair @ ( sk5 @ A ) @ A ) @ sk3 )
| ~ sk4 ),
inference(rewrite,[status(thm)],[43,138]) ).
thf(224,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 )
| ( member @ ( ordered_pair @ ( sk5 @ A ) @ A ) @ sk3 )
| ~ sk4 ),
inference(simp,[status(thm)],[223]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ sk2 )
| ~ sk4
| ~ ( empty @ B )
| ( ( member @ ( ordered_pair @ ( sk5 @ A ) @ A ) @ sk3 )
!= ( member @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[224,237]) ).
thf(239,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( ordered_pair @ ( sk5 @ E ) @ E ))]]) ).
thf(242,plain,
! [A: $i] :
( ~ ( member @ A @ sk2 )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(simp,[status(thm)],[239]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ~ sk4
| ~ ( empty @ sk3 )
| ( ( member @ C @ B )
!= ( member @ D @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[265,242]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( member @ B @ A )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ sk2 )
| ~ ( member @ B @ A )
| ~ sk4
| ~ ( empty @ sk3 ) ),
inference(simp,[status(thm)],[281]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ( ilf_type @ sk3 @ ( relation_type @ sk1 @ sk2 ) )
!= ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,302]) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( sk3 != C )
| ( ( relation_type @ sk1 @ sk2 )
!= ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(317,plain,
! [B: $i,A: $i] :
( ( ilf_type @ sk3 @ ( relation_type @ A @ B ) )
| ( ( relation_type @ sk1 @ sk2 )
!= ( subset_type @ ( cross_product @ A @ B ) ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(33,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
thf(169,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,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(141,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)],[24]) ).
thf(21,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',p24) ).
thf(134,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)],[21]) ).
thf(32,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( range @ A @ B @ C )
= ( range_of @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
thf(166,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( range @ A @ B @ C )
= ( range_of @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,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',p6) ).
thf(148,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)],[26]) ).
thf(107,plain,
ilf_type @ sk11 @ binary_relation_type,
inference(cnf,[status(esa)],[106]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( ilf_type @ sk11 @ binary_relation_type )
!= ( ilf_type @ C @ ( relation_type @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,348]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( sk11 != C )
| ( ( relation_type @ A @ B )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[366]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( ilf_type @ sk11 @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( relation_type @ A @ B )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[367]) ).
thf(27,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(150,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ ( sk19 @ A ) @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(262,plain,
! [A: $i] :
( ~ $true
| ( ilf_type @ ( sk19 @ A ) @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[151,138]) ).
thf(263,plain,
! [A: $i] : ( ilf_type @ ( sk19 @ A ) @ ( subset_type @ A ) ),
inference(simp,[status(thm)],[262]) ).
thf(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( ( ilf_type @ ( sk19 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,302]) ).
thf(307,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk19 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) ),
inference(pattern_uni,[status(thm)],[306:[bind(A,$thf( cross_product @ F @ G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( sk19 @ ( cross_product @ F @ G ) ))]]) ).
thf(313,plain,
! [B: $i,A: $i] : ( ilf_type @ ( sk19 @ ( cross_product @ A @ B ) ) @ ( relation_type @ A @ B ) ),
inference(simp,[status(thm)],[307]) ).
thf(46,plain,
( ( ( range @ sk1 @ sk2 @ sk3 )
!= sk2 )
| ~ sk4 ),
inference(cnf,[status(esa)],[37]) ).
thf(49,plain,
( ( ( range @ sk1 @ sk2 @ sk3 )
!= sk2 )
| ~ sk4 ),
inference(lifteq,[status(thm)],[46]) ).
thf(35,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( member @ ( ordered_pair @ A @ B ) @ C )
=> ( ( member @ A @ ( domain_of @ C ) )
& ( member @ B @ ( range_of @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
thf(181,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ binary_relation_type )
=> ( ( member @ ( ordered_pair @ A @ B ) @ C )
=> ( ( member @ A @ ( domain_of @ C ) )
& ( member @ B @ ( range_of @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(75,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ ( power_set @ A ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(212,plain,
! [A: $i] :
( ~ $true
| ~ ( empty @ ( power_set @ A ) ) ),
inference(rewrite,[status(thm)],[75,138]) ).
thf(213,plain,
! [A: $i] :
~ ( empty @ ( power_set @ A ) ),
inference(simp,[status(thm)],[212]) ).
thf(42,plain,
! [A: $i] :
( sk4
| ~ ( ilf_type @ A @ set_type )
| ~ ( member @ ( ordered_pair @ A @ sk6 ) @ sk3 ) ),
inference(cnf,[status(esa)],[37]) ).
thf(48,plain,
! [A: $i] :
( sk4
| ~ ( ilf_type @ A @ set_type )
| ~ ( member @ ( ordered_pair @ A @ sk6 ) @ sk3 ) ),
inference(simp,[status(thm)],[42]) ).
thf(250,plain,
! [A: $i] :
( sk4
| ~ $true
| ~ ( member @ ( ordered_pair @ A @ sk6 ) @ sk3 ) ),
inference(rewrite,[status(thm)],[48,138]) ).
thf(251,plain,
! [A: $i] :
( sk4
| ~ ( member @ ( ordered_pair @ A @ sk6 ) @ sk3 ) ),
inference(simp,[status(thm)],[250]) ).
thf(15,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ ( range_of @ A ) )
<=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(108,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ B @ ( range_of @ A ) )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) )
& ( ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) )
=> ( member @ B @ ( range_of @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
thf(162,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(254,plain,
! [A: $i] :
( sk4
| ( ( member @ ( ordered_pair @ A @ sk6 ) @ sk3 )
!= ( member @ sk6 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[47,251]) ).
thf(255,plain,
! [A: $i] :
( sk4
| ( ( ordered_pair @ A @ sk6 )
!= sk6 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[254]) ).
thf(45,plain,
( sk4
| ( ( range @ sk1 @ sk2 @ sk3 )
= sk2 ) ),
inference(cnf,[status(esa)],[37]) ).
thf(50,plain,
( ( ( range @ sk1 @ sk2 @ sk3 )
= sk2 )
| sk4 ),
inference(lifteq,[status(thm)],[45]) ).
thf(18,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',p25) ).
thf(127,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)],[18]) ).
thf(8,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
thf(72,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ( ilf_type @ sk11 @ binary_relation_type )
!= ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[107,302]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( sk11 != C )
| ( ( subset_type @ ( cross_product @ A @ B ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[308]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ilf_type @ sk11 @ ( relation_type @ A @ B ) )
| ( ( subset_type @ ( cross_product @ A @ B ) )
!= binary_relation_type ) ),
inference(simp,[status(thm)],[309]) ).
thf(12,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( A = B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
<=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
thf(87,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( A = B )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) ) )
& ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
thf(104,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
thf(55,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( ( ilf_type @ A @ set_type )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,302]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ilf_type @ D @ ( relation_type @ B @ C ) )
| ( A != D )
| ( ( subset_type @ ( cross_product @ B @ C ) )
!= set_type ) ),
inference(simp,[status(thm)],[303]) ).
thf(315,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ( subset_type @ ( cross_product @ A @ B ) )
!= set_type ) ),
inference(simp,[status(thm)],[310]) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( sk4
| ~ ( subset @ A @ B )
| ~ ( empty @ B )
| ( ( member @ sk6 @ sk2 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,275]) ).
thf(335,plain,
! [A: $i] :
( sk4
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ A ) ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(341,plain,
! [A: $i] :
( sk4
| ~ ( subset @ sk2 @ A )
| ~ ( empty @ A ) ),
inference(simp,[status(thm)],[335]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( sk4
| ~ ( subset @ A @ B )
| ( member @ C @ B )
| ( ( member @ sk6 @ sk2 )
!= ( member @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,265]) ).
thf(277,plain,
! [A: $i] :
( sk4
| ~ ( subset @ sk2 @ A )
| ( member @ sk6 @ A ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(283,plain,
! [A: $i] :
( sk4
| ~ ( subset @ sk2 @ A )
| ( member @ sk6 @ A ) ),
inference(simp,[status(thm)],[277]) ).
thf(34,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( domain @ A @ B @ C )
= ( domain_of @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
thf(178,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( domain @ A @ B @ C )
= ( domain_of @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(20,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
thf(131,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(514,plain,
$false,
inference(e,[status(thm)],[138,184,117,77,129,59,39,241,82,354,37,257,152,57,164,106,348,61,265,74,302,160,275,137,285,224,317,169,141,134,237,166,148,375,313,144,49,181,213,251,108,162,255,112,150,263,50,127,72,314,87,104,55,139,315,51,107,242,341,283,178,131,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET660+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 18:58:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (141ms).
% 1.40/0.98 % [INFO] Running in sequential loop mode.
% 1.73/1.18 % [INFO] eprover registered as external prover.
% 1.73/1.18 % [INFO] cvc4 registered as external prover.
% 1.73/1.19 % [INFO] Scanning for conjecture ...
% 1.93/1.26 % [INFO] Found a conjecture and 34 axioms. Running axiom selection ...
% 2.02/1.31 % [INFO] Axiom selection finished. Selected 34 axioms (removed 0 axioms).
% 2.26/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.37 % [INFO] Type checking passed.
% 2.39/1.37 % [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 ...
% 8.07/2.67 % External prover 'e' found a proof!
% 8.07/2.67 % [INFO] Killing All external provers ...
% 8.07/2.67 % Time passed: 2156ms (effective reasoning time: 1683ms)
% 8.07/2.67 % 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)>
% 8.07/2.67 % Axioms used in derivation (34): p27, p12, p34, p18, p26, p22, p11, p2, p17, p9, p24, p16, p20, p10, p19, p4, p7, p5, p23, p32, p21, p29, p15, p3, p33, p25, p14, p28, p1, p31, p30, p13, p6, p8
% 8.07/2.67 % No. of inferences in proof: 144
% 8.07/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2156 ms resp. 1683 ms w/o parsing
% 8.07/2.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.07/2.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------