TSTP Solution File: SET646+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 11:53:57 EDT 2023
% Result : Theorem 7.25s 2.49s
% Output : Refutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 45
% Syntax : Number of formulae : 149 ( 24 unt; 19 typ; 0 def)
% Number of atoms : 470 ( 84 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1640 ( 129 ~; 88 |; 37 &;1203 @)
% ( 13 <=>; 170 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 7 con; 0-2 aty)
% Number of variables : 264 ( 0 ^; 252 !; 12 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_type,type,
ilf_type: $i > $i > $o ).
thf(set_type_type,type,
set_type: $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(relation_type_type,type,
relation_type: $i > $i > $i ).
thf(subset_type_type,type,
subset_type: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(member_type_type,type,
member_type: $i > $i ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(relation_like_type,type,
relation_like: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
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 > $i ).
thf(11,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(69,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)],[11]) ).
thf(20,axiom,
! [A: $i] : ( ilf_type @ A @ set_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
thf(115,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(116,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(cnf,[status(esa)],[115]) ).
thf(4,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',p12) ).
thf(40,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)],[4]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[41,116]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(simp,[status(thm)],[294]) ).
thf(297,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ B ) )
| ( ( ilf_type @ A @ set_type )
!= ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[116,295]) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( subset_type @ B ) )
| ( A != C )
| ( ( member_type @ ( power_set @ B ) )
!= set_type ) ),
inference(simp,[status(thm)],[297]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( subset_type @ A ) )
| ( ( member_type @ ( power_set @ A ) )
!= set_type ) ),
inference(simp,[status(thm)],[301]) ).
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/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(36,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(38,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)],[36]) ).
thf(1,conjecture,
! [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 )
=> ( ( ( member @ C @ A )
& ( member @ D @ B ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( relation_type @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_8) ).
thf(2,negated_conjecture,
~ ! [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 )
=> ( ( ( member @ C @ A )
& ( member @ D @ B ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( relation_type @ A @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,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 )
=> ( ( ( member @ C @ A )
& ( member @ D @ B ) )
=> ( ilf_type @ ( singleton @ ( ordered_pair @ C @ D ) ) @ ( relation_type @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,plain,
~ ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[28]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ( ilf_type @ C @ ( relation_type @ A @ B ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,30]) ).
thf(180,plain,
( ~ ( ilf_type @ sk1 @ set_type )
| ~ ( ilf_type @ sk2 @ set_type )
| ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( singleton @ ( ordered_pair @ sk3 @ sk4 ) ))]]) ).
thf(225,plain,
( ~ $true
| ~ $true
| ~ ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ),
inference(rewrite,[status(thm)],[180,116]) ).
thf(226,plain,
~ ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ( ( member_type @ ( power_set @ A ) )
!= set_type )
| ( ( ilf_type @ B @ ( subset_type @ A ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,226]) ).
thf(316,plain,
( ( member_type @ ( power_set @ ( cross_product @ sk1 @ sk2 ) ) )
!= set_type ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( cross_product @ sk1 @ sk2 )),bind(B,$thf( singleton @ ( ordered_pair @ sk3 @ sk4 ) ))]]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( ( member_type @ ( power_set @ A ) )
!= set_type )
| ( ( ilf_type @ B @ ( subset_type @ A ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,30]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( ( member_type @ ( power_set @ A ) )
!= set_type )
| ( B
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( subset_type @ A )
!= ( relation_type @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[311]) ).
thf(321,plain,
! [A: $i] :
( ( ( member_type @ ( power_set @ A ) )
!= set_type )
| ( ( subset_type @ A )
!= ( relation_type @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(8,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
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)],[8]) ).
thf(53,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(269,plain,
! [A: $i] :
( ~ $true
| ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) ) ),
inference(rewrite,[status(thm)],[53,116]) ).
thf(270,plain,
! [A: $i] : ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) ),
inference(simp,[status(thm)],[269]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(371,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(rewrite,[status(thm)],[42,116]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ B @ ( subset_type @ A ) )
| ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ C @ ( subset_type @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,372]) ).
thf(385,plain,
! [A: $i] : ( ilf_type @ ( sk5 @ A ) @ ( member_type @ ( power_set @ A ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk5 @ D ))]]) ).
thf(403,plain,
! [A: $i] : ( ilf_type @ ( sk5 @ A ) @ ( member_type @ ( power_set @ A ) ) ),
inference(simp,[status(thm)],[385]) ).
thf(17,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',p4) ).
thf(103,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)],[17]) ).
thf(5,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 )
=> ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
<=> ( ( member @ A @ C )
& ( member @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(43,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 )
=> ( ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) )
=> ( ( member @ A @ C )
& ( member @ B @ D ) ) )
& ( ( ( member @ A @ C )
& ( member @ B @ D ) )
=> ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,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)],[36]) ).
thf(39,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)],[37]) ).
thf(246,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)],[39,116]) ).
thf(247,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)],[246]) ).
thf(25,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',p20) ).
thf(142,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)],[25]) ).
thf(29,plain,
ilf_type @ sk3 @ set_type,
inference(cnf,[status(esa)],[28]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ilf_type @ B @ set_type )
| ~ ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
| ( ilf_type @ C @ ( relation_type @ A @ B ) )
| ( ( ilf_type @ sk3 @ set_type )
!= ( ilf_type @ A @ set_type ) ) ),
inference(paramod_ordered,[status(thm)],[29,38]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ ( subset_type @ ( cross_product @ sk3 @ A ) ) )
| ( ilf_type @ B @ ( relation_type @ sk3 @ A ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk3 ))]]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( ilf_type @ B @ ( subset_type @ ( cross_product @ sk3 @ A ) ) )
| ( ilf_type @ B @ ( relation_type @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( ilf_type @ B @ ( subset_type @ ( cross_product @ sk3 @ A ) ) )
| ( ilf_type @ B @ ( relation_type @ sk3 @ A ) ) ),
inference(rewrite,[status(thm)],[198,116]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( ilf_type @ B @ ( subset_type @ ( cross_product @ sk3 @ A ) ) )
| ( ilf_type @ B @ ( relation_type @ sk3 @ A ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ sk3 @ B ) )
| ( ( ilf_type @ A @ set_type )
!= ( ilf_type @ C @ ( subset_type @ ( cross_product @ sk3 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[116,233]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ sk3 @ B ) )
| ( A != C )
| ( ( subset_type @ ( cross_product @ sk3 @ B ) )
!= set_type ) ),
inference(simp,[status(thm)],[234]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( relation_type @ sk3 @ A ) )
| ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type ) ),
inference(simp,[status(thm)],[238]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( ( ilf_type @ B @ ( relation_type @ sk3 @ A ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,30]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( B
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( relation_type @ sk3 @ A )
!= ( relation_type @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(335,plain,
! [A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( ( relation_type @ sk3 @ A )
!= ( relation_type @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(339,plain,
! [A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( sk3 != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[335]) ).
thf(340,plain,
( ( ( subset_type @ ( cross_product @ sk3 @ sk2 ) )
!= set_type )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[339]) ).
thf(13,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',p17) ).
thf(74,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)],[13]) ).
thf(21,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',p14) ).
thf(117,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)],[21]) ).
thf(16,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( C
= ( singleton @ B ) )
<=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( member @ D @ C )
<=> ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(85,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( ( C
= ( singleton @ B ) )
=> ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( member @ D @ C )
=> ( D = B ) )
& ( ( D = B )
=> ( member @ D @ C ) ) ) ) )
& ( ! [D: $i] :
( ( ilf_type @ D @ set_type )
=> ( ( ( member @ D @ C )
=> ( D = B ) )
& ( ( D = B )
=> ( member @ D @ C ) ) ) )
=> ( C
= ( singleton @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,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',p8) ).
thf(137,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)],[23]) ).
thf(227,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[116,226]) ).
thf(228,plain,
! [A: $i] :
( ( A
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( subset_type @ ( cross_product @ sk1 @ sk2 ) )
!= set_type ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
( ( subset_type @ ( cross_product @ sk1 @ sk2 ) )
!= set_type ),
inference(simp,[status(thm)],[228]) ).
thf(6,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',p18) ).
thf(47,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)],[6]) ).
thf(48,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ~ ( empty @ ( power_set @ A ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(223,plain,
! [A: $i] :
( ~ $true
| ~ ( empty @ ( power_set @ A ) ) ),
inference(rewrite,[status(thm)],[48,116]) ).
thf(224,plain,
! [A: $i] :
~ ( empty @ ( power_set @ A ) ),
inference(simp,[status(thm)],[223]) ).
thf(22,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( subset @ ( singleton @ A ) @ B )
<=> ( member @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(134,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( subset @ ( singleton @ A ) @ B )
=> ( member @ A @ B ) )
& ( ( member @ A @ B )
=> ( subset @ ( singleton @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,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',p9) ).
thf(105,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)],[18]) ).
thf(34,plain,
member @ sk3 @ sk1,
inference(cnf,[status(esa)],[28]) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( relation_type @ sk3 @ B ) )
| ( ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ C @ ( subset_type @ ( cross_product @ sk3 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,233]) ).
thf(275,plain,
! [A: $i] : ( ilf_type @ ( sk5 @ ( cross_product @ sk3 @ A ) ) @ ( relation_type @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( cross_product @ sk3 @ F )),bind(B,$thf( F )),bind(C,$thf( sk5 @ ( cross_product @ sk3 @ F ) ))]]) ).
thf(279,plain,
! [A: $i] : ( ilf_type @ ( sk5 @ ( cross_product @ sk3 @ A ) ) @ ( relation_type @ sk3 @ A ) ),
inference(simp,[status(thm)],[275]) ).
thf(10,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( subset @ A @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(64,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)],[10]) ).
thf(12,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',p19) ).
thf(71,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)],[12]) ).
thf(9,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(54,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)],[9]) ).
thf(26,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
thf(144,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(273,plain,
! [A: $i] :
( ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[270,30]) ).
thf(278,plain,
! [A: $i] :
( ( ( sk5 @ A )
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( subset_type @ A )
!= ( relation_type @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(272,plain,
! [A: $i] :
( ( ilf_type @ ( sk5 @ A ) @ ( subset_type @ A ) )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[270,226]) ).
thf(277,plain,
! [A: $i] :
( ( ( sk5 @ A )
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( subset_type @ A )
!= ( subset_type @ ( cross_product @ sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(281,plain,
! [A: $i] :
( ( ( sk5 @ A )
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( A
!= ( cross_product @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(282,plain,
( ( sk5 @ ( cross_product @ sk1 @ sk2 ) )
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( ilf_type @ E @ ( subset_type @ ( cross_product @ C @ D ) ) )
| ( ( ilf_type @ B @ ( relation_type @ sk3 @ A ) )
!= ( ilf_type @ E @ ( relation_type @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,247]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( ( subset_type @ ( cross_product @ sk3 @ A ) )
!= set_type )
| ( ilf_type @ B @ ( subset_type @ ( cross_product @ sk3 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk3 )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(7,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',p10) ).
thf(50,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)],[7]) ).
thf(31,plain,
member @ sk4 @ sk2,
inference(cnf,[status(esa)],[28]) ).
thf(24,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',p11) ).
thf(139,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)],[24]) ).
thf(27,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(146,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( ( ilf_type @ A @ set_type )
!= ( ilf_type @ C @ ( subset_type @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[116,372]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) )
| ( A != C )
| ( ( subset_type @ B )
!= set_type ) ),
inference(simp,[status(thm)],[374]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
| ( ( subset_type @ A )
!= set_type ) ),
inference(simp,[status(thm)],[398]) ).
thf(19,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',p7) ).
thf(107,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)],[19]) ).
thf(147,plain,
! [A: $i] :
( ~ ( ilf_type @ A @ set_type )
| ( subset @ A @ A ) ),
inference(cnf,[status(esa)],[146]) ).
thf(267,plain,
! [A: $i] :
( ~ $true
| ( subset @ A @ A ) ),
inference(rewrite,[status(thm)],[147,116]) ).
thf(268,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[267]) ).
thf(14,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',p21) ).
thf(79,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)],[14]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( member_type @ ( power_set @ A ) )
!= set_type )
| ( ilf_type @ D @ ( relation_type @ sk3 @ C ) )
| ( ( ilf_type @ B @ ( subset_type @ A ) )
!= ( ilf_type @ D @ ( subset_type @ ( cross_product @ sk3 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,233]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( member_type @ ( power_set @ ( cross_product @ sk3 @ B ) ) )
!= set_type )
| ( ilf_type @ A @ ( relation_type @ sk3 @ B ) ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( cross_product @ sk3 @ F )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( ( member_type @ ( power_set @ ( cross_product @ sk3 @ B ) ) )
!= set_type )
| ( ilf_type @ A @ ( relation_type @ sk3 @ B ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(15,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(83,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ilf_type @ ( singleton @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(220,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
!= ( ilf_type @ ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) @ ( relation_type @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[116,30]) ).
thf(221,plain,
! [A: $i] :
( ( A
!= ( singleton @ ( ordered_pair @ sk3 @ sk4 ) ) )
| ( ( relation_type @ sk1 @ sk2 )
!= set_type ) ),
inference(simp,[status(thm)],[220]) ).
thf(222,plain,
( ( relation_type @ sk1 @ sk2 )
!= set_type ),
inference(simp,[status(thm)],[221]) ).
thf(465,plain,
$false,
inference(e,[status(thm)],[69,316,321,403,103,43,115,308,247,142,340,52,372,116,74,233,117,270,85,28,137,229,224,134,105,244,34,279,64,71,54,144,335,278,226,295,282,327,50,31,40,139,146,30,410,36,107,268,79,47,277,322,83,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n025.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 19:25:35 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.92/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (125ms).
% 1.24/0.97 % [INFO] Running in sequential loop mode.
% 1.68/1.15 % [INFO] eprover registered as external prover.
% 1.68/1.16 % [INFO] cvc4 registered as external prover.
% 1.68/1.16 % [INFO] Scanning for conjecture ...
% 1.77/1.22 % [INFO] Found a conjecture and 25 axioms. Running axiom selection ...
% 1.97/1.27 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.12/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 2.12/1.32 % [INFO] Type checking passed.
% 2.12/1.32 % [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 ...
% 7.25/2.49 % External prover 'e' found a proof!
% 7.25/2.49 % [INFO] Killing All external provers ...
% 7.25/2.49 % Time passed: 1979ms (effective reasoning time: 1520ms)
% 7.25/2.49 % 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)>
% 7.25/2.49 % Axioms used in derivation (25): p12, p18, p15, p3, p22, p11, p2, p17, p9, p1, p24, p13, p16, p20, p10, p19, p4, p7, p5, p23, p21, p25, p14, p6, p8
% 7.25/2.49 % No. of inferences in proof: 130
% 7.25/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1979 ms resp. 1520 ms w/o parsing
% 7.25/2.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.25/2.55 % [INFO] Killing All external provers ...
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