TSTP Solution File: SEV488^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV488^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 : Tue May 21 04:10:39 EDT 2024
% Result : Theorem 146.68s 29.05s
% Output : Refutation 146.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 29
% Syntax : Number of formulae : 481 ( 98 unt; 23 typ; 0 def)
% Number of atoms : 1785 ( 385 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 3994 ( 554 ~; 386 |; 48 &;2987 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 603 ( 603 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 9 con; 0-4 aty)
% Number of variables : 1255 ( 203 ^1016 !; 30 ?;1255 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/trivia/I\'_type',type,
'\'const/trivia/I\'':
!>[TA: $tType] : ( TA > TA ) ).
thf('\'const/sets/UNIONS\'_type',type,
'\'const/sets/UNIONS\'':
!>[TA: $tType] : ( ( ( TA > $o ) > $o ) > TA > $o ) ).
thf('\'const/sets/SUBSET\'_type',type,
'\'const/sets/SUBSET\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/pairwise\'_type',type,
'\'const/sets/pairwise\'':
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > skt1 > $o ).
thf(sk2_type,type,
sk2: ( skt1 > $o ) > $o ).
thf(sk3_type,type,
sk3:
!>[TA: $tType] : ( TA > ( ( TA > $o ) > $o ) > TA > $o ) ).
thf(sk7_type,type,
sk7: skt1 ).
thf(sk8_type,type,
sk8: skt1 ).
thf(sk9_type,type,
sk9: skt1 > $o ).
thf(sk10_type,type,
sk10: skt1 > $o ).
thf(sk18_type,type,
sk18: skt1 ).
thf(sk24_type,type,
sk24: skt1 ).
thf(sk25_type,type,
sk25: skt1 > $o ).
thf(sk26_type,type,
sk26: skt1 > $o ).
thf(sk27_type,type,
sk27: skt1 ).
thf(sk28_type,type,
sk28: skt1 ).
thf(sk51_type,type,
sk51: skt1 > $o ).
thf(sk52_type,type,
sk52: skt1 > $o ).
thf(sk65_type,type,
sk65: skt1 > $o ).
thf(sk96_type,type,
sk96: skt1 ).
thf(1,conjecture,
! [TA: $tType,A: TA > TA > $o,B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ C ) )
& ! [C: TA > $o,D: TA > $o] :
( ( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
& ( '\'const/sets/IN\'' @ ( TA > $o ) @ D @ B ) )
=> ( ( '\'const/sets/SUBSET\'' @ TA @ C @ D )
| ( '\'const/sets/SUBSET\'' @ TA @ D @ C ) ) ) )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/UNIONS\'' @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/PAIRWISE_CHAIN_UNIONS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > TA > $o,B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ C ) )
& ! [C: TA > $o,D: TA > $o] :
( ( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
& ( '\'const/sets/IN\'' @ ( TA > $o ) @ D @ B ) )
=> ( ( '\'const/sets/SUBSET\'' @ TA @ C @ D )
| ( '\'const/sets/SUBSET\'' @ TA @ D @ C ) ) ) )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/UNIONS\'' @ TA @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,A: TA > TA > $o,B: ( TA > $o ) > $o] :
( ( ! [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ C ) )
& ! [C: TA > $o,D: TA > $o] :
( ( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
& ( '\'const/sets/IN\'' @ ( TA > $o ) @ D @ B ) )
=> ( ( '\'const/sets/SUBSET\'' @ TA @ C @ D )
| ( '\'const/sets/SUBSET\'' @ TA @ D @ C ) ) ) )
=> ( '\'const/sets/pairwise\'' @ TA @ A @ ( '\'const/sets/UNIONS\'' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).
thf(13,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(lifteq,[status(thm)],[14]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(16,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(32,plain,
! [TB: $tType,C: TB,B: TB > $o,A: $o] :
( ( A
= ( '\'const/sets/IN\'' @ TB @ C @ B ) )
| ( ( '\'const/trivia/I\'' @ $o @ A )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,18]) ).
thf(33,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [C: TB] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( D @ C )),bind(B,$thf( ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ))]]) ).
thf(35,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(43,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ D @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,18]) ).
thf(57,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( C @ A @ ( B @ A ) )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [D: TB] :
( '\'const/sets/IN\'' @ TA @ ( B @ D )
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( C @ D @ E ) ) ) ) ),
inference(pre_uni,[status(thm)],[43:[bind(A,$thf( E @ D )),bind(B,$thf( G @ D )),bind(C,$thf( ^ [G: TB] : ( '\'const/sets/IN\'' @ TA @ ( E @ G ) @ ^ [H: TA] : ( '\'const/trivia/I\'' @ $o @ ( G @ G @ H ) ) ) )),bind(D,$thf( D ))]]) ).
thf(69,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( C @ A @ ( B @ A ) )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [D: TB] :
( '\'const/sets/IN\'' @ TA @ ( B @ D )
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( C @ D @ E ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(41,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( C @ D ) )
| ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
!= ( '\'const/sets/IN\'' @ TB @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,18]) ).
thf(42,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
= ( B @ A ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( ^ [F: TB] : ( '\'const/trivia/I\'' @ $o @ ( E @ F ) ) )),bind(D,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(63,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
= ( B @ A ) ),
inference(simp,[status(thm)],[42]) ).
thf(101,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ~ ( B @ A ) ),
inference(bool_ext,[status(thm)],[63]) ).
thf(7,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/pairwise_') ).
thf(25,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
= ( ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(9,plain,
~ ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(829,plain,
! [TA: $tType,B: TA > TA > $o,A: TA > $o] :
( ~ ! [C: TA,D: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ D @ A )
& ( C != D ) )
=> ( B @ C @ D ) )
| ( ( '\'const/sets/pairwise\'' @ TA @ B @ A )
!= ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,9]) ).
thf(830,plain,
~ ! [A: skt1,B: skt1] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
& ( '\'const/sets/IN\'' @ skt1 @ B @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
& ( A != B ) )
=> ( sk1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[829:[bind(A,$thf( '\'const/sets/UNIONS\'' @ skt1 @ sk2 )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(884,plain,
'\'const/sets/IN\'' @ skt1 @ sk8 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ),
inference(cnf,[status(esa)],[830]) ).
thf(5,axiom,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_UNIONS_') ).
thf(19,plain,
! [TA: $tType,A: ( TA > $o ) > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(894,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[884,21]) ).
thf(895,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(932,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk10 @ sk2,
inference(cnf,[status(esa)],[895]) ).
thf(11,plain,
! [A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(71,plain,
! [A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(72,plain,
~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ))]]) ).
thf(1711,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk10 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[932,72]) ).
thf(1730,plain,
( ( sk10
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1711]) ).
thf(1735,plain,
( sk10
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[1730]) ).
thf(1992,plain,
( ( sk10 @ sk24 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ),
inference(func_ext,[status(esa)],[1735]) ).
thf(4877,plain,
( ~ ( sk10 @ sk24 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ),
inference(bool_ext,[status(thm)],[1992]) ).
thf(885,plain,
'\'const/sets/IN\'' @ skt1 @ sk7 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ),
inference(cnf,[status(esa)],[830]) ).
thf(28,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(2273,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk7 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[885,28]) ).
thf(2274,plain,
'\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7,
inference(pattern_uni,[status(thm)],[2273:[bind(A,$thf( '\'const/sets/UNIONS\'' @ skt1 @ sk2 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(6329,plain,
( ~ ( sk10 @ sk24 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[2274,4877]) ).
thf(6358,plain,
( ~ ( sk10 @ sk24 )
| ( sk2 != sk2 )
| ( sk24 != sk7 ) ),
inference(simp,[status(thm)],[6329]) ).
thf(6374,plain,
( ~ ( sk10 @ sk24 )
| ( sk24 != sk7 ) ),
inference(simp,[status(thm)],[6358]) ).
thf(74,plain,
! [TA: $tType,C: skt1 > $o,B: TA > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ D ) ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ C )
| ( ( B @ A )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[35,11]) ).
thf(82,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ C ) @ sk2 ) ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( D @ E ) @ sk2 ) )),bind(C,$thf( D @ A ))]]) ).
thf(88,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ C ) @ sk2 ) ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(10,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(156,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(162,plain,
! [A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( B ))]]) ).
thf(170,plain,
! [A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A ) ),
inference(simp,[status(thm)],[162]) ).
thf(896,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
!= ( '\'const/sets/IN\'' @ skt1 @ sk8 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,884]) ).
thf(897,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(928,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk9 @ sk2,
inference(cnf,[status(esa)],[897]) ).
thf(16134,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk9 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[928,170]) ).
thf(16135,plain,
'\'const/sets/SUBSET\'' @ skt1 @ sk9 @ sk9,
inference(pattern_uni,[status(thm)],[16134:[bind(A,$thf( sk9 ))]]) ).
thf(250,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
| ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ),
inference(bool_ext,[status(thm)],[21]) ).
thf(276,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( sk3 @ TA @ B @ A ) )
| ~ ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(2271,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
!= ( '\'const/sets/IN\'' @ skt1 @ sk7 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,885]) ).
thf(2272,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[2271:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(2312,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk25 @ sk2,
inference(cnf,[status(esa)],[2272]) ).
thf(2762,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk25 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2312,72]) ).
thf(2786,plain,
( ( sk25
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[2762]) ).
thf(2791,plain,
( sk25
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[2786]) ).
thf(3380,plain,
( ( sk25 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 ) ),
inference(func_ext,[status(esa)],[2791]) ).
thf(5547,plain,
( ( sk25 @ sk27 )
| ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 ) ),
inference(bool_ext,[status(thm)],[3380]) ).
thf(99,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TA @ A @ B ) ),
inference(rewrite,[status(thm)],[35,63]) ).
thf(902,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[884,99]) ).
thf(903,plain,
'\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8,
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( sk8 )),bind(B,$thf( '\'const/sets/UNIONS\'' @ skt1 @ sk2 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(5546,plain,
( ~ ( sk25 @ sk27 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 ) ),
inference(bool_ext,[status(thm)],[3380]) ).
thf(6839,plain,
( ~ ( sk25 @ sk27 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[903,5546]) ).
thf(6867,plain,
( ~ ( sk25 @ sk27 )
| ( sk2 != sk2 )
| ( sk27 != sk8 ) ),
inference(simp,[status(thm)],[6839]) ).
thf(6872,plain,
( ~ ( sk25 @ sk27 )
| ( sk27 != sk8 ) ),
inference(simp,[status(thm)],[6867]) ).
thf(7197,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
| ( sk27 != sk8 )
| ( ( sk25 @ sk27 )
!= ( sk25 @ sk27 ) ) ),
inference(paramod_ordered,[status(thm)],[5547,6872]) ).
thf(7198,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
| ( sk27 != sk8 ) ),
inference(pattern_uni,[status(thm)],[7197:[]]) ).
thf(1200,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk9 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[928,72]) ).
thf(1211,plain,
( ( sk9
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1200]) ).
thf(1220,plain,
( sk9
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[1211]) ).
thf(1427,plain,
( ( sk9 @ sk18 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ),
inference(func_ext,[status(esa)],[1220]) ).
thf(1655,plain,
( ( sk9 @ sk18 )
| ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ),
inference(bool_ext,[status(thm)],[1427]) ).
thf(1654,plain,
( ~ ( sk9 @ sk18 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ),
inference(bool_ext,[status(thm)],[1427]) ).
thf(2325,plain,
( ~ ( sk9 @ sk18 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[2274,1654]) ).
thf(2334,plain,
( ~ ( sk9 @ sk18 )
| ( sk2 != sk2 )
| ( sk18 != sk7 ) ),
inference(simp,[status(thm)],[2325]) ).
thf(2340,plain,
( ~ ( sk9 @ sk18 )
| ( sk18 != sk7 ) ),
inference(simp,[status(thm)],[2334]) ).
thf(6426,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
| ( sk18 != sk7 )
| ( ( sk9 @ sk18 )
!= ( sk9 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[1655,2340]) ).
thf(6427,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
| ( sk18 != sk7 ) ),
inference(pattern_uni,[status(thm)],[6426:[]]) ).
thf(17179,plain,
( ( sk18 != sk7 )
| ~ ( sk25 @ sk27 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[6427,5546]) ).
thf(17213,plain,
( ( sk18 != sk7 )
| ~ ( sk25 @ sk27 )
| ( sk2 != sk2 )
| ( sk27 != sk18 ) ),
inference(simp,[status(thm)],[17179]) ).
thf(17253,plain,
( ( sk18 != sk7 )
| ~ ( sk25 @ sk27 )
| ( sk27 != sk18 ) ),
inference(simp,[status(thm)],[17213]) ).
thf(6385,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A @ B )
| ( sk24 != sk7 )
| ( ( B @ A )
!= ( sk10 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[99,6374]) ).
thf(6391,plain,
! [TA: $tType,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk10 @ sk24 ) )
| ( sk24 != sk7 ) ),
inference(pre_uni,[status(thm)],[6385:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk10 @ sk24 ) ))]]) ).
thf(2269,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk7 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[885,21]) ).
thf(2270,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[2269:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(2316,plain,
'\'const/sets/IN\'' @ skt1 @ sk7 @ sk26,
inference(cnf,[status(esa)],[2270]) ).
thf(257,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA,A: ( TA > $o ) > $o] :
( ( ( ? [E: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ E @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ E ) ) )
= ( C @ D ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
!= ( '\'const/sets/IN\'' @ TB @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,18]) ).
thf(258,plain,
! [TB: $tType,B: TB,A: ( TB > $o ) > $o] :
( ( ? [C: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TB @ B @ C ) ) )
= ( '\'const/sets/UNIONS\'' @ TB @ A @ B ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( '\'const/sets/UNIONS\'' @ TB @ A )),bind(D,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(274,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) )
= ( '\'const/sets/UNIONS\'' @ TA @ A @ B ) ),
inference(simp,[status(thm)],[258]) ).
thf(20684,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/UNIONS\'' @ TA @ A @ B )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[274,903]) ).
thf(20685,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[20684:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(20819,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk51 @ sk2,
inference(cnf,[status(esa)],[20685]) ).
thf(21220,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk51 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[20819,72]) ).
thf(21261,plain,
( ( sk51
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[21220]) ).
thf(21311,plain,
( sk51
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[21261]) ).
thf(20600,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/UNIONS\'' @ TA @ A @ B )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[274,2274]) ).
thf(20601,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[20600:[bind(A,$thf( sk2 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(20862,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk65 @ sk2,
inference(cnf,[status(esa)],[20601]) ).
thf(4878,plain,
( ( sk10 @ sk24 )
| ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ),
inference(bool_ext,[status(thm)],[1992]) ).
thf(6908,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( sk24 != sk7 )
| ( ( sk10 @ sk24 )
!= ( sk10 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[4878,6374]) ).
thf(6909,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( sk24 != sk7 ) ),
inference(pattern_uni,[status(thm)],[6908:[]]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_') ).
thf(22,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(20818,plain,
'\'const/sets/IN\'' @ skt1 @ sk8 @ sk51,
inference(cnf,[status(esa)],[20685]) ).
thf(931,plain,
'\'const/sets/IN\'' @ skt1 @ sk8 @ sk10,
inference(cnf,[status(esa)],[895]) ).
thf(1433,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ sk10 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[931,28]) ).
thf(1434,plain,
sk10 @ sk8,
inference(pattern_uni,[status(thm)],[1433:[bind(A,$thf( sk10 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(6343,plain,
( ~ ( sk10 @ sk24 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[903,4877]) ).
thf(6361,plain,
( ~ ( sk10 @ sk24 )
| ( sk2 != sk2 )
| ( sk24 != sk8 ) ),
inference(simp,[status(thm)],[6343]) ).
thf(6375,plain,
( ~ ( sk10 @ sk24 )
| ( sk24 != sk8 ) ),
inference(simp,[status(thm)],[6361]) ).
thf(6464,plain,
( ( sk24 != sk8 )
| ( ( sk10 @ sk24 )
!= ( sk10 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[1434,6375]) ).
thf(6474,plain,
( ( sk24 != sk8 )
| ( sk24 != sk8 ) ),
inference(simp,[status(thm)],[6464]) ).
thf(6483,plain,
sk24 != sk8,
inference(simp,[status(thm)],[6474]) ).
thf(37,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( B @ A )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[35]) ).
thf(2317,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk26 @ sk2,
inference(cnf,[status(esa)],[2270]) ).
thf(4110,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk26 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[2317,72]) ).
thf(4135,plain,
( ( sk26
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[4110]) ).
thf(4149,plain,
( sk26
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[4135]) ).
thf(4154,plain,
( ( sk26 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 ) ),
inference(func_ext,[status(esa)],[4149]) ).
thf(5571,plain,
( ( sk26 @ sk28 )
| ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 ) ),
inference(bool_ext,[status(thm)],[4154]) ).
thf(5570,plain,
( ~ ( sk26 @ sk28 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 ) ),
inference(bool_ext,[status(thm)],[4154]) ).
thf(7494,plain,
( ~ ( sk26 @ sk28 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[903,5570]) ).
thf(7509,plain,
( ~ ( sk26 @ sk28 )
| ( sk2 != sk2 )
| ( sk28 != sk8 ) ),
inference(simp,[status(thm)],[7494]) ).
thf(7525,plain,
( ~ ( sk26 @ sk28 )
| ( sk28 != sk8 ) ),
inference(simp,[status(thm)],[7509]) ).
thf(7616,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
| ( sk28 != sk8 )
| ( ( sk26 @ sk28 )
!= ( sk26 @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[5571,7525]) ).
thf(7617,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
| ( sk28 != sk8 ) ),
inference(pattern_uni,[status(thm)],[7616:[]]) ).
thf(17815,plain,
( ( sk28 != sk8 )
| ~ ( sk10 @ sk24 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[7617,4877]) ).
thf(17861,plain,
( ( sk28 != sk8 )
| ~ ( sk10 @ sk24 )
| ( sk2 != sk2 )
| ( sk28 != sk24 ) ),
inference(simp,[status(thm)],[17815]) ).
thf(17888,plain,
( ( sk28 != sk8 )
| ~ ( sk10 @ sk24 )
| ( sk28 != sk24 ) ),
inference(simp,[status(thm)],[17861]) ).
thf(29,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[18]) ).
thf(38,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ),
inference(bool_ext,[status(thm)],[35]) ).
thf(1838,plain,
! [TA: $tType,A: TA] :
( $false
| ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ $false ) ) ),
inference(prim_subst,[status(thm)],[38:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : $false ))]]) ).
thf(1912,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ $false ) ),
inference(simp,[status(thm)],[1838]) ).
thf(7824,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/trivia/I\'' @ $o @ $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,1912]) ).
thf(7825,plain,
~ ( '\'const/trivia/I\'' @ $o @ $false ),
inference(pattern_uni,[status(thm)],[7824:[bind(A,$thf( ^ [D: TB] : ( '\'const/trivia/I\'' @ $o @ $false ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(108,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( D @ C ) )
| ( ( A @ B )
!= ( '\'const/trivia/I\'' @ $o @ ( D @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,63]) ).
thf(119,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TB > $o,B: TB,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )
= ( C @ B ) )
| ( ( D @ A )
!= ( C @ B ) ) ),
inference(pre_uni,[status(thm)],[108:[bind(A,$thf( ^ [F: TA] : ( '\'const/trivia/I\'' @ $o @ ( E @ F ) ) ))]]) ).
thf(120,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TB > $o,B: TB,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )
= ( C @ B ) )
| ( ( D @ A )
!= ( C @ B ) ) ),
inference(pre_uni,[status(thm)],[119:[]]) ).
thf(125,plain,
! [TA: $tType,TB: $tType,D: TA > $o,C: TB > $o,B: TB,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )
= ( C @ B ) )
| ( ( D @ A )
!= ( C @ B ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(2725,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A @ B )
| ( sk18 != sk7 )
| ( ( B @ A )
!= ( sk9 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[99,2340]) ).
thf(2730,plain,
! [TA: $tType,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk9 @ sk18 ) )
| ( sk18 != sk7 ) ),
inference(pre_uni,[status(thm)],[2725:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk9 @ sk18 ) ))]]) ).
thf(21744,plain,
( ( sk51 @ sk96 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk96 ) ),
inference(func_ext,[status(esa)],[21311]) ).
thf(22348,plain,
( ~ ( sk51 @ sk96 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk96 ) ),
inference(bool_ext,[status(thm)],[21744]) ).
thf(17605,plain,
( ( sk24 != sk7 )
| ~ ( sk26 @ sk28 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[6909,5570]) ).
thf(17640,plain,
( ( sk24 != sk7 )
| ~ ( sk26 @ sk28 )
| ( sk2 != sk2 )
| ( sk28 != sk24 ) ),
inference(simp,[status(thm)],[17605]) ).
thf(17667,plain,
( ( sk24 != sk7 )
| ~ ( sk26 @ sk28 )
| ( sk28 != sk24 ) ),
inference(simp,[status(thm)],[17640]) ).
thf(106,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ D @ C ) )
| ( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[63,18]) ).
thf(112,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( B @ A )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[106:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TB] : ( '\'const/trivia/I\'' @ $o @ ( E @ F ) ) ))]]) ).
thf(113,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( B @ A )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[112:[]]) ).
thf(121,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( B @ A )
!= ( D @ C ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(20686,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 )
!= ( '\'const/sets/UNIONS\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[903,274]) ).
thf(20687,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt1 @ sk8 @ A ) ),
inference(pattern_uni,[status(thm)],[20686:[bind(A,$thf( sk2 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(20820,plain,
'\'const/sets/IN\'' @ skt1 @ sk8 @ sk52,
inference(cnf,[status(esa)],[20687]) ).
thf(21773,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ sk52 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20820,28]) ).
thf(21774,plain,
sk52 @ sk8,
inference(pattern_uni,[status(thm)],[21773:[bind(A,$thf( sk52 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(77,plain,
! [TA: $tType,C: TA,B: TA > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ C @ B )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,18]) ).
thf(83,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ),
inference(pre_uni,[status(thm)],[77:[bind(A,$thf( E @ C )),bind(B,$thf( ^ [E: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( E @ E ) ) )),bind(C,$thf( C ))]]) ).
thf(89,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(109,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TA @ B @ A ) )
= ( D @ C ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,63]) ).
thf(115,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TA @ B @ A ) )
= ( D @ C ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[109:[]]) ).
thf(116,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TA @ B @ A ) )
= ( D @ C ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[115:[]]) ).
thf(20904,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ sk51 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20818,28]) ).
thf(20905,plain,
sk51 @ sk8,
inference(pattern_uni,[status(thm)],[20904:[bind(A,$thf( sk51 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(16108,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk25 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2312,170]) ).
thf(16109,plain,
'\'const/sets/SUBSET\'' @ skt1 @ sk25 @ sk25,
inference(pattern_uni,[status(thm)],[16108:[bind(A,$thf( sk25 ))]]) ).
thf(110,plain,
! [TA: $tType,C: TA > $o,B: TA,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( ( '\'const/trivia/I\'' @ $o @ $true )
= ( C @ B ) )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,63]) ).
thf(111,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(pre_uni,[status(thm)],[110:[bind(A,$thf( E @ B )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( E @ E ) ) ))]]) ).
thf(126,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(927,plain,
'\'const/sets/IN\'' @ skt1 @ sk8 @ sk9,
inference(cnf,[status(esa)],[897]) ).
thf(1132,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk8 @ sk9 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[927,28]) ).
thf(1133,plain,
sk9 @ sk8,
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( sk9 )),bind(B,$thf( sk8 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1160,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( ( '\'const/trivia/I\'' @ $o @ $true )
= ( B @ A ) )
| ( ( sk9 @ sk8 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1133,63]) ).
thf(1169,plain,
( ( sk9 @ sk8 )
= ( '\'const/trivia/I\'' @ $o @ $true ) ),
inference(pre_uni,[status(thm)],[1160:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk9 @ sk8 ) ))]]) ).
thf(4953,plain,
'\'const/trivia/I\'' @ $o @ $true,
inference(rewrite,[status(thm)],[1169,1133]) ).
thf(13228,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(rewrite,[status(thm)],[126,4953]) ).
thf(16118,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk10 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[932,170]) ).
thf(16119,plain,
'\'const/sets/SUBSET\'' @ skt1 @ sk10 @ sk10,
inference(pattern_uni,[status(thm)],[16118:[bind(A,$thf( sk10 ))]]) ).
thf(1198,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk9 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[928,11]) ).
thf(1199,plain,
'\'const/sets/pairwise\'' @ skt1 @ sk1 @ sk9,
inference(pattern_uni,[status(thm)],[1198:[bind(A,$thf( sk9 ))]]) ).
thf(17186,plain,
( ( sk18 != sk7 )
| ~ ( sk26 @ sk28 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[6427,5570]) ).
thf(17226,plain,
( ( sk18 != sk7 )
| ~ ( sk26 @ sk28 )
| ( sk2 != sk2 )
| ( sk28 != sk18 ) ),
inference(simp,[status(thm)],[17186]) ).
thf(17242,plain,
( ( sk18 != sk7 )
| ~ ( sk26 @ sk28 )
| ( sk28 != sk18 ) ),
inference(simp,[status(thm)],[17226]) ).
thf(31,plain,
! [TA: $tType,C: $o,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= C )
| ( ( A @ B )
!= ( '\'const/trivia/I\'' @ $o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,15]) ).
thf(34,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) )
= ( B @ A ) ),
inference(pre_uni,[status(thm)],[31:[bind(A,$thf( ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(36,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) )
= ( B @ A ) ),
inference(simp,[status(thm)],[34]) ).
thf(1166,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) )
| ( ( B @ A )
!= ( sk9 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[36,1133]) ).
thf(1171,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ ( sk9 @ sk8 ) ) ),
inference(pre_uni,[status(thm)],[1166:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk9 @ sk8 ) ))]]) ).
thf(17902,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ $true ) ),
inference(rewrite,[status(thm)],[1171,1133]) ).
thf(261,plain,
! [TA: $tType,TB: $tType,D: TB,C: ( TB > $o ) > $o,B: TA,A: TA > $o] :
( ( ( A @ B )
= ( ? [E: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ E @ C )
& ( '\'const/sets/IN\'' @ TB @ D @ E ) ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ TB @ D @ ( '\'const/sets/UNIONS\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,21]) ).
thf(262,plain,
! [TB: $tType,B: ( TB > $o ) > $o,A: TB] :
( ( '\'const/sets/UNIONS\'' @ TB @ B @ A )
= ( ? [C: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ C @ B )
& ( '\'const/sets/IN\'' @ TB @ A @ C ) ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( '\'const/sets/UNIONS\'' @ TB @ C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(275,plain,
! [TA: $tType,B: ( TA > $o ) > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ TA @ B @ A )
= ( ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ B )
& ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(78,plain,
! [TA: $tType,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ C )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(79,plain,
! [A: skt1 > $o] :
( ~ ( sk2 @ A )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(94,plain,
! [A: skt1 > $o] :
( ~ ( sk2 @ A )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A ) ),
inference(simp,[status(thm)],[79]) ).
thf(132,plain,
! [TA: $tType,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( sk2 @ C )
| ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,94]) ).
thf(133,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( sk2 @ ( B @ A ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ),
inference(pre_uni,[status(thm)],[132:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( E @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ B ))]]) ).
thf(137,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( sk2 @ ( B @ A ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(44,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( A @ B )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,35]) ).
thf(53,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( C @ A @ ( B @ A ) )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [D: TB] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TA @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(pre_uni,[status(thm)],[44:[bind(A,$thf( F @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: TB] : ( '\'const/sets/IN\'' @ TA @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(65,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( C @ A @ ( B @ A ) )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [D: TB] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TA @ ( B @ D ) @ ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(17614,plain,
( ( sk24 != sk7 )
| ~ ( sk9 @ sk18 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[6909,1654]) ).
thf(17627,plain,
( ( sk24 != sk7 )
| ~ ( sk9 @ sk18 )
| ( sk2 != sk2 )
| ( sk24 != sk18 ) ),
inference(simp,[status(thm)],[17614]) ).
thf(17659,plain,
( ( sk24 != sk7 )
| ~ ( sk9 @ sk18 )
| ( sk24 != sk18 ) ),
inference(simp,[status(thm)],[17627]) ).
thf(17842,plain,
( ( sk28 != sk8 )
| ~ ( sk9 @ sk18 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[7617,1654]) ).
thf(17857,plain,
( ( sk28 != sk8 )
| ~ ( sk9 @ sk18 )
| ( sk2 != sk2 )
| ( sk28 != sk18 ) ),
inference(simp,[status(thm)],[17842]) ).
thf(17887,plain,
( ( sk28 != sk8 )
| ~ ( sk9 @ sk18 )
| ( sk28 != sk18 ) ),
inference(simp,[status(thm)],[17857]) ).
thf(8317,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( sk9 @ sk18 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1655,101]) ).
thf(8651,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
| ( '\'const/trivia/I\'' @ $o @ ( sk9 @ sk18 ) ) ),
inference(pre_uni,[status(thm)],[8317:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk9 @ sk18 ) ))]]) ).
thf(20861,plain,
'\'const/sets/IN\'' @ skt1 @ sk7 @ sk65,
inference(cnf,[status(esa)],[20601]) ).
thf(147,plain,
! [TA: $tType,D: TA,C: TA > $o,B: skt1 > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/IN\'' @ TA @ D @ C )
| ( ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[12,18]) ).
thf(161,plain,
! [TA: $tType,C: TA > skt1 > $o,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ A ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ ( B @ A ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/sets/SUBSET\'' @ skt1 @ ( B @ D ) @ ( C @ D ) ) ) ),
inference(pre_uni,[status(thm)],[147:[bind(A,$thf( F @ D )),bind(B,$thf( E @ D )),bind(C,$thf( ^ [G: TA] : ( '\'const/sets/SUBSET\'' @ skt1 @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(169,plain,
! [TA: $tType,C: TA > skt1 > $o,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ A ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ ( B @ A ) )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/sets/SUBSET\'' @ skt1 @ ( B @ D ) @ ( C @ D ) ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(17681,plain,
( ( sk27 != sk8 )
| ~ ( sk10 @ sk24 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[7198,4877]) ).
thf(17749,plain,
( ( sk27 != sk8 )
| ~ ( sk10 @ sk24 )
| ( sk2 != sk2 )
| ( sk27 != sk24 ) ),
inference(simp,[status(thm)],[17681]) ).
thf(17763,plain,
( ( sk27 != sk8 )
| ~ ( sk10 @ sk24 )
| ( sk27 != sk24 ) ),
inference(simp,[status(thm)],[17749]) ).
thf(17598,plain,
( ( sk24 != sk7 )
| ~ ( sk25 @ sk27 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ) ),
inference(paramod_ordered,[status(thm)],[6909,5546]) ).
thf(17635,plain,
( ( sk24 != sk7 )
| ~ ( sk25 @ sk27 )
| ( sk2 != sk2 )
| ( sk27 != sk24 ) ),
inference(simp,[status(thm)],[17598]) ).
thf(17663,plain,
( ( sk24 != sk7 )
| ~ ( sk25 @ sk27 )
| ( sk27 != sk24 ) ),
inference(simp,[status(thm)],[17635]) ).
thf(17169,plain,
( ( sk18 != sk7 )
| ~ ( sk10 @ sk24 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[6427,4877]) ).
thf(17214,plain,
( ( sk18 != sk7 )
| ~ ( sk10 @ sk24 )
| ( sk2 != sk2 )
| ( sk24 != sk18 ) ),
inference(simp,[status(thm)],[17169]) ).
thf(17254,plain,
( ( sk18 != sk7 )
| ~ ( sk10 @ sk24 )
| ( sk24 != sk18 ) ),
inference(simp,[status(thm)],[17214]) ).
thf(1699,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk10 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[932,28]) ).
thf(1700,plain,
sk2 @ sk10,
inference(pattern_uni,[status(thm)],[1699:[bind(A,$thf( sk2 )),bind(B,$thf( sk10 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(127,plain,
! [A: skt1 > $o] :
( ~ ( sk2 @ A )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[94,9]) ).
thf(128,plain,
~ ( sk2 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ))]]) ).
thf(8355,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( sk26 @ sk28 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5571,101]) ).
thf(8614,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
| ( '\'const/trivia/I\'' @ $o @ ( sk26 @ sk28 ) ) ),
inference(pre_uni,[status(thm)],[8355:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk26 @ sk28 ) ))]]) ).
thf(21169,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk51 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20819,28]) ).
thf(21170,plain,
sk2 @ sk51,
inference(pattern_uni,[status(thm)],[21169:[bind(A,$thf( sk2 )),bind(B,$thf( sk51 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(148,plain,
! [TA: $tType,D: skt1 > $o,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ D @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ C @ D )
| ( '\'const/sets/SUBSET\'' @ skt1 @ D @ C )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18,12]) ).
thf(149,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ~ ( sk2 @ A )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(176,plain,
! [B: skt1 > $o,A: skt1 > $o] :
( ~ ( sk2 @ A )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A ) ),
inference(simp,[status(thm)],[149]) ).
thf(40,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
= ( '\'const/sets/IN\'' @ TB @ D @ C ) )
| ( ( B @ A )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[35,18]) ).
thf(58,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
= ( '\'const/sets/IN\'' @ TB @ D @ C ) )
| ( ( B @ A )
!= ( C @ D ) ) ),
inference(pre_uni,[status(thm)],[40:[]]) ).
thf(59,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
= ( '\'const/sets/IN\'' @ TB @ D @ C ) )
| ( ( B @ A )
!= ( C @ D ) ) ),
inference(pre_uni,[status(thm)],[58:[]]) ).
thf(129,plain,
! [TA: $tType,C: TA > $o,B: TA,A: skt1 > $o] :
( ~ ( sk2 @ A )
| ( ( '\'const/trivia/I\'' @ $o @ $true )
= ( C @ B ) )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[94,63]) ).
thf(134,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( sk2 @ ( B @ A ) )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(pre_uni,[status(thm)],[129:[bind(A,$thf( E @ B )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( E @ E ) ) ))]]) ).
thf(138,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( sk2 @ ( B @ A ) )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(13745,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( sk2 @ ( B @ A ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(rewrite,[status(thm)],[138,4953]) ).
thf(23265,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk7 @ sk65 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20861,28]) ).
thf(23266,plain,
sk65 @ sk7,
inference(pattern_uni,[status(thm)],[23265:[bind(A,$thf( sk65 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(4111,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk26 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2317,11]) ).
thf(4112,plain,
'\'const/sets/pairwise\'' @ skt1 @ sk1 @ sk26,
inference(pattern_uni,[status(thm)],[4111:[bind(A,$thf( sk26 ))]]) ).
thf(1674,plain,
( ~ ( sk9 @ sk18 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[903,1654]) ).
thf(1684,plain,
( ~ ( sk9 @ sk18 )
| ( sk2 != sk2 )
| ( sk18 != sk8 ) ),
inference(simp,[status(thm)],[1674]) ).
thf(1690,plain,
( ~ ( sk9 @ sk18 )
| ( sk18 != sk8 ) ),
inference(simp,[status(thm)],[1684]) ).
thf(2348,plain,
( ( sk18 != sk8 )
| ( ( sk9 @ sk18 )
!= ( sk9 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[1133,1690]) ).
thf(2350,plain,
( ( sk18 != sk8 )
| ( sk18 != sk8 ) ),
inference(simp,[status(thm)],[2348]) ).
thf(2358,plain,
sk18 != sk8,
inference(simp,[status(thm)],[2350]) ).
thf(2311,plain,
'\'const/sets/IN\'' @ skt1 @ sk7 @ sk25,
inference(cnf,[status(esa)],[2272]) ).
thf(2741,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk25 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2312,28]) ).
thf(2742,plain,
sk2 @ sk25,
inference(pattern_uni,[status(thm)],[2741:[bind(A,$thf( sk2 )),bind(B,$thf( sk25 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(131,plain,
! [TA: $tType,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ C )
| ( ( A @ B )
!= ( sk2 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,94]) ).
thf(136,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk2 @ ( B @ C ) ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[131:[bind(A,$thf( ^ [E: TA] : ( sk2 @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(140,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk2 @ ( B @ C ) ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(141,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( sk2 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,128]) ).
thf(142,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk2 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[141:[bind(A,$thf( ^ [C: TA] : ( sk2 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) )),bind(B,$thf( B ))]]) ).
thf(143,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk2 @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(180,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[143,128]) ).
thf(184,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,180]) ).
thf(186,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[184:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(188,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[186]) ).
thf(190,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[188,180]) ).
thf(194,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,190]) ).
thf(196,plain,
! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TC @ ( B @ C )
@ ^ [D: TC] : $false ) ),
inference(pre_uni,[status(thm)],[194:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TC @ ( D @ E ) @ ^ [F: TC] : $false ) )),bind(B,$thf( A )),bind(C,$thf( D @ A ))]]) ).
thf(198,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[196]) ).
thf(200,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[198,190]) ).
thf(205,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,200]) ).
thf(207,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[205:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(209,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[207]) ).
thf(204,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,200]) ).
thf(206,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(pre_uni,[status(thm)],[204:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ ^ [F: TB] : $false ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(208,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[206]) ).
thf(195,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,190]) ).
thf(197,plain,
! [TA: $tType,TC: $tType,B: TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TC @ B
@ ^ [C: TC] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[195:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(199,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[197]) ).
thf(210,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[199,200]) ).
thf(220,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[208,210]) ).
thf(230,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[209,220]) ).
thf(234,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,230]) ).
thf(236,plain,
! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TC @ ( B @ C )
@ ^ [D: TC] : $false ) ),
inference(pre_uni,[status(thm)],[234:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TC @ ( D @ E ) @ ^ [F: TC] : $false ) )),bind(B,$thf( A )),bind(C,$thf( D @ A ))]]) ).
thf(238,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[236]) ).
thf(225,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,220]) ).
thf(227,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[225:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(229,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[227]) ).
thf(224,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,220]) ).
thf(226,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(pre_uni,[status(thm)],[224:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ ^ [F: TB] : $false ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(228,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[226]) ).
thf(215,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,210]) ).
thf(217,plain,
! [TA: $tType,TC: $tType,B: TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TC @ B
@ ^ [C: TC] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[215:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(219,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[217]) ).
thf(214,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,210]) ).
thf(216,plain,
! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TC @ ( B @ C )
@ ^ [D: TC] : $false ) ),
inference(pre_uni,[status(thm)],[214:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TC @ ( D @ E ) @ ^ [F: TC] : $false ) )),bind(B,$thf( A )),bind(C,$thf( D @ A ))]]) ).
thf(218,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[216]) ).
thf(240,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[218,230]) ).
thf(281,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[219,240]) ).
thf(292,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[228,281]) ).
thf(303,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[229,292]) ).
thf(314,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[238,303]) ).
thf(319,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,314]) ).
thf(322,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(pre_uni,[status(thm)],[319:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ ^ [F: TB] : $false ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(324,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[322]) ).
thf(309,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,303]) ).
thf(311,plain,
! [TA: $tType,TC: $tType,B: TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TC @ B
@ ^ [C: TC] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[309:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(313,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[311]) ).
thf(308,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,303]) ).
thf(310,plain,
! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TC @ ( B @ C )
@ ^ [D: TC] : $false ) ),
inference(pre_uni,[status(thm)],[308:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TC @ ( D @ E ) @ ^ [F: TC] : $false ) )),bind(B,$thf( A )),bind(C,$thf( D @ A ))]]) ).
thf(312,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[310]) ).
thf(298,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,292]) ).
thf(300,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[298:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(302,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[300]) ).
thf(297,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,292]) ).
thf(299,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(pre_uni,[status(thm)],[297:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ ^ [F: TB] : $false ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(301,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[299]) ).
thf(287,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,281]) ).
thf(289,plain,
! [TA: $tType,TC: $tType,B: TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TC @ B
@ ^ [C: TC] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[287:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(291,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[289]) ).
thf(286,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,281]) ).
thf(288,plain,
! [TA: $tType,TC: $tType,B: TA > TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TC @ ( B @ C )
@ ^ [D: TC] : $false ) ),
inference(pre_uni,[status(thm)],[286:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TC @ ( D @ E ) @ ^ [F: TC] : $false ) )),bind(B,$thf( A )),bind(C,$thf( D @ A ))]]) ).
thf(290,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[288]) ).
thf(245,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,240]) ).
thf(247,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[245:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(249,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[247]) ).
thf(244,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [D: TB] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[18,240]) ).
thf(246,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(pre_uni,[status(thm)],[244:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ TB @ ( D @ E ) @ ^ [F: TB] : $false ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(248,plain,
! [TA: $tType,TB: $tType,B: TA > TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ C )
@ ^ [D: TB] : $false ) ),
inference(simp,[status(thm)],[246]) ).
thf(235,plain,
! [TA: $tType,TC: $tType,C: TC,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TC @ C
@ ^ [D: TC] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
| ( A @ B ) ),
inference(paramod_ordered,[status(thm)],[18,230]) ).
thf(237,plain,
! [TA: $tType,TC: $tType,B: TC,A: TA] :
~ ( '\'const/sets/IN\'' @ TC @ B
@ ^ [C: TC] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(pre_uni,[status(thm)],[235:[bind(A,$thf( ^ [D: TA] : $false ))]]) ).
thf(239,plain,
! [TA: $tType,TB: $tType,B: TB,A: TA] :
~ ( '\'const/sets/IN\'' @ TB @ B
@ ^ [C: TB] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : $false ) ),
inference(simp,[status(thm)],[237]) ).
thf(325,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[239,314]) ).
thf(336,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[248,325]) ).
thf(465,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[249,336]) ).
thf(536,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[290,465]) ).
thf(555,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[291,536]) ).
thf(574,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[301,555]) ).
thf(593,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[302,574]) ).
thf(612,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[312,593]) ).
thf(631,plain,
! [TB: $tType,A: TB] :
~ ( '\'const/sets/IN\'' @ TB @ A
@ ^ [B: TB] : $false ),
inference(rewrite,[status(thm)],[313,612]) ).
thf(799,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(rewrite,[status(thm)],[324,631]) ).
thf(80,plain,
! [TA: $tType,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ C )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(85,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ C ) @ sk2 ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[80:[bind(A,$thf( ^ [E: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( D @ E ) @ sk2 ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(91,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ C ) @ sk2 ) )
| ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ A ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(3390,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk7 @ sk26 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2316,28]) ).
thf(3391,plain,
sk26 @ sk7,
inference(pattern_uni,[status(thm)],[3390:[bind(A,$thf( sk26 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(7480,plain,
( ~ ( sk26 @ sk28 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[2274,5570]) ).
thf(7503,plain,
( ~ ( sk26 @ sk28 )
| ( sk2 != sk2 )
| ( sk28 != sk7 ) ),
inference(simp,[status(thm)],[7480]) ).
thf(7523,plain,
( ~ ( sk26 @ sk28 )
| ( sk28 != sk7 ) ),
inference(simp,[status(thm)],[7503]) ).
thf(7533,plain,
( ( sk28 != sk7 )
| ( ( sk26 @ sk28 )
!= ( sk26 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[3391,7523]) ).
thf(7546,plain,
( ( sk28 != sk7 )
| ( sk28 != sk7 ) ),
inference(simp,[status(thm)],[7533]) ).
thf(7551,plain,
sk28 != sk7,
inference(simp,[status(thm)],[7546]) ).
thf(39,plain,
! [TA: $tType,TB: $tType,D: TB,C: TB > $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) )
= ( C @ D ) )
| ( ( B @ A )
!= ( '\'const/sets/IN\'' @ TB @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,18]) ).
thf(54,plain,
! [TA: $tType,TB: $tType,C: TA > TB > $o,B: TA > TB,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TB @ ( B @ D ) @ ( C @ D ) ) ) )
= ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[39:[bind(A,$thf( A )),bind(B,$thf( ^ [G: TA] : ( '\'const/sets/IN\'' @ TB @ ( E @ G ) @ ( F @ G ) ) )),bind(C,$thf( F @ A )),bind(D,$thf( E @ A ))]]) ).
thf(66,plain,
! [TA: $tType,TB: $tType,C: TA > TB > $o,B: TA > TB,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/IN\'' @ TB @ ( B @ D ) @ ( C @ D ) ) ) )
= ( C @ A @ ( B @ A ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(8333,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( sk10 @ sk24 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4878,101]) ).
thf(8584,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) ) ),
inference(pre_uni,[status(thm)],[8333:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk10 @ sk24 ) ))]]) ).
thf(14113,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8584,101]) ).
thf(14218,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
| ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) ) ) ),
inference(pre_uni,[status(thm)],[14113:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) ) ))]]) ).
thf(251,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) )
| ~ ? [C: TA > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
& ( '\'const/sets/IN\'' @ TA @ B @ C ) ) ),
inference(bool_ext,[status(thm)],[21]) ).
thf(278,plain,
! [TA: $tType,C: TA > $o,B: TA,A: ( TA > $o ) > $o] :
( ~ ( '\'const/sets/IN\'' @ ( TA > $o ) @ C @ A )
| ~ ( '\'const/sets/IN\'' @ TA @ B @ C )
| ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ),
inference(cnf,[status(esa)],[251]) ).
thf(4084,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk26 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2317,28]) ).
thf(4085,plain,
sk2 @ sk26,
inference(pattern_uni,[status(thm)],[4084:[bind(A,$thf( sk2 )),bind(B,$thf( sk26 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(17699,plain,
( ( sk27 != sk8 )
| ~ ( sk26 @ sk28 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 ) ) ),
inference(paramod_ordered,[status(thm)],[7198,5570]) ).
thf(17735,plain,
( ( sk27 != sk8 )
| ~ ( sk26 @ sk28 )
| ( sk2 != sk2 )
| ( sk28 != sk27 ) ),
inference(simp,[status(thm)],[17699]) ).
thf(17758,plain,
( ( sk27 != sk8 )
| ~ ( sk26 @ sk28 )
| ( sk28 != sk27 ) ),
inference(simp,[status(thm)],[17735]) ).
thf(17825,plain,
( ( sk28 != sk8 )
| ~ ( sk25 @ sk27 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk28 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 ) ) ),
inference(paramod_ordered,[status(thm)],[7617,5546]) ).
thf(17871,plain,
( ( sk28 != sk8 )
| ~ ( sk25 @ sk27 )
| ( sk2 != sk2 )
| ( sk28 != sk27 ) ),
inference(simp,[status(thm)],[17825]) ).
thf(17896,plain,
( ( sk28 != sk8 )
| ~ ( sk25 @ sk27 )
| ( sk28 != sk27 ) ),
inference(simp,[status(thm)],[17871]) ).
thf(16110,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/SUBSET\'' @ skt1 @ A @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk26 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2317,170]) ).
thf(16111,plain,
'\'const/sets/SUBSET\'' @ skt1 @ sk26 @ sk26,
inference(pattern_uni,[status(thm)],[16110:[bind(A,$thf( sk26 ))]]) ).
thf(107,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/trivia/I\'' @ $o @ ( A @ B ) )
= ( D @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,63]) ).
thf(117,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( '\'const/trivia/I\'' @ $o @ ( C @ A @ ( B @ A ) ) )
= ( '\'const/sets/IN\'' @ TA @ ( B @ A ) @ ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[107:[bind(A,$thf( F @ C )),bind(B,$thf( E @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: TB] : ( '\'const/sets/IN\'' @ TA @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(123,plain,
! [TA: $tType,TB: $tType,C: TB > TA > $o,B: TB > TA,A: TB] :
( ( '\'const/trivia/I\'' @ $o @ ( C @ A @ ( B @ A ) ) )
= ( '\'const/sets/IN\'' @ TA @ ( B @ A ) @ ( C @ A ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(14111,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8584,101]) ).
thf(14272,plain,
( ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) )
| ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ) ),
inference(pre_uni,[status(thm)],[14111:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) ))]]) ).
thf(48,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( D @ C ) )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,35]) ).
thf(55,plain,
! [TA: $tType,TB: $tType,C: TA > TB > $o,B: TA > TB,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ D )
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( C @ D @ E ) ) ) )
= ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[48:[bind(A,$thf( ^ [G: TA] : ( '\'const/sets/IN\'' @ TB @ ( E @ G ) @ ^ [H: TB] : ( '\'const/trivia/I\'' @ $o @ ( G @ G @ H ) ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ B )),bind(D,$thf( G @ B ))]]) ).
thf(67,plain,
! [TA: $tType,TB: $tType,C: TA > TB > $o,B: TA > TB,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] :
( '\'const/sets/IN\'' @ TB @ ( B @ D )
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( C @ D @ E ) ) ) )
= ( C @ A @ ( B @ A ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(1187,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk9 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[928,28]) ).
thf(1188,plain,
sk2 @ sk9,
inference(pattern_uni,[status(thm)],[1187:[bind(A,$thf( sk2 )),bind(B,$thf( sk9 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(7970,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) )
| ( ( B @ A )
!= ( '\'const/trivia/I\'' @ $o @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[38,7825]) ).
thf(8000,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ $false ) ) ),
inference(pre_uni,[status(thm)],[7970:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ $false ) ))]]) ).
thf(9807,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( '\'const/trivia/I\'' @ $o @ $false ) ),
inference(rewrite,[status(thm)],[8000,7825]) ).
thf(19568,plain,
! [A: $o] :
( ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) )
| A
| ( ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) )
!= ( '\'const/trivia/I\'' @ $o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14272,15]) ).
thf(19569,plain,
( ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk24 ) )
| ( sk10 @ sk24 ) ),
inference(pattern_uni,[status(thm)],[19568:[bind(A,$thf( sk10 @ sk24 ))]]) ).
thf(17708,plain,
( ( sk27 != sk8 )
| ~ ( sk9 @ sk18 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[7198,1654]) ).
thf(17743,plain,
( ( sk27 != sk8 )
| ~ ( sk9 @ sk18 )
| ( sk2 != sk2 )
| ( sk27 != sk18 ) ),
inference(simp,[status(thm)],[17708]) ).
thf(17760,plain,
( ( sk27 != sk8 )
| ~ ( sk9 @ sk18 )
| ( sk27 != sk18 ) ),
inference(simp,[status(thm)],[17743]) ).
thf(2763,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk25 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2312,11]) ).
thf(2764,plain,
'\'const/sets/pairwise\'' @ skt1 @ sk1 @ sk25,
inference(pattern_uni,[status(thm)],[2763:[bind(A,$thf( sk25 ))]]) ).
thf(20821,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk52 @ sk2,
inference(cnf,[status(esa)],[20687]) ).
thf(22569,plain,
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk52 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[20821,72]) ).
thf(22611,plain,
( ( sk52
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[22569]) ).
thf(22660,plain,
( sk52
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 ) ),
inference(simp,[status(thm)],[22611]) ).
thf(152,plain,
! [TA: $tType,D: skt1 > $o,C: skt1 > $o,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ D @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ C @ D )
| ( '\'const/sets/SUBSET\'' @ skt1 @ D @ C )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18,12]) ).
thf(160,plain,
! [TA: $tType,C: TA > skt1 > $o,B: skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ D ) @ sk2 ) )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ ( C @ A ) ) ),
inference(pre_uni,[status(thm)],[152:[bind(A,$thf( ^ [F: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( E @ F ) @ sk2 ) )),bind(B,$thf( B )),bind(C,$thf( E @ B )),bind(D,$thf( D ))]]) ).
thf(168,plain,
! [TA: $tType,C: TA > skt1 > $o,B: skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ D ) @ sk2 ) )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ ( C @ A ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(1164,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ B )
| ( ( B @ A )
!= ( sk9 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[99,1133]) ).
thf(1167,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : ( sk9 @ sk8 ) ),
inference(pre_uni,[status(thm)],[1164:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk9 @ sk8 ) ))]]) ).
thf(6490,plain,
! [TA: $tType,A: TA] :
( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $true ),
inference(rewrite,[status(thm)],[1167,1133]) ).
thf(263,plain,
! [TA: $tType,TB: $tType,D: TB,C: ( TB > $o ) > $o,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( ? [E: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ E @ C )
& ( '\'const/sets/IN\'' @ TB @ D @ E ) ) ) )
| ( ( A @ B )
!= ( '\'const/sets/IN\'' @ TB @ D @ ( '\'const/sets/UNIONS\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,21]) ).
thf(271,plain,
! [TA: $tType,TB: $tType,D: TA > TB > ( TB > $o ) > $o,C: TA > TB,B: ( TB > $o ) > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] :
( '\'const/sets/IN\'' @ TB @ ( C @ E )
@ ^ [F: TB] : ( '\'const/sets/UNIONS\'' @ TB @ ( D @ E @ F ) @ F ) ) )
= ( ? [E: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ E @ B )
& ( '\'const/sets/IN\'' @ TB @ ( C @ A ) @ E ) ) ) )
| ( ( D @ A )
!= ( ^ [E: TB] : B ) ) ),
inference(pre_uni,[status(thm)],[263:[bind(A,$thf( ^ [G: TA] : ( '\'const/sets/IN\'' @ TB @ ( E @ G ) @ ^ [H: TB] : ( '\'const/sets/UNIONS\'' @ TB @ ( G @ G @ H ) @ H ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( E @ B ))]]) ).
thf(272,plain,
! [TA: $tType,TB: $tType,D: TA > TB > ( TB > $o ) > $o,C: TA > TB,B: ( TB > $o ) > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] :
( '\'const/sets/IN\'' @ TB @ ( C @ E )
@ ^ [F: TB] : ( '\'const/sets/UNIONS\'' @ TB @ ( D @ E @ F ) @ F ) ) )
= ( ? [E: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ E @ B )
& ( '\'const/sets/IN\'' @ TB @ ( C @ A ) @ E ) ) ) )
| ( ( D @ A )
!= ( ^ [E: TB] : B ) ) ),
inference(pre_uni,[status(thm)],[271:[]]) ).
thf(273,plain,
! [TA: $tType,TB: $tType,D: TA > TB > ( TB > $o ) > $o,C: TA > TB,B: ( TB > $o ) > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] :
( '\'const/sets/IN\'' @ TB @ ( C @ E )
@ ^ [F: TB] : ( '\'const/sets/UNIONS\'' @ TB @ ( D @ E @ F ) @ F ) ) )
= ( ? [E: TB > $o] :
( ( '\'const/sets/IN\'' @ ( TB > $o ) @ E @ B )
& ( '\'const/sets/IN\'' @ TB @ ( C @ A ) @ E ) ) ) )
| ( ( D @ A )
!= ( ^ [E: TB] : B ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(8349,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
| ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( ( sk25 @ sk27 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5547,101]) ).
thf(8589,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
| ( '\'const/trivia/I\'' @ $o @ ( sk25 @ sk27 ) ) ),
inference(pre_uni,[status(thm)],[8349:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk25 @ sk27 ) ))]]) ).
thf(14010,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TB > TA > $o,B: TB > TA,A: TB] :
( ~ ( '\'const/trivia/I\'' @ $o @ ( C @ A @ ( B @ A ) ) )
| ( sk18 != sk7 )
| ( ( '\'const/sets/IN\'' @ TA @ ( B @ A ) @ ( C @ A ) )
!= ( '\'const/sets/IN\'' @ TC @ D
@ ^ [E: TC] : ( sk9 @ sk18 ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,2730]) ).
thf(14050,plain,
( ~ ( '\'const/trivia/I\'' @ $o @ ( sk9 @ sk18 ) )
| ( sk18 != sk7 ) ),
inference(pre_uni,[status(thm)],[14010:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TB] : ^ [F: TC] : ( sk9 @ sk18 ) )),bind(D,$thf( B @ A )),bind_type(TA,$thf( TC ))]]) ).
thf(2365,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk7 @ sk25 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2311,28]) ).
thf(2366,plain,
sk25 @ sk7,
inference(pattern_uni,[status(thm)],[2365:[bind(A,$thf( sk25 )),bind(B,$thf( sk7 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(144,plain,
! [TA: $tType,D: TA > $o,C: TA,B: skt1 > $o,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ B @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ B @ A )
| ( ( '\'const/trivia/I\'' @ $o @ $true )
= ( D @ C ) )
| ( ( '\'const/sets/SUBSET\'' @ skt1 @ A @ B )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,63]) ).
thf(163,plain,
! [TA: $tType,C: TA > skt1 > $o,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ A ) @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ ( B @ A ) )
| ( ( '\'const/sets/SUBSET\'' @ skt1 @ ( B @ A ) @ ( C @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(pre_uni,[status(thm)],[144:[bind(A,$thf( E @ C )),bind(B,$thf( F @ C )),bind(C,$thf( C )),bind(D,$thf( ^ [G: TA] : ( '\'const/sets/SUBSET\'' @ skt1 @ ( E @ G ) @ ( F @ G ) ) ))]]) ).
thf(171,plain,
! [TA: $tType,C: TA > skt1 > $o,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ A ) @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ ( B @ A ) )
| ( ( '\'const/sets/SUBSET\'' @ skt1 @ ( B @ A ) @ ( C @ A ) )
= ( '\'const/trivia/I\'' @ $o @ $true ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(16642,plain,
! [TA: $tType,C: TA > skt1 > $o,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( C @ A ) @ sk2 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( C @ A ) @ ( B @ A ) )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( B @ A ) @ ( C @ A ) ) ),
inference(rewrite,[status(thm)],[171,4953]) ).
thf(883,plain,
sk7 != sk8,
inference(cnf,[status(esa)],[830]) ).
thf(886,plain,
sk8 != sk7,
inference(lifteq,[status(thm)],[883]) ).
thf(47,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[18,35]) ).
thf(61,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[47:[]]) ).
thf(62,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA,A: TA > $o] :
( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ) )
| ( ( A @ B )
!= ( D @ C ) ) ),
inference(pre_uni,[status(thm)],[61:[]]) ).
thf(277,plain,
! [TA: $tType,B: TA,A: ( TA > $o ) > $o] :
( ( '\'const/sets/IN\'' @ ( TA > $o ) @ ( sk3 @ TA @ B @ A ) @ A )
| ~ ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(1712,plain,
! [A: skt1 > $o] :
( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk10 @ sk2 )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[932,11]) ).
thf(1713,plain,
'\'const/sets/pairwise\'' @ skt1 @ sk1 @ sk10,
inference(pattern_uni,[status(thm)],[1712:[bind(A,$thf( sk10 ))]]) ).
thf(50,plain,
! [TA: $tType,C: $o,B: TA > $o,A: TA] :
( ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [D: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ D ) ) )
= C )
| ( ( B @ A )
!= ( '\'const/trivia/I\'' @ $o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,15]) ).
thf(56,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) )
= ( B @ A ) ),
inference(pre_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )),bind(C,$thf( D @ A ))]]) ).
thf(68,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) )
= ( B @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(73,plain,
! [TA: $tType,C: TA > $o,B: TA,A: skt1 > $o] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ B
@ ^ [D: TA] : ( '\'const/trivia/I\'' @ $o @ ( C @ D ) ) )
| ( ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ A )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,35]) ).
thf(84,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[73:[bind(A,$thf( E @ B )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TA] : ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( E @ E ) ) ))]]) ).
thf(90,plain,
! [TA: $tType,B: TA > skt1 > $o,A: TA] :
( ~ ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ ( B @ A ) @ sk2 )
| ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/sets/pairwise\'' @ skt1 @ sk1 @ ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(22518,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk52 @ sk2 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20821,28]) ).
thf(22519,plain,
sk2 @ sk52,
inference(pattern_uni,[status(thm)],[22518:[bind(A,$thf( sk2 )),bind(B,$thf( sk52 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(16004,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: TC,C: TB > TA > $o,B: TB > TA,A: TB] :
( ~ ( '\'const/trivia/I\'' @ $o @ ( C @ A @ ( B @ A ) ) )
| ( sk24 != sk7 )
| ( ( '\'const/sets/IN\'' @ TA @ ( B @ A ) @ ( C @ A ) )
!= ( '\'const/sets/IN\'' @ TC @ D
@ ^ [E: TC] : ( sk10 @ sk24 ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,6391]) ).
thf(16046,plain,
( ~ ( '\'const/trivia/I\'' @ $o @ ( sk10 @ sk24 ) )
| ( sk24 != sk7 ) ),
inference(pre_uni,[status(thm)],[16004:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TB] : ^ [F: TC] : ( sk10 @ sk24 ) )),bind(D,$thf( B @ A )),bind_type(TA,$thf( TC ))]]) ).
thf(6826,plain,
( ~ ( sk25 @ sk27 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk27 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ sk2 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[2274,5546]) ).
thf(6853,plain,
( ~ ( sk25 @ sk27 )
| ( sk2 != sk2 )
| ( sk27 != sk7 ) ),
inference(simp,[status(thm)],[6826]) ).
thf(6871,plain,
( ~ ( sk25 @ sk27 )
| ( sk27 != sk7 ) ),
inference(simp,[status(thm)],[6853]) ).
thf(6883,plain,
( ( sk27 != sk7 )
| ( ( sk25 @ sk27 )
!= ( sk25 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[2366,6871]) ).
thf(6885,plain,
( ( sk27 != sk7 )
| ( sk27 != sk7 ) ),
inference(simp,[status(thm)],[6883]) ).
thf(6896,plain,
sk27 != sk7,
inference(simp,[status(thm)],[6885]) ).
thf(882,plain,
~ ( sk1 @ sk7 @ sk8 ),
inference(cnf,[status(esa)],[830]) ).
thf(100,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
| ( B @ A ) ),
inference(bool_ext,[status(thm)],[63]) ).
thf(27411,plain,
$false,
inference(e,[status(thm)],[8,69,101,4877,6374,88,170,16135,276,7198,17253,6391,1655,1735,2316,21311,20862,6909,6872,24,885,20818,6483,37,17888,25,7825,2274,125,1992,2730,22348,29,17667,121,21774,89,116,20905,16109,13228,16119,1199,17242,4878,17902,28,38,275,21,137,20819,65,17659,17887,8651,6427,20861,9,169,884,17763,17663,2312,17254,2317,5547,1700,13,4953,1434,128,8614,5571,21170,176,22,2791,59,27,20820,13745,23266,4112,4149,2358,12,5546,2311,274,4154,2742,140,799,91,7551,66,14218,932,278,4085,17758,17896,16111,3380,927,123,5570,3391,63,18,14272,67,1188,16,9807,1220,19569,72,11,1427,99,931,903,17760,1654,8584,2764,1133,22660,36,168,19,6490,273,8589,20821,14050,2366,16642,2340,94,7525,886,928,15,7617,62,277,1713,68,90,21744,22519,16046,6896,882,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV488^1 : TPTP v8.2.0. Released v7.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n011.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 : Sun May 19 18:22:23 EDT 2024
% 0.23/0.37 % CPUTime :
% 1.01/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.11 % [INFO] Parsing done (168ms).
% 1.35/1.12 % [INFO] Running in sequential loop mode.
% 2.02/1.47 % [INFO] eprover registered as external prover.
% 2.02/1.47 % [INFO] cvc4 registered as external prover.
% 2.02/1.48 % [INFO] Scanning for conjecture ...
% 2.26/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.26/1.60 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.42/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.42/1.62 % [INFO] Type checking passed.
% 2.42/1.63 % [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 ...
% 146.68/29.04 % External prover 'e' found a proof!
% 146.68/29.04 % [INFO] Killing All external provers ...
% 146.68/29.05 % Time passed: 28514ms (effective reasoning time: 27922ms)
% 146.68/29.05 % 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)>
% 146.68/29.05 % Axioms used in derivation (5): thm/sets/pairwise_, thm/sets/IN_UNIONS_, thm/trivia/I_THM_, thm/sets/SUBSET_, thm/sets/IN_
% 146.68/29.05 % No. of inferences in proof: 458
% 146.68/29.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28514 ms resp. 27922 ms w/o parsing
% 146.82/29.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 146.82/29.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------