TSTP Solution File: SEV462^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV462^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n032.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 : Mon Jun 24 15:59:05 EDT 2024
% Result : Theorem 119.39s 29.89s
% Output : Refutation 119.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 168 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 839 ( 167 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1717 ( 141 ~; 91 |; 20 &;1453 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 261 ( 261 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-5 aty)
% Number of variables : 448 ( 68 ^ 360 !; 20 ?; 448 :)
% 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/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/IMAGE\'_type',type,
'\'const/sets/IMAGE\'':
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > TA > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(sk1_type,type,
sk1: skt2 > skt1 > $o ).
thf(sk2_type,type,
sk2: skt2 > skt1 > $o ).
thf(sk3_type,type,
sk3: skt2 > $o ).
thf(sk15_type,type,
sk15: skt1 ).
thf(sk16_type,type,
sk16: skt1 > $o ).
thf(sk17_type,type,
sk17: skt1 > $o ).
thf(sk23_type,type,
sk23: skt2 ).
thf(sk24_type,type,
sk24: skt1 ).
thf(sk29_type,type,
sk29: skt1 ).
thf(sk30_type,type,
sk30: skt1 ).
thf(sk37_type,type,
sk37: skt2 ).
thf(sk38_type,type,
sk38: skt2 ).
thf(sk41_type,type,
sk41: skt2 ).
thf(sk42_type,type,
sk42: skt1 ).
thf(sk47_type,type,
sk47: skt2 ).
thf(sk48_type,type,
sk48: skt2 ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
= ( ? [D: TA] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_') ).
thf(17,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
= ( ? [D: TA] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) )
= ( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_') ).
thf(23,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)],[7]) ).
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(cnf,[status(esa)],[23]) ).
thf(25,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)],[24]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > $o] :
( ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ C )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( A @ D ) @ ( B @ D ) ) )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ A @ C ) ) @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/UNIONS_MONO_IMAGE_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > $o] :
( ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ C )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( A @ D ) @ ( B @ D ) ) )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ A @ C ) ) @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o,C: TA > $o] :
( ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ C )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( A @ D ) @ ( B @ D ) ) )
=> ( '\'const/sets/SUBSET\'' @ TB @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ A @ C ) ) @ ( '\'const/sets/UNIONS\'' @ TB @ ( '\'const/sets/IMAGE\'' @ TA @ ( TB > $o ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ( '\'const/sets/SUBSET\'' @ skt1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(943,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ~ ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
=> ( '\'const/sets/IN\'' @ TA @ C @ B ) )
| ( ( '\'const/sets/SUBSET\'' @ TA @ A @ B )
!= ( '\'const/sets/SUBSET\'' @ skt1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,9]) ).
thf(944,plain,
~ ! [A: skt1] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
=> ( '\'const/sets/IN\'' @ skt1 @ A @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )),bind(B,$thf( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1020,plain,
'\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[944]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_UNIONS_') ).
thf(20,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)],[6]) ).
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(cnf,[status(esa)],[20]) ).
thf(22,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)],[21]) ).
thf(1048,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 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/UNIONS\'' @ TA @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[1020,22]) ).
thf(1049,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
& ( '\'const/sets/IN\'' @ skt1 @ sk15 @ A ) ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 )),bind(B,$thf( sk15 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1071,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk16 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ),
inference(cnf,[status(esa)],[1049]) ).
thf(1927,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) )
| ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk16 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1071]) ).
thf(1928,plain,
? [A: skt2] :
( ( sk16
= ( sk1 @ A ) )
& ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1927:[bind(A,$thf( sk16 )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 > $o )),bind_type(TB,$thf( skt2 ))]]) ).
thf(1933,plain,
'\'const/sets/IN\'' @ skt2 @ sk38 @ sk3,
inference(cnf,[status(esa)],[1928]) ).
thf(3,axiom,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/trivia/I_THM_') ).
thf(11,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,A: TA] :
( ( '\'const/trivia/I\'' @ TA @ A )
= A ),
inference(lifteq,[status(thm)],[12]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(14,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(15,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(30,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)],[13,16]) ).
thf(32,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [C: TB] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ),
inference(pre_uni,[status(thm)],[30:[bind(A,$thf( D @ C )),bind(B,$thf( ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ))]]) ).
thf(33,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)],[32]) ).
thf(39,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)],[33,16]) ).
thf(40,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
= ( B @ A ) ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$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(61,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/trivia/I\'' @ $o @ ( B @ A ) )
= ( B @ A ) ),
inference(simp,[status(thm)],[40]) ).
thf(108,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TA @ A @ B ) ),
inference(rewrite,[status(thm)],[33,61]) ).
thf(2294,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt2 @ sk38 @ sk3 )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1933,108]) ).
thf(2295,plain,
sk3 @ sk38,
inference(pattern_uni,[status(thm)],[2294:[bind(A,$thf( sk38 )),bind(B,$thf( sk3 )),bind_type(TA,$thf( skt2 ))]]) ).
thf(1050,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 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,1020]) ).
thf(1051,plain,
? [A: skt1 > $o] :
( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ A @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
& ( '\'const/sets/IN\'' @ skt1 @ sk15 @ A ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 )),bind(B,$thf( sk15 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1073,plain,
'\'const/sets/IN\'' @ ( skt1 > $o ) @ sk17 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ),
inference(cnf,[status(esa)],[1051]) ).
thf(1019,plain,
~ ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[944]) ).
thf(1068,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) )
!= ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1020,1019]) ).
thf(1069,plain,
( ( sk15 != sk15 )
| ( ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1074,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[1069]) ).
thf(3110,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk17 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1073,19]) ).
thf(3111,plain,
? [A: skt2] :
( ( sk17
= ( sk1 @ A ) )
& ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3110:[bind(A,$thf( sk17 )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 > $o )),bind_type(TB,$thf( skt2 ))]]) ).
thf(3117,plain,
'\'const/sets/IN\'' @ skt2 @ sk47 @ sk3,
inference(cnf,[status(esa)],[3111]) ).
thf(3153,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt2 @ sk47 @ sk3 )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3117,108]) ).
thf(3154,plain,
sk3 @ sk47,
inference(pattern_uni,[status(thm)],[3153:[bind(A,$thf( sk47 )),bind(B,$thf( sk3 )),bind_type(TA,$thf( skt2 ))]]) ).
thf(10,plain,
! [A: skt2] :
( ~ ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ A ) @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(75,plain,
! [TA: $tType,C: skt2,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ C ) @ ( sk2 @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ skt2 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,10]) ).
thf(76,plain,
! [A: skt2] :
( ~ ( sk3 @ A )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ A ) @ ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( skt2 ))]]) ).
thf(96,plain,
! [A: skt2] :
( ~ ( sk3 @ A )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ A ) @ ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(1070,plain,
'\'const/sets/IN\'' @ skt1 @ sk15 @ sk16,
inference(cnf,[status(esa)],[1049]) ).
thf(1107,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ sk16 )
!= ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1070,1019]) ).
thf(1116,plain,
( ( sk15 != sk15 )
| ( sk16
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[1107]) ).
thf(1119,plain,
( sk16
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[1116]) ).
thf(1396,plain,
( ( sk16 @ sk29 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk29 ) ),
inference(func_ext,[status(esa)],[1119]) ).
thf(2738,plain,
( ~ ( sk16 @ sk29 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk29 ) ),
inference(bool_ext,[status(thm)],[1396]) ).
thf(1925,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk16 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1071,19]) ).
thf(1926,plain,
? [A: skt2] :
( ( sk16
= ( sk1 @ A ) )
& ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( sk16 )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 > $o )),bind_type(TB,$thf( skt2 ))]]) ).
thf(1930,plain,
'\'const/sets/IN\'' @ skt2 @ sk37 @ sk3,
inference(cnf,[status(esa)],[1926]) ).
thf(1947,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt2 @ sk37 @ sk3 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1930,16]) ).
thf(1948,plain,
sk3 @ sk37,
inference(pattern_uni,[status(thm)],[1947:[bind(A,$thf( sk3 )),bind(B,$thf( sk37 )),bind_type(TA,$thf( skt2 ))]]) ).
thf(73,plain,
! [A: skt2] :
( ~ ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 )
| ( ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ A ) @ ( sk2 @ A ) )
!= ( '\'const/sets/SUBSET\'' @ skt1 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,9]) ).
thf(87,plain,
! [A: skt2] :
( ~ ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 )
| ( ( sk1 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(1053,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1020,108]) ).
thf(1054,plain,
'\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) @ sk15,
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk15 )),bind(B,$thf( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1029,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ~ ( B @ A )
| ( ( '\'const/sets/IN\'' @ TA @ A @ B )
!= ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,1019]) ).
thf(1030,plain,
~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk15 ),
inference(pattern_uni,[status(thm)],[1029:[bind(A,$thf( sk15 )),bind(B,$thf( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )),bind_type(TA,$thf( skt1 ))]]) ).
thf(1714,plain,
( ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk15 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) @ sk15 ) ),
inference(paramod_ordered,[status(thm)],[1054,1030]) ).
thf(1715,plain,
( ( ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 )
!= ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
| ( sk15 != sk15 ) ),
inference(simp,[status(thm)],[1714]) ).
thf(1716,plain,
( ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 )
!= ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ),
inference(simp,[status(thm)],[1715]) ).
thf(2015,plain,
( ( ( ^ [A: skt1 > $o] : sk2 )
!= ( ^ [A: skt1 > $o] : sk1 ) )
| ( ( ^ [A: skt1 > $o] : sk3 )
!= ( ^ [A: skt1 > $o] : sk3 ) )
| ( ( ^ [A: skt1 > $o] : A )
!= ( ^ [A: skt1 > $o] : A ) ) ),
inference(simp,[status(thm)],[1716]) ).
thf(2017,plain,
( ( ^ [A: skt1 > $o] : sk2 )
!= ( ^ [A: skt1 > $o] : sk1 ) ),
inference(simp,[status(thm)],[2015]) ).
thf(2018,plain,
( ( sk2 @ sk41 @ sk42 )
!= ( sk1 @ sk41 @ sk42 ) ),
inference(func_ext,[status(esa)],[2017]) ).
thf(45,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)],[16,33]) ).
thf(55,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)],[45:[]]) ).
thf(56,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)],[55:[]]) ).
thf(3112,plain,
! [TA: $tType,TB: $tType,C: TB > TA,B: TB > $o,A: TA] :
( ? [D: TB] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TB @ D @ B ) )
| ( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/IMAGE\'' @ TB @ TA @ C @ B ) )
!= ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk17 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,1073]) ).
thf(3113,plain,
? [A: skt2] :
( ( sk17
= ( sk1 @ A ) )
& ( '\'const/sets/IN\'' @ skt2 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3112:[bind(A,$thf( sk17 )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 > $o )),bind_type(TB,$thf( skt2 ))]]) ).
thf(3120,plain,
'\'const/sets/IN\'' @ skt2 @ sk48 @ sk3,
inference(cnf,[status(esa)],[3113]) ).
thf(1934,plain,
( sk16
= ( sk1 @ sk38 ) ),
inference(cnf,[status(esa)],[1928]) ).
thf(1935,plain,
( ( sk1 @ sk38 )
= sk16 ),
inference(lifteq,[status(thm)],[1934]) ).
thf(100,plain,
! [TA: $tType,C: skt2,B: TA,A: TA > $o] :
( ~ ( A @ B )
| ( ( sk1 @ C )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ C )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ B @ A )
!= ( '\'const/sets/IN\'' @ skt2 @ C @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[16,87]) ).
thf(101,plain,
! [A: skt2] :
( ~ ( sk3 @ A )
| ( ( sk1 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( skt2 ))]]) ).
thf(105,plain,
! [A: skt2] :
( ~ ( sk3 @ A )
| ( ( sk1 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ A )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(155,plain,
! [TA: $tType,C: skt2,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( ( sk1 @ C )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ C )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) )
| ( ( A @ B )
!= ( sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,105]) ).
thf(156,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk3 @ ( B @ C ) ) )
| ( ( sk1 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(pre_uni,[status(thm)],[155:[bind(A,$thf( ^ [E: TA] : ( sk3 @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(157,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk3 @ ( B @ C ) ) )
| ( ( sk1 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(423,plain,
! [TA: $tType,TB: $tType,D: TB > skt2,C: TB,B: TA > $o,A: TA] :
( ~ ( B @ A )
| ( ( sk1 @ ( D @ C ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ ( D @ C ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( sk3 @ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,157]) ).
thf(424,plain,
! [TB: $tType,B: TB > skt2,A: TB] :
( ~ ( sk3 @ ( B @ A ) )
| ( ( sk1 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[423:[bind(A,$thf( A )),bind(B,$thf( ^ [F: TB] : ( sk3 @ ( E @ F ) ) )),bind(C,$thf( A )),bind(D,$thf( E )),bind_type(TA,$thf( TB ))]]) ).
thf(436,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( sk3 @ ( B @ A ) )
| ( ( sk1 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( sk2 @ ( B @ A ) )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(2356,plain,
( ~ ( sk2 @ sk41 @ sk42 )
| ~ ( sk1 @ sk41 @ sk42 ) ),
inference(bool_ext,[status(thm)],[2018]) ).
thf(140,plain,
! [TA: $tType,C: skt2,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ C ) @ ( sk2 @ C ) )
| ( ( A @ B )
!= ( sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,96]) ).
thf(147,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk3 @ ( B @ C ) ) )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ ( B @ A ) ) @ ( sk2 @ ( B @ A ) ) ) ),
inference(pre_uni,[status(thm)],[140:[bind(A,$thf( ^ [E: TA] : ( sk3 @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
thf(152,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( sk3 @ ( B @ C ) ) )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ ( B @ A ) ) @ ( sk2 @ ( B @ A ) ) ) ),
inference(simp,[status(thm)],[147]) ).
thf(452,plain,
! [TA: $tType,TB: $tType,D: TB > skt2,C: TB,B: TA > $o,A: TA] :
( ~ ( B @ A )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ ( D @ C ) ) @ ( sk2 @ ( D @ C ) ) )
| ( ( '\'const/sets/IN\'' @ TA @ A @ B )
!= ( '\'const/sets/IN\'' @ TB @ C
@ ^ [E: TB] : ( sk3 @ ( D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,152]) ).
thf(453,plain,
! [TB: $tType,B: TB > skt2,A: TB] :
( ~ ( sk3 @ ( B @ A ) )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ ( B @ A ) ) @ ( sk2 @ ( B @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( A )),bind(B,$thf( ^ [F: TB] : ( sk3 @ ( E @ F ) ) )),bind(C,$thf( A )),bind(D,$thf( E )),bind_type(TA,$thf( TB ))]]) ).
thf(480,plain,
! [TA: $tType,B: TA > skt2,A: TA] :
( ~ ( sk3 @ ( B @ A ) )
| ( '\'const/sets/SUBSET\'' @ skt1 @ ( sk1 @ ( B @ A ) ) @ ( sk2 @ ( B @ A ) ) ) ),
inference(simp,[status(thm)],[453]) ).
thf(1072,plain,
'\'const/sets/IN\'' @ skt1 @ sk15 @ sk17,
inference(cnf,[status(esa)],[1051]) ).
thf(1092,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ sk16 )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1070,108]) ).
thf(1093,plain,
sk16 @ sk15,
inference(pattern_uni,[status(thm)],[1092:[bind(A,$thf( sk15 )),bind(B,$thf( sk16 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(2751,plain,
( ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk29 )
| ( ( sk16 @ sk29 )
!= ( sk16 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[1093,1396]) ).
thf(2758,plain,
( ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk29 )
| ( sk29 != sk15 ) ),
inference(simp,[status(thm)],[2751]) ).
thf(1364,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ sk17 )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1072,16]) ).
thf(1365,plain,
sk17 @ sk15,
inference(pattern_uni,[status(thm)],[1364:[bind(A,$thf( sk17 )),bind(B,$thf( sk15 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(3121,plain,
( sk17
= ( sk1 @ sk48 ) ),
inference(cnf,[status(esa)],[3113]) ).
thf(3122,plain,
( ( sk1 @ sk48 )
= sk17 ),
inference(lifteq,[status(thm)],[3121]) ).
thf(38,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)],[33,16]) ).
thf(52,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)],[38:[]]) ).
thf(53,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)],[52:[]]) ).
thf(3118,plain,
( sk17
= ( sk1 @ sk47 ) ),
inference(cnf,[status(esa)],[3111]) ).
thf(3119,plain,
( ( sk1 @ sk47 )
= sk17 ),
inference(lifteq,[status(thm)],[3118]) ).
thf(1383,plain,
( ( '\'const/sets/IN\'' @ skt1 @ sk15 @ sk17 )
!= ( '\'const/sets/IN\'' @ skt1 @ sk15 @ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1072,1019]) ).
thf(1392,plain,
( ( sk15 != sk15 )
| ( sk17
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[1383]) ).
thf(1395,plain,
( sk17
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1397,plain,
( ( sk17 @ sk30 )
!= ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk30 ) ),
inference(func_ext,[status(esa)],[1395]) ).
thf(26,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(1207,plain,
! [TA: $tType,A: TA] :
( ~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false )
| $false ),
inference(prim_subst,[status(thm)],[26:[bind(A,$thf( ^ [C: TA] : $false ))]]) ).
thf(1297,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A
@ ^ [B: TA] : $false ),
inference(simp,[status(thm)],[1207]) ).
thf(1931,plain,
( sk16
= ( sk1 @ sk37 ) ),
inference(cnf,[status(esa)],[1926]) ).
thf(1932,plain,
( ( sk1 @ sk37 )
= sk16 ),
inference(lifteq,[status(thm)],[1931]) ).
thf(1121,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( ( '\'const/trivia/I\'' @ $o @ $true )
= ( B @ A ) )
| ( ( sk16 @ sk15 )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1093,61]) ).
thf(1132,plain,
( ( sk16 @ sk15 )
= ( '\'const/trivia/I\'' @ $o @ $true ) ),
inference(pre_uni,[status(thm)],[1121:[bind(A,$thf( A )),bind(B,$thf( ^ [C: TA] : ( sk16 @ sk15 ) ))]]) ).
thf(1627,plain,
'\'const/trivia/I\'' @ $o @ $true,
inference(rewrite,[status(thm)],[1132,1093]) ).
thf(3902,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ skt2 @ sk48 @ sk3 )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3120,108]) ).
thf(3903,plain,
sk3 @ sk48,
inference(pattern_uni,[status(thm)],[3902:[bind(A,$thf( sk48 )),bind(B,$thf( sk3 )),bind_type(TA,$thf( skt2 ))]]) ).
thf(1905,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( A @ B )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk16 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
!= ( '\'const/sets/IN\'' @ TA @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1071,16]) ).
thf(1906,plain,
'\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 @ sk16,
inference(pattern_uni,[status(thm)],[1905:[bind(A,$thf( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 )),bind(B,$thf( sk16 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(29,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)],[16,13]) ).
thf(31,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) )
= ( B @ A ) ),
inference(pre_uni,[status(thm)],[29:[bind(A,$thf( ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )),bind(B,$thf( B )),bind(C,$thf( D @ B ))]]) ).
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(simp,[status(thm)],[31]) ).
thf(41,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)],[33,16]) ).
thf(54,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\'' @ $o @ ( C @ D @ E ) ) ) ) ),
inference(pre_uni,[status(thm)],[41:[bind(A,$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(64,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)],[54]) ).
thf(3187,plain,
( ~ ( sk17 @ sk30 )
| ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk30 ) ),
inference(bool_ext,[status(thm)],[1397]) ).
thf(27,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(1075,plain,
( ( ( ^ [A: skt1] : ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )
!= ( ^ [A: skt1] : ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) )
| ( ( ^ [A: skt1] : A )
!= ( ^ [A: skt1] : A ) ) ),
inference(simp,[status(thm)],[1074]) ).
thf(1077,plain,
( ( ^ [A: skt1] : ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) )
!= ( ^ [A: skt1] : ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(1078,plain,
( ( ( ^ [A: skt1,B: skt1 > $o] : sk2 )
!= ( ^ [A: skt1,B: skt1 > $o] : sk1 ) )
| ( ( ^ [A: skt1,B: skt1 > $o] : sk3 )
!= ( ^ [A: skt1,B: skt1 > $o] : sk3 ) )
| ( ( ^ [A: skt1,B: skt1 > $o] : B )
!= ( ^ [A: skt1,B: skt1 > $o] : B ) ) ),
inference(simp,[status(thm)],[1077]) ).
thf(1080,plain,
( ( ^ [A: skt1,B: skt1 > $o] : sk2 )
!= ( ^ [A: skt1,B: skt1 > $o] : sk1 ) ),
inference(simp,[status(thm)],[1078]) ).
thf(48,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)],[33,13]) ).
thf(58,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) )
= ( B @ A ) ),
inference(pre_uni,[status(thm)],[48:[bind(A,$thf( A )),bind(B,$thf( ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) )),bind(C,$thf( D @ A ))]]) ).
thf(66,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)],[58]) ).
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(bool_ext,[status(thm)],[33]) ).
thf(46,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)],[16,33]) ).
thf(51,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\'' @ $o @ ( C @ D @ E ) ) ) )
= ( C @ A @ ( B @ A ) ) ),
inference(pre_uni,[status(thm)],[46:[bind(A,$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(63,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)],[51]) ).
thf(3094,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
| ( ( '\'const/sets/IN\'' @ ( skt1 > $o ) @ sk17 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 ) )
!= ( '\'const/sets/IN\'' @ TA @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1073,108]) ).
thf(3095,plain,
'\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 @ sk17,
inference(pattern_uni,[status(thm)],[3094:[bind(A,$thf( sk17 )),bind(B,$thf( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk1 @ sk3 )),bind_type(TA,$thf( skt1 > $o ))]]) ).
thf(49,plain,
! [TB: $tType,C: TB > $o,B: TB,A: $o] :
( ( A
= ( '\'const/sets/IN\'' @ TB @ B
@ ^ [D: TB] : ( '\'const/trivia/I\'' @ $o @ ( C @ D ) ) ) )
| ( ( '\'const/trivia/I\'' @ $o @ A )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13,33]) ).
thf(57,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TB @ A
@ ^ [C: TB] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( D @ B )),bind(B,$thf( B )),bind(C,$thf( ^ [E: TB] : ( '\'const/trivia/I\'' @ $o @ ( D @ E ) ) ))]]) ).
thf(65,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( B @ A )
= ( '\'const/sets/IN\'' @ TA @ A
@ ^ [C: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ C ) ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(653,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TB,B: TA > $o,A: TA] :
( ( ( B @ A )
= ( D @ C ) )
| ( ( '\'const/sets/IN\'' @ TA @ A
@ ^ [E: TA] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ E ) ) ) )
!= ( '\'const/sets/IN\'' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[65,108]) ).
thf(654,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ A ) ) )
= ( B @ A ) ),
inference(pattern_uni,[status(thm)],[653:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( ^ [F: TB] : ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( F @ F ) ) ) )),bind_type(TA,$thf( TB ))]]) ).
thf(748,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/trivia/I\'' @ $o @ ( '\'const/trivia/I\'' @ $o @ ( B @ A ) ) )
= ( B @ A ) ),
inference(simp,[status(thm)],[654]) ).
thf(36,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)],[33]) ).
thf(3189,plain,
( ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk30 )
| ( ( sk17 @ sk30 )
!= ( sk17 @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[1365,1397]) ).
thf(3203,plain,
( ~ ( '\'const/sets/UNIONS\'' @ skt1 @ ( '\'const/sets/IMAGE\'' @ skt2 @ ( skt1 > $o ) @ sk2 @ sk3 ) @ sk30 )
| ( sk30 != sk15 ) ),
inference(simp,[status(thm)],[3189]) ).
thf(1120,plain,
( ( sk2 @ sk23 @ sk24 )
!= ( sk1 @ sk23 @ sk24 ) ),
inference(func_ext,[status(esa)],[1080]) ).
thf(1673,plain,
( ~ ( sk2 @ sk23 @ sk24 )
| ~ ( sk1 @ sk23 @ sk24 ) ),
inference(bool_ext,[status(thm)],[1120]) ).
thf(25112,plain,
$false,
inference(e,[status(thm)],[2295,1073,1074,3154,96,2738,1933,1948,87,2018,10,56,3120,1935,436,25,14,2356,157,20,152,1020,2017,480,61,1072,1119,2758,1365,3122,9,53,3119,1397,1297,1932,13,1627,3903,105,1054,1071,1906,34,64,17,3187,22,27,1080,66,108,1396,35,63,1070,1716,16,3095,11,3117,748,26,23,8,1030,1077,36,1395,3203,19,1673,1019,1120,1093,1930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEV462^1 : TPTP v8.2.0. Released v7.0.0.
% 0.02/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri Jun 21 18:51:40 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.79/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.94 % [INFO] Parsing done (122ms).
% 1.18/0.95 % [INFO] Running in sequential loop mode.
% 1.56/1.19 % [INFO] eprover registered as external prover.
% 1.56/1.19 % [INFO] Scanning for conjecture ...
% 1.69/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.69/1.30 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.85/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.33 % [INFO] Type checking passed.
% 1.85/1.33 % [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 ...
% 119.39/29.88 % External prover 'e' found a proof!
% 119.39/29.88 % [INFO] Killing All external provers ...
% 119.39/29.89 % Time passed: 29459ms (effective reasoning time: 28933ms)
% 119.39/29.89 % 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)>
% 119.39/29.89 % Axioms used in derivation (5): thm/sets/IN_UNIONS_, thm/sets/IN_IMAGE_, thm/trivia/I_THM_, thm/sets/SUBSET_, thm/sets/IN_
% 119.39/29.89 % No. of inferences in proof: 168
% 119.39/29.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29459 ms resp. 28933 ms w/o parsing
% 119.45/29.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 119.45/29.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------