TSTP Solution File: DAT327^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT327^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 7 07:39:58 EDT 2024
% Result : Theorem 71.70s 11.74s
% Output : Refutation 71.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 277 ( 156 unt; 9 typ; 0 def)
% Number of atoms : 1114 ( 382 equ; 12 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 3714 ( 392 ~; 232 |; 2 &;3084 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 747 ( 78 ^ 662 !; 0 ?; 747 :)
% ( 7 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/set_of_list\'_type',type,
'\'const/sets/set_of_list\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > TA > $o ) ).
thf('\'const/sets/INSERT\'_type',type,
'\'const/sets/INSERT\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/ind_types/NIL\'_type',type,
'\'const/ind_types/NIL\'':
!>[TA: $tType] : ( '\'type/ind_types/list\'' @ TA ) ).
thf('\'const/ind_types/CONS\'_type',type,
'\'const/ind_types/CONS\'':
!>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: '\'type/ind_types/list\'' @ skt1 ).
thf(sk2_type,type,
sk2:
!>[TA: $tType] : ( ( ( '\'type/ind_types/list\'' @ TA ) > $o ) > TA ) ).
thf(sk3_type,type,
sk3:
!>[TA: $tType] : ( ( ( '\'type/ind_types/list\'' @ TA ) > $o ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(7,axiom,
! [TA: $tType] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/set_of_list_0') ).
thf(29,plain,
! [TA: $tType] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,plain,
! [TA: $tType] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [TA: $tType] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/set_of_list_1') ).
thf(26,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ B )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_INSERT_EMPTY_') ).
thf(23,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ B )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ B )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ B )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(851,plain,
! [TB: $tType,D: TB > $o,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,25]) ).
thf(852,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[851:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( '\'const/sets/set_of_list\'' @ TB @ B ))]]) ).
thf(888,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[852]) ).
thf(921,plain,
! [TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,888]) ).
thf(922,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(939,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[922]) ).
thf(1163,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,939]) ).
thf(1164,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[1163:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ TB ))]]) ).
thf(1173,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[1164]) ).
thf(1179,plain,
! [TB: $tType,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1173]) ).
thf(1180,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[1179:[]]) ).
thf(1184,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1196,plain,
! [TB: $tType,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1184]) ).
thf(1197,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1196:[]]) ).
thf(1206,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[1197]) ).
thf(1236,plain,
! [TB: $tType,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,1206]) ).
thf(1237,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1236:[]]) ).
thf(1242,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[1237]) ).
thf(3,axiom,
! [TA: $tType,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
& ! [B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( A @ C )
=> ( A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) ) )
=> ! [B: '\'type/ind_types/list\'' @ TA] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_') ).
thf(11,plain,
! [TA: $tType,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
& ! [B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( A @ C )
=> ( A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) ) )
=> ! [B: '\'type/ind_types/list\'' @ TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(859,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ B ) ) ),
inference(paramod_ordered,[status(thm)],[31,28]) ).
thf(860,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[859:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ TB ))]]) ).
thf(889,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(simp,[status(thm)],[860]) ).
thf(1,conjecture,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/sets/set_of_list\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SET_OF_LIST_EQ_EMPTY_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/sets/set_of_list\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/sets/set_of_list\'' @ TA @ A )
= ( '\'const/sets/EMPTY\'' @ TA ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(34,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(39,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(33,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(38,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(51,plain,
( ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,38]) ).
thf(54,plain,
( ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( ^ [A: skt1] : sk1 )
!= ( ^ [A: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [A: skt1] : A )
!= ( ^ [A: skt1] : A ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(55,plain,
( ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( ^ [A: skt1] : sk1 )
!= ( ^ [A: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
( ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(func_ext,[status(esa)],[55]) ).
thf(57,plain,
( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(simp,[status(thm)],[56]) ).
thf(101,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simplifyReflect,[status(thm)],[39,57]) ).
thf(111,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[101,31]) ).
thf(112,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[111:[]]) ).
thf(173,plain,
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(rewrite,[status(thm)],[101,112]) ).
thf(855,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[173,28]) ).
thf(856,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(pattern_uni,[status(thm)],[855:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ skt1 ))]]) ).
thf(355,plain,
! [B: skt1 > $o,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ B ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,25]) ).
thf(356,plain,
! [B: skt1 > $o,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[355:[]]) ).
thf(648,plain,
! [B: skt1 > $o,A: skt1] :
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ B ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,356]) ).
thf(649,plain,
! [B: skt1 > $o,A: skt1] :
( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ B ) ),
inference(pattern_uni,[status(thm)],[648:[]]) ).
thf(844,plain,
! [D: skt1 > $o,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,649]) ).
thf(845,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[844:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( '\'const/sets/set_of_list\'' @ skt1 @ B ))]]) ).
thf(894,plain,
! [D: '\'type/ind_types/list\'' @ skt1,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,845]) ).
thf(895,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(952,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,895]) ).
thf(953,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) ) ),
inference(pattern_uni,[status(thm)],[952:[]]) ).
thf(1672,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[856,953]) ).
thf(1673,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[1672:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( '\'const/ind_types/CONS\'' @ skt1 @ D @ ( '\'const/ind_types/NIL\'' @ skt1 ) ))]]) ).
thf(1691,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[1673]) ).
thf(3007,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,1691]) ).
thf(3008,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[3007:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(950,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[173,895]) ).
thf(951,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[950:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ skt1 ))]]) ).
thf(963,plain,
! [A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,951]) ).
thf(964,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[963:[]]) ).
thf(982,plain,
! [A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,964]) ).
thf(983,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[982:[]]) ).
thf(1104,plain,
! [A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,983]) ).
thf(1105,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[1104:[]]) ).
thf(902,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[31,845]) ).
thf(906,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( ^ [C: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( ^ [C: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [C: skt1] : C )
!= ( ^ [C: skt1] : C ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(909,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ^ [C: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( ^ [C: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(1540,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
= ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ C ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[856,28]) ).
thf(1541,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
= ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1540:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'const/ind_types/NIL\'' @ skt1 ))]]) ).
thf(3011,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1541,1691]) ).
thf(3012,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[3011:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(174,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
= ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(rewrite,[status(thm)],[10,112]) ).
thf(185,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ A )
= ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(func_ext,[status(esa)],[173]) ).
thf(121,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(141,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(177,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 @ A )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ A ) ),
inference(func_ext,[status(esa)],[112]) ).
thf(1297,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(rewrite,[status(thm)],[141,177]) ).
thf(1298,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(simplifyReflect,[status(thm)],[1297,173]) ).
thf(353,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ A @ B ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,25]) ).
thf(354,plain,
! [TB: $tType,B: TB > $o,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ A @ B ) ),
inference(pattern_uni,[status(thm)],[353:[]]) ).
thf(357,plain,
! [TA: $tType,B: TA > $o,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/sets/INSERT\'' @ TA @ A @ B ) ),
inference(simp,[status(thm)],[354]) ).
thf(1730,plain,
! [TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
= ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ C ) ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,28]) ).
thf(1731,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
= ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[1730:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( '\'const/ind_types/NIL\'' @ TB ))]]) ).
thf(1873,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) )
= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(simp,[status(thm)],[1731]) ).
thf(1165,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,939]) ).
thf(1166,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) ) ),
inference(pattern_uni,[status(thm)],[1165:[]]) ).
thf(1174,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ B ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1898,plain,
! [TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[889,1174]) ).
thf(1899,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1898:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ ( '\'const/ind_types/NIL\'' @ TB ) ))]]) ).
thf(1944,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[1899]) ).
thf(3794,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/EMPTY\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[1873,1944]) ).
thf(3795,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[3794:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(3840,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[3795]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ B )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/NOT_CONS_NIL_') ).
thf(20,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ B )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(130,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(152,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(134,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( ( B @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ~ ( ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [E: '\'type/ind_types/list\'' @ TA] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(160,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(164,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(929,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,888]) ).
thf(933,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( ^ [C: TB] : ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( ^ [C: TB] : ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( ^ [C: TB] : C )
!= ( ^ [C: TB] : C ) ) ),
inference(simp,[status(thm)],[929]) ).
thf(937,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ^ [C: TA] : ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( ^ [C: TA] : ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[933]) ).
thf(1560,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[856,895]) ).
thf(1561,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( '\'const/ind_types/CONS\'' @ skt1 @ D @ ( '\'const/ind_types/NIL\'' @ skt1 ) ))]]) ).
thf(1619,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simp,[status(thm)],[1561]) ).
thf(2534,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,1619]) ).
thf(2535,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(3884,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,2535]) ).
thf(3885,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[3884:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(3923,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simp,[status(thm)],[3885]) ).
thf(13,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ ( sk3 @ TA @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[11]) ).
thf(36,plain,
( ( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[31,10]) ).
thf(37,plain,
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[36:[]]) ).
thf(108,plain,
( ( ( ( '\'const/sets/EMPTY\'' @ skt1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[101,37]) ).
thf(109,plain,
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[108:[]]) ).
thf(234,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ ( sk3 @ TA @ A ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,109]) ).
thf(268,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ ( sk3 @ TA @ A ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(12474,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ ( sk3 @ TA @ A ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(simplifyReflect,[status(thm)],[268,173]) ).
thf(3881,plain,
! [D: skt1,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ D @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ C @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,2535]) ).
thf(3882,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[3881:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ skt1 @ E @ ( '\'const/ind_types/NIL\'' @ skt1 ) )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).
thf(3922,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simp,[status(thm)],[3882]) ).
thf(7335,plain,
! [D: skt1,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ C @ ( '\'const/ind_types/CONS\'' @ skt1 @ D @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,3922]) ).
thf(7336,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[7335:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ skt1 @ E @ ( '\'const/ind_types/NIL\'' @ skt1 ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(7357,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simp,[status(thm)],[7336]) ).
thf(1188,plain,
! [TB: $tType,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,1184]) ).
thf(1189,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[1188:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ TB )),bind(C,$thf( A ))]]) ).
thf(1204,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[1189]) ).
thf(1213,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1204]) ).
thf(1220,plain,
! [TB: $tType,A: TB] :
( ( ( ^ [B: TB] : ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( ^ [B: TB] : ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( ^ [B: TB] : B )
!= ( ^ [B: TB] : B ) ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1223,plain,
! [TA: $tType,A: TA] :
( ( ^ [B: TA] : ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( ^ [B: TA] : ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[1220]) ).
thf(161,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(165,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(7338,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,3922]) ).
thf(7353,plain,
! [B: skt1,A: skt1] :
( ( ( ^ [C: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( ^ [C: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [C: skt1] : C )
!= ( ^ [C: skt1] : C ) ) ),
inference(simp,[status(thm)],[7338]) ).
thf(7361,plain,
! [B: skt1,A: skt1] :
( ( ^ [C: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( ^ [C: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[7353]) ).
thf(841,plain,
! [D: skt1 > $o,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,356]) ).
thf(842,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[841:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( '\'const/sets/set_of_list\'' @ skt1 @ B ))]]) ).
thf(1718,plain,
! [TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[889,939]) ).
thf(1719,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[1718:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ ( '\'const/ind_types/NIL\'' @ TB ) ))]]) ).
thf(1870,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[1719]) ).
thf(2568,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/EMPTY\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,1870]) ).
thf(2569,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[2568:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(2592,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[2569]) ).
thf(4644,plain,
! [TB: $tType,D: TB,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/INSERT\'' @ TB @ D @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,2592]) ).
thf(4645,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[4644:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ TB @ E @ ( '\'const/ind_types/NIL\'' @ TB ) )),bind(C,$thf( E )),bind(D,$thf( A ))]]) ).
thf(4680,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[4645]) ).
thf(125,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TB ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,12]) ).
thf(135,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( '\'const/ind_types/NIL\'' @ TB )
!= ( '\'const/ind_types/NIL\'' @ TB ) )
| ( ( '\'const/ind_types/NIL\'' @ TB )
= C )
| ( ( A @ B )
!= ( ( '\'const/ind_types/NIL\'' @ TB )
= ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) @ ( sk3 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ) ) ),
inference(replace_leibeq,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ))]]) ).
thf(145,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/ind_types/NIL\'' @ TB )
!= ( '\'const/ind_types/NIL\'' @ TB ) )
| ( ( '\'const/ind_types/NIL\'' @ TB )
= C )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ( '\'const/ind_types/NIL\'' @ TB )
= ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) @ ( sk3 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(169,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/ind_types/NIL\'' @ TB )
= C )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ( '\'const/ind_types/NIL\'' @ TB )
= ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) @ ( sk3 @ TB @ ( (=) @ ( '\'type/ind_types/list\'' @ TB ) @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(3777,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/EMPTY\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,1944]) ).
thf(3778,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[3777:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(3839,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[3778]) ).
thf(11988,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,3839]) ).
thf(11989,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[11988:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(12033,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[11989]) ).
thf(7365,plain,
! [B: skt1,A: skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(func_ext,[status(esa)],[7361]) ).
thf(9471,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,3008]) ).
thf(9472,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[9471:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9508,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[9472]) ).
thf(7339,plain,
! [B: skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,3922]) ).
thf(7340,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[7339:[]]) ).
thf(102,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 @ A )
= ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(func_ext,[status(esa)],[101]) ).
thf(433,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 @ A )
| ~ ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(bool_ext,[status(thm)],[102]) ).
thf(1050,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ A )
| ~ ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(rewrite,[status(thm)],[433,177]) ).
thf(911,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B )
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(func_ext,[status(esa)],[909]) ).
thf(162,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(166,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(32,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) @ A )
= ( '\'const/sets/EMPTY\'' @ TA @ A ) ),
inference(func_ext,[status(esa)],[31]) ).
thf(147,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TB ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[125:[]]) ).
thf(148,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( C @ D )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TB ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[147:[]]) ).
thf(974,plain,
! [C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,964]) ).
thf(975,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[974:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ skt1 )),bind(C,$thf( A ))]]) ).
thf(1000,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[31,975]) ).
thf(1004,plain,
! [A: skt1] :
( ( ( ^ [B: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( ^ [B: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [B: skt1] : B )
!= ( ^ [B: skt1] : B ) ) ),
inference(simp,[status(thm)],[1000]) ).
thf(1007,plain,
! [A: skt1] :
( ( ^ [B: skt1] : ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( ^ [B: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[1004]) ).
thf(21,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ B )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ B )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(942,plain,
! [D: '\'type/ind_types/list\'' @ skt1,C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ B ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,895]) ).
thf(943,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ C ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( '\'const/ind_types/CONS\'' @ skt1 @ E @ F ))]]) ).
thf(958,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ C ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(simp,[status(thm)],[943]) ).
thf(1214,plain,
! [TB: $tType,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1204]) ).
thf(1215,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1214:[]]) ).
thf(1226,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[1215]) ).
thf(9322,plain,
! [TB: $tType,D: TB,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ ( '\'const/ind_types/CONS\'' @ TB @ D @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,4680]) ).
thf(9323,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[9322:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ TB @ E @ ( '\'const/ind_types/NIL\'' @ TB ) )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(9344,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[9323]) ).
thf(2537,plain,
! [C: skt1,B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) )
!= ( '\'const/sets/INSERT\'' @ skt1 @ C @ ( '\'const/sets/EMPTY\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1541,1619]) ).
thf(2538,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[2537:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(836,plain,
! [TB: $tType,D: TB > $o,C: TB,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ B ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28,357]) ).
thf(837,plain,
! [TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[836:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( '\'const/sets/set_of_list\'' @ TB @ B ))]]) ).
thf(880,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[837]) ).
thf(2581,plain,
! [TB: $tType,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1870]) ).
thf(2582,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[2581:[]]) ).
thf(2593,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[2582]) ).
thf(9330,plain,
! [TB: $tType,B: TB,A: TB] :
( ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,4680]) ).
thf(9331,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[9330:[]]) ).
thf(9345,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[9331]) ).
thf(1509,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/EMPTY\'' @ skt1 ) @ B )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) @ B ) ),
inference(func_ext,[status(esa)],[856]) ).
thf(3801,plain,
! [TB: $tType,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,1944]) ).
thf(3802,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[3801:[]]) ).
thf(3842,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[3802]) ).
thf(124,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,12]) ).
thf(149,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pre_uni,[status(thm)],[124:[]]) ).
thf(150,plain,
! [TA: $tType,TB: $tType,D: '\'type/ind_types/list\'' @ TB,C: ( '\'type/ind_types/list\'' @ TB ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( C @ D )
| ~ ( C @ ( '\'const/ind_types/CONS\'' @ TB @ ( sk2 @ TB @ C ) @ ( sk3 @ TB @ C ) ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( A @ B )
!= ( C @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pre_uni,[status(thm)],[149:[]]) ).
thf(3184,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) )
!= ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/EMPTY\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[1873,1870]) ).
thf(3185,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[3184:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(3260,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[3185]) ).
thf(3018,plain,
! [B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,1691]) ).
thf(3019,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[3018:[]]) ).
thf(15,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/ind_types/NIL\'' @ TA )
!= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( '\'const/ind_types/NIL\'' @ TA )
= ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
| ( ( '\'const/ind_types/NIL\'' @ TA )
= A ) ),
inference(replace_leibeq,[status(thm)],[13:[bind(A,$thf( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ))]]) ).
thf(18,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/ind_types/NIL\'' @ TA )
!= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( '\'const/ind_types/NIL\'' @ TA )
= A ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(19,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( '\'const/ind_types/NIL\'' @ TA )
= A ) ),
inference(simp,[status(thm)],[18]) ).
thf(727,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( '\'const/ind_types/NIL\'' @ TA )
!= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A
!= ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(744,plain,
! [TA: $tType] :
( ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(pattern_uni,[status(thm)],[727:[bind(A,$thf( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) ))]]) ).
thf(127,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ B )
| ( ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
!= ( A @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(153,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A @ B )
| ( ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
!= ( A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(pre_uni,[status(thm)],[127:[]]) ).
thf(154,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( A @ B )
| ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
!= ( A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(pre_uni,[status(thm)],[153:[]]) ).
thf(1774,plain,
! [TB: $tType,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
| ( ( '\'const/sets/EMPTY\'' @ TB )
!= ( '\'const/sets/EMPTY\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,889]) ).
thf(1775,plain,
! [TB: $tType,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[1774:[]]) ).
thf(1881,plain,
! [TA: $tType,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/sets/set_of_list\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(simp,[status(thm)],[1775]) ).
thf(2542,plain,
! [B: skt1,A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,1619]) ).
thf(2543,plain,
! [B: skt1,A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/INSERT\'' @ skt1 @ B @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ),
inference(pattern_uni,[status(thm)],[2542:[]]) ).
thf(9329,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[31,4680]) ).
thf(9341,plain,
! [TB: $tType,B: TB,A: TB] :
( ( ( ^ [C: TB] : ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
!= ( ^ [C: TB] : ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( ^ [C: TB] : C )
!= ( ^ [C: TB] : C ) ) ),
inference(simp,[status(thm)],[9329]) ).
thf(9350,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ^ [C: TA] : ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( ^ [C: TA] : ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[9341]) ).
thf(9353,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(func_ext,[status(esa)],[9350]) ).
thf(432,plain,
! [A: skt1] :
( ~ ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 @ A )
| ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(bool_ext,[status(thm)],[102]) ).
thf(1010,plain,
! [A: skt1] :
( ~ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) @ A )
| ( '\'const/sets/EMPTY\'' @ skt1 @ A ) ),
inference(rewrite,[status(thm)],[432,177]) ).
thf(131,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [D: '\'type/ind_types/list\'' @ TA] : ~ ( C @ D ) ))]]) ).
thf(157,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( B @ A )
| ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(158,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( B @ A )
| ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(126,plain,
! [TA: $tType,D: '\'type/ind_types/list\'' @ $o,C: ( '\'type/ind_types/list\'' @ $o ) > $o,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ $o ) )
| ~ ( C @ ( '\'const/ind_types/CONS\'' @ $o @ $true @ ( sk3 @ $o @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( sk2 @ $o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,12]) ).
thf(155,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ $o ) > $o,B: '\'type/ind_types/list\'' @ $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( sk2 @ $o @ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ~ ( sk2 @ $o
@ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] : ( sk2 @ $o @ ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] : ( sk2 @ $o @ ( C @ D ) ) ) ) ) )
| ~ ( C @ A @ ( '\'const/ind_types/NIL\'' @ $o ) )
| ~ ( C @ A @ ( '\'const/ind_types/CONS\'' @ $o @ $true @ ( sk3 @ $o @ ( C @ A ) ) ) )
| ( C @ A @ B ) ),
inference(pre_uni,[status(thm)],[126:[bind(A,$thf( ^ [F: '\'type/ind_types/list\'' @ TA] : ( sk2 @ $o @ ( E @ F ) ) )),bind(B,$thf( B )),bind(C,$thf( E @ B ))]]) ).
thf(171,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ $o ) > $o,B: '\'type/ind_types/list\'' @ $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( sk2 @ $o @ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ~ ( sk2 @ $o
@ ( C
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] : ( sk2 @ $o @ ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] : ( sk2 @ $o @ ( C @ D ) ) ) ) ) )
| ~ ( C @ A @ ( '\'const/ind_types/NIL\'' @ $o ) )
| ~ ( C @ A @ ( '\'const/ind_types/CONS\'' @ $o @ $true @ ( sk3 @ $o @ ( C @ A ) ) ) )
| ( C @ A @ B ) ),
inference(simp,[status(thm)],[155]) ).
thf(4647,plain,
! [TB: $tType,C: TB,B: TB,A: TB] :
( ( ( '\'const/sets/INSERT\'' @ TB @ C @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) )
| ( ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/sets/set_of_list\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[889,2592]) ).
thf(4648,plain,
! [TB: $tType,B: TB,A: TB] :
( ( '\'const/sets/INSERT\'' @ TB @ B @ ( '\'const/sets/INSERT\'' @ TB @ A @ ( '\'const/sets/EMPTY\'' @ TB ) ) )
!= ( '\'const/sets/EMPTY\'' @ TB ) ),
inference(pattern_uni,[status(thm)],[4647:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(4681,plain,
! [TA: $tType,B: TA,A: TA] :
( ( '\'const/sets/INSERT\'' @ TA @ B @ ( '\'const/sets/INSERT\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ) )
!= ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(simp,[status(thm)],[4648]) ).
thf(129,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(151,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(998,plain,
! [A: skt1] :
( ( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,975]) ).
thf(999,plain,
! [A: skt1] :
( ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[998:[]]) ).
thf(1229,plain,
! [TA: $tType,A: TA] :
( ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(func_ext,[status(esa)],[1223]) ).
thf(179,plain,
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/sets/set_of_list\'' @ skt1 @ sk1 )
!= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,112]) ).
thf(181,plain,
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [A: skt1] : sk1 )
!= ( ^ [A: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [A: skt1] : A )
!= ( ^ [A: skt1] : A ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(183,plain,
( ( ( '\'const/sets/EMPTY\'' @ skt1 )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( ^ [A: skt1] : sk1 )
!= ( ^ [A: skt1] : ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(1549,plain,
! [A: skt1] :
( ( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) )
| ( ( '\'const/sets/EMPTY\'' @ skt1 )
!= ( '\'const/sets/EMPTY\'' @ skt1 ) ) ),
inference(paramod_ordered,[status(thm)],[173,856]) ).
thf(1550,plain,
! [A: skt1] :
( ( '\'const/sets/INSERT\'' @ skt1 @ A @ ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
= ( '\'const/sets/set_of_list\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1549:[]]) ).
thf(159,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(163,plain,
! [TA: $tType,C: ( '\'type/ind_types/list\'' @ TA ) > $o,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk3 @ TA
@ ^ [D: '\'type/ind_types/list\'' @ TA] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(1009,plain,
! [A: skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(func_ext,[status(esa)],[1007]) ).
thf(18981,plain,
$false,
inference(e,[status(thm)],[1242,12,3008,1105,909,3012,1173,174,185,25,1298,357,3840,20,152,57,29,164,937,3923,1206,1691,12474,7357,1223,1619,165,1174,28,7361,889,842,4680,1541,356,169,12033,109,7365,3922,9508,7340,1050,13,173,911,953,888,166,32,148,856,3839,975,1007,22,958,1226,9344,2538,880,649,964,2593,895,983,2592,2535,9345,1873,1509,939,3842,150,3260,3019,177,951,31,744,154,11,1881,2543,9353,845,1010,158,171,23,26,4681,8,9350,151,999,1229,183,1550,163,1944,1009,1184,1204,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT327^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 11:32:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (114ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.65/1.20 % [INFO] eprover registered as external prover.
% 1.65/1.20 % [INFO] cvc4 registered as external prover.
% 1.65/1.20 % [INFO] Scanning for conjecture ...
% 1.80/1.25 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.80/1.28 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.80/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.80/1.29 % [INFO] Type checking passed.
% 1.80/1.29 % [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 ...
% 71.51/11.73 % External prover 'e' found a proof!
% 71.51/11.73 % [INFO] Killing All external provers ...
% 71.70/11.74 % Time passed: 11207ms (effective reasoning time: 10749ms)
% 71.70/11.74 % 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)>
% 71.70/11.74 % Axioms used in derivation (5): thm/sets/NOT_INSERT_EMPTY_, thm/sets/set_of_list_1, thm/ind_types/list_INDUCT_, thm/sets/set_of_list_0, thm/lists/NOT_CONS_NIL_
% 71.70/11.74 % No. of inferences in proof: 268
% 71.70/11.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11207 ms resp. 10749 ms w/o parsing
% 71.94/11.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 71.94/11.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------