TSTP Solution File: DAT290^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT290^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 07:39:54 EDT 2024
% Result : Theorem 26.96s 6.18s
% Output : Refutation 26.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of formulae : 197 ( 112 unt; 10 typ; 0 def)
% Number of atoms : 323 ( 278 equ; 6 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 2615 ( 268 ~; 164 |; 2 &;2177 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 593 ( 22 ^ 566 !; 1 ?; 593 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/nums/SUC\'_type',type,
'\'const/nums/SUC\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/NUMERAL\'_type',type,
'\'const/nums/NUMERAL\'': '\'type/nums/num\'' > '\'type/nums/num\'' ).
thf('\'const/nums/_0\'_type',type,
'\'const/nums/_0\'': '\'type/nums/num\'' ).
thf('\'const/lists/LENGTH\'_type',type,
'\'const/lists/LENGTH\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > '\'type/nums/num\'' ) ).
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(sk3_type,type,
sk3:
!>[TA: $tType] : ( ( ( '\'type/ind_types/list\'' @ TA ) > $o ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/LENGTH_1') ).
thf(27,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(5,axiom,
! [A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
!= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/nums/NOT_SUC_') ).
thf(23,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
!= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
~ ? [A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
!= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
!= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(7,axiom,
! [TA: $tType] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/LENGTH_0') ).
thf(30,plain,
! [TA: $tType] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [TA: $tType] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [TA: $tType] :
( ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(33,plain,
! [TA: $tType,A: '\'type/nums/num\''] :
( ( '\'const/nums/SUC\'' @ A )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(rewrite,[status(thm)],[26,32]) ).
thf(263,plain,
! [TA: $tType,TB: $tType,C: '\'type/nums/num\'',B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,33]) ).
thf(264,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( A )),bind(B,$thf( D )),bind(C,$thf( '\'const/lists/LENGTH\'' @ TA @ D ))]]) ).
thf(269,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(271,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: '\'type/ind_types/list\'' @ TB,C: TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,269]) ).
thf(272,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(291,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,284]) ).
thf(292,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(301,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(309,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,301]) ).
thf(310,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(321,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(434,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,321]) ).
thf(435,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(447,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[435]) ).
thf(456,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,447]) ).
thf(457,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(474,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[457]) ).
thf(710,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,474]) ).
thf(711,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[710:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(729,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[711]) ).
thf(754,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,729]) ).
thf(755,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[754:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(776,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(919,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,776]) ).
thf(920,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[919:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(945,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[920]) ).
thf(1,conjecture,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ A )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/LENGTH_EQ_NIL_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ A )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ A )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) )
= ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/nums/NUMERAL\'' @ '\'const/nums/_0\'' ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(34,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(rewrite,[status(thm)],[10,32]) ).
thf(36,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(bool_ext,[status(thm)],[34]) ).
thf(38,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(35,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(bool_ext,[status(thm)],[34]) ).
thf(37,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(94,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[38,37]) ).
thf(95,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[94:[]]) ).
thf(1101,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[95,37]) ).
thf(1102,plain,
! [TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[1101:[bind_type(TA,$thf( TC ))]]) ).
thf(1184,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1564,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[38,1184]) ).
thf(1565,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/NIL\'' @ skt1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[1564:[]]) ).
thf(1858,plain,
! [TA: $tType] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(pattern_uni,[status(thm)],[1565:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2440,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,284]) ).
thf(2441,plain,
! [TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2440:[bind(A,$thf( '\'const/ind_types/NIL\'' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(2508,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[2441]) ).
thf(2471,plain,
! [TA: $tType,TB: $tType] :
( ( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1858,34]) ).
thf(2472,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[2471:[]]) ).
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/sandbox/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(48,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(72,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)],[48]) ).
thf(73,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)],[72]) ).
thf(4078,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(bool_ext,[status(thm)],[2472]) ).
thf(4117,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(lifteq,[status(thm)],[4078]) ).
thf(2400,plain,
( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(simplifyReflect,[status(thm)],[37,1858]) ).
thf(4252,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simplifyReflect,[status(thm)],[4117,2400]) ).
thf(2438,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,284]) ).
thf(2439,plain,
! [TA: $tType,TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2438:[bind(A,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2507,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[2439]) ).
thf(2529,plain,
! [TA: $tType,TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2507]) ).
thf(2530,plain,
! [TB: $tType,TC: $tType,A: TB] :
( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2529:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(2534,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[2530]) ).
thf(4382,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC] :
( ( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/CONS\'' @ TC @ A @ ( '\'const/ind_types/NIL\'' @ TC ) ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TD @ ( '\'const/ind_types/NIL\'' @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[4252,2534]) ).
thf(4383,plain,
! [TB: $tType,TC: $tType,A: TC] :
( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/CONS\'' @ TC @ A @ ( '\'const/ind_types/NIL\'' @ TC ) ) ) ),
inference(pattern_uni,[status(thm)],[4382:[bind_type(TA,$thf( TD ))]]) ).
thf(4419,plain,
! [TA: $tType,TB: $tType,A: TB] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(simp,[status(thm)],[4383]) ).
thf(46,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(69,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)],[46]) ).
thf(756,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,729]) ).
thf(757,plain,
! [TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(777,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(712,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,474]) ).
thf(713,plain,
! [TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(730,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[713]) ).
thf(2403,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,301]) ).
thf(2404,plain,
! [TA: $tType,TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2403:[bind(A,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2516,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[2404]) ).
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/sandbox/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(436,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,321]) ).
thf(437,plain,
! [TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[436:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(448,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[437]) ).
thf(51,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(74,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)],[51]) ).
thf(78,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)],[74]) ).
thf(458,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,447]) ).
thf(459,plain,
! [TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(475,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[459]) ).
thf(3883,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1858,2534]) ).
thf(3884,plain,
! [TB: $tType,A: TB] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[3883:[bind_type(TA,$thf( TC ))]]) ).
thf(3886,plain,
! [TA: $tType,A: TA] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ),
inference(simp,[status(thm)],[3884]) ).
thf(6268,plain,
! [TA: $tType,TB: $tType,C: TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,3886]) ).
thf(6269,plain,
! [TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6268:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/NIL\'' @ TB )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).
thf(6282,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ),
inference(simp,[status(thm)],[6269]) ).
thf(786,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: '\'type/ind_types/list\'' @ TB,C: TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,448]) ).
thf(787,plain,
! [TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ C ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[786:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ TB @ E @ F )),bind(C,$thf( E )),bind(D,$thf( F )),bind_type(TA,$thf( TB ))]]) ).
thf(793,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TA,B: TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[787]) ).
thf(39,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(64,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)],[39:[]]) ).
thf(65,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)],[64:[]]) ).
thf(2537,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2508]) ).
thf(2538,plain,
! [TB: $tType,A: skt1] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(pattern_uni,[status(thm)],[2537:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(2542,plain,
! [TA: $tType,A: skt1] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[2538]) ).
thf(3893,plain,
! [TA: $tType,TB: $tType,A: skt1] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[1858,2542]) ).
thf(3894,plain,
! [A: skt1] :
( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3893:[bind_type(TA,$thf( TB ))]]) ).
thf(971,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ),
inference(paramod_ordered,[status(thm)],[29,945]) ).
thf(972,plain,
! [TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[971:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( '\'const/ind_types/CONS\'' @ TB @ D @ E )),bind_type(TA,$thf( TB ))]]) ).
thf(997,plain,
! [TA: $tType,TB: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ A ) ) ) ) ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[972]) ).
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(312,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,301]) ).
thf(313,plain,
! [TB: $tType,TC: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).
thf(322,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[313]) ).
thf(740,plain,
! [TA: $tType,TB: $tType,TC: $tType,D: '\'type/ind_types/list\'' @ TB,C: TB,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ B ) )
!= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ C @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,322]) ).
thf(741,plain,
! [TB: $tType,TC: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: TB] :
( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ ( '\'const/ind_types/CONS\'' @ TB @ B @ C ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[740:[bind(A,$thf( A )),bind(B,$thf( '\'const/ind_types/CONS\'' @ TB @ E @ F )),bind(C,$thf( E )),bind(D,$thf( F )),bind_type(TA,$thf( TB ))]]) ).
thf(745,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TA,B: TA,A: TA] :
( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[741]) ).
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(43,plain,
! [TA: $tType,TB: $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/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ( ( A @ B )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,34]) ).
thf(59,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
| ~ ( 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)],[43]) ).
thf(44,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(70,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)],[44:[]]) ).
thf(71,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)],[70:[]]) ).
thf(2454,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,321]) ).
thf(2455,plain,
! [TA: $tType,TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2454:[bind(A,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2510,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[2455]) ).
thf(2413,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,447]) ).
thf(2414,plain,
! [TA: $tType,TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2413:[bind(A,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2521,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ),
inference(simp,[status(thm)],[2414]) ).
thf(2445,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1858,29]) ).
thf(2446,plain,
! [TA: $tType,A: skt1] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[2445:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
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(383,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(399,plain,
! [TA: $tType] :
( ( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/ind_types/NIL\'' @ TA ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( sk3 @ TA @ ( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ ( '\'const/ind_types/NIL\'' @ TA ) ) ))]]) ).
thf(6287,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(paramod_ordered,[status(thm)],[1858,6282]) ).
thf(6288,plain,
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[6287:[bind_type(TA,$thf( TB ))]]) ).
thf(76,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)],[51]) ).
thf(80,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)],[76]) ).
thf(40,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(66,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)],[40:[]]) ).
thf(67,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)],[66:[]]) ).
thf(4089,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ) ),
inference(paramod_ordered,[status(thm)],[1858,2472]) ).
thf(4090,plain,
! [TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[4089:[bind_type(TA,$thf( TC ))]]) ).
thf(4132,plain,
! [TA: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[4090]) ).
thf(258,plain,
! [TA: $tType,TB: $tType,B: '\'type/ind_types/list\'' @ TB,A: TB] :
( ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ A @ B ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ TB @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,29]) ).
thf(259,plain,
! [TA: $tType,A: skt1] :
( ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[258:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(1670,plain,
! [TA: $tType,TB: $tType,C: '\'type/ind_types/list\'' @ TB,B: TB,A: skt1] :
( ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ C ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/CONS\'' @ TB @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[259,29]) ).
thf(1671,plain,
! [TA: $tType] :
( ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).
thf(2543,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ),
inference(simplifyReflect,[status(thm)],[1671,2400]) ).
thf(2456,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,321]) ).
thf(2457,plain,
! [TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2456:[bind(A,$thf( '\'const/ind_types/NIL\'' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(2511,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[2457]) ).
thf(7082,plain,
! [A: skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ sk1 )
!= sk1 ),
inference(simp,[status(thm)],[3894]) ).
thf(2415,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,447]) ).
thf(2416,plain,
! [TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2415:[bind(A,$thf( '\'const/ind_types/NIL\'' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(2522,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ) ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[2416]) ).
thf(2405,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: '\'type/ind_types/list\'' @ TB] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TB @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1858,301]) ).
thf(2406,plain,
! [TC: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) )
!= ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) ) ),
inference(pattern_uni,[status(thm)],[2405:[bind(A,$thf( '\'const/ind_types/NIL\'' @ TB )),bind_type(TA,$thf( TB ))]]) ).
thf(2517,plain,
! [TA: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) )
!= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[2406]) ).
thf(75,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)],[51]) ).
thf(79,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)],[75]) ).
thf(2667,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) )
| ( ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 )
!= ( '\'const/lists/LENGTH\'' @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1858,2543]) ).
thf(2668,plain,
! [TA: $tType,TB: $tType] :
( ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
= ( '\'const/nums/SUC\'' @ ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) ) ),
inference(pattern_uni,[status(thm)],[2667:[]]) ).
thf(47,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(68,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)],[47]) ).
thf(4263,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) )
| ( ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) )
!= ( '\'const/lists/LENGTH\'' @ TD @ ( '\'const/ind_types/NIL\'' @ TD ) ) ) ),
inference(paramod_ordered,[status(thm)],[4252,2472]) ).
thf(4264,plain,
! [TB: $tType,TC: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TC @ ( '\'const/ind_types/NIL\'' @ TC ) )
= ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(pattern_uni,[status(thm)],[4263:[bind_type(TA,$thf( TD ))]]) ).
thf(4423,plain,
! [TA: $tType,TB: $tType] :
( ( ( '\'const/lists/LENGTH\'' @ TB @ ( '\'const/ind_types/NIL\'' @ TB ) )
= ( '\'const/lists/LENGTH\'' @ TA @ ( '\'const/ind_types/NIL\'' @ TA ) ) )
!= ( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ) ),
inference(simp,[status(thm)],[4264]) ).
thf(7287,plain,
$false,
inference(e,[status(thm)],[945,2508,2472,73,776,4419,8,69,777,730,269,301,2516,2400,20,284,448,78,29,475,321,1858,6282,793,4252,729,33,65,3894,997,13,745,32,34,22,59,27,71,12,2510,2521,2446,2542,399,6288,80,67,4132,2543,11,2511,7082,23,2534,30,2522,2517,447,79,474,2668,2507,3886,68,322,4423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT290^1 : TPTP v8.1.2. Released v7.0.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 6 11:30:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.85/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.93 % [INFO] Parsing done (127ms).
% 1.23/0.94 % [INFO] Running in sequential loop mode.
% 1.61/1.21 % [INFO] eprover registered as external prover.
% 1.69/1.22 % [INFO] cvc4 registered as external prover.
% 1.69/1.22 % [INFO] Scanning for conjecture ...
% 1.77/1.28 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.77/1.30 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.77/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.32 % [INFO] Type checking passed.
% 1.77/1.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 26.96/6.17 % External prover 'e' found a proof!
% 26.96/6.17 % [INFO] Killing All external provers ...
% 26.96/6.18 % Time passed: 5705ms (effective reasoning time: 5234ms)
% 26.96/6.18 % 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)>
% 26.96/6.18 % Axioms used in derivation (5): thm/nums/NOT_SUC_, thm/lists/LENGTH_1, thm/ind_types/list_INDUCT_, thm/lists/LENGTH_0, thm/lists/NOT_CONS_NIL_
% 26.96/6.18 % No. of inferences in proof: 187
% 26.96/6.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5705 ms resp. 5234 ms w/o parsing
% 26.96/6.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.96/6.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------