TSTP Solution File: DAT251^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT251^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 07:39:51 EDT 2024
% Result : Theorem 34.34s 15.34s
% Output : Refutation 34.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 268
% Syntax : Number of formulae : 491 ( 293 unt; 47 typ; 0 def)
% Number of atoms : 1127 ( 861 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 6855 ( 202 ~; 37 |; 122 &;6130 @)
% ( 0 <=>; 364 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 342 ( 342 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 6 con; 0-5 aty)
% Number of variables : 1824 ( 48 ^1641 !; 80 ?;1824 :)
% ( 55 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(bNF_Greatest_Shift_type,type,
bNF_Greatest_Shift:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > TA > ( set @ ( list @ TA ) ) ) ).
thf(bNF_Greatest_Succ_type,type,
bNF_Greatest_Succ:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > ( list @ TA ) > ( set @ TA ) ) ).
thf(bNF_Greatest_shift_type,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(butlast_type,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(fold_type,type,
fold:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > ( list @ TB ) > TA > TA ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(case_list_type,type,
case_list:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( list @ TA ) > TB ) > ( list @ TA ) > TB ) ).
thf(hd_type,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(tl_type,type,
tl:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(listrelp_type,type,
listrelp:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o ) ).
thf(map_tailrec_type,type,
map_tailrec:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(map_tailrec_rev_type,type,
map_tailrec_rev:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TB > ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( ( list @ TA ) > TA > $o ) ).
thf(lexordp_eq_type,type,
lexordp_eq:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(remdups_adj_type,type,
remdups_adj:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(replicate_type,type,
replicate:
!>[TA: $tType] : ( nat > TA > ( list @ TA ) ) ).
thf(rev_type,type,
rev:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(union_type,type,
union:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(stream317748790_cycle_type,type,
stream317748790_cycle:
!>[TA: $tType] : ( ( list @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream942386729e_flat_type,type,
stream942386729e_flat:
!>[TA: $tType] : ( ( stream170649215stream @ ( list @ TA ) ) > ( stream170649215stream @ TA ) ) ).
thf(stream1195056575_while_type,type,
stream1195056575_while:
!>[TA: $tType] : ( ( TA > $o ) > ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream1035003186_shift_type,type,
stream1035003186_shift:
!>[TA: $tType] : ( ( list @ TA ) > ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream1586597341member_type,type,
stream1586597341member:
!>[TA: $tType] : ( TA > ( stream170649215stream @ TA ) > $o ) ).
thf(stream641971652_SCons_type,type,
stream641971652_SCons:
!>[TA: $tType] : ( TA > ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream1342653232stream_type,type,
stream1342653232stream:
!>[TA: $tType,TB: $tType] : ( ( TB > ( stream170649215stream @ TB ) > TA ) > ( stream170649215stream @ TB ) > TA ) ).
thf(stream_Mirabelle_shd_type,type,
stream_Mirabelle_shd:
!>[TA: $tType] : ( ( stream170649215stream @ TA ) > TA ) ).
thf(stream2128578057e_smap_type,type,
stream2128578057e_smap:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( stream170649215stream @ TB ) > ( stream170649215stream @ TA ) ) ).
thf(stream_Mirabelle_stl_type,type,
stream_Mirabelle_stl:
!>[TA: $tType] : ( ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) ) ).
thf(stream2015131171treams_type,type,
stream2015131171treams:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( stream170649215stream @ TA ) ) ) ).
thf(member2_type,type,
member2:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(ws_type,type,
ws: stream170649215stream @ ( list @ a ) ).
thf(209,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( append @ TA @ A @ B ) @ C )
= ( stream1035003186_shift @ TA @ A @ ( stream1035003186_shift @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_shift__append) ).
thf(1031,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( append @ TA @ A @ B ) @ C )
= ( stream1035003186_shift @ TA @ A @ ( stream1035003186_shift @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(185,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( list @ TA ),C: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( bNF_Greatest_Shift @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_ShiftD) ).
thf(962,plain,
! [TA: $tType,A: list @ TA,B: set @ ( list @ TA ),C: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( bNF_Greatest_Shift @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( list @ TB ) > TA] :
( ( case_list @ TA @ TB @ A @ B @ ( nil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_list_Osimps_I4_J) ).
thf(234,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( list @ TB ) > TA] :
( ( case_list @ TA @ TB @ A @ B @ ( nil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_stl @ TB @ ( stream2128578057e_smap @ TA @ TB @ A @ B ) )
= ( stream2128578057e_smap @ TA @ TB @ A @ ( stream_Mirabelle_stl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_stream_Omap__sel_I2_J) ).
thf(941,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_stl @ TB @ ( stream2128578057e_smap @ TA @ TB @ A @ B ) )
= ( stream2128578057e_smap @ TA @ TB @ A @ ( stream_Mirabelle_stl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(190,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( stream317748790_cycle @ TA @ A )
= ( stream1035003186_shift @ TA @ A @ ( stream317748790_cycle @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_cycle__decomp) ).
thf(977,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( stream317748790_cycle @ TA @ A )
= ( stream1035003186_shift @ TA @ A @ ( stream317748790_cycle @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( list @ TA ) > TB,C: TA,D: list @ TA] :
( ( case_list @ TB @ TA @ A @ B @ ( cons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_list_Osimps_I5_J) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( list @ TA ) > TB,C: TA,D: list @ TA] :
( ( case_list @ TB @ TA @ A @ B @ ( cons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(219,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: set @ ( list @ TA )] :
( ( member2 @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ C )
=> ( member2 @ TA @ B @ ( bNF_Greatest_Succ @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_SuccI) ).
thf(1068,plain,
! [TA: $tType,A: list @ TA,B: TA,C: set @ ( list @ TA )] :
( ( member2 @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ C )
=> ( member2 @ TA @ B @ ( bNF_Greatest_Succ @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_map__tailrec__rev_Oinduct) ).
thf(308,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(221,axiom,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( ( stream1035003186_shift @ TA @ A @ B )
= ( stream1035003186_shift @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_shift__left__inj) ).
thf(1073,plain,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( ( stream1035003186_shift @ TA @ A @ B )
= ( stream1035003186_shift @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_splice__Nil2) ).
thf(247,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(92,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_same__append__eq) ).
thf(523,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_list_Osel_I1_J) ).
thf(582,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(171,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA] :
( ( fold @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_fold__simps_I1_J) ).
thf(873,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TA] :
( ( fold @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(71,axiom,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ B @ ( append @ TA @ ( replicate @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_replicate__app__Cons__same) ).
thf(449,plain,
! [TA: $tType,A: nat,B: TA,C: list @ TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ C ) )
= ( cons @ TA @ B @ ( append @ TA @ ( replicate @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(68,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_append__assoc) ).
thf(440,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [TA: $tType,A: ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: stream170649215stream @ TA] :
( ( A @ D )
=> ? [E: TA,F: stream170649215stream @ TA] :
( ( D
= ( stream641971652_SCons @ TA @ E @ F ) )
& ( member2 @ TA @ E @ C )
& ( ( A @ F )
| ( member2 @ ( stream170649215stream @ TA ) @ F @ ( stream2015131171treams @ TA @ C ) ) ) ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ B @ ( stream2015131171treams @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_streams_Ocoinduct) ).
thf(655,plain,
! [TA: $tType,A: ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: set @ TA] :
( ( A @ B )
=> ( ! [D: stream170649215stream @ TA] :
( ( A @ D )
=> ? [E: TA,F: stream170649215stream @ TA] :
( ( D
= ( stream641971652_SCons @ TA @ E @ F ) )
& ( member2 @ TA @ E @ C )
& ( ( A @ F )
| ( member2 @ ( stream170649215stream @ TA ) @ F @ ( stream2015131171treams @ TA @ C ) ) ) ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ B @ ( stream2015131171treams @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(54,axiom,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_rev_Osimps_I1_J) ).
thf(384,plain,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(174,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_append__self__conv2) ).
thf(913,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(127,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( ( tl @ TA @ A )
!= ( nil @ TA ) ) )
=> ( ( last @ TA @ ( tl @ TA @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_last__tl) ).
thf(670,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( ( tl @ TA @ A )
!= ( nil @ TA ) ) )
=> ( ( last @ TA @ ( tl @ TA @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: TB,D: list @ TB] :
( ( ( map @ TA @ TB @ A @ B )
= ( cons @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TA @ TB @ A @ F )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_map__eq__Cons__conv) ).
thf(404,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: TB,D: list @ TB] :
( ( ( map @ TA @ TB @ A @ B )
= ( cons @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TA @ TB @ A @ F )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream2128578057e_smap @ TA @ TB @ A @ ( stream1035003186_shift @ TA @ B @ C ) )
= ( stream1035003186_shift @ TB @ ( map @ TA @ TB @ A @ B ) @ ( stream2128578057e_smap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_smap__shift) ).
thf(1001,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream2128578057e_smap @ TA @ TB @ A @ ( stream1035003186_shift @ TA @ B @ C ) )
= ( stream1035003186_shift @ TB @ ( map @ TA @ TB @ A @ B ) @ ( stream2128578057e_smap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(148,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rev @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_rev_Osimps_I2_J) ).
thf(782,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rev @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(160,axiom,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( replicate @ TA @ C @ B ) )
= ( append @ TA @ ( replicate @ TA @ C @ B ) @ ( replicate @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_append__replicate__commute) ).
thf(841,plain,
! [TA: $tType,A: nat,B: TA,C: nat] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( replicate @ TA @ C @ B ) )
= ( append @ TA @ ( replicate @ TA @ C @ B ) @ ( replicate @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_hd__Cons__tl) ).
thf(288,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_rotate1_Osimps_I2_J) ).
thf(320,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
=> ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Cons__eq__map__D) ).
thf(785,plain,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
=> ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(86,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_self__append__conv2) ).
thf(504,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_map__is__Nil__conv) ).
thf(838,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(49,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: stream170649215stream @ TA] :
( ( ( A @ B )
=> ( ( stream1195056575_while @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream1195056575_while @ TA @ A @ C ) ) )
& ( ~ ( A @ B )
=> ( ( stream1195056575_while @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream641971652_SCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_sdrop__while__SCons) ).
thf(357,plain,
! [TA: $tType,A: TA > $o,B: TA,C: stream170649215stream @ TA] :
( ( ( A @ B )
=> ( ( stream1195056575_while @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream1195056575_while @ TA @ A @ C ) ) )
& ( ~ ( A @ B )
=> ( ( stream1195056575_while @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream641971652_SCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(216,axiom,
! [TA: $tType,A: stream170649215stream @ TA] :
( A
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ ( stream_Mirabelle_stl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_stream_Oexhaust__sel) ).
thf(1059,plain,
! [TA: $tType,A: stream170649215stream @ TA] :
( A
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ ( stream_Mirabelle_stl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Nil__is__map__conv) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(132,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list_Ocollapse) ).
thf(702,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(138,axiom,
! [TA: $tType,A: list @ TA] :
( ( remdups_adj @ TA @ ( rev @ TA @ A ) )
= ( rev @ TA @ ( remdups_adj @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_remdups__adj__rev) ).
thf(751,plain,
! [TA: $tType,A: list @ TA] :
( ( remdups_adj @ TA @ ( rev @ TA @ A ) )
= ( rev @ TA @ ( remdups_adj @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(164,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( rev @ TA @ A ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Nil__is__rev__conv) ).
thf(853,plain,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( rev @ TA @ A ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(170,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
= ( ? [C: TA,D: stream170649215stream @ TA] :
( ( A
= ( stream641971652_SCons @ TA @ C @ D ) )
& ( member2 @ TA @ C @ B )
& ( member2 @ ( stream170649215stream @ TA ) @ D @ ( stream2015131171treams @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_streams_Osimps) ).
thf(870,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
= ( ? [C: TA,D: stream170649215stream @ TA] :
( ( A
= ( stream641971652_SCons @ TA @ C @ D ) )
& ( member2 @ TA @ C @ B )
& ( member2 @ ( stream170649215stream @ TA ) @ D @ ( stream2015131171treams @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(188,axiom,
! [TA: $tType,A: ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream170649215stream @ TA,E: stream170649215stream @ TA] :
( ( A @ D @ E )
=> ( ( ( stream_Mirabelle_shd @ TA @ D )
= ( stream_Mirabelle_shd @ TA @ E ) )
& ( A @ ( stream_Mirabelle_stl @ TA @ D ) @ ( stream_Mirabelle_stl @ TA @ E ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_stream_Ocoinduct) ).
thf(969,plain,
! [TA: $tType,A: ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream170649215stream @ TA,E: stream170649215stream @ TA] :
( ( A @ D @ E )
=> ( ( ( stream_Mirabelle_shd @ TA @ D )
= ( stream_Mirabelle_shd @ TA @ E ) )
& ( A @ ( stream_Mirabelle_stl @ TA @ D ) @ ( stream_Mirabelle_stl @ TA @ E ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(144,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member2 @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(770,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member2 @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(62,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( cons @ TA @ B @ ( replicate @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_replicate__append__same) ).
thf(416,plain,
! [TA: $tType,A: nat,B: TA] :
( ( append @ TA @ ( replicate @ TA @ A @ B ) @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( cons @ TA @ B @ ( replicate @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA] :
( ( butlast @ TA @ ( tl @ TA @ A ) )
= ( tl @ TA @ ( butlast @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_butlast__tl) ).
thf(261,plain,
! [TA: $tType,A: list @ TA] :
( ( butlast @ TA @ ( tl @ TA @ A ) )
= ( tl @ TA @ ( butlast @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,axiom,
! [TA: $tType,A: stream170649215stream @ TA] :
~ ! [B: TA,C: stream170649215stream @ TA] :
( A
!= ( stream641971652_SCons @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_stream_Oexhaust) ).
thf(443,plain,
! [TA: $tType,A: stream170649215stream @ TA] :
~ ! [B: TA,C: stream170649215stream @ TA] :
( A
!= ( stream641971652_SCons @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_last__snoc) ).
thf(485,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( tl @ TA @ A )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_tl__Nil) ).
thf(348,plain,
! [TA: $tType,A: list @ TA] :
( ( ( tl @ TA @ A )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(187,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_product__lists_Osimps_I1_J) ).
thf(966,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: list @ TB,C: list @ TA,D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( listrelp @ TB @ TA @ A @ B @ C )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( A @ E @ F )
=> ( ( listrelp @ TB @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_listrelp_Oinducts) ).
thf(480,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: list @ TB,C: list @ TA,D: ( list @ TB ) > ( list @ TA ) > $o] :
( ( listrelp @ TB @ TA @ A @ B @ C )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: TA,G: list @ TB,H: list @ TA] :
( ( A @ E @ F )
=> ( ( listrelp @ TB @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TB @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( append @ TA @ B @ C ) )
= ( append @ TB @ ( map @ TA @ TB @ A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_map__append) ).
thf(646,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( append @ TA @ B @ C ) )
= ( append @ TB @ ( map @ TA @ TB @ A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( butlast @ TA @ B ) )
= ( butlast @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_map__butlast) ).
thf(253,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( butlast @ TA @ B ) )
= ( butlast @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(115,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ord_Olexordp__eq_Ocases) ).
thf(602,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: stream170649215stream @ TA,C: TA,D: stream170649215stream @ TA] :
( ( ( stream641971652_SCons @ TA @ A @ B )
= ( stream641971652_SCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_stream_Oinject) ).
thf(634,plain,
! [TA: $tType,A: TA,B: stream170649215stream @ TA,C: TA,D: stream170649215stream @ TA] :
( ( ( stream641971652_SCons @ TA @ A @ B )
= ( stream641971652_SCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(197,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ~ ( ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B )
=> ~ ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_streamsE) ).
thf(998,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ~ ( ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B )
=> ~ ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(10,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord_Olexordp__eq__simps_I1_J) ).
thf(243,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= ( rev @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev__is__rev__conv) ).
thf(507,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= ( rev @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: stream170649215stream @ TA,C: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ ( stream641971652_SCons @ TA @ A @ B ) @ ( stream2015131171treams @ TA @ C ) )
= ( ( member2 @ TA @ A @ C )
& ( member2 @ ( stream170649215stream @ TA ) @ B @ ( stream2015131171treams @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_streams__Stream) ).
thf(293,plain,
! [TA: $tType,A: TA,B: stream170649215stream @ TA,C: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ ( stream641971652_SCons @ TA @ A @ B ) @ ( stream2015131171treams @ TA @ C ) )
= ( ( member2 @ TA @ A @ C )
& ( member2 @ ( stream170649215stream @ TA ) @ B @ ( stream2015131171treams @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(184,axiom,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( stream_Mirabelle_stl @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream_Mirabelle_stl @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( stream_Mirabelle_stl @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream1035003186_shift @ TA @ ( tl @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_shift__simps_I2_J) ).
thf(956,plain,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( stream_Mirabelle_stl @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream_Mirabelle_stl @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( stream_Mirabelle_stl @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream1035003186_shift @ TA @ ( tl @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TB @ ( A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_list_Osimps_I9_J) ).
thf(452,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TB @ ( A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType] :
( ( map_tailrec_rev @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( append @ TB @ ( rev @ TB @ ( map @ TA @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_map__tailrec__rev) ).
thf(661,plain,
! [TA: $tType,TB: $tType] :
( ( map_tailrec_rev @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( append @ TB @ ( rev @ TB @ ( map @ TA @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(141,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_list_Oexhaust) ).
thf(761,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(152,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_append__butlast__last__id) ).
thf(810,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(53,axiom,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_remdups__adj_Osimps_I1_J) ).
thf(381,plain,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( list @ TA ) > TB,D: list @ TA] :
( ( A @ ( case_list @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( nil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( cons @ TA @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) )
=> ( A @ ( C @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_list_Osplit__sel) ).
thf(714,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( list @ TA ) > TB,D: list @ TA] :
( ( A @ ( case_list @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( nil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( cons @ TA @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) )
=> ( A @ ( C @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_map__tailrec__rev_Osimps_I1_J) ).
thf(270,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_append1__eq__conv) ).
thf(529,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( listrelp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: list @ TA,C: list @ TB] :
( ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TB @ E @ G ) )
& ( A @ D @ E )
& ( listrelp @ TA @ TB @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_listrelp_Osimps) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( listrelp @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: list @ TA,C: list @ TB] :
( ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TB ) ) )
| ? [D: TA,E: TB,F: list @ TA,G: list @ TB] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TB @ E @ G ) )
& ( A @ D @ E )
& ( listrelp @ TA @ TB @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(167,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_member__rec_I2_J) ).
thf(862,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_list_Osel_I3_J) ).
thf(407,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(65,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ~ ! [C: TA,D: stream170649215stream @ TA] :
( ( A
= ( stream641971652_SCons @ TA @ C @ D ) )
=> ( ( member2 @ TA @ C @ B )
=> ~ ( member2 @ ( stream170649215stream @ TA ) @ D @ ( stream2015131171treams @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_streams_Ocases) ).
thf(429,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ~ ! [C: TA,D: stream170649215stream @ TA] :
( ( A
= ( stream641971652_SCons @ TA @ C @ D ) )
=> ( ( member2 @ TA @ C @ B )
=> ~ ( member2 @ ( stream170649215stream @ TA ) @ D @ ( stream2015131171treams @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(173,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( splice @ TA @ A @ B )
= C )
=> ( ( ( A
= ( nil @ TA ) )
=> ( C != B ) )
=> ( ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ( ( B
= ( nil @ TA ) )
=> ( C
!= ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( B
= ( cons @ TA @ F @ G ) )
=> ( C
!= ( cons @ TA @ D @ ( cons @ TA @ F @ ( splice @ TA @ E @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_splice_Oelims) ).
thf(879,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( splice @ TA @ A @ B )
= C )
=> ( ( ( A
= ( nil @ TA ) )
=> ( C != B ) )
=> ( ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ( ( B
= ( nil @ TA ) )
=> ( C
!= ( cons @ TA @ D @ E ) ) ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( B
= ( cons @ TA @ F @ G ) )
=> ( C
!= ( cons @ TA @ D @ ( cons @ TA @ F @ ( splice @ TA @ E @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_rev__nonempty__induct) ).
thf(329,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_maps__simps_I2_J) ).
thf(461,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(140,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_last__appendL) ).
thf(757,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) )
= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_splice_Osimps_I2_J) ).
thf(551,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) )
= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(189,axiom,
! [TA: $tType,A: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_shift_Osimps_I1_J) ).
thf(974,plain,
! [TA: $tType,A: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(202,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
= ( append @ TA @ ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) @ ( if @ ( list @ TA ) @ ( B = C ) @ ( nil @ TA ) @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_remdups__adj__append__two) ).
thf(1012,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
= ( append @ TA @ ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) @ ( if @ ( list @ TA ) @ ( B = C ) @ ( nil @ TA ) @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(26,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_neq__Nil__conv) ).
thf(285,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: list @ TA,D: list @ TA] :
( ( ( map_tailrec_rev @ TB @ TA @ A @ B @ C )
= D )
=> ( ( ( B
= ( nil @ TB ) )
=> ( D != C ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
=> ( D
!= ( map_tailrec_rev @ TB @ TA @ A @ F @ ( cons @ TA @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_map__tailrec__rev_Oelims) ).
thf(916,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: list @ TA,D: list @ TA] :
( ( ( map_tailrec_rev @ TB @ TA @ A @ B @ C )
= D )
=> ( ( ( B
= ( nil @ TB ) )
=> ( D != C ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
=> ( D
!= ( map_tailrec_rev @ TB @ TA @ A @ F @ ( cons @ TA @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_bind__simps_I2_J) ).
thf(467,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(162,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_list_Oinject) ).
thf(847,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: list @ TB,D: TA] :
( ( fold @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( fold @ TB @ TA @ A @ C @ ( A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_fold__simps_I2_J) ).
thf(566,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: TB,C: list @ TB,D: TA] :
( ( fold @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( fold @ TB @ TA @ A @ C @ ( A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(137,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ( ( hd @ TA @ A )
= ( hd @ TA @ B ) )
& ( ( tl @ TA @ A )
= ( tl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_list_Oexpand) ).
thf(742,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) )
=> ( ( ( A
!= ( nil @ TA ) )
=> ( ( B
!= ( nil @ TA ) )
=> ( ( ( hd @ TA @ A )
= ( hd @ TA @ B ) )
& ( ( tl @ TA @ A )
= ( tl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(37,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_splice_Oinduct) ).
thf(317,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(204,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_streams__stl) ).
thf(1017,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( stream170649215stream @ TA ) > TB,C: stream170649215stream @ TA] :
( ( A @ ( stream1342653232stream @ TA @ TB @ B @ C ) )
= ( ( C
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) )
=> ( A @ ( B @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_stream_Osplit__sel) ).
thf(980,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( stream170649215stream @ TA ) > TB,C: stream170649215stream @ TA] :
( ( A @ ( stream1342653232stream @ TA @ TB @ B @ C ) )
= ( ( C
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) )
=> ( A @ ( B @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(200,axiom,
! [TA: $tType,A: stream170649215stream @ ( list @ TA )] :
( ( stream_Mirabelle_stl @ TA @ ( stream942386729e_flat @ TA @ A ) )
= ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
= ( nil @ TA ) )
@ ( stream_Mirabelle_stl @ ( list @ TA ) @ A )
@ ( stream641971652_SCons @ ( list @ TA ) @ ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) @ ( stream_Mirabelle_stl @ ( list @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_flat_Osimps_I2_J) ).
thf(1006,plain,
! [TA: $tType,A: stream170649215stream @ ( list @ TA )] :
( ( stream_Mirabelle_stl @ TA @ ( stream942386729e_flat @ TA @ A ) )
= ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
= ( nil @ TA ) )
@ ( stream_Mirabelle_stl @ ( list @ TA ) @ A )
@ ( stream641971652_SCons @ ( list @ TA ) @ ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) @ ( stream_Mirabelle_stl @ ( list @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(114,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_list_Oinducts) ).
thf(593,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(194,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( stream317748790_cycle @ TA @ B )
= ( stream1035003186_shift @ TA @ A @ C ) )
=> ( ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ B ) @ ( cons @ TA @ ( hd @ TA @ B ) @ ( nil @ TA ) ) ) )
= ( stream1035003186_shift @ TA @ ( tl @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_cycle__rotated) ).
thf(989,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( ( stream317748790_cycle @ TA @ B )
= ( stream1035003186_shift @ TA @ A @ C ) )
=> ( ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ B ) @ ( cons @ TA @ ( hd @ TA @ B ) @ ( nil @ TA ) ) ) )
= ( stream1035003186_shift @ TA @ ( tl @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(15,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord_Olexordp__eq_OCons) ).
thf(256,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(208,axiom,
! [TA: $tType,A: stream170649215stream @ TA] :
( ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ ( stream_Mirabelle_stl @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_stream_Ocollapse) ).
thf(1028,plain,
! [TA: $tType,A: stream170649215stream @ TA] :
( ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ ( stream_Mirabelle_stl @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_bind__simps_I1_J) ).
thf(488,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_ord_Olexordp__eq_ONil) ).
thf(225,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( tl @ TA @ B ) )
= ( tl @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_map__tl) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( tl @ TA @ B ) )
= ( tl @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( list @ TA ) > TB,D: list @ TA] :
( ( A @ ( case_list @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( nil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( cons @ TA @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list_Osplit__sel__asm) ).
thf(554,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( list @ TA ) > TB,D: list @ TA] :
( ( A @ ( case_list @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( nil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( cons @ TA @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( hd @ TA @ D ) @ ( tl @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(93,axiom,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_rotate1_Osimps_I1_J) ).
thf(526,plain,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Nil__is__append__conv) ).
thf(637,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(113,axiom,
! [TA: $tType,A: list @ TA] :
( ( hd @ TA @ ( remdups_adj @ TA @ A ) )
= ( hd @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_hd__remdups__adj) ).
thf(590,plain,
! [TA: $tType,A: list @ TA] :
( ( hd @ TA @ ( remdups_adj @ TA @ A ) )
= ( hd @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: list @ TB,C: list @ TA] :
( ( listrelp @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TB ) )
=> ( C
!= ( nil @ TA ) ) )
=> ~ ! [D: TB,E: TA,F: list @ TB] :
( ( B
= ( cons @ TB @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp @ TB @ TA @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_listrelp_Ocases) ).
thf(679,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: list @ TB,C: list @ TA] :
( ( listrelp @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TB ) )
=> ( C
!= ( nil @ TA ) ) )
=> ~ ! [D: TB,E: TA,F: list @ TB] :
( ( B
= ( cons @ TB @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp @ TB @ TA @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(213,axiom,
! [TA: $tType] :
( ( stream1195056575_while @ TA )
= ( ^ [A: TA > $o,B: stream170649215stream @ TA] : ( if @ ( stream170649215stream @ TA ) @ ( A @ ( stream_Mirabelle_shd @ TA @ B ) ) @ ( stream1195056575_while @ TA @ A @ ( stream_Mirabelle_stl @ TA @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sdrop__while_Osimps) ).
thf(1050,plain,
! [TA: $tType] :
( ( stream1195056575_while @ TA )
= ( ^ [A: TA > $o,B: stream170649215stream @ TA] : ( if @ ( stream170649215stream @ TA ) @ ( A @ ( stream_Mirabelle_shd @ TA @ B ) ) @ ( stream1195056575_while @ TA @ A @ ( stream_Mirabelle_stl @ TA @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(107,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_longest__common__suffix) ).
thf(569,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(147,axiom,
! [TA: $tType,A: nat,B: TA] :
( ( rev @ TA @ ( replicate @ TA @ A @ B ) )
= ( replicate @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_rev__replicate) ).
thf(779,plain,
! [TA: $tType,A: nat,B: TA] :
( ( rev @ TA @ ( replicate @ TA @ A @ B ) )
= ( replicate @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( cons @ TA @ A @ ( cons @ TA @ C @ ( splice @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_splice_Osimps_I3_J) ).
thf(237,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( cons @ TA @ A @ ( cons @ TA @ C @ ( splice @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(150,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_remdups__adj_Oinduct) ).
thf(792,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( rev @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_rev__append) ).
thf(311,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( rev @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_remdups__adj__Nil__iff) ).
thf(398,plain,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_shd @ TB @ ( stream2128578057e_smap @ TA @ TB @ A @ B ) )
= ( A @ ( stream_Mirabelle_shd @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_stream_Omap__sel_I1_J) ).
thf(953,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_shd @ TB @ ( stream2128578057e_smap @ TA @ TB @ A @ B ) )
= ( A @ ( stream_Mirabelle_shd @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType] :
( ( map_tailrec @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( rev @ TB @ ( map_tailrec_rev @ TA @ TB @ A @ B @ ( nil @ TB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_map__tailrec__def) ).
thf(773,plain,
! [TA: $tType,TB: $tType] :
( ( map_tailrec @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( rev @ TB @ ( map_tailrec_rev @ TA @ TB @ A @ B @ ( nil @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(89,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_eq__Nil__appendI) ).
thf(513,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(18,axiom,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_butlast_Osimps_I1_J) ).
thf(264,plain,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(165,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_rev__singleton__conv) ).
thf(856,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(24,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_tl__append2) ).
thf(279,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_append__is__Nil__conv) ).
thf(296,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(52,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_butlast__append) ).
thf(375,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(99,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_insert__Nil) ).
thf(545,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(61,axiom,
! [TA: $tType] :
( ( stream317748790_cycle @ TA )
= ( ^ [A: list @ TA] : ( stream641971652_SCons @ TA @ ( hd @ TA @ A ) @ ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_cycle_Ocode) ).
thf(413,plain,
! [TA: $tType] :
( ( stream317748790_cycle @ TA )
= ( ^ [A: list @ TA] : ( stream641971652_SCons @ TA @ ( hd @ TA @ A ) @ ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(109,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_remdups__adj_Ocases) ).
thf(579,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(28,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ord_Olexordp__eq__simps_I3_J) ).
thf(291,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(177,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: stream170649215stream @ ( list @ TA )] :
( ( stream942386729e_flat @ TA @ ( stream641971652_SCons @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) )
= ( stream641971652_SCons @ TA @ A
@ ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( B
= ( nil @ TA ) )
@ C
@ ( stream641971652_SCons @ ( list @ TA ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_flat__Cons) ).
thf(936,plain,
! [TA: $tType,A: TA,B: list @ TA,C: stream170649215stream @ ( list @ TA )] :
( ( stream942386729e_flat @ TA @ ( stream641971652_SCons @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ C ) )
= ( stream641971652_SCons @ TA @ A
@ ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( B
= ( nil @ TA ) )
@ C
@ ( stream641971652_SCons @ ( list @ TA ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(181,axiom,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ ( list @ TA )] :
( ( A
!= ( nil @ TA ) )
=> ( ( stream942386729e_flat @ TA @ ( stream641971652_SCons @ ( list @ TA ) @ A @ B ) )
= ( stream1035003186_shift @ TA @ A @ ( stream942386729e_flat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_flat__Stream) ).
thf(947,plain,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ ( list @ TA )] :
( ( A
!= ( nil @ TA ) )
=> ( ( stream942386729e_flat @ TA @ ( stream641971652_SCons @ ( list @ TA ) @ A @ B ) )
= ( stream1035003186_shift @ TA @ A @ ( stream942386729e_flat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(142,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_butlast__snoc) ).
thf(764,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(157,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_append__eq__appendI) ).
thf(831,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: TA,D: list @ TA] :
( ( ( map @ TB @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ? [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TB @ TA @ A @ F )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_map__eq__Cons__D) ).
thf(419,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: TA,D: list @ TA] :
( ( ( map @ TB @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ? [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TB @ TA @ A @ F )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( listrelp @ TB @ TA @ A @ ( nil @ TB ) @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_listrelp_ONil) ).
thf(230,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( listrelp @ TB @ TA @ A @ ( nil @ TB ) @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_butlast_Osimps_I2_J) ).
thf(362,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(11,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ord_Olexordp__eq__refl) ).
thf(245,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(121,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( A
= ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_list_Oexhaust__sel) ).
thf(649,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( A
= ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(212,axiom,
! [TA: $tType,A: ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream170649215stream @ TA,E: stream170649215stream @ TA] :
( ( A @ D @ E )
=> ( ( ( stream_Mirabelle_shd @ TA @ D )
= ( stream_Mirabelle_shd @ TA @ E ) )
& ( ( A @ ( stream_Mirabelle_stl @ TA @ D ) @ ( stream_Mirabelle_stl @ TA @ E ) )
| ( ( stream_Mirabelle_stl @ TA @ D )
= ( stream_Mirabelle_stl @ TA @ E ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_stream_Ocoinduct__strong) ).
thf(1043,plain,
! [TA: $tType,A: ( stream170649215stream @ TA ) > ( stream170649215stream @ TA ) > $o,B: stream170649215stream @ TA,C: stream170649215stream @ TA] :
( ( A @ B @ C )
=> ( ! [D: stream170649215stream @ TA,E: stream170649215stream @ TA] :
( ( A @ D @ E )
=> ( ( ( stream_Mirabelle_shd @ TA @ D )
= ( stream_Mirabelle_shd @ TA @ E ) )
& ( ( A @ ( stream_Mirabelle_stl @ TA @ D ) @ ( stream_Mirabelle_stl @ TA @ E ) )
| ( ( stream_Mirabelle_stl @ TA @ D )
= ( stream_Mirabelle_stl @ TA @ E ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_hd__rev) ).
thf(434,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(55,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_ord_Olexordp__eq_Oinducts) ).
thf(387,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(45,axiom,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list_Osel_I2_J) ).
thf(345,plain,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_list_OdiscI) ).
thf(535,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(154,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_last_Osimps) ).
thf(816,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member2 @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(323,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member2 @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: stream170649215stream @ TB,B: set @ TB,C: TB > TA,D: set @ TA] :
( ( member2 @ ( stream170649215stream @ TB ) @ A @ ( stream2015131171treams @ TB @ B ) )
=> ( ! [E: TB] :
( ( member2 @ TB @ E @ B )
=> ( member2 @ TA @ ( C @ E ) @ D ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ ( stream2128578057e_smap @ TB @ TA @ C @ A ) @ ( stream2015131171treams @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_smap__streams) ).
thf(520,plain,
! [TA: $tType,TB: $tType,A: stream170649215stream @ TB,B: set @ TB,C: TB > TA,D: set @ TA] :
( ( member2 @ ( stream170649215stream @ TB ) @ A @ ( stream2015131171treams @ TB @ B ) )
=> ( ! [E: TB] :
( ( member2 @ TB @ E @ B )
=> ( member2 @ TA @ ( C @ E ) @ D ) )
=> ( member2 @ ( stream170649215stream @ TA ) @ ( stream2128578057e_smap @ TB @ TA @ C @ A ) @ ( stream2015131171treams @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(9,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ord_Olexordp__eq__simps_I4_J) ).
thf(240,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: set @ ( list @ TA ),C: list @ TA] :
( ( member2 @ TA @ A @ ( bNF_Greatest_Succ @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( append @ TA @ C @ ( cons @ TA @ A @ ( nil @ TA ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_SuccD) ).
thf(964,plain,
! [TA: $tType,A: TA,B: set @ ( list @ TA ),C: list @ TA] :
( ( member2 @ TA @ A @ ( bNF_Greatest_Succ @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( append @ TA @ C @ ( cons @ TA @ A @ ( nil @ TA ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(206,axiom,
! [TA: $tType,A: list @ TA] :
( ( fold @ TA @ ( list @ TA ) @ ( cons @ TA ) @ A )
= ( append @ TA @ ( rev @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_fold__Cons__rev) ).
thf(1022,plain,
! [TA: $tType,A: list @ TA] :
( ( fold @ TA @ ( list @ TA ) @ ( cons @ TA ) @ A )
= ( append @ TA @ ( rev @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(192,axiom,
! [TA: $tType,A: TA,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_stl @ TA @ ( stream641971652_SCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_stream_Osel_I2_J) ).
thf(983,plain,
! [TA: $tType,A: TA,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_stl @ TA @ ( stream641971652_SCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(73,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( append @ TA @ ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) @ ( tl @ TA @ ( remdups_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_remdups__adj__append) ).
thf(455,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( append @ TA @ ( remdups_adj @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) @ ( tl @ TA @ ( remdups_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(203,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_streams__shd) ).
thf(1015,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) )
=> ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1,conjecture,
( ( stream942386729e_flat @ a @ ws )
= ( stream1035003186_shift @ a @ ( stream_Mirabelle_shd @ ( list @ a ) @ ws ) @ ( stream942386729e_flat @ a @ ( stream_Mirabelle_stl @ ( list @ a ) @ ws ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( stream942386729e_flat @ a @ ws )
!= ( stream1035003186_shift @ a @ ( stream_Mirabelle_shd @ ( list @ a ) @ ws ) @ ( stream942386729e_flat @ a @ ( stream_Mirabelle_stl @ ( list @ a ) @ ws ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(223,plain,
( ( stream942386729e_flat @ a @ ws )
!= ( stream1035003186_shift @ a @ ( stream_Mirabelle_shd @ ( list @ a ) @ ws ) @ ( stream942386729e_flat @ a @ ( stream_Mirabelle_stl @ ( list @ a ) @ ws ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: stream170649215stream @ TB,C: TA,D: stream170649215stream @ TA] :
( ( ( stream2128578057e_smap @ TB @ TA @ A @ B )
= ( stream641971652_SCons @ TA @ C @ D ) )
= ( ( ( A @ ( stream_Mirabelle_shd @ TB @ B ) )
= C )
& ( ( stream2128578057e_smap @ TB @ TA @ A @ ( stream_Mirabelle_stl @ TB @ B ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_smap__ctr) ).
thf(986,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: stream170649215stream @ TB,C: TA,D: stream170649215stream @ TA] :
( ( ( stream2128578057e_smap @ TB @ TA @ A @ B )
= ( stream641971652_SCons @ TA @ C @ D ) )
= ( ( ( A @ ( stream_Mirabelle_shd @ TB @ B ) )
= C )
& ( ( stream2128578057e_smap @ TB @ TA @ A @ ( stream_Mirabelle_stl @ TB @ B ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( rev @ TA @ A ) )
= ( hd @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_last__rev) ).
thf(563,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( rev @ TA @ A ) )
= ( hd @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_maps__simps_I1_J) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(267,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(222,axiom,
( ( stream_Mirabelle_shd @ ( list @ a ) @ ws )
!= ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1076,plain,
( ( stream_Mirabelle_shd @ ( list @ a ) @ ws )
!= ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( stream170649215stream @ TA ) > TB,C: stream170649215stream @ TA] :
( ( A @ ( stream1342653232stream @ TA @ TB @ B @ C ) )
= ( ~ ( ( C
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) )
& ~ ( A @ ( B @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_stream_Osplit__sel__asm) ).
thf(1034,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( stream170649215stream @ TA ) > TB,C: stream170649215stream @ TA] :
( ( A @ ( stream1342653232stream @ TA @ TB @ B @ C ) )
= ( ~ ( ( C
= ( stream641971652_SCons @ TA @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) )
& ~ ( A @ ( B @ ( stream_Mirabelle_shd @ TA @ C ) @ ( stream_Mirabelle_stl @ TA @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(64,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_append__Nil2) ).
thf(426,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(180,axiom,
! [TA: $tType,A: list @ TA] :
( ( stream_Mirabelle_shd @ TA @ ( stream317748790_cycle @ TA @ A ) )
= ( hd @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_cycle_Osimps_I1_J) ).
thf(944,plain,
! [TA: $tType,A: list @ TA] :
( ( stream_Mirabelle_shd @ TA @ ( stream317748790_cycle @ TA @ A ) )
= ( hd @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(100,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_append__same__eq) ).
thf(548,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(178,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) )
=> ( ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B )
=> ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_in__streams) ).
thf(939,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: set @ TA] :
( ( member2 @ ( stream170649215stream @ TA ) @ ( stream_Mirabelle_stl @ TA @ A ) @ ( stream2015131171treams @ TA @ B ) )
=> ( ( member2 @ TA @ ( stream_Mirabelle_shd @ TA @ A ) @ B )
=> ( member2 @ ( stream170649215stream @ TA ) @ A @ ( stream2015131171treams @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_map__eq__map__tailrec) ).
thf(342,plain,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(139,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_snoc__eq__iff__butlast) ).
thf(754,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(74,axiom,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_rev__rev__ident) ).
thf(458,plain,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(146,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_append__eq__Cons__conv) ).
thf(776,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(103,axiom,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord_Olexordp__eq_Osimps) ).
thf(557,plain,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(118,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_last__ConsR) ).
thf(640,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(207,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_sublists_Osimps_I1_J) ).
thf(1025,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(220,axiom,
! [TA: $tType] :
( ( stream942386729e_flat @ TA )
= ( ^ [A: stream170649215stream @ ( list @ TA )] :
( stream641971652_SCons @ TA @ ( hd @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
@ ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
= ( nil @ TA ) )
@ ( stream_Mirabelle_stl @ ( list @ TA ) @ A )
@ ( stream641971652_SCons @ ( list @ TA ) @ ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) @ ( stream_Mirabelle_stl @ ( list @ TA ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_flat_Ocode) ).
thf(1070,plain,
! [TA: $tType] :
( ( stream942386729e_flat @ TA )
= ( ^ [A: stream170649215stream @ ( list @ TA )] :
( stream641971652_SCons @ TA @ ( hd @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
@ ( stream942386729e_flat @ TA
@ ( if @ ( stream170649215stream @ ( list @ TA ) )
@ ( ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) )
= ( nil @ TA ) )
@ ( stream_Mirabelle_stl @ ( list @ TA ) @ A )
@ ( stream641971652_SCons @ ( list @ TA ) @ ( tl @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) @ ( stream_Mirabelle_stl @ ( list @ TA ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(133,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_rev__induct) ).
thf(705,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_rotate1__is__Nil__conv) ).
thf(282,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(214,axiom,
! [TA: $tType,A: list @ TA] :
( ( stream_Mirabelle_stl @ TA @ ( stream317748790_cycle @ TA @ A ) )
= ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_cycle_Osimps_I2_J) ).
thf(1053,plain,
! [TA: $tType,A: list @ TA] :
( ( stream_Mirabelle_stl @ TA @ ( stream317748790_cycle @ TA @ A ) )
= ( stream317748790_cycle @ TA @ ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(111,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( tl @ TA @ A ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Nil__tl) ).
thf(585,plain,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( tl @ TA @ A ) )
= ( ( A
= ( nil @ TA ) )
| ? [B: TA] :
( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(135,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_append__Nil) ).
thf(717,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(643,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_last__ConsL) ).
thf(470,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(108,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( rev @ TA @ B ) )
= ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_singleton__rev__conv) ).
thf(576,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( rev @ TA @ B ) )
= ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_last__appendR) ).
thf(336,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(168,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_append__self__conv) ).
thf(864,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_last__map) ).
thf(314,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Cons__eq__map__conv) ).
thf(446,plain,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(166,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= B )
= ( A
= ( rev @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_rev__swap) ).
thf(859,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= B )
= ( A
= ( rev @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Cons__eq__appendI) ).
thf(497,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(172,axiom,
! [TA: $tType,A: TA] :
( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_remdups__adj_Osimps_I2_J) ).
thf(876,plain,
! [TA: $tType,A: TA] :
( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: list @ TB,D: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( map_tailrec_rev @ TB @ TA @ A @ C @ ( cons @ TA @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_map__tailrec__rev_Osimps_I2_J) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: list @ TB,D: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( map_tailrec_rev @ TB @ TA @ A @ C @ ( cons @ TA @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: nat,C: TA] :
( ( map @ TA @ TB @ A @ ( replicate @ TA @ B @ C ) )
= ( replicate @ TB @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_map__replicate) ).
thf(539,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: nat,C: TA] :
( ( map @ TA @ TB @ A @ ( replicate @ TA @ B @ C ) )
= ( replicate @ TB @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_list__nonempty__induct) ).
thf(368,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_BNF__Greatest__Fixpoint_Oshift__def) ).
thf(844,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(153,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ C ) )
= ( A
= ( append @ TA @ ( rev @ TA @ C ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rev__eq__Cons__iff) ).
thf(813,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ C ) )
= ( A
= ( append @ TA @ ( rev @ TA @ C ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(90,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_append__eq__append__conv2) ).
thf(517,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(217,axiom,
! [TA: $tType,A: stream170649215stream @ ( list @ TA )] :
( ( stream_Mirabelle_shd @ TA @ ( stream942386729e_flat @ TA @ A ) )
= ( hd @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_flat_Osimps_I1_J) ).
thf(1062,plain,
! [TA: $tType,A: stream170649215stream @ ( list @ TA )] :
( ( stream_Mirabelle_shd @ TA @ ( stream942386729e_flat @ TA @ A ) )
= ( hd @ TA @ ( stream_Mirabelle_shd @ ( list @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(16,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_splice_Osimps_I1_J) ).
thf(258,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( hd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_hd__map) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( hd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(196,axiom,
! [TA: $tType,A: TA,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_shd @ TA @ ( stream641971652_SCons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_stream_Osel_I1_J) ).
thf(995,plain,
! [TA: $tType,A: TA,B: stream170649215stream @ TA] :
( ( stream_Mirabelle_shd @ TA @ ( stream641971652_SCons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(112,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_list__ex1__simps_I1_J) ).
thf(588,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( map @ TA @ TB @ B @ ( tl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_list_Omap__sel_I2_J) ).
thf(699,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( tl @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( map @ TA @ TB @ B @ ( tl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( stream317748790_cycle @ TA @ ( cons @ TA @ A @ B ) )
= ( stream641971652_SCons @ TA @ A @ ( stream317748790_cycle @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_cycle__Cons) ).
thf(652,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( stream317748790_cycle @ TA @ ( cons @ TA @ A @ B ) )
= ( stream641971652_SCons @ TA @ A @ ( stream317748790_cycle @ TA @ ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Cons__eq__append__conv) ).
thf(351,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_list__induct2_H) ).
thf(510,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(126,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_not__Cons__self2) ).
thf(667,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(176,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ D ) )
& ( B
= ( append @ TA @ C @ E ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( hd @ TA @ D )
!= ( hd @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_longest__common__prefix) ).
thf(929,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ C @ D ) )
& ( B
= ( append @ TA @ C @ E ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( hd @ TA @ D )
!= ( hd @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_list_Odistinct_I1_J) ).
thf(410,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(182,axiom,
! [TA: $tType] :
( ( union @ TA )
= ( fold @ TA @ ( list @ TA ) @ ( insert @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_List_Ounion__def) ).
thf(950,plain,
! [TA: $tType] :
( ( union @ TA )
= ( fold @ TA @ ( list @ TA ) @ ( insert @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(158,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_self__append__conv) ).
thf(835,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: TA,C: stream170649215stream @ TA] :
( ( stream1586597341member @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( ( A != B )
=> ( stream1586597341member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_smember__code) ).
thf(867,plain,
! [TA: $tType,A: TA,B: TA,C: stream170649215stream @ TA] :
( ( stream1586597341member @ TA @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( ( A != B )
=> ( stream1586597341member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(22,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(273,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_list_Osimps_I8_J) ).
thf(305,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA > ( stream170649215stream @ TA ) > TB,B: TA,C: stream170649215stream @ TA] :
( ( stream1342653232stream @ TA @ TB @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_stream_Ocase) ).
thf(326,plain,
! [TA: $tType,TB: $tType,A: TA > ( stream170649215stream @ TA ) > TB,B: TA,C: stream170649215stream @ TA] :
( ( stream1342653232stream @ TA @ TB @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(20,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ord_Olexordp__eq_OCons__eq) ).
thf(268,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType] :
( ( case_list @ TA @ TB )
= ( ^ [A: TA,B: TB > ( list @ TB ) > TA,C: list @ TB] :
( if @ TA
@ ( C
= ( nil @ TB ) )
@ A
@ ( B @ ( hd @ TB @ C ) @ ( tl @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_list_Ocase__eq__if) ).
thf(807,plain,
! [TA: $tType,TB: $tType] :
( ( case_list @ TA @ TB )
= ( ^ [A: TA,B: TB > ( list @ TB ) > TA,C: list @ TB] :
( if @ TA
@ ( C
= ( nil @ TB ) )
@ A
@ ( B @ ( hd @ TB @ C ) @ ( tl @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(67,axiom,
! [TA: $tType,A: set @ ( list @ TA ),B: TA,C: list @ TA] :
( ( bNF_Greatest_Succ @ TA @ ( bNF_Greatest_Shift @ TA @ A @ B ) @ C )
= ( bNF_Greatest_Succ @ TA @ A @ ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Succ__Shift) ).
thf(437,plain,
! [TA: $tType,A: set @ ( list @ TA ),B: TA,C: list @ TA] :
( ( bNF_Greatest_Succ @ TA @ ( bNF_Greatest_Shift @ TA @ A @ B ) @ C )
= ( bNF_Greatest_Succ @ TA @ A @ ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: stream170649215stream @ TA] :
( ( stream2128578057e_smap @ TA @ TB @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream641971652_SCons @ TB @ ( A @ B ) @ ( stream2128578057e_smap @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_stream_Omap) ).
thf(828,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: stream170649215stream @ TA] :
( ( stream2128578057e_smap @ TA @ TB @ A @ ( stream641971652_SCons @ TA @ B @ C ) )
= ( stream641971652_SCons @ TB @ ( A @ B ) @ ( stream2128578057e_smap @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_list_Omap__disc__iff) ).
thf(696,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(136,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= B )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [C: TA] :
( ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdups_adj @ TA @ ( cons @ TA @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons @ TA @ C @ ( remdups_adj @ TA @ ( cons @ TA @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_remdups__adj_Oelims) ).
thf(720,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= B )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [C: TA] :
( ( A
= ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdups_adj @ TA @ ( cons @ TA @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons @ TA @ C @ ( remdups_adj @ TA @ ( cons @ TA @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(79,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_last__append) ).
thf(474,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ ( tl @ TA @ ( remdups_adj @ TA @ ( cons @ TA @ A @ B ) ) ) )
= ( remdups_adj @ TA @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_remdups__adj__Cons__alt) ).
thf(767,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ ( tl @ TA @ ( remdups_adj @ TA @ ( cons @ TA @ A @ B ) ) ) )
= ( remdups_adj @ TA @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(215,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( stream641971652_SCons @ TA @ A @ ( stream1035003186_shift @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_shift_Osimps_I2_J) ).
thf(1056,plain,
! [TA: $tType,A: TA,B: list @ TA,C: stream170649215stream @ TA] :
( ( stream1035003186_shift @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( stream641971652_SCons @ TA @ A @ ( stream1035003186_shift @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rev @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rev__is__Nil__conv) ).
thf(664,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rev @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(95,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_rev__exhaust) ).
thf(532,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(218,axiom,
! [TA: $tType,A: stream170649215stream @ TA,B: stream170649215stream @ TA] :
( ( ( ( stream_Mirabelle_shd @ TA @ A )
= ( stream_Mirabelle_shd @ TA @ B ) )
& ( ( stream_Mirabelle_stl @ TA @ A )
= ( stream_Mirabelle_stl @ TA @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_stream_Oexpand) ).
thf(1065,plain,
! [TA: $tType,A: stream170649215stream @ TA,B: stream170649215stream @ TA] :
( ( ( ( stream_Mirabelle_shd @ TA @ A )
= ( stream_Mirabelle_shd @ TA @ B ) )
& ( ( stream_Mirabelle_stl @ TA @ A )
= ( stream_Mirabelle_stl @ TA @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_append__Cons) ).
thf(464,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType] :
( ( stream1342653232stream @ TA @ TB )
= ( ^ [A: TA > ( stream170649215stream @ TA ) > TB,B: stream170649215stream @ TA] : ( A @ ( stream_Mirabelle_shd @ TA @ B ) @ ( stream_Mirabelle_stl @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_stream_Ocase__eq__if) ).
thf(1019,plain,
! [TA: $tType,TB: $tType] :
( ( stream1342653232stream @ TA @ TB )
= ( ^ [A: TA > ( stream170649215stream @ TA ) > TB,B: stream170649215stream @ TA] : ( A @ ( stream_Mirabelle_shd @ TA @ B ) @ ( stream_Mirabelle_stl @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(195,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_transpose_Ocases) ).
thf(992,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(155,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_hd__append) ).
thf(822,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(163,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_hd__append2) ).
thf(850,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(199,axiom,
! [TA: $tType,A: set @ ( list @ TA ),B: TA] :
( ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ A )
=> ( ( member2 @ TA @ B @ ( bNF_Greatest_Succ @ TA @ A @ ( nil @ TA ) ) )
=> ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( bNF_Greatest_Shift @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_empty__Shift) ).
thf(1004,plain,
! [TA: $tType,A: set @ ( list @ TA ),B: TA] :
( ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ A )
=> ( ( member2 @ TA @ B @ ( bNF_Greatest_Succ @ TA @ A @ ( nil @ TA ) ) )
=> ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( bNF_Greatest_Shift @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(85,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( rotate1 @ TA @ A )
= ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_rotate1__hd__tl) ).
thf(501,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( rotate1 @ TA @ A )
= ( append @ TA @ ( tl @ TA @ A ) @ ( cons @ TA @ ( hd @ TA @ A ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ord_Olexordp__eq__simps_I2_J) ).
thf(227,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(354,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(201,axiom,
! [TA: $tType] :
( ( rev @ TA )
= ( ^ [A: list @ TA] : ( fold @ TA @ ( list @ TA ) @ ( cons @ TA ) @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_rev__conv__fold) ).
thf(1009,plain,
! [TA: $tType] :
( ( rev @ TA )
= ( ^ [A: list @ TA] : ( fold @ TA @ ( list @ TA ) @ ( cons @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( hd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_list_Omap__sel_I1_J) ).
thf(676,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( hd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( ( A = B )
=> ( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( remdups_adj @ TA @ ( cons @ TA @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( cons @ TA @ A @ ( remdups_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_remdups__adj_Osimps_I3_J) ).
thf(491,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( ( A = B )
=> ( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( remdups_adj @ TA @ ( cons @ TA @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdups_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( cons @ TA @ A @ ( remdups_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: list @ TB,E: list @ TA] :
( ( A @ B @ C )
=> ( ( listrelp @ TB @ TA @ A @ D @ E )
=> ( listrelp @ TB @ TA @ A @ ( cons @ TB @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_listrelp_OCons) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: list @ TB,E: list @ TA] :
( ( A @ B @ C )
=> ( ( listrelp @ TB @ TA @ A @ D @ E )
=> ( listrelp @ TB @ TA @ A @ ( cons @ TB @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(211,axiom,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( stream_Mirabelle_shd @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream_Mirabelle_shd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( stream_Mirabelle_shd @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_shift__simps_I1_J) ).
thf(1037,plain,
! [TA: $tType,A: list @ TA,B: stream170649215stream @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( stream_Mirabelle_shd @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( stream_Mirabelle_shd @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( stream_Mirabelle_shd @ TA @ ( stream1035003186_shift @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( ( A = C )
| ( member @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_member__rec_I1_J) ).
thf(560,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA] :
( ( member @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( ( A = C )
| ( member @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1082,plain,
$false,
inference(e,[status(thm)],[1031,962,234,941,977,276,1068,308,1073,247,523,582,873,449,440,655,384,913,670,404,1001,782,841,288,320,785,504,838,357,1059,542,702,751,853,870,969,770,416,261,443,485,348,966,480,646,253,602,634,998,243,507,293,956,452,661,761,810,381,714,270,529,302,862,407,429,879,329,461,757,551,974,1012,285,916,467,847,566,742,317,1017,980,1006,593,989,256,1028,488,225,339,554,526,637,590,679,1050,569,779,237,792,311,398,953,773,513,264,856,279,296,375,545,413,579,291,936,947,764,831,419,230,362,245,649,1043,434,387,345,535,816,323,520,240,964,1022,983,455,1015,223,986,563,299,267,1076,1034,426,944,548,939,342,754,458,776,557,640,1025,1070,705,282,1053,585,717,643,470,576,336,864,314,446,859,497,876,250,539,368,844,813,517,1062,258,401,995,588,699,652,351,510,667,929,410,950,835,867,273,305,326,268,807,437,828,696,720,474,767,1056,664,532,1065,464,1019,992,822,850,1004,501,227,354,1009,676,491,232,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : DAT251^1 : TPTP v8.1.2. Released v7.0.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % 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 11:31:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.91/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.01/1.28 % [INFO] Parsing done (352ms).
% 2.01/1.30 % [INFO] Running in sequential loop mode.
% 3.09/1.62 % [INFO] eprover registered as external prover.
% 3.09/1.62 % [INFO] cvc4 registered as external prover.
% 3.09/1.63 % [INFO] Scanning for conjecture ...
% 3.37/1.73 % [INFO] Found a conjecture and 266 axioms. Running axiom selection ...
% 3.86/1.83 % [INFO] Axiom selection finished. Selected 220 axioms (removed 46 axioms).
% 4.29/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 4.62/2.07 % [INFO] Type checking passed.
% 4.62/2.07 % [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 ...
% 34.34/15.33 % External prover 'e' found a proof!
% 34.34/15.33 % [INFO] Killing All external provers ...
% 34.34/15.33 % Time passed: 14790ms (effective reasoning time: 14030ms)
% 34.34/15.33 % 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)>
% 34.34/15.34 % Axioms used in derivation (220): fact_28_stream_Osel_I2_J, fact_30_stream_Osplit__sel__asm, fact_253_append__replicate__commute, fact_113_ord_Olexordp__eq_ONil, fact_15_in__streams, fact_164_BNF__Greatest__Fixpoint_Oshift__def, fact_105_ord_Olexordp__eq__refl, fact_54_not__Cons__self2, fact_245_replicate__app__Cons__same, fact_115_splice_Osimps_I1_J, fact_75_Nil__tl, fact_80_insert__Nil, fact_169_listrelp_Oinducts, fact_197_fold__simps_I1_J, fact_144_maps__simps_I2_J, fact_16_stream_Oinject, fact_181_listrelp_OCons, fact_183_rev_Osimps_I2_J, fact_184_last__rev, fact_124_longest__common__prefix, fact_171_rev__is__rev__conv, fact_95_shift__append, fact_150_last__appendR, fact_67_list_Osel_I3_J, fact_27_flat_Ocode, fact_5_flat__Stream, fact_82_ord_Olexordp__eq__simps_I3_J, fact_177_rev__singleton__conv, fact_185_hd__rev, fact_74_tl__Nil, fact_2_stream_Oexpand, fact_108_Cons__eq__appendI, fact_154_butlast__tl, fact_58_list_Oexhaust, fact_43_list_Oexhaust__sel, fact_50_stream_Omap__sel_I2_J, fact_110_eq__Nil__appendI, fact_107_append__Cons, fact_168_rev__eq__Cons__iff, fact_142_remdups__adj_Oelims, fact_121_map__tailrec__rev_Osimps_I2_J, fact_25_list_Osel_I2_J, fact_6_shift__simps_I1_J, fact_152_append__butlast__last__id, fact_73_list_Osplit__sel, fact_59_list_Oinducts, fact_34_stream_Oexhaust__sel, fact_156_butlast_Osimps_I2_J, fact_111_ord_Olexordp__eq_OCons__eq, fact_137_rotate1__is__Nil__conv, fact_251_list_Osimps_I8_J, fact_83_map__tailrec__rev_Oelims, fact_69_stream_Omap, fact_254_map__butlast, fact_24_sdrop__while__SCons, fact_125_ord_Olexordp__eq_Ocases, fact_186_listrelp_Ocases, fact_100_append1__eq__conv, fact_145_remdups__adj__append__two, fact_138_remdups__adj__Cons__alt, fact_159_last__ConsR, fact_51_stream_Omap__sel_I1_J, fact_248_map__eq__Cons__D, fact_94_append__Nil2, fact_33_streams__shd, fact_231_map__tailrec__rev, fact_61_list__induct2_H, fact_78_cycle_Osimps_I2_J, fact_173_Nil__is__rev__conv, fact_53_member__rec_I1_J, fact_246_list_Osimps_I9_J, fact_160_longest__common__suffix, fact_89_Nil__is__append__conv, help_If_1_1_T, fact_153_butlast_Osimps_I1_J, fact_14_streamsE, fact_13_stream_Ocollapse, fact_232_replicate__append__same, fact_249_Cons__eq__map__conv, fact_119_rev__exhaust, fact_123_hd__append, fact_91_append__self__conv2, fact_242_hd__map, fact_187_map__tailrec__def, fact_20_streams_Osimps, fact_112_ord_Olexordp__eq_OCons, fact_120_rev__induct, fact_17_list_Oexpand, fact_36_flat__Cons, fact_56_list_Odistinct_I1_J, fact_114_splice_Osimps_I3_J, fact_99_splice__Nil2, fact_157_last_Osimps, fact_236_map__append, fact_161_butlast__append, fact_68_list_Osel_I1_J, fact_49_list_Oinject, fact_170_listrelp_Osimps, fact_12_cycle__decomp, fact_241_list_Omap__sel_I2_J, fact_252_map__tl, fact_98_ord_Olexordp__eq__simps_I2_J, fact_18_stream_Ocase, fact_147_butlast__snoc, fact_26_cycle_Osimps_I1_J, fact_62_splice_Oinduct, fact_23_streams_Ocoinduct, fact_76_shift_Osimps_I2_J, fact_233_Nil__is__map__conv, fact_244_last__map, fact_235_list_Omap__disc__iff, fact_11_flat_Osimps_I2_J, fact_19_streams_Ocases, fact_37_list_Ocase__eq__if, fact_106_append__eq__appendI, fact_101_tl__append2, fact_81_cycle__Cons, fact_97_ord_Olexordp__eq__simps_I1_J, fact_176_remdups__adj__rev, fact_200_List_Ounion__def, fact_134_remdups__adj__append, fact_238_rev__replicate, fact_240_map__eq__map__tailrec, fact_52_list_Osimps_I5_J, fact_103_bind__simps_I2_J, fact_199_rev__conv__fold, fact_60_neq__Nil__conv, fact_239_smap__shift, fact_148_SuccD, fact_166_Succ__Shift, fact_234_map__is__Nil__conv, fact_136_hd__remdups__adj, fact_79_cycle_Ocode, fact_126_ord_Olexordp__eq_Osimps, fact_167_ShiftD, fact_4_stream_Ocoinduct__strong, fact_21_stream_Oexhaust, help_If_3_1_T, fact_87_append__assoc, fact_96_ord_Olexordp__eq__simps_I4_J, help_If_2_1_T, fact_104_append__eq__append__conv2, fact_141_rotate1_Osimps_I1_J, fact_1_shift_Osimps_I1_J, fact_88_append__is__Nil__conv, fact_122_map__tailrec__rev_Osimps_I1_J, fact_175_rev__append, fact_8_stream_Ocase__eq__if, fact_128_splice_Osimps_I2_J, fact_243_list_Omap__sel_I1_J, fact_149_SuccI, fact_9_shift__simps_I2_J, fact_143_remdups__adj_Osimps_I2_J, fact_55_transpose_Ocases, fact_45_Collect__mem__eq, fact_66_map__tailrec__rev_Oinduct, fact_86_append__same__eq, fact_72_list_Osplit__sel__asm, fact_198_fold__simps_I2_J, fact_146_last__snoc, fact_180_rev__swap, fact_130_sublists_Osimps_I1_J, fact_0_shift__left__inj, fact_32_streams__stl, fact_22_streams__Stream, fact_71_list_Osimps_I4_J, fact_90_self__append__conv2, fact_237_map__replicate, fact_63_remdups__adj_Ocases, fact_7_flat_Osimps_I1_J, fact_40_list_Ocollapse, fact_3_stream_Ocoinduct, fact_57_list_OdiscI, fact_116_rev__nonempty__induct, fact_10_sdrop__while_Osimps, fact_172_rev__rev__ident, fact_174_rev__is__Nil__conv, fact_64_remdups__adj_Oinduct, fact_35_smember__code, fact_84_splice_Oelims, fact_102_hd__append2, fact_77_cycle__rotated, fact_155_snoc__eq__iff__butlast, fact_92_self__append__conv, fact_133_rotate1_Osimps_I2_J, fact_132_maps__simps_I1_J, fact_129_rotate1__hd__tl, fact_117_append__eq__Cons__conv, fact_151_last__appendL, fact_127_ord_Olexordp__eq_Oinducts, fact_250_map__eq__Cons__conv, fact_178_singleton__rev__conv, fact_109_append__Nil, fact_31_stream_Osplit__sel, fact_38_list__ex1__simps_I1_J, fact_41_smap__ctr, fact_139_remdups__adj_Osimps_I3_J, fact_42_bind__simps_I1_J, fact_182_listrelp_ONil, fact_39_hd__Cons__tl, fact_65_list__nonempty__induct, conj_0, fact_135_remdups__adj__Nil__iff, fact_140_remdups__adj_Osimps_I1_J, fact_189_fold__Cons__rev, fact_247_Cons__eq__map__D, fact_165_empty__Shift, fact_118_Cons__eq__append__conv, fact_46_Collect__cong, fact_131_product__lists_Osimps_I1_J, fact_48_member__rec_I2_J, fact_85_same__append__eq, fact_29_stream_Osel_I1_J, fact_70_smap__streams, fact_163_last__tl, fact_93_append__self__conv, fact_162_last__append, fact_158_last__ConsL, fact_44_mem__Collect__eq, fact_179_rev_Osimps_I1_J
% 34.34/15.34 % No. of inferences in proof: 444
% 34.34/15.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14790 ms resp. 14030 ms w/o parsing
% 34.96/15.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.96/15.50 % [INFO] Killing All external provers ...
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