%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP100^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:45 AM UTC 2026
% Result : Theorem 120.69s 84.95s
% Output : Refutation 123.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 272
% Syntax : Number of formulae : 546 ( 257 unt; 0 typ; 0 def)
% Number of atoms : 1697 ( 928 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 9283 ( 328 ~; 83 |; 182 &;7902 @)
% ( 0 <=>; 788 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 424 ( 424 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 6 con; 0-6 aty)
% Number of variables : 2384 ( 54 ^;2188 !; 142 ?;2384 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(bNF_Greatest_Shift_decl,type,
bNF_Greatest_Shift:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > TA > ( set @ ( list @ TA ) ) ) ).
thf(bNF_Greatest_Succ_decl,type,
bNF_Greatest_Succ:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > ( list @ TA ) > ( set @ TA ) ) ).
thf(bNF_Greatest_shift_decl,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(list_asc_decl,type,
list_asc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(list_ord_decl,type,
list_ord:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > $o ) ).
thf(list_strict_asc_decl,type,
list_strict_asc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(map2_decl,type,
map2:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( list @ TC ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(listIn521021761append_decl,type,
listIn521021761append:
!>[TA: $tType] : ( ( list @ TA ) > ( nat > TA ) > nat > TA ) ).
thf(append_decl,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(arg_min_list_decl,type,
arg_min_list:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > TB ) ).
thf(bind_decl,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(butlast_decl,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(concat_decl,type,
concat:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ TA ) ) ).
thf(distinct_adj_decl,type,
distinct_adj:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(foldr_decl,type,
foldr:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > TA ) > ( list @ TB ) > TA > TA ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_decl,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(case_list_decl,type,
case_list:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( list @ TA ) > TB ) > ( list @ TA ) > TB ) ).
thf(hd_decl,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(tl_decl,type,
tl:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(listrelp_decl,type,
listrelp:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o ) ).
thf(map_tailrec_rev_decl,type,
map_tailrec_rev:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(maps_decl,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TB > ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( ( list @ TA ) > TA > $o ) ).
thf(lexordp_eq_decl,type,
lexordp_eq:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(ord_lexordp_decl,type,
ord_lexordp:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(ord_lexordp_eq_decl,type,
ord_lexordp_eq:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(product_lists_decl,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(remdups_adj_decl,type,
remdups_adj:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(rotate1_decl,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(shuffles_decl,type,
shuffles:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( set @ ( list @ TA ) ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(subseqs_decl,type,
subseqs:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(successively_decl,type,
successively:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > $o ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member2_decl,type,
member2:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_decl,type,
f: nat > a ).
thf(x_decl,type,
x: a ).
thf(xs_decl,type,
xs: list @ a ).
thf(147,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( list_ord @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( list_ord @ TA @ A @ B )
& ( ( C
= ( nil @ TA ) )
| ( ( list_ord @ TA @ A @ C )
& ( ( B
= ( nil @ TA ) )
| ( A @ ( last @ TA @ B ) @ ( hd @ TA @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_list__ord__append) ).
thf(809,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( list_ord @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( list_ord @ TA @ A @ B )
& ( ( C
= ( nil @ TA ) )
| ( ( list_ord @ TA @ A @ C )
& ( ( B
= ( nil @ TA ) )
| ( A @ ( last @ TA @ B ) @ ( hd @ TA @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(169,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_209_list_Osplit__sel) ).
thf(893,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)],[169]) ).
thf(200,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_lexordp__eq__simps_I2_J) ).
thf(1083,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA,B: list @ TC] :
( ( map2 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ B )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_map2_Osimps_I1_J) ).
thf(1179,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA,B: list @ TC] :
( ( map2 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ B )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(115,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( B
= ( nil @ TA ) )
=> ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( shuffles @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Nil__in__shufflesI) ).
thf(666,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( B
= ( nil @ TA ) )
=> ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( shuffles @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( B
= ( nil @ TA ) )
| ( ( last @ TA @ A )
!= ( hd @ TA @ B ) ) )
=> ( ( remdups_adj @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( remdups_adj @ TA @ A ) @ ( remdups_adj @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_remdups__adj__append_H) ).
thf(479,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( B
= ( nil @ TA ) )
| ( ( last @ TA @ A )
!= ( hd @ TA @ B ) ) )
=> ( ( remdups_adj @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( remdups_adj @ TA @ A ) @ ( remdups_adj @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(205,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: TA] :
( ( list_ord @ TA @ A @ B )
=> ( ( A @ C @ ( hd @ TA @ B ) )
=> ( list_ord @ TA @ A @ ( cons @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_list__ord__Cons__imp) ).
thf(1105,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: TA] :
( ( list_ord @ TA @ A @ B )
=> ( ( A @ C @ ( hd @ TA @ B ) )
=> ( list_ord @ TA @ A @ ( cons @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] : ( member2 @ ( list @ TA ) @ ( splice @ TA @ A @ B ) @ ( shuffles @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_splice__in__shuffles) ).
thf(333,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] : ( member2 @ ( list @ TA ) @ ( splice @ TA @ A @ B ) @ ( shuffles @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(193,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( shuffles @ TA @ B @ ( cons @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Cons__in__shuffles__rightI) ).
thf(1031,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( shuffles @ TA @ B @ ( cons @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_lexordp__into__lexordp__eq) ).
thf(408,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(84,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_109_butlast__snoc) ).
thf(523,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)],[84]) ).
thf(3,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4) ).
thf(276,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(185,axiom,
! [TA: $tType,A: TA > TA > $o] : ( successively @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_successively_Osimps_I1_J) ).
thf(994,plain,
! [TA: $tType,A: TA > TA > $o] : ( successively @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(72,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_shuffles_Oinduct) ).
thf(449,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ ( cons @ TA @ F @ G ) )
=> ( ( A @ ( cons @ TA @ D @ E ) @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TC,B: TC > TA > TB,C: TA,D: list @ TA] :
( ( A
!= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( cons @ TB @ ( B @ ( hd @ TC @ A ) @ C ) @ ( map2 @ TC @ TA @ TB @ B @ ( tl @ TC @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_map2__Cons__not__empty) ).
thf(597,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TC,B: TC > TA > TB,C: TA,D: list @ TA] :
( ( A
!= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( cons @ TB @ ( B @ ( hd @ TC @ A ) @ C ) @ ( map2 @ TC @ TA @ TB @ B @ ( tl @ TC @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(160,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_30_bind__simps_I1_J) ).
thf(861,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)],[160]) ).
thf(224,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_115_last__appendR) ).
thf(1173,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)],[224]) ).
thf(48,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(385,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member2 @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(214,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_77_self__append__conv2) ).
thf(1137,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)],[214]) ).
thf(89,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_100_Cons__eq__append__conv) ).
thf(550,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)],[89]) ).
thf(234,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_130_maps__simps_I2_J) ).
thf(1233,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)],[234]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_append__eq__Cons) ).
thf(698,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) @ B )
= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(31,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
| ( ord_lexordp_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lexordp__eq__linear) ).
thf(340,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
| ( ord_lexordp_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: list @ TC,D: list @ TA] :
( ( map2 @ TC @ TA @ TB @ A @ ( cons @ TC @ B @ C ) @ D )
= ( cons @ TB @ ( A @ B @ ( hd @ TA @ D ) ) @ ( map2 @ TC @ TA @ TB @ A @ C @ ( tl @ TA @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_map2_Osimps_I2_J) ).
thf(670,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: list @ TC,D: list @ TA] :
( ( map2 @ TC @ TA @ TB @ A @ ( cons @ TC @ B @ C ) @ D )
= ( cons @ TB @ ( A @ B @ ( hd @ TA @ D ) ) @ ( map2 @ TC @ TA @ TB @ A @ C @ ( tl @ TA @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(231,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_list_Osel_I3_J) ).
thf(1196,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( tl @ TA @ ( cons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( B
= ( append @ TA @ A @ ( cons @ TA @ C @ D ) ) )
| ? [C: list @ TA,D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
& ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ F ) ) )
& ( B
= ( append @ TA @ C @ ( cons @ TA @ E @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_lexordp__iff) ).
thf(1243,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( B
= ( append @ TA @ A @ ( cons @ TA @ C @ D ) ) )
| ? [C: list @ TA,D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
& ( A
= ( append @ TA @ C @ ( cons @ TA @ D @ F ) ) )
& ( B
= ( append @ TA @ C @ ( cons @ TA @ E @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(60,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_distinct__adj__appendD2) ).
thf(417,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(166,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_185_tl__append2) ).
thf(885,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)],[166]) ).
thf(10,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ( list_asc @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_list__strict__asc__imp__list__asc) ).
thf(288,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ( list_asc @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(251,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_lexordp_Oinducts) ).
thf(1359,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(256,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_231_remdups__adj__append) ).
thf(1386,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)],[256]) ).
thf(14,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_73_append_Oassoc) ).
thf(301,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)],[14]) ).
thf(22,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_71_append__same__eq) ).
thf(320,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)],[22]) ).
thf(68,axiom,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_butlast_Osimps_I1_J) ).
thf(436,plain,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(44,axiom,
! [TA: $tType,A: list @ TA] :
( ( butlast @ TA @ ( tl @ TA @ A ) )
= ( tl @ TA @ ( butlast @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_butlast__tl) ).
thf(372,plain,
! [TA: $tType,A: list @ TA] :
( ( butlast @ TA @ ( tl @ TA @ A ) )
= ( tl @ TA @ ( butlast @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(177,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp @ TA @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_lexordp_Ocases) ).
thf(917,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp @ TA @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(33,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_neq__if__length__neq) ).
thf(344,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(212,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( successively @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_successively_Osimps_I2_J) ).
thf(1132,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] : ( successively @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(75,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_append_Oleft__neutral) ).
thf(460,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(92,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_splice__Nil2) ).
thf(559,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(255,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_167_hd__append) ).
thf(1379,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)],[255]) ).
thf(164,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_54_listrelp_OCons) ).
thf(881,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)],[164]) ).
thf(20,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: list @ TA] :
~ ( ord_lexordp @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_lexordp__irreflexive_H) ).
thf(316,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: list @ TA] :
~ ( ord_lexordp @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(150,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o] : ( list_ord @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_list__ord_Osimps_I2_J) ).
thf(817,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o] : ( list_ord @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(172,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_59_ord_Olexordp__eq_Osimps) ).
thf(902,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)],[172]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(284,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(140,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_append__Nil) ).
thf(770,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(209,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_168_longest__common__prefix) ).
thf(1115,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)],[209]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
& ~ ( ord_lexordp_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_lexordp__conv__lexordp__eq) ).
thf(325,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
& ~ ( ord_lexordp_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(260,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp @ TA @ C @ D )
=> ( ord_lexordp @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_lexordp_OCons__eq) ).
thf(1415,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp @ TA @ C @ D )
=> ( ord_lexordp @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: list @ TC,D: TA,E: list @ TA] :
( ( map2 @ TC @ TA @ TB @ A @ ( cons @ TC @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( cons @ TB @ ( A @ B @ D ) @ ( map2 @ TC @ TA @ TB @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_map2__Cons__Cons) ).
thf(1465,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: list @ TC,D: TA,E: list @ TA] :
( ( map2 @ TC @ TA @ TB @ A @ ( cons @ TC @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( cons @ TB @ ( A @ B @ D ) @ ( map2 @ TC @ TA @ TB @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(137,axiom,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( concat @ TA @ ( cons @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ A @ ( concat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_concat_Osimps_I2_J) ).
thf(756,plain,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( concat @ TA @ ( cons @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ A @ ( concat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA] : ( ord_lexordp @ TA @ ( nil @ TA ) @ ( cons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_lexordp_ONil) ).
thf(591,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA] : ( ord_lexordp @ TA @ ( nil @ TA ) @ ( cons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA,B: list @ TC] :
( ( map2 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ B )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_map2__Nil) ).
thf(1109,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA,B: list @ TC] :
( ( map2 @ TB @ TC @ TA @ A @ ( nil @ TB ) @ B )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_append__eq__append__conv) ).
thf(376,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(109,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 ) )
=> ( C
!= ( cons @ TA @ D @ ( splice @ TA @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_splice_Oelims) ).
thf(623,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 ) )
=> ( C
!= ( cons @ TA @ D @ ( splice @ TA @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(153,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA] :
( ( listIn521021761append @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( append @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_i__append__assoc) ).
thf(834,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA] :
( ( listIn521021761append @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( append @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(219,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ord_less @ TA @ D @ F )
=> ( C @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( ord_lexordp @ TA @ E @ F )
=> ( ( C @ E @ F )
=> ( C @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ D @ F ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_lexordp__induct) ).
thf(1151,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ! [D: TA,E: list @ TA] : ( C @ ( nil @ TA ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ord_less @ TA @ D @ F )
=> ( C @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: TA,E: list @ TA,F: list @ TA] :
( ( ord_lexordp @ TA @ E @ F )
=> ( ( C @ E @ F )
=> ( C @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ D @ F ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(34,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_87_append__eq__append__conv2) ).
thf(348,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)],[34]) ).
thf(146,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_6_neq__Nil__conv) ).
thf(806,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)],[146]) ).
thf(36,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] : ( lexordp_eq @ TA @ A @ B @ ( append @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord_Olexordp__eq__pref) ).
thf(353,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] : ( lexordp_eq @ TA @ A @ B @ ( append @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(173,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_206_list_Oexhaust__sel) ).
thf(905,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)],[173]) ).
thf(222,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_133_empty__Shift) ).
thf(1169,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)],[222]) ).
thf(254,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_distinct__adj__ConsD) ).
thf(1377,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(163,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_122_last__ConsL) ).
thf(877,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)],[163]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_list_Osel_I1_J) ).
thf(734,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( hd @ TA @ ( cons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(52,axiom,
! [TA: $tType,A: list @ TA] :
( ( last @ TA @ ( remdups_adj @ TA @ A ) )
= ( last @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_last__remdups__adj) ).
thf(396,plain,
! [TA: $tType,A: list @ TA] :
( ( last @ TA @ ( remdups_adj @ TA @ A ) )
= ( last @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(187,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_125_longest__common__suffix) ).
thf(998,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)],[187]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_not__Cons__self2) ).
thf(1345,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( append @ TA @ C @ A ) @ ( append @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_lexordp__append__leftI) ).
thf(307,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( append @ TA @ C @ A ) @ ( append @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( rotate1 @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_length__rotate1) ).
thf(292,plain,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( rotate1 @ TA @ A ) )
= ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,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_22_remdups__adj_Ocases) ).
thf(439,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)],[69]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_lexordp__eq__simps_I1_J) ).
thf(529,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(232,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_lexordp__eq_Ocases) ).
thf(1199,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
=> ! [F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ( ~ ( ord_less @ TA @ C @ D )
=> ( ~ ( ord_less @ TA @ D @ C )
=> ~ ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(247,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_242_remdups__adj_Osimps_I3_J) ).
thf(1338,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)],[247]) ).
thf(88,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_20_remdups__adj_Oinduct) ).
thf(534,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)],[88]) ).
thf(195,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( splice @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_split__Nil__iff) ).
thf(1047,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( splice @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(210,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_121_last_Osimps) ).
thf(1123,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)],[210]) ).
thf(149,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_51_ord_Olexordp__eq_OCons) ).
thf(815,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)],[149]) ).
thf(132,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_199_Nil__tl) ).
thf(729,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)],[132]) ).
thf(40,axiom,
! [TA: $tType,A: list @ TA] :
( ( hd @ TA @ ( remdups_adj @ TA @ A ) )
= ( hd @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_hd__remdups__adj) ).
thf(361,plain,
! [TA: $tType,A: list @ TA] :
( ( hd @ TA @ ( remdups_adj @ TA @ A ) )
= ( hd @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(220,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_strict__sorted_Ocases) ).
thf(1159,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(120,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B = C ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lexordp__eq_Osimps) ).
thf(682,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B = C ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp_eq @ TA @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(258,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_132_shift__def) ).
thf(1392,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)],[258]) ).
thf(127,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( shuffles @ TA @ ( cons @ TA @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Cons__in__shuffles__leftI) ).
thf(710,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( member2 @ ( list @ TA ) @ ( cons @ TA @ D @ A ) @ ( shuffles @ TA @ ( cons @ TA @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(190,axiom,
! [TA: $tType,A: TA] : ( distinct_adj @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_distinct__adj__singleton) ).
thf(1012,plain,
! [TA: $tType,A: TA] : ( distinct_adj @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(98,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( successively @ TA @ A @ B )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_successively_Oelims_I2_J) ).
thf(578,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( successively @ TA @ A @ B )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] :
( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(216,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ( ( hd @ ( list @ TA ) @ A )
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( concat @ TA @ A ) )
= ( hd @ TA @ ( hd @ ( list @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_hd__concat) ).
thf(1143,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ( ( hd @ ( list @ TA ) @ A )
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( concat @ TA @ A ) )
= ( hd @ TA @ ( hd @ ( list @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(188,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_list_Odistinct_I1_J) ).
thf(1006,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(49,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ~ ( ord_lexordp @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_lexordp__antisym) ).
thf(388,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ~ ( ord_lexordp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(102,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( B
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_length__greater__imp__not__empty) ).
thf(593,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( B
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(62,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ ( list @ TA )] :
( ( concat @ TA @ ( append @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ ( concat @ TA @ A ) @ ( concat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_concat__append) ).
thf(420,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ ( list @ TA )] :
( ( concat @ TA @ ( append @ ( list @ TA ) @ A @ B ) )
= ( append @ TA @ ( concat @ TA @ A ) @ ( concat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(25,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6) ).
thf(328,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(243,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_29_ord_Olexordp__eq__simps_I3_J) ).
thf(1329,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)],[243]) ).
thf(192,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_101_rev__exhaust) ).
thf(1028,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)],[192]) ).
thf(227,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA] : ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_list__ord_Osimps_I3_J) ).
thf(1182,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA] : ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(269,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_3_list_OdiscI) ).
thf(1461,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)],[269]) ).
thf(85,axiom,
! [TA: $tType,A: nat > TA] :
( ( listIn521021761append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_i__append__Nil) ).
thf(526,plain,
! [TA: $tType,A: nat > TA] :
( ( listIn521021761append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,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_124_last__append) ).
thf(637,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)],[110]) ).
thf(79,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_111_SuccI) ).
thf(489,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)],[79]) ).
thf(119,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_57_map__tailrec__rev_Osimps_I1_J) ).
thf(679,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)],[119]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TC,B: TC > TA > TB,C: TA,D: list @ TA] :
( ( ( A
= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( nil @ TB ) ) )
& ( ( A
!= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( cons @ TB @ ( B @ ( hd @ TC @ A ) @ C ) @ ( map2 @ TC @ TA @ TB @ B @ ( tl @ TC @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_map2__Cons__if) ).
thf(837,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TC,B: TC > TA > TB,C: TA,D: list @ TA] :
( ( ( A
= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( nil @ TB ) ) )
& ( ( A
!= ( nil @ TC ) )
=> ( ( map2 @ TC @ TA @ TB @ B @ A @ ( cons @ TA @ C @ D ) )
= ( cons @ TB @ ( B @ ( hd @ TC @ A ) @ C ) @ ( map2 @ TC @ TA @ TB @ B @ ( tl @ TC @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(51,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(393,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member2 @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ! [D: list @ TA] : ( C @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp_eq @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lexordp__eq_Oinducts) ).
thf(647,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ! [D: list @ TA] : ( C @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( ord_less @ TA @ D @ E )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) )
=> ( ! [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ~ ( ord_less @ TA @ D @ E )
=> ( ~ ( ord_less @ TA @ E @ D )
=> ( ( ord_lexordp_eq @ TA @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ TA @ D @ F ) @ ( cons @ TA @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: TB > TC > TA,D: TB,E: TC] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( map2 @ TB @ TC @ TA @ C @ ( append @ TB @ A @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TC @ B @ ( cons @ TC @ E @ ( nil @ TC ) ) ) )
= ( append @ TA @ ( map2 @ TB @ TC @ TA @ C @ A @ B ) @ ( cons @ TA @ ( C @ D @ E ) @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_map2__snoc__snoc) ).
thf(701,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: TB > TC > TA,D: TB,E: TC] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( map2 @ TB @ TC @ TA @ C @ ( append @ TB @ A @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TC @ B @ ( cons @ TC @ E @ ( nil @ TC ) ) ) )
= ( append @ TA @ ( map2 @ TB @ TC @ TA @ C @ A @ B ) @ ( cons @ TA @ ( C @ D @ E ) @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(239,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_80_append__self__conv) ).
thf(1249,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)],[239]) ).
thf(242,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [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_58_ord_Olexordp__eq_Ocases) ).
thf(1297,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( B
!= ( nil @ TA ) )
=> ( ! [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)],[242]) ).
thf(268,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_5_list_Oinducts) ).
thf(1451,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)],[268]) ).
thf(233,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA] : ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_list__ord__one) ).
thf(1231,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA] : ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(175,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_rotate1__is__Nil__conv) ).
thf(911,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(238,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_69_bind__simps_I2_J) ).
thf(1246,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)],[238]) ).
thf(196,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_53_ord_Olexordp__eq_ONil) ).
thf(1050,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)],[196]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > TB,B: TA] :
( ( arg_min_list @ TA @ TB @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_arg__min__list_Osimps_I1_J) ).
thf(457,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: TA > TB,B: TA] :
( ( arg_min_list @ TA @ TB @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(245,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_123_last__ConsR) ).
thf(1333,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)],[245]) ).
thf(201,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_member__rec_I2_J) ).
thf(1086,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ ( nil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(39,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(360,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(18,axiom,
! [TA: $tType] :
( ( shuffles @ TA )
= ( ^ [A: list @ TA,B: list @ TA] : ( shuffles @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_shuffles__commutes) ).
thf(311,plain,
! [TA: $tType] :
( ( shuffles @ TA )
= ( ^ [A: list @ TA,B: list @ TA] : ( shuffles @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(229,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_31_listrelp_Oinducts) ).
thf(1187,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)],[229]) ).
thf(179,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_129_butlast__append) ).
thf(953,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)],[179]) ).
thf(141,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA,C: list @ TA] :
( ( list_ord @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( C
= ( nil @ TA ) )
| ( ( A @ B @ ( hd @ TA @ C ) )
& ( list_ord @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_list__ord__Cons) ).
thf(773,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA,C: list @ TA] :
( ( list_ord @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( C
= ( nil @ TA ) )
| ( ( A @ B @ ( hd @ TA @ C ) )
& ( list_ord @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_lexordp__eq_OCons) ).
thf(586,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(114,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_90_Cons__eq__appendI) ).
thf(662,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)],[114]) ).
thf(167,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).
thf(888,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(182,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__Nil) ).
thf(965,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(108,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA] :
( ~ ( list_ord @ TA @ A @ B )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( list_ord @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_list__ord_Oelims_I3_J) ).
thf(618,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA] :
( ~ ( list_ord @ TA @ A @ B )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( list_ord @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(5,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(279,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)],[5]) ).
thf(253,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( successively @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( successively @ TA @ A @ B )
& ( successively @ TA @ A @ C )
& ( ( B
= ( nil @ TA ) )
| ( C
= ( nil @ TA ) )
| ( A @ ( last @ TA @ B ) @ ( hd @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_successively__append__iff) ).
thf(1374,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( successively @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( successively @ TA @ A @ B )
& ( successively @ TA @ A @ C )
& ( ( B
= ( nil @ TA ) )
| ( C
= ( nil @ TA ) )
| ( A @ ( last @ TA @ B ) @ ( hd @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(45,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_8) ).
thf(375,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(217,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_186_hd__Cons__tl) ).
thf(1146,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)],[217]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ord_lexordp @ TA @ B @ C )
=> ( ord_lexordp @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_lexordp__trans) ).
thf(430,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ord_lexordp @ TA @ B @ C )
=> ( ord_lexordp @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(151,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_108_rotate1_Osimps_I2_J) ).
thf(819,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)],[151]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_lexordp_OCons) ).
thf(562,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_lexordp__eq__antisym) ).
thf(423,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,axiom,
! [TA: $tType] :
( ( distinct_adj @ TA )
= ( ^ [A: list @ TA] :
( ( remdups_adj @ TA @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_distinct__adj__altdef) ).
thf(402,plain,
! [TA: $tType] :
( ( distinct_adj @ TA )
= ( ^ [A: list @ TA] :
( ( remdups_adj @ TA @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(133,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_39_ord_Olexordp__eq__simps_I1_J) ).
thf(732,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)],[133]) ).
thf(257,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_append__Nil2) ).
thf(1389,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(286,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(59,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_88_append__eq__appendI) ).
thf(413,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)],[59]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( A = B )
| ( ord_lexordp @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_lexordp__eq__conv__lexord) ).
thf(382,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_lexordp_eq @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( A = B )
| ( ord_lexordp @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(96,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_198_tl__Nil) ).
thf(572,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)],[96]) ).
thf(252,axiom,
! [TA: $tType] :
( ( concat @ TA )
= ( ^ [A: list @ ( list @ TA )] : ( foldr @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA ) @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_concat__conv__foldr) ).
thf(1371,plain,
! [TA: $tType] :
( ( concat @ TA )
= ( ^ [A: list @ ( list @ TA )] : ( foldr @ ( list @ TA ) @ ( list @ TA ) @ ( append @ TA ) @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(206,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_55_listrelp_ONil) ).
thf(1107,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)],[206]) ).
thf(236,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_successively_Oinduct) ).
thf(1239,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_list__induct3) ).
thf(1092,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: list @ TB,B: list @ TC,C: list @ TA,D: ( list @ TB ) > ( list @ TC ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TC ) @ B ) )
=> ( ( ( size_size @ ( list @ TC ) @ B )
= ( size_size @ ( list @ TA ) @ C ) )
=> ( ( D @ ( nil @ TB ) @ ( nil @ TC ) @ ( nil @ TA ) )
=> ( ! [E: TB,F: list @ TB,G: TC,H: list @ TC,I: TA,J: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ F )
= ( size_size @ ( list @ TC ) @ H ) )
=> ( ( ( size_size @ ( list @ TC ) @ H )
= ( size_size @ ( list @ TA ) @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons @ TB @ E @ F ) @ ( cons @ TC @ G @ H ) @ ( cons @ TA @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA] :
~ ( ord_less @ TA @ B @ B )
=> ~ ( ord_lexordp @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_lexordp__irreflexive) ).
thf(335,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA] :
~ ( ord_less @ TA @ B @ B )
=> ~ ( ord_lexordp @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(125,axiom,
! [TA: $tType] :
( ( concat @ TA @ ( nil @ ( list @ TA ) ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_concat_Osimps_I1_J) ).
thf(704,plain,
! [TA: $tType] :
( ( concat @ TA @ ( nil @ ( list @ TA ) ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(250,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_99_append__eq__Cons__conv) ).
thf(1356,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)],[250]) ).
thf(1,conjecture,
( ( listIn521021761append @ a @ ( cons @ a @ x @ xs ) @ f )
= ( listIn521021761append @ a @ ( cons @ a @ x @ ( nil @ a ) ) @ ( listIn521021761append @ a @ xs @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( listIn521021761append @ a @ ( cons @ a @ x @ xs ) @ f )
!= ( listIn521021761append @ a @ ( cons @ a @ x @ ( nil @ a ) ) @ ( listIn521021761append @ a @ xs @ f ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(274,plain,
( ( listIn521021761append @ a @ ( cons @ a @ x @ xs ) @ f )
!= ( listIn521021761append @ a @ ( cons @ a @ x @ ( nil @ a ) ) @ ( listIn521021761append @ a @ xs @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(419,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(186,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
~ ( ord_lexordp @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_lexordp__simps_I2_J) ).
thf(996,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
~ ( ord_lexordp @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o] : ( list_ord @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_list__ord__Nil) ).
thf(616,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o] : ( list_ord @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(264,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_117_append__butlast__last__id) ).
thf(1439,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)],[264]) ).
thf(135,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_201_last__tl) ).
thf(737,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)],[135]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lexordp__eq__refl) ).
thf(318,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(168,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: TA] :
( ( list_ord @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
= ( ( B
= ( nil @ TA ) )
| ( ( A @ ( last @ TA @ B ) @ C )
& ( list_ord @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_list__ord__snoc) ).
thf(890,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: TA] :
( ( list_ord @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
= ( ( B
= ( nil @ TA ) )
| ( ( A @ ( last @ TA @ B ) @ C )
& ( list_ord @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(272,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ B ) )
= ( ( B
= ( nil @ TA ) )
| ( ( A
!= ( hd @ TA @ B ) )
& ( distinct_adj @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_distinct__adj__Cons) ).
thf(1471,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ B ) )
= ( ( B
= ( nil @ TA ) )
| ( ( A
!= ( hd @ TA @ B ) )
& ( distinct_adj @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(81,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_239_remdups__adj_Oelims) ).
thf(494,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)],[81]) ).
thf(23,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_ord_Olexordp__eq__refl) ).
thf(323,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(218,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_lexordp__eq_ONil) ).
thf(1149,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] : ( ord_lexordp_eq @ TA @ ( nil @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(241,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_16_map__tailrec__rev_Oinduct) ).
thf(1293,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)],[241]) ).
thf(26,axiom,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( lexordp_eq @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ord_Olexordp__eq_Ocong) ).
thf(330,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA,D: list @ TA] :
( ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( list_ord @ TA @ A @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__ord_Osimps_I1_J) ).
thf(1112,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA,D: list @ TA] :
( ( list_ord @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( list_ord @ TA @ A @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(159,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_89_append__Cons) ).
thf(858,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)],[159]) ).
thf(42,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_70_same__append__eq) ).
thf(367,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)],[42]) ).
thf(221,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_126_butlast_Osimps_I2_J) ).
thf(1162,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)],[221]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( splice @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_splice_Osimps_I2_J) ).
thf(726,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( splice @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( splice @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(156,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_67_member__rec_I1_J) ).
thf(848,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)],[156]) ).
thf(83,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_210_list_Osplit__sel__asm) ).
thf(520,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)],[83]) ).
thf(53,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ C )
=> ( ord_lexordp_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_lexordp__eq__trans) ).
thf(399,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp_eq @ TA @ A @ B )
=> ( ( ord_lexordp_eq @ TA @ B @ C )
=> ( ord_lexordp_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(273,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_240_remdups__adj_Osimps_I2_J) ).
thf(1474,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)],[273]) ).
thf(143,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: $o] :
( ( ( list_ord @ TA @ A @ B )
= C )
=> ( ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( list_ord @ TA @ A @ ( cons @ TA @ E @ F ) ) ) ) ) )
=> ( ( ( B
= ( nil @ TA ) )
=> ~ C )
=> ~ ( ? [D: TA] :
( B
= ( cons @ TA @ D @ ( nil @ TA ) ) )
=> ~ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_list__ord_Oelims_I1_J) ).
thf(780,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA,C: $o] :
( ( ( list_ord @ TA @ A @ B )
= C )
=> ( ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( list_ord @ TA @ A @ ( cons @ TA @ E @ F ) ) ) ) ) )
=> ( ( ( B
= ( nil @ TA ) )
=> ~ C )
=> ~ ( ? [D: TA] :
( B
= ( cons @ TA @ D @ ( nil @ TA ) ) )
=> ~ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(165,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp_eq @ TA @ C @ D )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_lexordp__eq_OCons__eq) ).
thf(883,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ( ord_lexordp_eq @ TA @ C @ D )
=> ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ C ) @ ( cons @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(225,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_85_append1__eq__conv) ).
thf(1176,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)],[225]) ).
thf(121,axiom,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_list_Osel_I2_J) ).
thf(685,plain,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(223,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) @ ( append @ TA @ C @ ( cons @ TA @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_lexordp__append__left__rightI) ).
thf(1171,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_lexordp @ TA @ ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) @ ( append @ TA @ C @ ( cons @ TA @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(4,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_9) ).
thf(278,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(266,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_243_remdups__adj__append__two) ).
thf(1445,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)],[266]) ).
thf(157,axiom,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_remdups__adj_Osimps_I1_J) ).
thf(851,plain,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(204,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_213_list_Osimps_I4_J) ).
thf(1102,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)],[204]) ).
thf(64,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(426,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(87,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_235_remdups__adj__Cons__alt) ).
thf(531,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)],[87]) ).
thf(213,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
= ( ( ( A
= ( nil @ ( list @ TA ) ) )
=> ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TA ) ) ) )
& ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_concat__eq__append__conv) ).
thf(1134,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
= ( ( ( A
= ( nil @ ( list @ TA ) ) )
=> ( ( B
= ( nil @ TA ) )
& ( C
= ( nil @ TA ) ) ) )
& ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(148,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_32_listrelp_Osimps) ).
thf(812,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)],[148]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(342,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( A @ D @ E )
=> ( B @ D @ E ) )
=> ( ( list_ord @ TA @ A @ C )
=> ( list_ord @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_list__ord__imp) ).
thf(355,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA,E: TA] :
( ( A @ D @ E )
=> ( B @ D @ E ) )
=> ( ( list_ord @ TA @ A @ C )
=> ( list_ord @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_append_Oright__neutral) ).
thf(553,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(183,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_lexordp__simps_I3_J) ).
thf(968,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(142,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_93_eq__Nil__appendI) ).
thf(776,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)],[142]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_list__induct2) ).
thf(712,plain,
! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TB ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( C @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( ( size_size @ ( list @ TB ) @ E )
= ( size_size @ ( list @ TA ) @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(13,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_length__induct) ).
thf(295,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).
thf(282,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp @ TA @ E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_lexordp_Osimps) ).
thf(707,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_lexordp @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
( ? [C: TA,D: list @ TA] :
( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ( ord_less @ TA @ C @ D ) )
| ? [C: TA,D: TA,E: list @ TA,F: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( B
= ( cons @ TA @ D @ F ) )
& ~ ( ord_less @ TA @ C @ D )
& ~ ( ord_less @ TA @ D @ C )
& ( ord_lexordp @ TA @ E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(184,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: list @ TA] :
( ( B
= ( cons @ TA @ C @ E ) )
=> ~ ( ord_lexordp @ TA @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_lexordp__cases) ).
thf(971,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
=> ( ( ( A
= ( nil @ TA ) )
=> ! [C: TA,D: list @ TA] :
( B
!= ( cons @ TA @ C @ D ) ) )
=> ( ! [C: TA] :
( ? [D: list @ TA] :
( A
= ( cons @ TA @ C @ D ) )
=> ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ~ ( ord_less @ TA @ C @ D ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ! [E: list @ TA] :
( ( B
= ( cons @ TA @ C @ E ) )
=> ~ ( ord_lexordp @ TA @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(240,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( ( ( A = B )
=> ( C
!= ( nil @ TA ) ) )
=> ( ( ( A = C )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( A
= ( cons @ TA @ F @ G ) )
=> ( ( D = F )
=> ~ ( member2 @ ( list @ TA ) @ G @ ( shuffles @ TA @ E @ C ) ) ) ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( C
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( A
= ( cons @ TA @ F @ G ) )
=> ( ( D = F )
=> ~ ( member2 @ ( list @ TA ) @ G @ ( shuffles @ TA @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_shufflesE) ).
thf(1252,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( member2 @ ( list @ TA ) @ A @ ( shuffles @ TA @ B @ C ) )
=> ( ( ( A = B )
=> ( C
!= ( nil @ TA ) ) )
=> ( ( ( A = C )
=> ( B
!= ( nil @ TA ) ) )
=> ( ! [D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( A
= ( cons @ TA @ F @ G ) )
=> ( ( D = F )
=> ~ ( member2 @ ( list @ TA ) @ G @ ( shuffles @ TA @ E @ C ) ) ) ) )
=> ~ ! [D: TA,E: list @ TA] :
( ( C
= ( cons @ TA @ D @ E ) )
=> ! [F: TA,G: list @ TA] :
( ( A
= ( cons @ TA @ F @ G ) )
=> ( ( D = F )
=> ~ ( member2 @ ( list @ TA ) @ G @ ( shuffles @ TA @ B @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_splice_Osimps_I1_J) ).
thf(673,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA] : ( distinct_adj @ TA @ ( remdups_adj @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_distinct__adj__remdups__adj) ).
thf(331,plain,
! [TA: $tType,A: list @ TA] : ( distinct_adj @ TA @ ( remdups_adj @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_distinct__adj__appendD1) ).
thf(370,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
=> ( distinct_adj @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,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_112_SuccD) ).
thf(463,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)],[76]) ).
thf(38,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).
thf(359,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(211,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA] :
~ ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_lexordp__eq__simps_I3_J) ).
thf(1130,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA] :
~ ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(246,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_52_ord_Olexordp__eq_OCons__eq) ).
thf(1336,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)],[246]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: list @ TC,B: list @ TB,C: list @ TD,D: list @ TA,E: ( list @ TC ) > ( list @ TB ) > ( list @ TD ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TC ) @ A )
= ( size_size @ ( list @ TB ) @ B ) )
=> ( ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TD ) @ C ) )
=> ( ( ( size_size @ ( list @ TD ) @ C )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( ( E @ ( nil @ TC ) @ ( nil @ TB ) @ ( nil @ TD ) @ ( nil @ TA ) )
=> ( ! [F: TC,G: list @ TC,H: TB,I: list @ TB,J: TD,K: list @ TD,L: TA,M: list @ TA] :
( ( ( size_size @ ( list @ TC ) @ G )
= ( size_size @ ( list @ TB ) @ I ) )
=> ( ( ( size_size @ ( list @ TB ) @ I )
= ( size_size @ ( list @ TD ) @ K ) )
=> ( ( ( size_size @ ( list @ TD ) @ K )
= ( size_size @ ( list @ TA ) @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons @ TC @ F @ G ) @ ( cons @ TB @ H @ I ) @ ( cons @ TD @ J @ K ) @ ( cons @ TA @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_list__induct4) ).
thf(744,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: list @ TC,B: list @ TB,C: list @ TD,D: list @ TA,E: ( list @ TC ) > ( list @ TB ) > ( list @ TD ) > ( list @ TA ) > $o] :
( ( ( size_size @ ( list @ TC ) @ A )
= ( size_size @ ( list @ TB ) @ B ) )
=> ( ( ( size_size @ ( list @ TB ) @ B )
= ( size_size @ ( list @ TD ) @ C ) )
=> ( ( ( size_size @ ( list @ TD ) @ C )
= ( size_size @ ( list @ TA ) @ D ) )
=> ( ( E @ ( nil @ TC ) @ ( nil @ TB ) @ ( nil @ TD ) @ ( nil @ TA ) )
=> ( ! [F: TC,G: list @ TC,H: TB,I: list @ TB,J: TD,K: list @ TD,L: TA,M: list @ TA] :
( ( ( size_size @ ( list @ TC ) @ G )
= ( size_size @ ( list @ TB ) @ I ) )
=> ( ( ( size_size @ ( list @ TB ) @ I )
= ( size_size @ ( list @ TD ) @ K ) )
=> ( ( ( size_size @ ( list @ TD ) @ K )
= ( size_size @ ( list @ TA ) @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons @ TC @ F @ G ) @ ( cons @ TB @ H @ I ) @ ( cons @ TD @ J @ K ) @ ( cons @ TA @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(106,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp_eq @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_lexordp__eq__simps_I4_J) ).
thf(613,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ord_lexordp_eq @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
= ( ( ord_less @ TA @ A @ C )
| ( ~ ( ord_less @ TA @ C @ A )
& ( ord_lexordp_eq @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(104,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_38_ord_Olexordp__eq__simps_I2_J) ).
thf(600,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)],[104]) ).
thf(197,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_102_rev__induct) ).
thf(1052,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)],[197]) ).
thf(161,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_79_self__append__conv) ).
thf(864,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)],[161]) ).
thf(215,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_75_append__is__Nil__conv) ).
thf(1140,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)],[215]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) )
=> ( ! [D: TA] :
~ ( ord_less @ TA @ D @ D )
=> ( ord_lexordp @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lexordp__append__leftD) ).
thf(314,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ord_lexordp @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) )
=> ( ! [D: TA] :
~ ( ord_less @ TA @ D @ D )
=> ( ord_lexordp @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,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_155_hd__append2) ).
thf(446,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)],[71]) ).
thf(77,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_98_rev__nonempty__induct) ).
thf(465,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)],[77]) ).
thf(91,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( shuffles @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Nil__in__shuffles) ).
thf(556,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( member2 @ ( list @ TA ) @ ( nil @ TA ) @ ( shuffles @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(122,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [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_14_strict__sorted_Oinduct) ).
thf(688,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [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)],[122]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA] :
( ( list_ord @ TA @ A @ B )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( list_ord @ TA @ A @ ( cons @ TA @ D @ E ) ) ) )
=> ( ( B
!= ( nil @ TA ) )
=> ~ ! [C: TA] :
( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_list__ord_Oelims_I2_J) ).
thf(759,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA > TA > $o,B: list @ TA] :
( ( list_ord @ TA @ A @ B )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( list_ord @ TA @ A @ ( cons @ TA @ D @ E ) ) ) )
=> ( ( B
!= ( nil @ TA ) )
=> ~ ! [C: TA] :
( B
!= ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(267,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ord_lexordp @ TA @ B @ ( append @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lexordp__append__rightI) ).
thf(1448,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ord_lexordp @ TA @ B @ ( append @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_list__ord_Oinduct) ).
thf(844,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(100,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_37_ord_Olexordp__eq__simps_I4_J) ).
thf(588,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)],[100]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: list @ TA,C: list @ TB] :
( ( ( map2 @ TA @ TB @ TC @ A @ B @ C )
= ( nil @ TC ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_map2__empty__conv) ).
thf(896,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: list @ TA,C: list @ TB] :
( ( ( map2 @ TA @ TB @ TC @ A @ B @ C )
= ( nil @ TC ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(15,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_72_append__assoc) ).
thf(304,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)],[15]) ).
thf(198,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( member2 @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( shuffles @ TA @ C @ D ) )
= ( ( ( C
!= ( nil @ TA ) )
& ( ( hd @ TA @ C )
= A )
& ( member2 @ ( list @ TA ) @ B @ ( shuffles @ TA @ ( tl @ TA @ C ) @ D ) ) )
| ( ( D
!= ( nil @ TA ) )
& ( ( hd @ TA @ D )
= A )
& ( member2 @ ( list @ TA ) @ B @ ( shuffles @ TA @ C @ ( tl @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_Cons__in__shuffles__iff) ).
thf(1062,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( member2 @ ( list @ TA ) @ ( cons @ TA @ A @ B ) @ ( shuffles @ TA @ C @ D ) )
= ( ( ( C
!= ( nil @ TA ) )
& ( ( hd @ TA @ C )
= A )
& ( member2 @ ( list @ TA ) @ B @ ( shuffles @ TA @ ( tl @ TA @ C ) @ D ) ) )
| ( ( D
!= ( nil @ TA ) )
& ( ( hd @ TA @ D )
= A )
& ( member2 @ ( list @ TA ) @ B @ ( shuffles @ TA @ C @ ( tl @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] : ( ord_lexordp_eq @ TA @ A @ ( append @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_lexordp__eq__pref) ).
thf(351,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA,B: list @ TA] : ( ord_lexordp_eq @ TA @ A @ ( append @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( list_strict_asc @ TA )
= ( list_ord @ TA @ ( ord_less @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_list__strict__asc__def) ).
thf(390,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( list_strict_asc @ TA )
= ( list_ord @ TA @ ( ord_less @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(54,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(401,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(181,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_147_ShiftD) ).
thf(963,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)],[181]) ).
thf(82,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_212_list_Osimps_I5_J) ).
thf(517,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)],[82]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: list @ TA,C: list @ TB] :
( ( ( map2 @ TA @ TB @ TC @ A @ B @ C )
!= ( nil @ TC ) )
= ( B
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_map2__not__empty__conv) ).
thf(568,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: list @ TA,C: list @ TB] :
( ( ( map2 @ TA @ TB @ TC @ A @ B @ C )
!= ( nil @ TC ) )
= ( B
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(230,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_56_map__tailrec__rev_Osimps_I2_J) ).
thf(1193,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)],[230]) ).
thf(171,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ( ord_lexordp @ TA @ ( nil @ TA ) @ A )
= ( A
!= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_lexordp__simps_I1_J) ).
thf(899,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ( ord_lexordp @ TA @ ( nil @ TA ) @ A )
= ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(265,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_min__list_Ocases) ).
thf(1442,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: list @ TA] :
( ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) )
=> ( A
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(144,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_1_list_Oinject) ).
thf(800,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)],[144]) ).
thf(11,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5) ).
thf(290,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(176,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA] :
( ( successively @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively @ TA @ A @ ( cons @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_successively_Osimps_I3_J) ).
thf(914,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA] :
( ( successively @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively @ TA @ A @ ( cons @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(249,axiom,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
=> ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_concat__eq__appendD) ).
thf(1348,plain,
! [TA: $tType,A: list @ ( list @ TA ),B: list @ TA,C: list @ TA] :
( ( ( concat @ TA @ A )
= ( append @ TA @ B @ C ) )
=> ( ( A
!= ( nil @ ( list @ TA ) ) )
=> ? [D: list @ ( list @ TA ),E: list @ TA,F: list @ TA,G: list @ ( list @ TA )] :
( ( A
= ( append @ ( list @ TA ) @ D @ ( cons @ ( list @ TA ) @ ( append @ TA @ E @ F ) @ G ) ) )
& ( B
= ( append @ TA @ ( concat @ TA @ D ) @ E ) )
& ( C
= ( append @ TA @ F @ ( concat @ TA @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(67,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_7_list__induct2_H) ).
thf(432,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)],[67]) ).
thf(58,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(410,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(178,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_211_list_Ocase__eq__if) ).
thf(950,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)],[178]) ).
thf(259,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: $o] :
( ( ( successively @ TA @ A @ B )
= C )
=> ( ( ( B
= ( nil @ TA ) )
=> ~ C )
=> ( ( ? [D: TA] :
( B
= ( cons @ TA @ D @ ( nil @ TA ) ) )
=> ~ C )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively @ TA @ A @ ( cons @ TA @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_successively_Oelims_I1_J) ).
thf(1395,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: $o] :
( ( ( successively @ TA @ A @ B )
= C )
=> ( ( ( B
= ( nil @ TA ) )
=> ~ C )
=> ( ( ? [D: TA] :
( B
= ( cons @ TA @ D @ ( nil @ TA ) ) )
=> ~ C )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively @ TA @ A @ ( cons @ TA @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(56,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(405,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(158,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_114_last__appendL) ).
thf(854,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)],[158]) ).
thf(162,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_200_list_Oexpand) ).
thf(867,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)],[162]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_min__list_Oinduct) ).
thf(603,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: TA,D: list @ TA] :
( ! [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
=> ( A @ D ) )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( ( A @ ( nil @ TA ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_arg__min__list_Oinduct) ).
thf(564,plain,
! [TA: $tType,TB: $tType] :
( ( linorder @ TB )
=> ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
=> ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
( ( A @ D @ ( cons @ TA @ F @ G ) )
=> ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
=> ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(263,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
= ( ( distinct_adj @ TA @ A )
& ( distinct_adj @ TA @ B )
& ( ( A
= ( nil @ TA ) )
| ( B
= ( nil @ TA ) )
| ( ( last @ TA @ A )
!= ( hd @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_distinct__adj__append__iff) ).
thf(1436,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( distinct_adj @ TA @ ( append @ TA @ A @ B ) )
= ( ( distinct_adj @ TA @ A )
& ( distinct_adj @ TA @ B )
& ( ( A
= ( nil @ TA ) )
| ( B
= ( nil @ TA ) )
| ( ( last @ TA @ A )
!= ( hd @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(139,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_61_product__lists_Osimps_I1_J) ).
thf(767,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)],[139]) ).
thf(194,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] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_induct__list012) ).
thf(1033,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] :
( ( A @ E )
=> ( ( A @ ( cons @ TA @ D @ E ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(180,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_182_rotate1__hd__tl) ).
thf(960,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)],[180]) ).
thf(199,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_33_listrelp_Ocases) ).
thf(1065,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)],[199]) ).
thf(129,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_23_transpose_Ocases) ).
thf(720,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)],[129]) ).
thf(7,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(283,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(235,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_106_maps__simps_I1_J) ).
thf(1236,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)],[235]) ).
thf(97,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_187_list_Ocollapse) ).
thf(575,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)],[97]) ).
thf(65,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Ex__list__of__length) ).
thf(427,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(111,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_119_snoc__eq__iff__butlast) ).
thf(644,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)],[111]) ).
thf(174,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_76_Nil__is__append__conv) ).
thf(908,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)],[174]) ).
thf(130,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_4_list_Oexhaust) ).
thf(723,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)],[130]) ).
thf(152,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_60_ord_Olexordp__eq_Oinducts) ).
thf(822,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)],[152]) ).
thf(262,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ~ ( successively @ TA @ A @ B )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_successively_Oelims_I3_J) ).
thf(1431,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ~ ( successively @ TA @ A @ B )
=> ~ ! [C: TA,D: TA,E: list @ TA] :
( ( B
= ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively @ TA @ A @ ( cons @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(70,axiom,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_sorted__wrt_Oinduct) ).
thf(442,plain,
! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
=> ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
( ( A @ D @ F )
=> ( A @ D @ ( cons @ TA @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(244,axiom,
! [TA: $tType] : ( distinct_adj @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_distinct__adj__Nil) ).
thf(1331,plain,
! [TA: $tType] : ( distinct_adj @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(145,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_remdups__adj__Nil__iff) ).
thf(803,plain,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(30,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
| ( A = B )
| ( ord_lexordp @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_lexordp__linear) ).
thf(337,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: list @ TA,B: list @ TA] :
( ( ord_lexordp @ TA @ A @ B )
| ( A = B )
| ( ord_lexordp @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(189,axiom,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_subseqs_Osimps_I1_J) ).
thf(1009,plain,
! [TA: $tType] :
( ( subseqs @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(228,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_78_append__self__conv2) ).
thf(1184,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)],[228]) ).
thf(118,axiom,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_distinct__adj__Cons__Cons) ).
thf(676,plain,
! [TA: $tType,A: TA,B: TA,C: list @ TA] :
( ( distinct_adj @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj @ TA @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(271,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_134_Succ__Shift) ).
thf(1468,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)],[271]) ).
thf(73,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_110_last__snoc) ).
thf(454,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)],[73]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: list @ TB,C: list @ TB,D: TA] :
( ( foldr @ TB @ TA @ A @ ( append @ TB @ B @ C ) @ D )
= ( foldr @ TB @ TA @ A @ B @ ( foldr @ TB @ TA @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_foldr__append) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: TB > TA > TA,B: list @ TB,C: list @ TB,D: TA] :
( ( foldr @ TB @ TA @ A @ ( append @ TB @ B @ C ) @ D )
= ( foldr @ TB @ TA @ A @ B @ ( foldr @ TB @ TA @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( successively @ TA @ A @ B )
=> ( successively @ TA @ A @ ( remdups_adj @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_successively__remdups__adjI) ).
thf(309,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( successively @ TA @ A @ B )
=> ( successively @ TA @ A @ ( remdups_adj @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(113,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
( ( successively @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( C
= ( nil @ TA ) )
| ( ( A @ B @ ( hd @ TA @ C ) )
& ( successively @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_successively__Cons) ).
thf(659,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
( ( successively @ TA @ A @ ( cons @ TA @ B @ C ) )
= ( ( C
= ( nil @ TA ) )
| ( ( A @ B @ ( hd @ TA @ C ) )
& ( successively @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(80,axiom,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_rotate1_Osimps_I1_J) ).
thf(491,plain,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(202,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,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_splice_Oinduct) ).
thf(1088,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,F: list @ TA] :
( ( A @ F @ E )
=> ( A @ ( cons @ TA @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(191,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_27_map__tailrec__rev_Oelims) ).
thf(1014,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)],[191]) ).
thf(261,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_17_list__nonempty__induct) ).
thf(1417,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)],[261]) ).
thf(1477,plain,
$false,
inference(e,[status(thm)],[809,893,1083,1179,666,479,1105,333,1031,408,523,276,994,449,597,861,1173,385,1137,550,1233,698,340,670,1196,1243,417,885,288,1359,1386,301,320,436,372,917,344,1132,460,559,1379,881,316,817,902,284,770,1115,325,1415,1465,756,591,1109,376,623,834,1151,348,806,353,905,1169,1377,877,734,396,998,1345,307,292,439,529,1199,1338,534,1047,1123,815,729,361,1159,682,1392,710,1012,578,1143,1006,388,593,420,328,1329,1028,1182,1461,526,637,489,679,837,393,647,701,1249,1297,1451,1231,911,1246,1050,457,1333,1086,360,311,1187,953,773,586,662,888,965,618,279,1374,375,1146,430,819,562,423,402,732,1389,286,413,382,572,1371,1107,1239,1092,335,704,1356,274,419,996,616,1439,737,318,890,1471,494,323,1149,1293,330,1112,858,367,1162,726,848,520,399,1474,780,883,1176,685,1171,278,1445,851,1102,426,531,1134,812,342,355,553,968,776,712,295,282,707,971,1252,673,331,370,463,359,1130,1336,744,613,600,1052,864,1140,314,446,465,556,688,759,1448,844,588,896,304,1062,351,390,401,963,517,568,1193,899,1442,800,290,914,1348,432,410,950,1395,405,854,867,603,564,1436,767,1033,960,1065,720,283,1236,575,427,644,908,723,822,1431,442,1331,803,337,1009,1184,676,1468,454,364,309,659,491,1088,1014,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP100^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.27 % Computer : n017.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8046.5625MB
% 0.08/0.27 % OS : Linux 6.8.0-71-generic
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Sep 29 19:48:52 UTC 2026
% 0.26/0.27 % CPUTime :
% 0.26/0.28 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/0.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/0.93 % [INFO] Parsing done (296ms).
% 1.96/0.94 % [INFO] Running in sequential loop mode.
% 2.94/1.26 % [INFO] eprover registered as external prover.
% 2.94/1.27 % [INFO] Scanning for conjecture ...
% 3.42/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 272 axioms. Running axiom selection ...
% 3.65/1.58 % [INFO] Axiom selection finished. Selected 271 axioms (removed 1 axioms).
% 5.11/1.97 % [INFO] Problem is higher-order (TPTP THF).
% 5.11/2.01 % [INFO] Type checking passed.
% 5.11/2.02 % [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 ...
% 120.69/84.94 % External prover 'e' found a proof!
% 120.69/84.94 % [INFO] Killing All external provers ...
% 120.69/84.94 % Time passed: 84535ms (effective reasoning time: 84000ms)
% 120.69/84.94 % 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)>
% 120.69/84.95 % Axioms used in derivation (271): fact_143_list__ord__one, fact_209_list_Osplit__sel, fact_214_Cons__in__shuffles__iff, fact_110_last__snoc, fact_87_append__eq__append__conv2, tcon_HOL_Obool___Orderings_Opreorder_7, fact_176_lexordp_Ocases, fact_102_rev__induct, tcon_Nat_Onat___Orderings_Oorder_2, fact_97_splice_Osimps_I1_J, fact_66_member__rec_I2_J, fact_26_list__ex1__simps_I1_J, fact_202_successively_Osimps_I2_J, fact_113_rotate1__is__Nil__conv, fact_136_concat__conv__foldr, fact_89_append__Cons, tcon_Nat_Onat___Orderings_Olinorder, fact_131_concat__eq__appendD, fact_229_map2__Cons__if, fact_155_hd__append2, fact_75_append__is__Nil__conv, fact_77_self__append__conv2, fact_244_map2__snoc__snoc, fact_16_map__tailrec__rev_Oinduct, fact_49_lexordp__eq__antisym, fact_126_butlast_Osimps_I2_J, fact_147_ShiftD, fact_116_concat__append, fact_29_ord_Olexordp__eq__simps_I3_J, fact_175_list__ord__Cons, fact_28_arg__min__list_Osimps_I1_J, fact_79_self__append__conv, fact_154_lexordp__simps_I3_J, fact_115_last__appendR, fact_141_list__ord__Nil, fact_161_lexordp__irreflexive, fact_254_list__induct4, fact_125_longest__common__suffix, fact_251_length__induct, tcon_fun___Orderings_Oord, fact_185_tl__append2, fact_35_lexordp__eq__simps_I2_J, fact_123_last__ConsR, fact_197_butlast__tl, fact_38_ord_Olexordp__eq__simps_I2_J, fact_200_list_Oexpand, fact_226_Nil__in__shufflesI, fact_173_lexordp_ONil, fact_119_snoc__eq__iff__butlast, fact_183_successively__append__iff, fact_151_lexordp__append__left__rightI, fact_230_remdups__adj__append_H, fact_121_last_Osimps, fact_247_length__rotate1, fact_42_lexordp__eq__refl, fact_150_lexordp__iff, fact_93_eq__Nil__appendI, fact_187_list_Ocollapse, fact_142_list__ord__imp, tcon_HOL_Obool___Orderings_Oorder_9, fact_78_append__self__conv2, fact_241_remdups__adj_Osimps_I1_J, fact_51_ord_Olexordp__eq_OCons, fact_14_strict__sorted_Oinduct, fact_48_lexordp__eq__linear, fact_5_list_Oinducts, fact_233_hd__remdups__adj, fact_41_ord_Olexordp__eq__refl, fact_106_maps__simps_I1_J, fact_144_list__ord_Osimps_I3_J, fact_133_empty__Shift, fact_231_remdups__adj__append, fact_54_listrelp_OCons, fact_40_ord_Olexordp__eq_Ocong, fact_212_list_Osimps_I5_J, fact_120_rotate1_Osimps_I1_J, fact_22_remdups__adj_Ocases, fact_246_append__eq__append__conv, fact_207_successively__Cons, fact_85_append1__eq__conv, fact_227_shuffles__commutes, fact_118_butlast_Osimps_I1_J, fact_15_strict__sorted_Ocases, fact_96_splice_Osimps_I2_J, fact_33_listrelp_Ocases, fact_134_Succ__Shift, fact_57_map__tailrec__rev_Osimps_I1_J, fact_184_distinct__adj__Cons__Cons, fact_88_append__eq__appendI, fact_53_ord_Olexordp__eq_ONil, fact_219_map2__Cons__Cons, help_If_1_1_T, fact_206_list_Oexhaust__sel, fact_250_Ex__list__of__length, fact_224_Cons__in__shuffles__leftI, fact_138_list__ord_Oelims_I3_J, fact_228_map2_Osimps_I2_J, fact_17_list__nonempty__induct, fact_210_list_Osplit__sel__asm, fact_166_lexordp__conv__lexordp__eq, fact_127_concat_Osimps_I1_J, fact_146_list__ord_Oelims_I2_J, fact_50_lexordp__eq_ONil, fact_9_induct__list012, tcon_Set_Oset___Orderings_Oord_6, fact_36_lexordp__eq__simps_I1_J, fact_20_remdups__adj_Oinduct, fact_56_map__tailrec__rev_Osimps_I2_J, fact_105_lexordp__eq_OCons__eq, fact_178_lexordp_Oinducts, fact_99_append__eq__Cons__conv, fact_70_same__append__eq, fact_148_list__strict__asc__def, fact_2_list_Odistinct_I1_J, fact_249_neq__if__length__neq, fact_198_tl__Nil, fact_24_list__ord_Oinduct, fact_81_append__Nil2, fact_65_lexordp__eq_Oinducts, fact_232_remdups__adj__Nil__iff, fact_21_sorted__wrt_Oinduct, fact_179_lexordp__cases, fact_109_butlast__snoc, fact_204_successively_Oelims_I2_J, fact_168_longest__common__prefix, fact_34_lexordp__eq__simps_I3_J, fact_190_successively_Oelims_I3_J, fact_12_shuffles_Oinduct, fact_203_successively_Oelims_I1_J, fact_67_member__rec_I1_J, fact_72_append__assoc, tcon_HOL_Obool___Orderings_Oord_10, fact_186_hd__Cons__tl, fact_199_Nil__tl, fact_160_lexordp__irreflexive_H, fact_83_splice__Nil2, fact_196_distinct__adj__ConsD, fact_240_remdups__adj_Osimps_I2_J, fact_194_distinct__adj__appendD2, fact_171_lexordp_OCons__eq, fact_111_SuccI, fact_225_Cons__in__shuffles__rightI, fact_242_remdups__adj_Osimps_I3_J, fact_95_ord_Olexordp__eq__pref, fact_245_list__strict__asc__imp__list__asc, fact_103_append__eq__Cons, fact_58_ord_Olexordp__eq_Ocases, tcon_Nat_Onat___Orderings_Oord_3, fact_63_lexordp__eq_Ocases, fact_124_last__append, fact_82_split__Nil__iff, fact_60_ord_Olexordp__eq_Oinducts, fact_10_min__list_Ocases, fact_114_last__appendL, fact_59_ord_Olexordp__eq_Osimps, fact_31_listrelp_Oinducts, fact_68_splice_Oelims, fact_195_distinct__adj__Nil, fact_4_list_Oexhaust, fact_76_Nil__is__append__conv, fact_237_distinct__adj__remdups__adj, fact_139_list__ord_Osimps_I1_J, fact_243_remdups__adj__append__two, fact_91_append_Oleft__neutral, fact_235_remdups__adj__Cons__alt, fact_222_map2__empty__conv, help_If_2_1_T, tcon_Set_Oset___Orderings_Opreorder_4, fact_19_arg__min__list_Oinduct, fact_158_lexordp__trans, fact_140_list__ord_Osimps_I2_J, fact_193_distinct__adj__appendD1, fact_94_lexordp__eq__pref, help_If_3_1_T, fact_101_rev__exhaust, fact_52_ord_Olexordp__eq_OCons__eq, fact_98_rev__nonempty__induct, fact_156_lexordp__append__leftI, fact_25_insert__Nil, fact_145_list__ord_Oelims_I1_J, fact_137_foldr__append, fact_248_length__greater__imp__not__empty, fact_6_neq__Nil__conv, fact_23_transpose_Ocases, fact_252_list__induct2, fact_221_map2__Nil, fact_90_Cons__eq__appendI, tcon_fun___Orderings_Opreorder, fact_112_SuccD, tcon_Set_Oset___Orderings_Oorder_5, fact_18_successively_Oinduct, fact_172_lexordp__append__leftD, fact_238_distinct__adj__altdef, fact_73_append_Oassoc, fact_86_lexordp__eq__simps_I4_J, fact_122_last__ConsL, fact_45_Collect__mem__eq, tcon_Nat_Onat___Orderings_Opreorder_1, fact_180_lexordp__induct, fact_167_hd__append, fact_157_lexordp__antisym, fact_84_i__append__assoc, fact_37_ord_Olexordp__eq__simps_I4_J, fact_107_concat__eq__append__conv, fact_3_list_OdiscI, fact_130_maps__simps_I2_J, fact_92_append__Nil, fact_174_lexordp__append__rightI, fact_32_listrelp_Osimps, tcon_HOL_Obool___Orderings_Olinorder_8, fact_39_ord_Olexordp__eq__simps_I1_J, fact_69_bind__simps_I2_J, fact_129_butlast__append, fact_153_lexordp__simps_I1_J, fact_191_successively_Osimps_I3_J, fact_149_list__ord__append, tcon_fun___Orderings_Oorder, fact_236_successively__remdups__adjI, fact_220_map2_Osimps_I1_J, fact_217_splice__in__shuffles, fact_1_list_Oinject, fact_169_list__ord__Cons__imp, fact_211_list_Ocase__eq__if, fact_104_lexordp__eq_OCons, fact_135_list__ord__snoc, fact_162_list_Osel_I1_J, fact_128_concat_Osimps_I2_J, fact_64_lexordp__eq_Osimps, fact_253_list__induct3, fact_208_distinct__adj__Cons, fact_181_distinct__adj__append__iff, fact_100_Cons__eq__append__conv, fact_205_distinct__adj__singleton, fact_177_lexordp_Osimps, fact_164_lexordp__into__lexordp__eq, fact_80_append__self__conv, fact_108_rotate1_Osimps_I2_J, fact_62_subseqs_Osimps_I1_J, fact_27_map__tailrec__rev_Oelims, fact_132_shift__def, fact_55_listrelp_ONil, fact_201_last__tl, fact_117_append__butlast__last__id, fact_170_lexordp_OCons, fact_189_list_Osel_I2_J, fact_234_last__remdups__adj, fact_218_shufflesE, fact_61_product__lists_Osimps_I1_J, fact_192_successively_Osimps_I1_J, fact_163_hd__concat, fact_8_splice_Oinduct, fact_213_list_Osimps_I4_J, fact_182_rotate1__hd__tl, fact_239_remdups__adj_Oelims, fact_215_map2__Cons__not__empty, fact_216_Nil__in__shuffles, fact_46_Collect__cong, fact_74_append_Oright__neutral, fact_7_list__induct2_H, fact_44_mem__Collect__eq, fact_165_lexordp__eq__conv__lexord, fact_152_lexordp__simps_I2_J, fact_43_lexordp__eq__trans, fact_71_append__same__eq, fact_188_list_Osel_I3_J, fact_223_map2__not__empty__conv, fact_30_bind__simps_I1_J, fact_11_min__list_Oinduct, fact_159_lexordp__linear, fact_13_not__Cons__self2, fact_0_i__append__Nil
% 120.69/84.95 % No. of inferences in proof: 546
% 120.69/84.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 84535 ms resp. 84000 ms w/o parsing
% 123.06/85.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 123.06/85.42 % [INFO] Killing All external provers ...
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