TSTP Solution File: ITP100^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:54 EDT 2024
% Result : Theorem 21.24s 6.64s
% Output : Refutation 22.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 416
% Syntax : Number of formulae : 749 ( 377 unt; 85 typ; 0 def)
% Number of atoms : 1645 (1292 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 6445 ( 384 ~; 91 |; 224 &;4914 @)
% ( 0 <=>; 832 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 737 ( 737 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 7 con; 0-3 aty)
% Number of variables : 2233 ( 44 ^2041 !; 148 ?;2233 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_list_list_a_type,type,
list_list_list_a: $tType ).
thf(set_list_list_a_type,type,
set_list_list_a: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(set_list_a_type,type,
set_list_a: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(bNF_Gr1972240547list_a_type,type,
bNF_Gr1972240547list_a: set_list_list_a > list_a > set_list_list_a ).
thf(bNF_Greatest_Shift_a_type,type,
bNF_Greatest_Shift_a: set_list_a > a > set_list_a ).
thf(bNF_Gr1046450207list_a_type,type,
bNF_Gr1046450207list_a: set_list_list_a > list_list_a > set_list_a ).
thf(bNF_Greatest_Succ_a_type,type,
bNF_Greatest_Succ_a: set_list_a > list_a > set_a ).
thf(if_list_a_type,type,
if_list_a: $o > list_a > list_a > list_a ).
thf(list_ord_nat_type,type,
list_ord_nat: ( nat > nat > $o ) > list_nat > $o ).
thf(list_strict_asc_nat_type,type,
list_strict_asc_nat: list_nat > $o ).
thf(map2_a_a_a_type,type,
map2_a_a_a: ( a > a > a ) > list_a > list_a > list_a ).
thf(listIn1753026346list_a_type,type,
listIn1753026346list_a: list_list_a > ( nat > list_a ) > nat > list_a ).
thf(listIn1312259492pend_a_type,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(append_list_a_type,type,
append_list_a: list_list_a > list_list_a > list_list_a ).
thf(append_a_type,type,
append_a: list_a > list_a > list_a ).
thf(bind_list_a_list_a_type,type,
bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
thf(bind_list_a_a_type,type,
bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
thf(bind_a_list_a_type,type,
bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
thf(bind_a_a_type,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(butlast_list_a_type,type,
butlast_list_a: list_list_a > list_list_a ).
thf(butlast_a_type,type,
butlast_a: list_a > list_a ).
thf(concat_list_a_type,type,
concat_list_a: list_list_list_a > list_list_a ).
thf(concat_a_type,type,
concat_a: list_list_a > list_a ).
thf(distinct_adj_list_a_type,type,
distinct_adj_list_a: list_list_a > $o ).
thf(distinct_adj_a_type,type,
distinct_adj_a: list_a > $o ).
thf(foldr_769741863list_a_type,type,
foldr_769741863list_a: ( list_list_a > list_list_a > list_list_a ) > list_list_list_a > list_list_a > list_list_a ).
thf(foldr_list_a_list_a_type,type,
foldr_list_a_list_a: ( list_a > list_a > list_a ) > list_list_a > list_a > list_a ).
thf(insert_list_a_type,type,
insert_list_a: list_a > list_list_a > list_list_a ).
thf(insert_a_type,type,
insert_a: a > list_a > list_a ).
thf(last_list_a_type,type,
last_list_a: list_list_a > list_a ).
thf(last_a_type,type,
last_a: list_a > a ).
thf(cons_list_a_type,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(cons_a_type,type,
cons_a: a > list_a > list_a ).
thf(nil_list_list_a_type,type,
nil_list_list_a: list_list_list_a ).
thf(nil_list_a_type,type,
nil_list_a: list_list_a ).
thf(nil_a_type,type,
nil_a: list_a ).
thf(hd_list_list_a_type,type,
hd_list_list_a: list_list_list_a > list_list_a ).
thf(hd_list_a_type,type,
hd_list_a: list_list_a > list_a ).
thf(hd_a_type,type,
hd_a: list_a > a ).
thf(tl_list_a_type,type,
tl_list_a: list_list_a > list_list_a ).
thf(tl_a_type,type,
tl_a: list_a > list_a ).
thf(list_ex1_list_a_type,type,
list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(list_ex1_a_type,type,
list_ex1_a: ( a > $o ) > list_a > $o ).
thf(listre1221556159list_a_type,type,
listre1221556159list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
thf(listrelp_list_a_a_type,type,
listrelp_list_a_a: ( list_a > a > $o ) > list_list_a > list_a > $o ).
thf(listrelp_a_list_a_type,type,
listrelp_a_list_a: ( a > list_a > $o ) > list_a > list_list_a > $o ).
thf(listrelp_a_a_type,type,
listrelp_a_a: ( a > a > $o ) > list_a > list_a > $o ).
thf(map_ta982122357list_a_type,type,
map_ta982122357list_a: ( list_a > list_a ) > list_list_a > list_list_a > list_list_a ).
thf(map_ta2002079599st_a_a_type,type,
map_ta2002079599st_a_a: ( list_a > a ) > list_list_a > list_a > list_a ).
thf(map_ta41997947list_a_type,type,
map_ta41997947list_a: ( a > list_a ) > list_a > list_list_a > list_list_a ).
thf(map_tailrec_rev_a_a_type,type,
map_tailrec_rev_a_a: ( a > a ) > list_a > list_a > list_a ).
thf(maps_list_a_list_a_type,type,
maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
thf(maps_list_a_a_type,type,
maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
thf(maps_a_list_a_type,type,
maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
thf(maps_a_a_type,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(member_list_a_type,type,
member_list_a: list_list_a > list_a > $o ).
thf(member_a_type,type,
member_a: list_a > a > $o ).
thf(lexordp_eq_list_a_type,type,
lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).
thf(lexordp_eq_a_type,type,
lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).
thf(product_lists_a_type,type,
product_lists_a: list_list_a > list_list_a ).
thf(remdups_adj_a_type,type,
remdups_adj_a: list_a > list_a ).
thf(rotate1_list_a_type,type,
rotate1_list_a: list_list_a > list_list_a ).
thf(rotate1_a_type,type,
rotate1_a: list_a > list_a ).
thf(shuffles_a_type,type,
shuffles_a: list_a > list_a > set_list_a ).
thf(splice_list_a_type,type,
splice_list_a: list_list_a > list_list_a > list_list_a ).
thf(splice_a_type,type,
splice_a: list_a > list_a > list_a ).
thf(subseqs_a_type,type,
subseqs_a: list_a > list_list_a ).
thf(successively_list_a_type,type,
successively_list_a: ( list_a > list_a > $o ) > list_list_a > $o ).
thf(successively_a_type,type,
successively_a: ( a > a > $o ) > list_a > $o ).
thf(size_size_list_a_type,type,
size_size_list_a: list_a > nat ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(collect_list_a_type,type,
collect_list_a: ( list_a > $o ) > set_list_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(member_list_list_a_type,type,
member_list_list_a: list_list_a > set_list_list_a > $o ).
thf(member_list_a2_type,type,
member_list_a2: list_a > set_list_a > $o ).
thf(member_a2_type,type,
member_a2: a > set_a > $o ).
thf(f_type,type,
f: nat > a ).
thf(x_type,type,
x: a ).
thf(xs_type,type,
xs: list_a ).
thf(116,axiom,
! [A: list_list_a,B: list_list_a] :
? [C: list_list_a,D: list_list_a,E: list_list_a] :
( ( A
= ( append_list_a @ D @ C ) )
& ( B
= ( append_list_a @ E @ C ) )
& ( ( D = nil_list_a )
| ( E = nil_list_a )
| ( ( last_list_a @ D )
!= ( last_list_a @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_longest__common__suffix) ).
thf(809,plain,
! [A: list_list_a,B: list_list_a] :
? [C: list_list_a,D: list_list_a,E: list_list_a] :
( ( A
= ( append_list_a @ D @ C ) )
& ( B
= ( append_list_a @ E @ C ) )
& ( ( D = nil_list_a )
| ( E = nil_list_a )
| ( ( last_list_a @ D )
!= ( last_list_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(229,axiom,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( butlast_a @ ( cons_a @ B @ A ) )
= nil_a ) )
& ( ( A != nil_a )
=> ( ( butlast_a @ ( cons_a @ B @ A ) )
= ( cons_a @ B @ ( butlast_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_butlast_Osimps_I2_J) ).
thf(1337,plain,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( butlast_a @ ( cons_a @ B @ A ) )
= nil_a ) )
& ( ( A != nil_a )
=> ( ( butlast_a @ ( cons_a @ B @ A ) )
= ( cons_a @ B @ ( butlast_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(162,axiom,
! [A: list_a,B: a,C: list_a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= C )
= ( ( C != nil_a )
& ( ( butlast_a @ C )
= A )
& ( ( last_a @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_snoc__eq__iff__butlast) ).
thf(1024,plain,
! [A: list_a,B: a,C: list_a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= C )
= ( ( C != nil_a )
& ( ( butlast_a @ C )
= A )
& ( ( last_a @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(194,axiom,
! [A: list_a] :
( ( nil_a
= ( tl_a @ A ) )
= ( ( A = nil_a )
| ? [B: a] :
( A
= ( cons_a @ B @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Nil__tl) ).
thf(1168,plain,
! [A: list_a] :
( ( nil_a
= ( tl_a @ A ) )
= ( ( A = nil_a )
| ? [B: a] :
( A
= ( cons_a @ B @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(286,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a > list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( ( size_size_list_a @ B )
= ( size_size_list_a @ C ) )
=> ( ( D @ nil_a @ nil_a @ nil_a )
=> ( ! [E: a,F: list_a,G: a,H: list_a,I: a,J: list_a] :
( ( ( size_size_list_a @ F )
= ( size_size_list_a @ H ) )
=> ( ( ( size_size_list_a @ H )
= ( size_size_list_a @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons_a @ E @ F ) @ ( cons_a @ G @ H ) @ ( cons_a @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_list__induct3) ).
thf(1633,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a > list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( ( size_size_list_a @ B )
= ( size_size_list_a @ C ) )
=> ( ( D @ nil_a @ nil_a @ nil_a )
=> ( ! [E: a,F: list_a,G: a,H: list_a,I: a,J: list_a] :
( ( ( size_size_list_a @ F )
= ( size_size_list_a @ H ) )
=> ( ( ( size_size_list_a @ H )
= ( size_size_list_a @ J ) )
=> ( ( D @ F @ H @ J )
=> ( D @ ( cons_a @ E @ F ) @ ( cons_a @ G @ H ) @ ( cons_a @ I @ J ) ) ) ) )
=> ( D @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(270,axiom,
! [A: a > a,B: a,C: list_a,D: list_a] :
( ( map_tailrec_rev_a_a @ A @ ( cons_a @ B @ C ) @ D )
= ( map_tailrec_rev_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_map__tailrec__rev_Osimps_I2_J) ).
thf(1559,plain,
! [A: a > a,B: a,C: list_a,D: list_a] :
( ( map_tailrec_rev_a_a @ A @ ( cons_a @ B @ C ) @ D )
= ( map_tailrec_rev_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(145,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
= ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_append_Oassoc) ).
thf(941,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
= ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(51,axiom,
! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
( ( ( cons_list_a @ A @ B )
= C )
=> ( ( D
= ( append_list_a @ B @ E ) )
=> ( ( cons_list_a @ A @ D )
= ( append_list_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Cons__eq__appendI) ).
thf(481,plain,
! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
( ( ( cons_list_a @ A @ B )
= C )
=> ( ( D
= ( append_list_a @ B @ E ) )
=> ( ( cons_list_a @ A @ D )
= ( append_list_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(224,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_append__self__conv2) ).
thf(1322,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= B )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(292,axiom,
! [A: a > a > $o] : ( listrelp_a_a @ A @ nil_a @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_listrelp_ONil) ).
thf(1665,plain,
! [A: a > a > $o] : ( listrelp_a_a @ A @ nil_a @ nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1,conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(333,plain,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(81,axiom,
! [A: list_a,B: list_list_a] :
( ( append_list_a @ ( cons_list_a @ A @ nil_list_a ) @ B )
= ( cons_list_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_append__eq__Cons) ).
thf(628,plain,
! [A: list_a,B: list_list_a] :
( ( append_list_a @ ( cons_list_a @ A @ nil_list_a ) @ B )
= ( cons_list_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(326,axiom,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ord_Olexordp__eq_ONil) ).
thf(1855,plain,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(198,axiom,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_hd__append2) ).
thf(1211,plain,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(192,axiom,
! [A: list_a,B: a > a > a,C: a,D: list_a] :
( ( ( A = nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= nil_a ) )
& ( ( A != nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_map2__Cons__if) ).
thf(1158,plain,
! [A: list_a,B: a > a > a,C: a,D: list_a] :
( ( ( A = nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= nil_a ) )
& ( ( A != nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(240,axiom,
! [A: nat > a] :
( ( listIn1312259492pend_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_i__append__Nil) ).
thf(1406,plain,
! [A: nat > a] :
( ( listIn1312259492pend_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(297,axiom,
! [A: a] :
~ ( member_a @ nil_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_member__rec_I2_J) ).
thf(1692,plain,
! [A: a] :
~ ( member_a @ nil_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(257,axiom,
( listrelp_list_a_a
= ( ^ [A: list_a > a > $o,B: list_list_a,C: list_a] :
( ( ( B = nil_list_a )
& ( C = nil_a ) )
| ? [D: list_a,E: a,F: list_list_a,G: list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_listrelp_Osimps) ).
thf(1486,plain,
( listrelp_list_a_a
= ( ^ [A: list_a > a > $o,B: list_list_a,C: list_a] :
( ( ( B = nil_list_a )
& ( C = nil_a ) )
| ? [D: list_a,E: a,F: list_list_a,G: list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(311,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_hd__Cons__tl) ).
thf(1750,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(31,axiom,
! [A: set_list_list_a,B: list_a] :
( ( member_list_list_a @ nil_list_a @ A )
=> ( ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ A @ nil_list_a ) )
=> ( member_list_list_a @ nil_list_a @ ( bNF_Gr1972240547list_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_empty__Shift) ).
thf(408,plain,
! [A: set_list_list_a,B: list_a] :
( ( member_list_list_a @ nil_list_a @ A )
=> ( ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ A @ nil_list_a ) )
=> ( member_list_list_a @ nil_list_a @ ( bNF_Gr1972240547list_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: list_a > list_a > $o,B: list_list_a] :
( ~ ( successively_list_a @ A @ B )
=> ~ ! [C: list_a,D: list_a,E: list_list_a] :
( ( B
= ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_successively_Oelims_I3_J) ).
thf(379,plain,
! [A: list_a > list_a > $o,B: list_list_a] :
( ~ ( successively_list_a @ A @ B )
=> ~ ! [C: list_a,D: list_a,E: list_list_a] :
( ( B
= ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(213,axiom,
! [A: list_a > a,B: list_a,C: list_list_a,D: list_a] :
( ( map_ta2002079599st_a_a @ A @ ( cons_list_a @ B @ C ) @ D )
= ( map_ta2002079599st_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_map__tailrec__rev_Osimps_I2_J) ).
thf(1269,plain,
! [A: list_a > a,B: list_a,C: list_list_a,D: list_a] :
( ( map_ta2002079599st_a_a @ A @ ( cons_list_a @ B @ C ) @ D )
= ( map_ta2002079599st_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(318,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( ( ( A = B )
=> ( C != nil_a ) )
=> ( ( ( A = C )
=> ( B != nil_a ) )
=> ( ! [D: a,E: list_a] :
( ( B
= ( cons_a @ D @ E ) )
=> ! [F: a,G: list_a] :
( ( A
= ( cons_a @ F @ G ) )
=> ( ( D = F )
=> ~ ( member_list_a2 @ G @ ( shuffles_a @ E @ C ) ) ) ) )
=> ~ ! [D: a,E: list_a] :
( ( C
= ( cons_a @ D @ E ) )
=> ! [F: a,G: list_a] :
( ( A
= ( cons_a @ F @ G ) )
=> ( ( D = F )
=> ~ ( member_list_a2 @ G @ ( shuffles_a @ B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_shufflesE) ).
thf(1788,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( ( ( A = B )
=> ( C != nil_a ) )
=> ( ( ( A = C )
=> ( B != nil_a ) )
=> ( ! [D: a,E: list_a] :
( ( B
= ( cons_a @ D @ E ) )
=> ! [F: a,G: list_a] :
( ( A
= ( cons_a @ F @ G ) )
=> ( ( D = F )
=> ~ ( member_list_a2 @ G @ ( shuffles_a @ E @ C ) ) ) ) )
=> ~ ! [D: a,E: list_a] :
( ( C
= ( cons_a @ D @ E ) )
=> ! [F: a,G: list_a] :
( ( A
= ( cons_a @ F @ G ) )
=> ( ( D = F )
=> ~ ( member_list_a2 @ G @ ( shuffles_a @ B @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(21,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__List__Olist_Itf__a_J_T) ).
thf(385,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(313,axiom,
! [A: a > a > $o,B: list_a] :
( ~ ( successively_a @ A @ B )
=> ~ ! [C: a,D: a,E: list_a] :
( ( B
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_successively_Oelims_I3_J) ).
thf(1756,plain,
! [A: a > a > $o,B: list_a] :
( ~ ( successively_a @ A @ B )
=> ~ ! [C: a,D: a,E: list_a] :
( ( B
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ( ( A @ C @ D )
& ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(56,axiom,
! [A: list_a > list_list_a] :
( ( maps_list_a_list_a @ A @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_maps__simps_I2_J) ).
thf(500,plain,
! [A: list_a > list_list_a] :
( ( maps_list_a_list_a @ A @ nil_list_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(331,axiom,
! [A: a,B: list_a] :
( ( rotate1_a @ ( cons_a @ A @ B ) )
= ( append_a @ B @ ( cons_a @ A @ nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rotate1_Osimps_I2_J) ).
thf(1872,plain,
! [A: a,B: list_a] :
( ( rotate1_a @ ( cons_a @ A @ B ) )
= ( append_a @ B @ ( cons_a @ A @ nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(205,axiom,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ( A @ B @ C )
=> ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ord_Olexordp__eq_OCons) ).
thf(1233,plain,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ( A @ B @ C )
=> ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(96,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ~ ! [B: list_a,C: list_list_a] :
( A
!= ( cons_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Oexhaust) ).
thf(698,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ~ ! [B: list_a,C: list_list_a] :
( A
!= ( cons_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(201,axiom,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_append__Cons) ).
thf(1222,plain,
! [A: a,B: list_a,C: list_a] :
( ( append_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(175,axiom,
! [A: a > list_a > $o,B: list_a,C: list_list_a,D: list_a > list_list_a > $o] :
( ( listrelp_a_list_a @ A @ B @ C )
=> ( ( D @ nil_a @ nil_list_a )
=> ( ! [E: a,F: list_a,G: list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( ( listrelp_a_list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_listrelp_Oinducts) ).
thf(1063,plain,
! [A: a > list_a > $o,B: list_a,C: list_list_a,D: list_a > list_list_a > $o] :
( ( listrelp_a_list_a @ A @ B @ C )
=> ( ( D @ nil_a @ nil_list_a )
=> ( ! [E: a,F: list_a,G: list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( ( listrelp_a_list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(5,axiom,
! [A: list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( cons_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_distinct__adj__ConsD) ).
thf(340,plain,
! [A: list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( cons_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(187,axiom,
! [A: a,B: list_a] :
( ( cons_a @ A @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ A @ B ) ) ) )
= ( remdups_adj_a @ ( cons_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_remdups__adj__Cons__alt) ).
thf(1127,plain,
! [A: a,B: list_a] :
( ( cons_a @ A @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ A @ B ) ) ) )
= ( remdups_adj_a @ ( cons_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(180,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_induct__list012) ).
thf(1095,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( A @ E )
=> ( ( A @ ( cons_a @ D @ E ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(29,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] : ( lexordp_eq_list_a @ A @ B @ ( append_list_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ord_Olexordp__eq__pref) ).
thf(404,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] : ( lexordp_eq_list_a @ A @ B @ ( append_list_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(203,axiom,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Nil__is__append__conv) ).
thf(1228,plain,
! [A: list_a,B: list_a] :
( ( nil_a
= ( append_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(256,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: list_a,C: a] :
( A
!= ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_rev__exhaust) ).
thf(1482,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: list_a,C: a] :
( A
!= ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(23,axiom,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_distinct__adj__appendD1) ).
thf(389,plain,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(241,axiom,
! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
( ( listrelp_a_a @ A @ B @ C )
=> ( ( D @ nil_a @ nil_a )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ( A @ E @ F )
=> ( ( listrelp_a_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_listrelp_Oinducts) ).
thf(1409,plain,
! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
( ( listrelp_a_a @ A @ B @ C )
=> ( ( D @ nil_a @ nil_a )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ( A @ E @ F )
=> ( ( listrelp_a_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(216,axiom,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_not__Cons__self2) ).
thf(1287,plain,
! [A: a,B: list_a] :
( ( cons_a @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(314,axiom,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Odistinct_I1_J) ).
thf(1760,plain,
! [A: a,B: list_a] :
( nil_a
!= ( cons_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(98,axiom,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ! [D: list_list_a] : ( A @ nil_list_a @ D )
=> ( ! [D: list_a,E: list_list_a,F: list_list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_list_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_splice_Oinduct) ).
thf(719,plain,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ! [D: list_list_a] : ( A @ nil_list_a @ D )
=> ( ! [D: list_a,E: list_list_a,F: list_list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_list_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(97,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( listre1221556159list_a @ A @ B @ C )
=> ( ( ( B = nil_list_a )
=> ( C != nil_list_a ) )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listre1221556159list_a @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_listrelp_Ocases) ).
thf(702,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( listre1221556159list_a @ A @ B @ C )
=> ( ( ( B = nil_list_a )
=> ( C != nil_list_a ) )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listre1221556159list_a @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(274,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_shuffles_Oinduct) ).
thf(1577,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: list_a] : ( A @ D @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ ( cons_a @ F @ G ) )
=> ( ( A @ ( cons_a @ D @ E ) @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(143,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( tl_list_a @ ( append_list_a @ A @ B ) )
= ( append_list_a @ ( tl_list_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_tl__append2) ).
thf(934,plain,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( tl_list_a @ ( append_list_a @ A @ B ) )
= ( append_list_a @ ( tl_list_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(249,axiom,
! [A: a > list_a,B: a,C: list_a,D: list_list_a] :
( ( map_ta41997947list_a @ A @ ( cons_a @ B @ C ) @ D )
= ( map_ta41997947list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_map__tailrec__rev_Osimps_I2_J) ).
thf(1462,plain,
! [A: a > list_a,B: a,C: list_a,D: list_list_a] :
( ( map_ta41997947list_a @ A @ ( cons_a @ B @ C ) @ D )
= ( map_ta41997947list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(328,axiom,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list_Oinject) ).
thf(1860,plain,
! [A: a,B: list_a,C: a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(211,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_append_Oleft__neutral) ).
thf(1264,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(67,axiom,
! [A: list_a > list_list_a] :
( ( bind_list_a_list_a @ nil_list_a @ A )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_bind__simps_I1_J) ).
thf(542,plain,
! [A: list_a > list_list_a] :
( ( bind_list_a_list_a @ nil_list_a @ A )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(47,axiom,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
=> ( distinct_adj_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_distinct__adj__appendD2) ).
thf(460,plain,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
=> ( distinct_adj_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(117,axiom,
! [A: list_a,B: list_a] :
( ( if_list_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__List__Olist_Itf__a_J_T) ).
thf(817,plain,
! [A: list_a,B: list_a] :
( ( if_list_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(72,axiom,
! [A: list_a > list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( map_ta982122357list_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_list_a )
=> ( D != C ) )
=> ~ ! [E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ E @ F ) )
=> ( D
!= ( map_ta982122357list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_map__tailrec__rev_Oelims) ).
thf(559,plain,
! [A: list_a > list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( map_ta982122357list_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_list_a )
=> ( D != C ) )
=> ~ ! [E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ E @ F ) )
=> ( D
!= ( map_ta982122357list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(301,axiom,
! [A: a,B: list_a] :
( ( append_a @ ( cons_a @ A @ nil_a ) @ B )
= ( cons_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_append__eq__Cons) ).
thf(1704,plain,
! [A: a,B: list_a] :
( ( append_a @ ( cons_a @ A @ nil_a ) @ B )
= ( cons_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(75,axiom,
! [A: list_a] : ( distinct_adj_list_a @ ( cons_list_a @ A @ nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_distinct__adj__singleton) ).
thf(606,plain,
! [A: list_a] : ( distinct_adj_list_a @ ( cons_list_a @ A @ nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(34,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_append__assoc) ).
thf(416,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(183,axiom,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ( A @ B @ C )
=> ( ( listrelp_a_a @ A @ D @ E )
=> ( listrelp_a_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_listrelp_OCons) ).
thf(1115,plain,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ( A @ B @ C )
=> ( ( listrelp_a_a @ A @ D @ E )
=> ( listrelp_a_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(332,axiom,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( lexordp_eq_a @ A @ B @ C )
=> ( ( B != nil_a )
=> ( ! [D: a] :
( ? [E: list_a] :
( B
= ( cons_a @ D @ E ) )
=> ! [E: a] :
( ? [F: list_a] :
( C
= ( cons_a @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq_a @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ord_Olexordp__eq_Ocases) ).
thf(1875,plain,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( lexordp_eq_a @ A @ B @ C )
=> ( ( B != nil_a )
=> ( ! [D: a] :
( ? [E: list_a] :
( B
= ( cons_a @ D @ E ) )
=> ! [E: a] :
( ? [F: list_a] :
( C
= ( cons_a @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq_a @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(85,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_last__append) ).
thf(638,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(124,axiom,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_a,E: list_list_a] :
( ( ( C = D )
=> ( A @ ( cons_list_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_list_a @ D @ E ) ) )
=> ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_remdups__adj_Oinduct) ).
thf(853,plain,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_a,E: list_list_a] :
( ( ( C = D )
=> ( A @ ( cons_list_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_list_a @ D @ E ) ) )
=> ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(255,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_self__append__conv) ).
thf(1479,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ A @ B ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(282,axiom,
! [A: a > a > $o,B: list_a] :
( ( successively_a @ A @ B )
=> ( ( B != nil_a )
=> ( ! [C: a] :
( B
!= ( cons_a @ C @ nil_a ) )
=> ~ ! [C: a,D: a,E: list_a] :
( ( B
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_successively_Oelims_I2_J) ).
thf(1609,plain,
! [A: a > a > $o,B: list_a] :
( ( successively_a @ A @ B )
=> ( ( B != nil_a )
=> ( ! [C: a] :
( B
!= ( cons_a @ C @ nil_a ) )
=> ~ ! [C: a,D: a,E: list_a] :
( ( B
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(159,axiom,
! [A: list_a,B: set_list_a,C: a] :
( ( member_list_a2 @ A @ ( bNF_Greatest_Shift_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ShiftD) ).
thf(1013,plain,
! [A: list_a,B: set_list_a,C: a] :
( ( member_list_a2 @ A @ ( bNF_Greatest_Shift_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(109,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( rotate1_list_a @ A )
= ( append_list_a @ ( tl_list_a @ A ) @ ( cons_list_a @ ( hd_list_a @ A ) @ nil_list_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_rotate1__hd__tl) ).
thf(770,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( rotate1_list_a @ A )
= ( append_list_a @ ( tl_list_a @ A ) @ ( cons_list_a @ ( hd_list_a @ A ) @ nil_list_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(113,axiom,
( listre1221556159list_a
= ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( ( B = nil_list_a )
& ( C = nil_list_a ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E )
& ( listre1221556159list_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_listrelp_Osimps) ).
thf(789,plain,
( listre1221556159list_a
= ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( ( B = nil_list_a )
& ( C = nil_list_a ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E )
& ( listre1221556159list_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(42,axiom,
! [A: list_list_list_a] :
( ( A != nil_list_list_a )
=> ( ( ( hd_list_list_a @ A )
!= nil_list_a )
=> ( ( hd_list_a @ ( concat_list_a @ A ) )
= ( hd_list_a @ ( hd_list_list_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_hd__concat) ).
thf(443,plain,
! [A: list_list_list_a] :
( ( A != nil_list_list_a )
=> ( ( ( hd_list_list_a @ A )
!= nil_list_a )
=> ( ( hd_list_a @ ( concat_list_a @ A ) )
= ( hd_list_a @ ( hd_list_list_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(181,axiom,
! [A: a > a > $o,B: a] : ( successively_a @ A @ ( cons_a @ B @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_successively_Osimps_I2_J) ).
thf(1109,plain,
! [A: a > a > $o,B: a] : ( successively_a @ A @ ( cons_a @ B @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(18,axiom,
! [A: list_a,B: list_a,C: list_list_a] :
( ( distinct_adj_list_a @ ( cons_list_a @ A @ ( cons_list_a @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj_list_a @ ( cons_list_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_distinct__adj__Cons__Cons) ).
thf(376,plain,
! [A: list_a,B: list_a,C: list_list_a] :
( ( distinct_adj_list_a @ ( cons_list_a @ A @ ( cons_list_a @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj_list_a @ ( cons_list_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(79,axiom,
! [A: a > a > $o,B: list_a,C: list_a] : ( lexordp_eq_a @ A @ B @ ( append_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ord_Olexordp__eq__pref) ).
thf(623,plain,
! [A: a > a > $o,B: list_a,C: list_a] : ( lexordp_eq_a @ A @ B @ ( append_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(296,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__induct2_H) ).
thf(1682,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ( A @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(319,axiom,
! [A: list_a,B: list_a,C: list_a,D: a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ B @ ( cons_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Cons__in__shuffles__rightI) ).
thf(1828,plain,
! [A: list_a,B: list_a,C: list_a,D: a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ B @ ( cons_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(9,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a] :
( ( successively_list_a @ A @ ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively_list_a @ A @ ( cons_list_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_successively_Osimps_I3_J) ).
thf(353,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a] :
( ( successively_list_a @ A @ ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively_list_a @ A @ ( cons_list_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,axiom,
! [A: list_a] :
( ( butlast_a @ ( tl_a @ A ) )
= ( tl_a @ ( butlast_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_butlast__tl) ).
thf(492,plain,
! [A: list_a] :
( ( butlast_a @ ( tl_a @ A ) )
= ( tl_a @ ( butlast_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(250,axiom,
! [A: list_a > a > $o] : ( listrelp_list_a_a @ A @ nil_list_a @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_listrelp_ONil) ).
thf(1465,plain,
! [A: list_a > a > $o] : ( listrelp_list_a_a @ A @ nil_list_a @ nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(228,axiom,
! [A: list_a] :
( ( ( tl_a @ A )
= nil_a )
= ( ( A = nil_a )
| ? [B: a] :
( A
= ( cons_a @ B @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_tl__Nil) ).
thf(1334,plain,
! [A: list_a] :
( ( ( tl_a @ A )
= nil_a )
= ( ( A = nil_a )
| ? [B: a] :
( A
= ( cons_a @ B @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(86,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
( ( listre1221556159list_a @ A @ B @ C )
=> ( ( D @ nil_list_a @ nil_list_a )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( ( listre1221556159list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_listrelp_Oinducts) ).
thf(646,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
( ( listre1221556159list_a @ A @ B @ C )
=> ( ( D @ nil_list_a @ nil_list_a )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( ( listre1221556159list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(161,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_splice_Oinduct) ).
thf(1020,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a] :
( ! [D: list_a] : ( A @ nil_a @ D )
=> ( ! [D: a,E: list_a,F: list_a] :
( ( A @ F @ E )
=> ( A @ ( cons_a @ D @ E ) @ F ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(7,axiom,
! [A: list_list_a] :
( ( splice_list_a @ A @ nil_list_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_splice__Nil2) ).
thf(348,plain,
! [A: list_list_a] :
( ( splice_list_a @ A @ nil_list_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(94,axiom,
! [A: list_a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
( ( map_ta982122357list_a @ A @ ( cons_list_a @ B @ C ) @ D )
= ( map_ta982122357list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__tailrec__rev_Osimps_I2_J) ).
thf(687,plain,
! [A: list_a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
( ( map_ta982122357list_a @ A @ ( cons_list_a @ B @ C ) @ D )
= ( map_ta982122357list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(128,axiom,
! [A: list_list_a,B: list_a,C: list_list_a,D: list_a] :
( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
= ( append_list_a @ C @ ( cons_list_a @ D @ nil_list_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_append1__eq__conv) ).
thf(877,plain,
! [A: list_list_a,B: list_a,C: list_list_a,D: list_a] :
( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
= ( append_list_a @ C @ ( cons_list_a @ D @ nil_list_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(148,axiom,
! [A: list_list_a,B: list_list_a] :
( ( concat_a @ ( append_list_a @ A @ B ) )
= ( append_a @ ( concat_a @ A ) @ ( concat_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_concat__append) ).
thf(956,plain,
! [A: list_list_a,B: list_list_a] :
( ( concat_a @ ( append_list_a @ A @ B ) )
= ( append_a @ ( concat_a @ A ) @ ( concat_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(26,axiom,
! [A: list_a > list_a > $o,B: list_list_a] :
( ( lexordp_eq_list_a @ A @ B @ nil_list_a )
= ( B = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ord_Olexordp__eq__simps_I2_J) ).
thf(396,plain,
! [A: list_a > list_a > $o,B: list_list_a] :
( ( lexordp_eq_list_a @ A @ B @ nil_list_a )
= ( B = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a > list_a > $o,E: list_a] : ( A @ D @ ( cons_list_a @ E @ nil_list_a ) )
=> ( ! [D: list_a > list_a > $o,E: list_a,F: list_a,G: list_list_a] :
( ( A @ D @ ( cons_list_a @ F @ G ) )
=> ( A @ D @ ( cons_list_a @ E @ ( cons_list_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_successively_Oinduct) ).
thf(428,plain,
! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a > list_a > $o,E: list_a] : ( A @ D @ ( cons_list_a @ E @ nil_list_a ) )
=> ( ! [D: list_a > list_a > $o,E: list_a,F: list_a,G: list_list_a] :
( ( A @ D @ ( cons_list_a @ F @ G ) )
=> ( A @ D @ ( cons_list_a @ E @ ( cons_list_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(279,axiom,
! [A: a,B: list_a,C: a > list_list_a] :
( ( bind_a_list_a @ ( cons_a @ A @ B ) @ C )
= ( append_list_a @ ( C @ A ) @ ( bind_a_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_bind__simps_I2_J) ).
thf(1600,plain,
! [A: a,B: list_a,C: a > list_list_a] :
( ( bind_a_list_a @ ( cons_a @ A @ B ) @ C )
= ( append_list_a @ ( C @ A ) @ ( bind_a_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(208,axiom,
! [A: list_a,B: list_a,C: list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( C @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( ( size_size_list_a @ E )
= ( size_size_list_a @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_list__induct2) ).
thf(1242,plain,
! [A: list_a,B: list_a,C: list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( C @ nil_a @ nil_a )
=> ( ! [D: a,E: list_a,F: a,G: list_a] :
( ( ( size_size_list_a @ E )
= ( size_size_list_a @ G ) )
=> ( ( C @ E @ G )
=> ( C @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(199,axiom,
! [A: list_a > list_list_a > $o,B: list_a,C: list_list_a] :
( ( A @ nil_a @ nil_list_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ nil_a @ ( cons_list_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: list_a,G: list_list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_list__induct2_H) ).
thf(1215,plain,
! [A: list_a > list_list_a > $o,B: list_a,C: list_list_a] :
( ( A @ nil_a @ nil_list_a )
=> ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ nil_a @ ( cons_list_a @ D @ E ) )
=> ( ! [D: a,E: list_a,F: list_a,G: list_list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(83,axiom,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord_Olexordp__eq__refl) ).
thf(634,plain,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(32,axiom,
! [A: list_list_a] :
( ( splice_list_a @ nil_list_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_splice_Osimps_I1_J) ).
thf(411,plain,
! [A: list_list_a] :
( ( splice_list_a @ nil_list_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(230,axiom,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( tl_a @ ( append_a @ A @ B ) )
= ( append_a @ ( tl_a @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_tl__append2) ).
thf(1345,plain,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( tl_a @ ( append_a @ A @ B ) )
= ( append_a @ ( tl_a @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(329,axiom,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_last__appendL) ).
thf(1863,plain,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(91,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
= ( ? [B: list_a,C: list_list_a] :
( A
= ( cons_list_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_neq__Nil__conv) ).
thf(678,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
= ( ? [B: list_a,C: list_list_a] :
( A
= ( cons_list_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(65,axiom,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
=> ( distinct_adj_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_distinct__adj__appendD1) ).
thf(529,plain,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
=> ( distinct_adj_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(190,axiom,
( ( subseqs_a @ nil_a )
= ( cons_list_a @ nil_a @ nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_subseqs_Osimps_I1_J) ).
thf(1153,plain,
( ( subseqs_a @ nil_a )
= ( cons_list_a @ nil_a @ nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(252,axiom,
! [A: a,B: list_a,C: a] :
( ( member_a @ ( cons_a @ A @ B ) @ C )
= ( ( A = C )
| ( member_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_member__rec_I1_J) ).
thf(1470,plain,
! [A: a,B: list_a,C: a] :
( ( member_a @ ( cons_a @ A @ B ) @ C )
= ( ( A = C )
| ( member_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(14,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_list_a,D: list_a,E: list_list_a] :
( ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ ( cons_list_a @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq_list_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ord_Olexordp__eq__simps_I4_J) ).
thf(366,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_list_a,D: list_a,E: list_list_a] :
( ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ ( cons_list_a @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq_list_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(330,axiom,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_last__appendR) ).
thf(1868,plain,
! [A: list_a,B: list_a] :
( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(60,axiom,
! [A: ( list_a > list_a ) > list_list_a > list_list_a > $o,B: list_a > list_a,C: list_list_a,D: list_list_a] :
( ! [E: list_a > list_a,F: list_list_a] : ( A @ E @ nil_list_a @ F )
=> ( ! [E: list_a > list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_map__tailrec__rev_Oinduct) ).
thf(512,plain,
! [A: ( list_a > list_a ) > list_list_a > list_list_a > $o,B: list_a > list_a,C: list_list_a,D: list_list_a] :
( ! [E: list_a > list_a,F: list_list_a] : ( A @ E @ nil_list_a @ F )
=> ( ! [E: list_a > list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(41,axiom,
! [A: list_a,B: list_list_a] :
( ( cons_list_a @ A @ B )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not__Cons__self2) ).
thf(439,plain,
! [A: list_a,B: list_list_a] :
( ( cons_list_a @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(169,axiom,
( ( rotate1_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_rotate1_Osimps_I1_J) ).
thf(1047,plain,
( ( rotate1_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(309,axiom,
! [A: a > a > $o,B: a,C: list_a] :
~ ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord_Olexordp__eq__simps_I3_J) ).
thf(1730,plain,
! [A: a > a > $o,B: a,C: list_a] :
~ ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(132,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_same__append__eq) ).
thf(894,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(105,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_list_Ocollapse) ).
thf(746,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(232,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_remdups__adj_Oinduct) ).
thf(1355,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: a,E: list_a] :
( ( ( C = D )
=> ( A @ ( cons_a @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons_a @ D @ E ) ) )
=> ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(118,axiom,
! [A: list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( cons_list_a @ A @ ( append_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_append__Cons) ).
thf(820,plain,
! [A: list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( cons_list_a @ A @ ( append_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(24,axiom,
distinct_adj_list_a @ nil_list_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_distinct__adj__Nil) ).
thf(392,plain,
distinct_adj_list_a @ nil_list_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(167,axiom,
( lexordp_eq_a
= ( ^ [A: a > a > $o,B: list_a,C: list_a] :
( ? [D: list_a] :
( ( B = nil_a )
& ( C = D ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord_Olexordp__eq_Osimps) ).
thf(1042,plain,
( lexordp_eq_a
= ( ^ [A: a > a > $o,B: list_a,C: list_a] :
( ? [D: list_a] :
( ( B = nil_a )
& ( C = D ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(147,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_last__appendR) ).
thf(952,plain,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(136,axiom,
! [A: list_a,B: list_list_a] :
( ( hd_list_a @ ( cons_list_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_list_Osel_I1_J) ).
thf(916,plain,
! [A: list_a,B: list_list_a] :
( ( hd_list_a @ ( cons_list_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(122,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= nil_list_a )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_append__is__Nil__conv) ).
thf(847,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= nil_list_a )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(80,axiom,
! [A: set_list_a] :
( ( collect_list_a
@ ^ [B: list_a] : ( member_list_a2 @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Collect__mem__eq) ).
thf(625,plain,
! [A: set_list_a] :
( ( collect_list_a
@ ^ [B: list_a] : ( member_list_a2 @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(40,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A = B )
=> ( A
= ( append_list_a @ nil_list_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_eq__Nil__appendI) ).
thf(435,plain,
! [A: list_list_a,B: list_list_a] :
( ( A = B )
=> ( A
= ( append_list_a @ nil_list_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(63,axiom,
! [A: list_list_a,B: list_list_a,C: nat > list_a] :
( ( listIn1753026346list_a @ A @ ( listIn1753026346list_a @ B @ C ) )
= ( listIn1753026346list_a @ ( append_list_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_i__append__assoc) ).
thf(522,plain,
! [A: list_list_a,B: list_list_a,C: nat > list_a] :
( ( listIn1753026346list_a @ A @ ( listIn1753026346list_a @ B @ C ) )
= ( listIn1753026346list_a @ ( append_list_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(197,axiom,
distinct_adj_a @ nil_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_distinct__adj__Nil) ).
thf(1210,plain,
distinct_adj_a @ nil_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(163,axiom,
! [A: a > list_list_a,B: a,C: list_a] :
( ( maps_a_list_a @ A @ ( cons_a @ B @ C ) )
= ( append_list_a @ ( A @ B ) @ ( maps_a_list_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_maps__simps_I1_J) ).
thf(1027,plain,
! [A: a > list_list_a,B: a,C: list_a] :
( ( maps_a_list_a @ A @ ( cons_a @ B @ C ) )
= ( append_list_a @ ( A @ B ) @ ( maps_a_list_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(108,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( splice_list_a @ A @ B )
= C )
=> ( ( ( A = nil_list_a )
=> ( C != B ) )
=> ~ ! [D: list_a,E: list_list_a] :
( ( A
= ( cons_list_a @ D @ E ) )
=> ( C
!= ( cons_list_a @ D @ ( splice_list_a @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_splice_Oelims) ).
thf(757,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( splice_list_a @ A @ B )
= C )
=> ( ( ( A = nil_list_a )
=> ( C != B ) )
=> ~ ! [D: list_a,E: list_list_a] :
( ( A
= ( cons_list_a @ D @ E ) )
=> ( C
!= ( cons_list_a @ D @ ( splice_list_a @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(70,axiom,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ! [D: list_list_a] : ( A @ nil_list_a @ D )
=> ( ! [D: list_list_a] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
( ( A @ E @ ( cons_list_a @ F @ G ) )
=> ( ( A @ ( cons_list_a @ D @ E ) @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_shuffles_Oinduct) ).
thf(551,plain,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ! [D: list_list_a] : ( A @ nil_list_a @ D )
=> ( ! [D: list_list_a] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
( ( A @ E @ ( cons_list_a @ F @ G ) )
=> ( ( A @ ( cons_list_a @ D @ E ) @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(217,axiom,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ D @ C ) )
& ( B
= ( append_a @ E @ C ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( last_a @ D )
!= ( last_a @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_longest__common__suffix) ).
thf(1291,plain,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ D @ C ) )
& ( B
= ( append_a @ E @ C ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( last_a @ D )
!= ( last_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(62,axiom,
! [A: list_list_a] :
( ( nil_list_a
= ( tl_list_a @ A ) )
= ( ( A = nil_list_a )
| ? [B: list_a] :
( A
= ( cons_list_a @ B @ nil_list_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_Nil__tl) ).
thf(519,plain,
! [A: list_list_a] :
( ( nil_list_a
= ( tl_list_a @ A ) )
= ( ( A = nil_list_a )
| ? [B: list_a] :
( A
= ( cons_list_a @ B @ nil_list_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(178,axiom,
! [A: a > list_a,B: a,C: list_a] :
( ( maps_a_a @ A @ ( cons_a @ B @ C ) )
= ( append_a @ ( A @ B ) @ ( maps_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_maps__simps_I1_J) ).
thf(1089,plain,
! [A: a > list_a,B: a,C: list_a] :
( ( maps_a_a @ A @ ( cons_a @ B @ C ) )
= ( append_a @ ( A @ B ) @ ( maps_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(77,axiom,
! [A: list_list_a,B: list_a,C: list_list_a] :
( ( A
= ( cons_list_a @ B @ C ) )
=> ( A != nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list_OdiscI) ).
thf(615,plain,
! [A: list_list_a,B: list_a,C: list_list_a] :
( ( A
= ( cons_list_a @ B @ C ) )
=> ( A != nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(226,axiom,
! [A: list_a,B: a] :
( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_last__snoc) ).
thf(1328,plain,
! [A: list_a,B: a] :
( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(185,axiom,
! [A: list_a,B: list_a,C: nat > a] :
( ( listIn1312259492pend_a @ A @ ( listIn1312259492pend_a @ B @ C ) )
= ( listIn1312259492pend_a @ ( append_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_i__append__assoc) ).
thf(1121,plain,
! [A: list_a,B: list_a,C: nat > a] :
( ( listIn1312259492pend_a @ A @ ( listIn1312259492pend_a @ B @ C ) )
= ( listIn1312259492pend_a @ ( append_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(182,axiom,
! [A: ( list_a > a ) > list_list_a > list_a > $o,B: list_a > a,C: list_list_a,D: list_a] :
( ! [E: list_a > a,F: list_a] : ( A @ E @ nil_list_a @ F )
=> ( ! [E: list_a > a,F: list_a,G: list_list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_map__tailrec__rev_Oinduct) ).
thf(1111,plain,
! [A: ( list_a > a ) > list_list_a > list_a > $o,B: list_a > a,C: list_list_a,D: list_a] :
( ! [E: list_a > a,F: list_a] : ( A @ E @ nil_list_a @ F )
=> ( ! [E: list_a > a,F: list_a,G: list_list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(267,axiom,
! [A: list_a > a,B: list_list_a,C: list_a,D: list_a] :
( ( ( map_ta2002079599st_a_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_list_a )
=> ( D != C ) )
=> ~ ! [E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ E @ F ) )
=> ( D
!= ( map_ta2002079599st_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_map__tailrec__rev_Oelims) ).
thf(1540,plain,
! [A: list_a > a,B: list_list_a,C: list_a,D: list_a] :
( ( ( map_ta2002079599st_a_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_list_a )
=> ( D != C ) )
=> ~ ! [E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ E @ F ) )
=> ( D
!= ( map_ta2002079599st_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(125,axiom,
! [A: list_a,B: list_list_a,C: list_a > list_list_a] :
( ( bind_list_a_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( append_list_a @ ( C @ A ) @ ( bind_list_a_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_bind__simps_I2_J) ).
thf(869,plain,
! [A: list_a,B: list_list_a,C: list_a > list_list_a] :
( ( bind_list_a_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( append_list_a @ ( C @ A ) @ ( bind_list_a_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(184,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( ( hd_list_a @ A )
!= nil_a )
=> ( ( hd_a @ ( concat_a @ A ) )
= ( hd_a @ ( hd_list_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_hd__concat) ).
thf(1118,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( ( hd_list_a @ A )
!= nil_a )
=> ( ( hd_a @ ( concat_a @ A ) )
= ( hd_a @ ( hd_list_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(316,axiom,
! [A: a,B: list_a,C: a > list_a] :
( ( bind_a_a @ ( cons_a @ A @ B ) @ C )
= ( append_a @ ( C @ A ) @ ( bind_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_bind__simps_I2_J) ).
thf(1772,plain,
! [A: a,B: list_a,C: a > list_a] :
( ( bind_a_a @ ( cons_a @ A @ B ) @ C )
= ( append_a @ ( C @ A ) @ ( bind_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(209,axiom,
( ( product_lists_a @ nil_list_a )
= ( cons_list_a @ nil_a @ nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_product__lists_Osimps_I1_J) ).
thf(1259,plain,
( ( product_lists_a @ nil_list_a )
= ( cons_list_a @ nil_a @ nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(306,axiom,
! [A: a > a > $o,B: a,C: list_a] :
( ( successively_a @ A @ ( cons_a @ B @ C ) )
= ( ( C = nil_a )
| ( ( A @ B @ ( hd_a @ C ) )
& ( successively_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_successively__Cons) ).
thf(1719,plain,
! [A: a > a > $o,B: a,C: list_a] :
( ( successively_a @ A @ ( cons_a @ B @ C ) )
= ( ( C = nil_a )
| ( ( A @ B @ ( hd_a @ C ) )
& ( successively_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(10,axiom,
! [A: list_a > list_a > $o] : ( successively_list_a @ A @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_successively_Osimps_I1_J) ).
thf(356,plain,
! [A: list_a > list_a > $o] : ( successively_list_a @ A @ nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(276,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_list_Oinducts) ).
thf(1584,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( cons_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(53,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_hd__Cons__tl) ).
thf(489,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(191,axiom,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_neq__Nil__conv) ).
thf(1155,plain,
! [A: list_a] :
( ( A != nil_a )
= ( ? [B: a,C: list_a] :
( A
= ( cons_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(25,axiom,
! [A: list_a,B: list_list_a,C: list_list_a] :
( ( splice_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( cons_list_a @ A @ ( splice_list_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_splice_Osimps_I2_J) ).
thf(393,plain,
! [A: list_a,B: list_list_a,C: list_list_a] :
( ( splice_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( cons_list_a @ A @ ( splice_list_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(247,axiom,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list__nonempty__induct) ).
thf(1451,plain,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( cons_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(235,axiom,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_append1__eq__conv) ).
thf(1382,plain,
! [A: list_a,B: a,C: list_a,D: a] :
( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
= ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(243,axiom,
! [A: a > a,B: list_a,C: list_a,D: list_a] :
( ( ( map_tailrec_rev_a_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_a )
=> ( D != C ) )
=> ~ ! [E: a,F: list_a] :
( ( B
= ( cons_a @ E @ F ) )
=> ( D
!= ( map_tailrec_rev_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_map__tailrec__rev_Oelims) ).
thf(1429,plain,
! [A: a > a,B: list_a,C: list_a,D: list_a] :
( ( ( map_tailrec_rev_a_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_a )
=> ( D != C ) )
=> ~ ! [E: a,F: list_a] :
( ( B
= ( cons_a @ E @ F ) )
=> ( D
!= ( map_tailrec_rev_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(112,axiom,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a,D: list_list_a] :
( ( A @ D )
=> ( A @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_rev__induct) ).
thf(779,plain,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a,D: list_list_a] :
( ( A @ D )
=> ( A @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(16,axiom,
! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ord_Olexordp__eq_ONil) ).
thf(371,plain,
! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(57,axiom,
! [A: list_a > list_list_a,B: list_a,C: list_list_a] :
( ( maps_list_a_list_a @ A @ ( cons_list_a @ B @ C ) )
= ( append_list_a @ ( A @ B ) @ ( maps_list_a_list_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_maps__simps_I1_J) ).
thf(503,plain,
! [A: list_a > list_list_a,B: list_a,C: list_list_a] :
( ( maps_list_a_list_a @ A @ ( cons_list_a @ B @ C ) )
= ( append_list_a @ ( A @ B ) @ ( maps_list_a_list_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(320,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_append__is__Nil__conv) ).
thf(1831,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(204,axiom,
! [A: a,B: set_list_a,C: list_a] :
( ( member_a2 @ A @ ( bNF_Greatest_Succ_a @ B @ C ) )
=> ( member_list_a2 @ ( append_a @ C @ ( cons_a @ A @ nil_a ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_SuccD) ).
thf(1231,plain,
! [A: a,B: set_list_a,C: list_a] :
( ( member_a2 @ A @ ( bNF_Greatest_Succ_a @ B @ C ) )
=> ( member_list_a2 @ ( append_a @ C @ ( cons_a @ A @ nil_a ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(174,axiom,
! [A: list_a] :
( ( splice_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_splice__Nil2) ).
thf(1060,plain,
! [A: list_a] :
( ( splice_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(46,axiom,
! [A: list_list_a,B: list_list_a] :
( ( nil_list_a
= ( append_list_a @ A @ B ) )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Nil__is__append__conv) ).
thf(457,plain,
! [A: list_list_a,B: list_list_a] :
( ( nil_list_a
= ( append_list_a @ A @ B ) )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(327,axiom,
! [A: list_a,B: a,C: list_a] :
( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) )
= ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_remdups__adj__append) ).
thf(1857,plain,
! [A: list_a,B: a,C: list_a] :
( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) )
= ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(12,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( splice_list_a @ A @ B )
= nil_list_a )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_split__Nil__iff) ).
thf(360,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( splice_list_a @ A @ B )
= nil_list_a )
= ( ( A = nil_list_a )
& ( B = nil_list_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(298,axiom,
! [A: a,B: list_a,C: list_a] :
( ( splice_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( splice_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_splice_Osimps_I2_J) ).
thf(1695,plain,
! [A: a,B: list_a,C: list_a] :
( ( splice_a @ ( cons_a @ A @ B ) @ C )
= ( cons_a @ A @ ( splice_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(90,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_hd__append2) ).
thf(674,plain,
! [A: list_list_a,B: list_list_a] :
( ( A != nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(110,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( successively_list_a @ A @ ( append_list_a @ B @ C ) )
= ( ( successively_list_a @ A @ B )
& ( successively_list_a @ A @ C )
& ( ( B = nil_list_a )
| ( C = nil_list_a )
| ( A @ ( last_list_a @ B ) @ ( hd_list_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_successively__append__iff) ).
thf(773,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( successively_list_a @ A @ ( append_list_a @ B @ C ) )
= ( ( successively_list_a @ A @ B )
& ( successively_list_a @ A @ C )
& ( ( B = nil_list_a )
| ( C = nil_list_a )
| ( A @ ( last_list_a @ B ) @ ( hd_list_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(140,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( append_list_a @ ( butlast_list_a @ A ) @ ( cons_list_a @ ( last_list_a @ A ) @ nil_list_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_append__butlast__last__id) ).
thf(926,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ( append_list_a @ ( butlast_list_a @ A ) @ ( cons_list_a @ ( last_list_a @ A ) @ nil_list_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(177,axiom,
! [A: a,B: list_a] :
( ( hd_a @ ( cons_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_list_Osel_I1_J) ).
thf(1086,plain,
! [A: a,B: list_a] :
( ( hd_a @ ( cons_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(144,axiom,
! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( cons_list_a @ A @ B )
= ( append_list_a @ C @ D ) )
= ( ( ( C = nil_list_a )
& ( ( cons_list_a @ A @ B )
= D ) )
| ? [E: list_list_a] :
( ( ( cons_list_a @ A @ E )
= C )
& ( B
= ( append_list_a @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Cons__eq__append__conv) ).
thf(938,plain,
! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( cons_list_a @ A @ B )
= ( append_list_a @ C @ D ) )
= ( ( ( C = nil_list_a )
& ( ( cons_list_a @ A @ B )
= D ) )
| ? [E: list_list_a] :
( ( ( cons_list_a @ A @ E )
= C )
& ( B
= ( append_list_a @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(324,axiom,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_append__self__conv) ).
thf(1846,plain,
! [A: list_a,B: list_a] :
( ( ( append_a @ A @ B )
= A )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(172,axiom,
! [A: list_a,B: list_a,C: a > a > a,D: a,E: a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( map2_a_a_a @ C @ ( append_a @ A @ ( cons_a @ D @ nil_a ) ) @ ( append_a @ B @ ( cons_a @ E @ nil_a ) ) )
= ( append_a @ ( map2_a_a_a @ C @ A @ B ) @ ( cons_a @ ( C @ D @ E ) @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_map2__snoc__snoc) ).
thf(1054,plain,
! [A: list_a,B: list_a,C: a > a > a,D: a,E: a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( map2_a_a_a @ C @ ( append_a @ A @ ( cons_a @ D @ nil_a ) ) @ ( append_a @ B @ ( cons_a @ E @ nil_a ) ) )
= ( append_a @ ( map2_a_a_a @ C @ A @ B ) @ ( cons_a @ ( C @ D @ E ) @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(308,axiom,
! [A: a > a > a,B: a,C: list_a,D: a,E: list_a] :
( ( map2_a_a_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
= ( cons_a @ ( A @ B @ D ) @ ( map2_a_a_a @ A @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_map2__Cons__Cons) ).
thf(1727,plain,
! [A: a > a > a,B: a,C: list_a,D: a,E: list_a] :
( ( map2_a_a_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
= ( cons_a @ ( A @ B @ D ) @ ( map2_a_a_a @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(315,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( butlast_a @ ( append_a @ B @ A ) )
= ( butlast_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( butlast_a @ ( append_a @ B @ A ) )
= ( append_a @ B @ ( butlast_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_butlast__append) ).
thf(1764,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( butlast_a @ ( append_a @ B @ A ) )
= ( butlast_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( butlast_a @ ( append_a @ B @ A ) )
= ( append_a @ B @ ( butlast_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(37,axiom,
! [A: list_list_a,B: list_a,C: list_list_a] :
( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
= C )
= ( ( C != nil_list_a )
& ( ( butlast_list_a @ C )
= A )
& ( ( last_list_a @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_snoc__eq__iff__butlast) ).
thf(425,plain,
! [A: list_list_a,B: list_a,C: list_list_a] :
( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
= C )
= ( ( C != nil_list_a )
& ( ( butlast_list_a @ C )
= A )
& ( ( last_list_a @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(299,axiom,
! [A: list_a,B: list_a,C: a,D: list_a] :
( ( ( append_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( ( A = nil_a )
& ( B
= ( cons_a @ C @ D ) ) )
| ? [E: list_a] :
( ( A
= ( cons_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_append__eq__Cons__conv) ).
thf(1698,plain,
! [A: list_a,B: list_a,C: a,D: list_a] :
( ( ( append_a @ A @ B )
= ( cons_a @ C @ D ) )
= ( ( ( A = nil_a )
& ( B
= ( cons_a @ C @ D ) ) )
| ? [E: list_a] :
( ( A
= ( cons_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(200,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_append__Nil2) ).
thf(1219,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(234,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_last__append) ).
thf(1374,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( append_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(152,axiom,
! [A: list_a > list_a > $o,B: list_list_a] :
( ( successively_list_a @ A @ B )
=> ( ( B != nil_list_a )
=> ( ! [C: list_a] :
( B
!= ( cons_list_a @ C @ nil_list_a ) )
=> ~ ! [C: list_a,D: list_a,E: list_list_a] :
( ( B
= ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_successively_Oelims_I2_J) ).
thf(975,plain,
! [A: list_a > list_a > $o,B: list_list_a] :
( ( successively_list_a @ A @ B )
=> ( ( B != nil_list_a )
=> ( ! [C: list_a] :
( B
!= ( cons_list_a @ C @ nil_list_a ) )
=> ~ ! [C: list_a,D: list_a,E: list_list_a] :
( ( B
= ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
=> ~ ( ( A @ C @ D )
& ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(157,axiom,
! [A: list_a,B: list_a > $o] :
( ( member_list_a2 @ A @ ( collect_list_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__Collect__eq) ).
thf(1007,plain,
! [A: list_a,B: list_a > $o] :
( ( member_list_a2 @ A @ ( collect_list_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(102,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_list_a] :
~ ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ord_Olexordp__eq__simps_I3_J) ).
thf(732,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_list_a] :
~ ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(237,axiom,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ C @ D ) )
& ( B
= ( append_a @ C @ E ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( hd_a @ D )
!= ( hd_a @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_longest__common__prefix) ).
thf(1388,plain,
! [A: list_a,B: list_a] :
? [C: list_a,D: list_a,E: list_a] :
( ( A
= ( append_a @ C @ D ) )
& ( B
= ( append_a @ C @ E ) )
& ( ( D = nil_a )
| ( E = nil_a )
| ( ( hd_a @ D )
!= ( hd_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(104,axiom,
! [A: list_list_a] :
( ( ( rotate1_list_a @ A )
= nil_list_a )
= ( A = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_rotate1__is__Nil__conv) ).
thf(743,plain,
! [A: list_list_a] :
( ( ( rotate1_list_a @ A )
= nil_list_a )
= ( A = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(265,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ( append_a @ ( butlast_a @ A ) @ ( cons_a @ ( last_a @ A ) @ nil_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_append__butlast__last__id) ).
thf(1535,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ( append_a @ ( butlast_a @ A ) @ ( cons_a @ ( last_a @ A ) @ nil_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(300,axiom,
! [A: a] :
( ( insert_a @ A @ nil_a )
= ( cons_a @ A @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_insert__Nil) ).
thf(1701,plain,
! [A: a] :
( ( insert_a @ A @ nil_a )
= ( cons_a @ A @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(186,axiom,
! [A: list_a,B: a] :
( ( butlast_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_butlast__snoc) ).
thf(1124,plain,
! [A: list_a,B: a] :
( ( butlast_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(127,axiom,
( lexordp_eq_list_a
= ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ? [D: list_list_a] :
( ( B = nil_list_a )
& ( C = D ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord_Olexordp__eq_Osimps) ).
thf(875,plain,
( lexordp_eq_list_a
= ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ? [D: list_list_a] :
( ( B = nil_list_a )
& ( C = D ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(120,axiom,
! [A: list_a > list_a > $o,B: list_a] : ( successively_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_successively_Osimps_I2_J) ).
thf(826,plain,
! [A: list_a > list_a > $o,B: list_a] : ( successively_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(68,axiom,
! [A: list_list_a] :
( ( append_list_a @ A @ nil_list_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_append__Nil2) ).
thf(545,plain,
! [A: list_list_a] :
( ( append_list_a @ A @ nil_list_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(258,axiom,
! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
( ( lexordp_eq_a @ A @ B @ C )
=> ( ! [E: list_a] : ( D @ nil_a @ E )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ( A @ E @ F )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ord_Olexordp__eq_Oinducts) ).
thf(1488,plain,
! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
( ( lexordp_eq_a @ A @ B @ C )
=> ( ! [E: list_a] : ( D @ nil_a @ E )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ( A @ E @ F )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) )
=> ( ! [E: a,F: a,G: list_a,H: list_a] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(73,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( lexordp_eq_list_a @ A @ B @ C )
=> ( ( B != nil_list_a )
=> ( ! [D: list_a] :
( ? [E: list_list_a] :
( B
= ( cons_list_a @ D @ E ) )
=> ! [E: list_a] :
( ? [F: list_list_a] :
( C
= ( cons_list_a @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord_Olexordp__eq_Ocases) ).
thf(572,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
( ( lexordp_eq_list_a @ A @ B @ C )
=> ( ( B != nil_list_a )
=> ( ! [D: list_a] :
( ? [E: list_list_a] :
( B
= ( cons_list_a @ D @ E ) )
=> ! [E: list_a] :
( ? [F: list_list_a] :
( C
= ( cons_list_a @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(302,axiom,
! [A: list_a,B: a,C: a] :
( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ ( cons_a @ C @ nil_a ) ) ) )
= ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( if_list_a @ ( B = C ) @ nil_a @ ( cons_a @ C @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_remdups__adj__append__two) ).
thf(1707,plain,
! [A: list_a,B: a,C: a] :
( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ ( cons_a @ C @ nil_a ) ) ) )
= ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( if_list_a @ ( B = C ) @ nil_a @ ( cons_a @ C @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(233,axiom,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( member_list_a2 @ ( cons_a @ A @ B ) @ ( shuffles_a @ C @ D ) )
= ( ( ( C != nil_a )
& ( ( hd_a @ C )
= A )
& ( member_list_a2 @ B @ ( shuffles_a @ ( tl_a @ C ) @ D ) ) )
| ( ( D != nil_a )
& ( ( hd_a @ D )
= A )
& ( member_list_a2 @ B @ ( shuffles_a @ C @ ( tl_a @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_Cons__in__shuffles__iff) ).
thf(1371,plain,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( member_list_a2 @ ( cons_a @ A @ B ) @ ( shuffles_a @ C @ D ) )
= ( ( ( C != nil_a )
& ( ( hd_a @ C )
= A )
& ( member_list_a2 @ B @ ( shuffles_a @ ( tl_a @ C ) @ D ) ) )
| ( ( D != nil_a )
& ( ( hd_a @ D )
= A )
& ( member_list_a2 @ B @ ( shuffles_a @ C @ ( tl_a @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(220,axiom,
! [A: a > a > $o] : ( successively_a @ A @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_successively_Osimps_I1_J) ).
thf(1312,plain,
! [A: a > a > $o] : ( successively_a @ A @ nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(310,axiom,
! [A: a > list_a > $o,B: list_a,C: list_list_a] :
( ( listrelp_a_list_a @ A @ B @ C )
=> ( ( ( B = nil_a )
=> ( C != nil_list_a ) )
=> ~ ! [D: a,E: list_a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_listrelp_Ocases) ).
thf(1733,plain,
! [A: a > list_a > $o,B: list_a,C: list_list_a] :
( ( listrelp_a_list_a @ A @ B @ C )
=> ( ( ( B = nil_a )
=> ( C != nil_list_a ) )
=> ~ ! [D: a,E: list_a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_list_a] :
( ( C
= ( cons_list_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(173,axiom,
( ( remdups_adj_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_remdups__adj_Osimps_I1_J) ).
thf(1058,plain,
( ( remdups_adj_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(207,axiom,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_append_Oright__neutral) ).
thf(1239,plain,
! [A: list_a] :
( ( append_a @ A @ nil_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(179,axiom,
! [A: list_a,B: list_a] :
( ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_Nil__in__shuffles) ).
thf(1092,plain,
! [A: list_a,B: list_a] :
( ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(3,axiom,
! [A: list_list_a,B: set_list_list_a,C: list_a] :
( ( member_list_list_a @ A @ ( bNF_Gr1972240547list_a @ B @ C ) )
=> ( member_list_list_a @ ( cons_list_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ShiftD) ).
thf(335,plain,
! [A: list_list_a,B: set_list_list_a,C: list_a] :
( ( member_list_list_a @ A @ ( bNF_Gr1972240547list_a @ B @ C ) )
=> ( member_list_list_a @ ( cons_list_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(137,axiom,
! [A: list_a] :
~ ( member_list_a @ nil_list_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_member__rec_I2_J) ).
thf(919,plain,
! [A: list_a] :
~ ( member_list_a @ nil_list_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(92,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_append__same__eq) ).
thf(681,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(35,axiom,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
= ( ( distinct_adj_list_a @ A )
& ( distinct_adj_list_a @ B )
& ( ( A = nil_list_a )
| ( B = nil_list_a )
| ( ( last_list_a @ A )
!= ( hd_list_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_distinct__adj__append__iff) ).
thf(419,plain,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
= ( ( distinct_adj_list_a @ A )
& ( distinct_adj_list_a @ B )
& ( ( A = nil_list_a )
| ( B = nil_list_a )
| ( ( last_list_a @ A )
!= ( hd_list_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(263,axiom,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq_a @ A @ D @ E )
=> ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ord_Olexordp__eq_OCons__eq) ).
thf(1524,plain,
! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq_a @ A @ D @ E )
=> ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(231,axiom,
! [A: list_a > a > $o,B: list_list_a,C: list_a,D: list_list_a > list_a > $o] :
( ( listrelp_list_a_a @ A @ B @ C )
=> ( ( D @ nil_list_a @ nil_a )
=> ( ! [E: list_a,F: a,G: list_list_a,H: list_a] :
( ( A @ E @ F )
=> ( ( listrelp_list_a_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_listrelp_Oinducts) ).
thf(1349,plain,
! [A: list_a > a > $o,B: list_list_a,C: list_a,D: list_list_a > list_a > $o] :
( ( listrelp_list_a_a @ A @ B @ C )
=> ( ( D @ nil_list_a @ nil_a )
=> ( ! [E: list_a,F: a,G: list_list_a,H: list_a] :
( ( A @ E @ F )
=> ( ( listrelp_list_a_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
=> ( D @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(155,axiom,
! [A: list_list_a] :
( ( append_list_a @ A @ nil_list_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_append_Oright__neutral) ).
thf(996,plain,
! [A: list_list_a] :
( ( append_list_a @ A @ nil_list_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(280,axiom,
! [A: a > list_a] :
( ( maps_a_a @ A @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_maps__simps_I2_J) ).
thf(1603,plain,
! [A: a > list_a] :
( ( maps_a_a @ A @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(44,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_append__eq__append__conv2) ).
thf(451,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a] :
( ( ( append_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ? [E: list_a] :
( ( ( A
= ( append_a @ C @ E ) )
& ( ( append_a @ E @ B )
= D ) )
| ( ( ( append_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(307,axiom,
! [A: list_a,B: a] :
( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_last__ConsL) ).
thf(1722,plain,
! [A: list_a,B: a] :
( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(134,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
( ( lexordp_eq_list_a @ A @ B @ C )
=> ( ! [E: list_list_a] : ( D @ nil_list_a @ E )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq_list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ord_Olexordp__eq_Oinducts) ).
thf(900,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
( ( lexordp_eq_list_a @ A @ B @ C )
=> ( ! [E: list_list_a] : ( D @ nil_list_a @ E )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ( A @ E @ F )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) )
=> ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq_list_a @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(30,axiom,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_distinct__adj__appendD2) ).
thf(406,plain,
! [A: list_list_a,B: list_list_a] :
( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
=> ( distinct_adj_list_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(59,axiom,
! [A: list_a,B: list_list_a] :
( ( concat_a @ ( cons_list_a @ A @ B ) )
= ( append_a @ A @ ( concat_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_concat_Osimps_I2_J) ).
thf(509,plain,
! [A: list_a,B: list_list_a] :
( ( concat_a @ ( cons_list_a @ A @ B ) )
= ( append_a @ A @ ( concat_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(129,axiom,
! [A: list_a,B: set_list_list_a,C: list_list_a] :
( ( member_list_a2 @ A @ ( bNF_Gr1046450207list_a @ B @ C ) )
=> ( member_list_list_a @ ( append_list_a @ C @ ( cons_list_a @ A @ nil_list_a ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_SuccD) ).
thf(880,plain,
! [A: list_a,B: set_list_list_a,C: list_list_a] :
( ( member_list_a2 @ A @ ( bNF_Gr1046450207list_a @ B @ C ) )
=> ( member_list_list_a @ ( append_list_a @ C @ ( cons_list_a @ A @ nil_list_a ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(293,axiom,
! [A: list_a] :
( ( ( remdups_adj_a @ A )
= nil_a )
= ( A = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_remdups__adj__Nil__iff) ).
thf(1667,plain,
! [A: list_a] :
( ( ( remdups_adj_a @ A )
= nil_a )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(82,axiom,
! [A: list_a,B: list_list_a,C: list_a] :
( ( member_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( ( A = C )
| ( member_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_member__rec_I1_J) ).
thf(631,plain,
! [A: list_a,B: list_list_a,C: list_a] :
( ( member_list_a @ ( cons_list_a @ A @ B ) @ C )
= ( ( A = C )
| ( member_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(100,axiom,
( concat_list_a
= ( ^ [A: list_list_list_a] : ( foldr_769741863list_a @ append_list_a @ A @ nil_list_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_concat__conv__foldr) ).
thf(726,plain,
( concat_list_a
= ( ^ [A: list_list_list_a] : ( foldr_769741863list_a @ append_list_a @ A @ nil_list_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(150,axiom,
! [A: list_list_a,B: list_list_a] :
? [C: list_list_a,D: list_list_a,E: list_list_a] :
( ( A
= ( append_list_a @ C @ D ) )
& ( B
= ( append_list_a @ C @ E ) )
& ( ( D = nil_list_a )
| ( E = nil_list_a )
| ( ( hd_list_a @ D )
!= ( hd_list_a @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_longest__common__prefix) ).
thf(964,plain,
! [A: list_list_a,B: list_list_a] :
? [C: list_list_a,D: list_list_a,E: list_list_a] :
( ( A
= ( append_list_a @ C @ D ) )
& ( B
= ( append_list_a @ C @ E ) )
& ( ( D = nil_list_a )
| ( E = nil_list_a )
| ( ( hd_list_a @ D )
!= ( hd_list_a @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(269,axiom,
! [A: list_a] :
( ( splice_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_splice_Osimps_I1_J) ).
thf(1556,plain,
! [A: list_a] :
( ( splice_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(322,axiom,
! [A: a,B: a,C: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj_a @ ( cons_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_distinct__adj__Cons__Cons) ).
thf(1838,plain,
! [A: a,B: a,C: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( ( A != B )
& ( distinct_adj_a @ ( cons_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(225,axiom,
! [A: a] :
( ( remdups_adj_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_remdups__adj_Osimps_I2_J) ).
thf(1325,plain,
! [A: a] :
( ( remdups_adj_a @ ( cons_a @ A @ nil_a ) )
= ( cons_a @ A @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(48,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A
= ( append_list_a @ A @ B ) )
= ( B = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_self__append__conv) ).
thf(462,plain,
! [A: list_list_a,B: list_list_a] :
( ( A
= ( append_list_a @ A @ B ) )
= ( B = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(142,axiom,
( ( rotate1_list_a @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_rotate1_Osimps_I1_J) ).
thf(932,plain,
( ( rotate1_list_a @ nil_list_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(153,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_append_Oassoc) ).
thf(983,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( append_a @ ( append_a @ A @ B ) @ C )
= ( append_a @ A @ ( append_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(27,axiom,
( ( tl_list_a @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_list_Osel_I2_J) ).
thf(399,plain,
( ( tl_list_a @ nil_list_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(277,axiom,
! [A: a > a > $o,B: list_a] :
( ( lexordp_eq_a @ A @ B @ nil_a )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ord_Olexordp__eq__simps_I2_J) ).
thf(1594,plain,
! [A: a > a > $o,B: list_a] :
( ( lexordp_eq_a @ A @ B @ nil_a )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(149,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_append__eq__appendI) ).
thf(959,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( append_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( append_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(287,axiom,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( successively_a @ A @ ( append_a @ B @ C ) )
= ( ( successively_a @ A @ B )
& ( successively_a @ A @ C )
& ( ( B = nil_a )
| ( C = nil_a )
| ( A @ ( last_a @ B ) @ ( hd_a @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_successively__append__iff) ).
thf(1643,plain,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( successively_a @ A @ ( append_a @ B @ C ) )
= ( ( successively_a @ A @ B )
& ( successively_a @ A @ C )
& ( ( B = nil_a )
| ( C = nil_a )
| ( A @ ( last_a @ B ) @ ( hd_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(160,axiom,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list_OdiscI) ).
thf(1015,plain,
! [A: list_a,B: a,C: list_a] :
( ( A
= ( cons_a @ B @ C ) )
=> ( A != nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(76,axiom,
! [A: list_list_a,B: list_a,C: list_a] :
( ( ( concat_a @ A )
= ( append_a @ B @ C ) )
=> ( ( A != nil_list_a )
=> ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
( ( A
= ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
& ( B
= ( append_a @ ( concat_a @ D ) @ E ) )
& ( C
= ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_concat__eq__appendD) ).
thf(608,plain,
! [A: list_list_a,B: list_a,C: list_a] :
( ( ( concat_a @ A )
= ( append_a @ B @ C ) )
=> ( ( A != nil_list_a )
=> ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
( ( A
= ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
& ( B
= ( append_a @ ( concat_a @ D ) @ E ) )
& ( C
= ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(154,axiom,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a,D: list_list_a] :
( ( A @ D )
=> ( A @ ( cons_list_a @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_list_Oinducts) ).
thf(986,plain,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a,D: list_list_a] :
( ( A @ D )
=> ( A @ ( cons_list_a @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(317,axiom,
! [A: list_a,B: list_a,C: list_a] :
( ( ( splice_a @ A @ B )
= C )
=> ( ( ( A = nil_a )
=> ( C != B ) )
=> ~ ! [D: a,E: list_a] :
( ( A
= ( cons_a @ D @ E ) )
=> ( C
!= ( cons_a @ D @ ( splice_a @ B @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_splice_Oelims) ).
thf(1775,plain,
! [A: list_a,B: list_a,C: list_a] :
( ( ( splice_a @ A @ B )
= C )
=> ( ( ( A = nil_a )
=> ( C != B ) )
=> ~ ! [D: a,E: list_a] :
( ( A
= ( cons_a @ D @ E ) )
=> ( C
!= ( cons_a @ D @ ( splice_a @ B @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(138,axiom,
lexordp_eq_a = lexordp_eq_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord_Olexordp__eq_Ocong) ).
thf(922,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(271,axiom,
! [A: list_list_a,B: list_a,C: list_a] :
( ( ( concat_a @ A )
= ( append_a @ B @ C ) )
= ( ( ( A = nil_list_a )
=> ( ( B = nil_a )
& ( C = nil_a ) ) )
& ( ( A != nil_list_a )
=> ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
( ( A
= ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
& ( B
= ( append_a @ ( concat_a @ D ) @ E ) )
& ( C
= ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_concat__eq__append__conv) ).
thf(1562,plain,
! [A: list_list_a,B: list_a,C: list_a] :
( ( ( concat_a @ A )
= ( append_a @ B @ C ) )
= ( ( ( A = nil_list_a )
=> ( ( B = nil_a )
& ( C = nil_a ) ) )
& ( ( A != nil_list_a )
=> ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
( ( A
= ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
& ( B
= ( append_a @ ( concat_a @ D ) @ E ) )
& ( C
= ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(135,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_a] :
( A
!= ( cons_list_a @ B @ nil_list_a ) )
=> ~ ! [B: list_a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_remdups__adj_Ocases) ).
thf(912,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_a] :
( A
!= ( cons_list_a @ B @ nil_list_a ) )
=> ~ ! [B: list_a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(195,axiom,
! [A: list_a > a > $o,B: list_list_a,C: list_a] :
( ( listrelp_list_a_a @ A @ B @ C )
=> ( ( ( B = nil_list_a )
=> ( C != nil_a ) )
=> ~ ! [D: list_a,E: a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_listrelp_Ocases) ).
thf(1171,plain,
! [A: list_a > a > $o,B: list_list_a,C: list_a] :
( ( listrelp_list_a_a @ A @ B @ C )
=> ( ( ( B = nil_list_a )
=> ( C != nil_a ) )
=> ~ ! [D: list_a,E: a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(323,axiom,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( B = nil_a )
=> ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Nil__in__shufflesI) ).
thf(1841,plain,
! [A: list_a,B: list_a] :
( ( A = nil_a )
=> ( ( B = nil_a )
=> ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(238,axiom,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_last_Osimps) ).
thf(1396,plain,
! [A: list_a,B: a] :
( ( ( A = nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= B ) )
& ( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(84,axiom,
! [A: list_list_a,B: list_a,C: set_list_list_a] :
( ( member_list_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) @ C )
=> ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_SuccI) ).
thf(636,plain,
! [A: list_list_a,B: list_a,C: set_list_list_a] :
( ( member_list_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) @ C )
=> ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(168,axiom,
! [A: a > list_list_a] :
( ( maps_a_list_a @ A @ nil_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_maps__simps_I2_J) ).
thf(1044,plain,
! [A: a > list_list_a] :
( ( maps_a_list_a @ A @ nil_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(50,axiom,
! [A: list_list_a,B: list_a] :
( ( ( A = nil_list_a )
=> ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
= nil_list_a ) )
& ( ( A != nil_list_a )
=> ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
= ( cons_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_butlast_Osimps_I2_J) ).
thf(473,plain,
! [A: list_list_a,B: list_a] :
( ( ( A = nil_list_a )
=> ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
= nil_list_a ) )
& ( ( A != nil_list_a )
=> ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
= ( cons_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(165,axiom,
! [A: list_a,B: a > a > a,C: a,D: list_a] :
( ( A != nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_map2__Cons__not__empty) ).
thf(1034,plain,
! [A: list_a,B: a > a > a,C: a,D: list_a] :
( ( A != nil_a )
=> ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
= ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(291,axiom,
! [A: a > a > $o,B: a,C: list_a,D: a,E: list_a] :
( ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_ord_Olexordp__eq__simps_I4_J) ).
thf(1662,plain,
! [A: a > a > $o,B: a,C: list_a,D: a,E: list_a] :
( ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(193,axiom,
( concat_a
= ( ^ [A: list_list_a] : ( foldr_list_a_list_a @ append_a @ A @ nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_concat__conv__foldr) ).
thf(1166,plain,
( concat_a
= ( ^ [A: list_list_a] : ( foldr_list_a_list_a @ append_a @ A @ nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(146,axiom,
! [A: list_list_a,B: list_list_a > $o] :
( ( A != nil_list_a )
=> ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_list_a] :
( ( D != nil_list_a )
=> ( ( B @ D )
=> ( B @ ( cons_list_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_list__nonempty__induct) ).
thf(944,plain,
! [A: list_list_a,B: list_list_a > $o] :
( ( A != nil_list_a )
=> ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_list_a] :
( ( D != nil_list_a )
=> ( ( B @ D )
=> ( B @ ( cons_list_a @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(251,axiom,
! [A: set_list_a,B: a] :
( ( member_list_a2 @ nil_a @ A )
=> ( ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ A @ nil_a ) )
=> ( member_list_a2 @ nil_a @ ( bNF_Greatest_Shift_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_empty__Shift) ).
thf(1467,plain,
! [A: set_list_a,B: a] :
( ( member_list_a2 @ nil_a @ A )
=> ( ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ A @ nil_a ) )
=> ( member_list_a2 @ nil_a @ ( bNF_Greatest_Shift_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(115,axiom,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_a,E: list_list_a] :
( ( A @ E )
=> ( ( A @ ( cons_list_a @ D @ E ) )
=> ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_induct__list012) ).
thf(795,plain,
! [A: list_list_a > $o,B: list_list_a] :
( ( A @ nil_list_a )
=> ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_a,E: list_list_a] :
( ( A @ E )
=> ( ( A @ ( cons_list_a @ D @ E ) )
=> ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(69,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= B )
= ( A = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_append__self__conv2) ).
thf(548,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= B )
= ( A = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(189,axiom,
! [A: a > a > $o,B: list_a,C: $o] :
( ( ( successively_a @ A @ B )
= C )
=> ( ( ( B = nil_a )
=> ~ C )
=> ( ( ? [D: a] :
( B
= ( cons_a @ D @ nil_a ) )
=> ~ C )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ ( cons_a @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively_a @ A @ ( cons_a @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_successively_Oelims_I1_J) ).
thf(1134,plain,
! [A: a > a > $o,B: list_a,C: $o] :
( ( ( successively_a @ A @ B )
= C )
=> ( ( ( B = nil_a )
=> ~ C )
=> ( ( ? [D: a] :
( B
= ( cons_a @ D @ nil_a ) )
=> ~ C )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ ( cons_a @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively_a @ A @ ( cons_a @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(106,axiom,
! [A: list_a > list_a,B: list_a,C: list_list_a] :
( ( maps_list_a_a @ A @ ( cons_list_a @ B @ C ) )
= ( append_a @ ( A @ B ) @ ( maps_list_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_maps__simps_I1_J) ).
thf(749,plain,
! [A: list_a > list_a,B: list_a,C: list_list_a] :
( ( maps_list_a_a @ A @ ( cons_list_a @ B @ C ) )
= ( append_a @ ( A @ B ) @ ( maps_list_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(61,axiom,
! [A: list_list_a,B: list_a] :
( ( last_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_last__snoc) ).
thf(516,plain,
! [A: list_list_a,B: list_a] :
( ( last_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6,axiom,
! [A: list_list_a] :
( ( ( A = nil_list_a )
| ( ( tl_list_a @ A )
!= nil_list_a ) )
=> ( ( last_list_a @ ( tl_list_a @ A ) )
= ( last_list_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_last__tl) ).
thf(342,plain,
! [A: list_list_a] :
( ( ( A = nil_list_a )
| ( ( tl_list_a @ A )
!= nil_list_a ) )
=> ( ( last_list_a @ ( tl_list_a @ A ) )
= ( last_list_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(119,axiom,
! [A: list_a > $o] :
~ ( list_ex1_list_a @ A @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list__ex1__simps_I1_J) ).
thf(823,plain,
! [A: list_a > $o] :
~ ( list_ex1_list_a @ A @ nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(170,axiom,
! [A: set_list_a,B: a,C: list_a] :
( ( bNF_Greatest_Succ_a @ ( bNF_Greatest_Shift_a @ A @ B ) @ C )
= ( bNF_Greatest_Succ_a @ A @ ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Succ__Shift) ).
thf(1049,plain,
! [A: set_list_a,B: a,C: list_a] :
( ( bNF_Greatest_Succ_a @ ( bNF_Greatest_Shift_a @ A @ B ) @ C )
= ( bNF_Greatest_Succ_a @ A @ ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(111,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a2 @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Collect__mem__eq) ).
thf(776,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a2 @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(64,axiom,
! [A: list_list_a,B: list_a] :
( ( A != nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_last__ConsR) ).
thf(525,plain,
! [A: list_list_a,B: list_a] :
( ( A != nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(95,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
= ( butlast_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
= ( append_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_butlast__append) ).
thf(690,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
= ( butlast_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
= ( append_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(126,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_same__append__eq) ).
thf(872,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(202,axiom,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_append__Nil) ).
thf(1225,plain,
! [A: list_a] :
( ( append_a @ nil_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(33,axiom,
( list_strict_asc_nat
= ( list_ord_nat @ ord_less_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_list__strict__asc__def) ).
thf(414,plain,
( list_strict_asc_nat
= ( list_ord_nat @ ord_less_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(312,axiom,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
= ( ( distinct_adj_a @ A )
& ( distinct_adj_a @ B )
& ( ( A = nil_a )
| ( B = nil_a )
| ( ( last_a @ A )
!= ( hd_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_distinct__adj__append__iff) ).
thf(1753,plain,
! [A: list_a,B: list_a] :
( ( distinct_adj_a @ ( append_a @ A @ B ) )
= ( ( distinct_adj_a @ A )
& ( distinct_adj_a @ B )
& ( ( A = nil_a )
| ( B = nil_a )
| ( ( last_a @ A )
!= ( hd_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(212,axiom,
( listrelp_a_list_a
= ( ^ [A: a > list_a > $o,B: list_a,C: list_list_a] :
( ( ( B = nil_a )
& ( C = nil_list_a ) )
| ? [D: a,E: list_a,F: list_a,G: list_list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_listrelp_Osimps) ).
thf(1267,plain,
( listrelp_a_list_a
= ( ^ [A: a > list_a > $o,B: list_a,C: list_list_a] :
( ( ( B = nil_a )
& ( C = nil_list_a ) )
| ? [D: a,E: list_a,F: list_a,G: list_list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_list_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(305,axiom,
! [A: a > a,B: list_a] :
( ( map_tailrec_rev_a_a @ A @ nil_a @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_map__tailrec__rev_Osimps_I1_J) ).
thf(1716,plain,
! [A: a > a,B: list_a] :
( ( map_tailrec_rev_a_a @ A @ nil_a @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(114,axiom,
! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a > list_a > $o,E: list_a,F: list_list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_list_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_sorted__wrt_Oinduct) ).
thf(791,plain,
! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
=> ( ! [D: list_a > list_a > $o,E: list_a,F: list_list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_list_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(196,axiom,
! [A: list_a,B: list_a] :
( ( ( remdups_adj_a @ A )
= B )
=> ( ( ( A = nil_a )
=> ( B != nil_a ) )
=> ( ! [C: a] :
( ( A
= ( cons_a @ C @ nil_a ) )
=> ( B
!= ( cons_a @ C @ nil_a ) ) )
=> ~ ! [C: a,D: a,E: list_a] :
( ( A
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdups_adj_a @ ( cons_a @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons_a @ C @ ( remdups_adj_a @ ( cons_a @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_remdups__adj_Oelims) ).
thf(1188,plain,
! [A: list_a,B: list_a] :
( ( ( remdups_adj_a @ A )
= B )
=> ( ( ( A = nil_a )
=> ( B != nil_a ) )
=> ( ! [C: a] :
( ( A
= ( cons_a @ C @ nil_a ) )
=> ( B
!= ( cons_a @ C @ nil_a ) ) )
=> ~ ! [C: a,D: a,E: list_a] :
( ( A
= ( cons_a @ C @ ( cons_a @ D @ E ) ) )
=> ~ ( ( ( C = D )
=> ( B
= ( remdups_adj_a @ ( cons_a @ C @ E ) ) ) )
& ( ( C != D )
=> ( B
= ( cons_a @ C @ ( remdups_adj_a @ ( cons_a @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(166,axiom,
! [A: list_list_a > list_a > $o,B: list_list_a,C: list_a] :
( ( A @ nil_list_a @ nil_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_list_a @ ( cons_a @ D @ E ) )
=> ( ! [D: list_a,E: list_list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_list__induct2_H) ).
thf(1038,plain,
! [A: list_list_a > list_a > $o,B: list_list_a,C: list_a] :
( ( A @ nil_list_a @ nil_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_a )
=> ( ! [D: a,E: list_a] : ( A @ nil_list_a @ ( cons_a @ D @ E ) )
=> ( ! [D: list_a,E: list_list_a,F: a,G: list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(222,axiom,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ( ( C = nil_a )
& ( ( cons_a @ A @ B )
= D ) )
| ? [E: list_a] :
( ( ( cons_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Cons__eq__append__conv) ).
thf(1317,plain,
! [A: a,B: list_a,C: list_a,D: list_a] :
( ( ( cons_a @ A @ B )
= ( append_a @ C @ D ) )
= ( ( ( C = nil_a )
& ( ( cons_a @ A @ B )
= D ) )
| ? [E: list_a] :
( ( ( cons_a @ A @ E )
= C )
& ( B
= ( append_a @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(266,axiom,
( ( tl_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_list_Osel_I2_J) ).
thf(1538,plain,
( ( tl_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(295,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ( rotate1_a @ A )
= ( append_a @ ( tl_a @ A ) @ ( cons_a @ ( hd_a @ A ) @ nil_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_rotate1__hd__tl) ).
thf(1679,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ( rotate1_a @ A )
= ( append_a @ ( tl_a @ A ) @ ( cons_a @ ( hd_a @ A ) @ nil_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(188,axiom,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_eq__Nil__appendI) ).
thf(1130,plain,
! [A: list_a,B: list_a] :
( ( A = B )
=> ( A
= ( append_a @ nil_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(215,axiom,
! [A: a,B: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ B ) )
=> ( distinct_adj_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_distinct__adj__ConsD) ).
thf(1285,plain,
! [A: a,B: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ B ) )
=> ( distinct_adj_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(239,axiom,
! [A: a] : ( distinct_adj_a @ ( cons_a @ A @ nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_distinct__adj__singleton) ).
thf(1404,plain,
! [A: a] : ( distinct_adj_a @ ( cons_a @ A @ nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(325,axiom,
! [A: list_a] :
( ( ( A = nil_a )
| ( ( tl_a @ A )
!= nil_a ) )
=> ( ( last_a @ ( tl_a @ A ) )
= ( last_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_last__tl) ).
thf(1849,plain,
! [A: list_a] :
( ( ( A = nil_a )
| ( ( tl_a @ A )
!= nil_a ) )
=> ( ( last_a @ ( tl_a @ A ) )
= ( last_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(171,axiom,
( ( concat_a @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_concat_Osimps_I1_J) ).
thf(1052,plain,
( ( concat_a @ nil_list_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(242,axiom,
! [A: list_a,B: a,C: set_list_a] :
( ( member_list_a2 @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) @ C )
=> ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_SuccI) ).
thf(1427,plain,
! [A: list_a,B: a,C: set_list_a] :
( ( member_list_a2 @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) @ C )
=> ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(260,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_sorted__wrt_Oinduct) ).
thf(1504,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a,F: list_a] :
( ( A @ D @ F )
=> ( A @ D @ ( cons_a @ E @ F ) ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(22,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( ( listre1221556159list_a @ A @ D @ E )
=> ( listre1221556159list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_listrelp_OCons) ).
thf(386,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( ( listre1221556159list_a @ A @ D @ E )
=> ( listre1221556159list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(294,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
| ( B = nil_a )
| ( ( last_a @ A )
!= ( hd_a @ B ) ) )
=> ( ( remdups_adj_a @ ( append_a @ A @ B ) )
= ( append_a @ ( remdups_adj_a @ A ) @ ( remdups_adj_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_remdups__adj__append_H) ).
thf(1670,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
| ( B = nil_a )
| ( ( last_a @ A )
!= ( hd_a @ B ) ) )
=> ( ( remdups_adj_a @ ( append_a @ A @ B ) )
= ( append_a @ ( remdups_adj_a @ A ) @ ( remdups_adj_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(43,axiom,
! [A: list_list_a,B: list_a] :
( ( A = nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_last__ConsL) ).
thf(446,plain,
! [A: list_list_a,B: list_a] :
( ( A = nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(214,axiom,
! [A: a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
( ( ( map_ta41997947list_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_a )
=> ( D != C ) )
=> ~ ! [E: a,F: list_a] :
( ( B
= ( cons_a @ E @ F ) )
=> ( D
!= ( map_ta41997947list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_map__tailrec__rev_Oelims) ).
thf(1272,plain,
! [A: a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
( ( ( map_ta41997947list_a @ A @ B @ C )
= D )
=> ( ( ( B = nil_a )
=> ( D != C ) )
=> ~ ! [E: a,F: list_a] :
( ( B
= ( cons_a @ E @ F ) )
=> ( D
!= ( map_ta41997947list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(283,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_hd__append) ).
thf(1617,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ B ) ) )
& ( ( A != nil_a )
=> ( ( hd_a @ ( append_a @ A @ B ) )
= ( hd_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(49,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_hd__append) ).
thf(465,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ B ) ) )
& ( ( A != nil_list_a )
=> ( ( hd_list_a @ ( append_list_a @ A @ B ) )
= ( hd_list_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(248,axiom,
! [A: a > list_a] :
( ( bind_a_a @ nil_a @ A )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_bind__simps_I1_J) ).
thf(1459,plain,
! [A: a > list_a] :
( ( bind_a_a @ nil_a @ A )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(268,axiom,
! [A: list_a,B: list_a] :
( ( ( splice_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_split__Nil__iff) ).
thf(1553,plain,
! [A: list_a,B: list_a] :
( ( ( splice_a @ A @ B )
= nil_a )
= ( ( A = nil_a )
& ( B = nil_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(89,axiom,
! [A: list_a > list_a > list_a,B: list_list_a,C: list_list_a,D: list_a] :
( ( foldr_list_a_list_a @ A @ ( append_list_a @ B @ C ) @ D )
= ( foldr_list_a_list_a @ A @ B @ ( foldr_list_a_list_a @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_foldr__append) ).
thf(671,plain,
! [A: list_a > list_a > list_a,B: list_list_a,C: list_list_a,D: list_a] :
( ( foldr_list_a_list_a @ A @ ( append_list_a @ B @ C ) @ D )
= ( foldr_list_a_list_a @ A @ B @ ( foldr_list_a_list_a @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(321,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_transpose_Ocases) ).
thf(1834,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ( ! [B: list_list_a] :
( A
!= ( cons_list_a @ nil_a @ B ) )
=> ~ ! [B: a,C: list_a,D: list_list_a] :
( A
!= ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(131,axiom,
! [A: list_list_a] :
( ( append_list_a @ nil_list_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_append_Oleft__neutral) ).
thf(891,plain,
! [A: list_list_a] :
( ( append_list_a @ nil_list_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(246,axiom,
! [A: a > list_a > $o,B: a,C: list_a,D: list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( ( listrelp_a_list_a @ A @ D @ E )
=> ( listrelp_a_list_a @ A @ ( cons_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_listrelp_OCons) ).
thf(1448,plain,
! [A: a > list_a > $o,B: a,C: list_a,D: list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( ( listrelp_a_list_a @ A @ D @ E )
=> ( listrelp_a_list_a @ A @ ( cons_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(13,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ord_Olexordp__eq_OCons) ).
thf(363,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ( A @ B @ C )
=> ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(71,axiom,
! [A: list_a,B: list_list_a,C: list_a > list_a] :
( ( bind_list_a_a @ ( cons_list_a @ A @ B ) @ C )
= ( append_a @ ( C @ A ) @ ( bind_list_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_bind__simps_I2_J) ).
thf(556,plain,
! [A: list_a,B: list_list_a,C: list_a > list_a] :
( ( bind_list_a_a @ ( cons_list_a @ A @ B ) @ C )
= ( append_a @ ( C @ A ) @ ( bind_list_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(55,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
( ( ( append_list_a @ A @ B )
= C )
=> ( ( D
= ( append_list_a @ B @ E ) )
=> ( ( append_list_a @ A @ D )
= ( append_list_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_append__eq__appendI) ).
thf(495,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
( ( ( append_list_a @ A @ B )
= C )
=> ( ( D
= ( append_list_a @ B @ E ) )
=> ( ( append_list_a @ A @ D )
= ( append_list_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(289,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_list_Ocollapse) ).
thf(1654,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(158,axiom,
! [A: a > a > $o,B: a,C: a,D: list_a] :
( ( successively_a @ A @ ( cons_a @ B @ ( cons_a @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively_a @ A @ ( cons_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_successively_Osimps_I3_J) ).
thf(1010,plain,
! [A: a > a > $o,B: a,C: a,D: list_a] :
( ( successively_a @ A @ ( cons_a @ B @ ( cons_a @ C @ D ) ) )
= ( ( A @ B @ C )
& ( successively_a @ A @ ( cons_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(273,axiom,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ord_Olexordp__eq__simps_I1_J) ).
thf(1575,plain,
! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(288,axiom,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_rev__nonempty__induct) ).
thf(1646,plain,
! [A: list_a,B: list_a > $o] :
( ( A != nil_a )
=> ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
=> ( ! [C: a,D: list_a] :
( ( D != nil_a )
=> ( ( B @ D )
=> ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(236,axiom,
! [A: list_a > list_a] :
( ( maps_list_a_a @ A @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_maps__simps_I2_J) ).
thf(1385,plain,
! [A: list_a > list_a] :
( ( maps_list_a_a @ A @ nil_list_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(254,axiom,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_self__append__conv2) ).
thf(1476,plain,
! [A: list_a,B: list_a] :
( ( A
= ( append_a @ B @ A ) )
= ( B = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(261,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_remdups__adj_Ocases) ).
thf(1508,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( ! [B: a] :
( A
!= ( cons_a @ B @ nil_a ) )
=> ~ ! [B: a,C: a,D: list_a] :
( A
!= ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(8,axiom,
! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ord_Olexordp__eq__simps_I1_J) ).
thf(351,plain,
! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(285,axiom,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_successively_Oinduct) ).
thf(1629,plain,
! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
( ! [D: a > a > $o] : ( A @ D @ nil_a )
=> ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
=> ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
( ( A @ D @ ( cons_a @ F @ G ) )
=> ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(28,axiom,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq_list_a @ A @ D @ E )
=> ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ord_Olexordp__eq_OCons__eq) ).
thf(401,plain,
! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq_list_a @ A @ D @ E )
=> ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(164,axiom,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( B != nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_length__greater__imp__not__empty) ).
thf(1030,plain,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( B != nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(88,axiom,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ~ ! [B: list_list_a,C: list_a] :
( A
!= ( append_list_a @ B @ ( cons_list_a @ C @ nil_list_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_rev__exhaust) ).
thf(667,plain,
! [A: list_list_a] :
( ( A != nil_list_a )
=> ~ ! [B: list_list_a,C: list_a] :
( A
!= ( append_list_a @ B @ ( cons_list_a @ C @ nil_list_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(141,axiom,
! [A: list_list_a] :
( ( ( tl_list_a @ A )
= nil_list_a )
= ( ( A = nil_list_a )
| ? [B: list_a] :
( A
= ( cons_list_a @ B @ nil_list_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_tl__Nil) ).
thf(929,plain,
! [A: list_list_a] :
( ( ( tl_list_a @ A )
= nil_list_a )
= ( ( A = nil_list_a )
| ? [B: list_a] :
( A
= ( cons_list_a @ B @ nil_list_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(219,axiom,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_map__tailrec__rev_Oinduct) ).
thf(1308,plain,
! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > a,F: a,G: list_a,H: list_a] :
( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(20,axiom,
( ( butlast_list_a @ nil_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_butlast_Osimps_I1_J) ).
thf(383,plain,
( ( butlast_list_a @ nil_list_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,axiom,
! [A: list_list_a] :
( ( append_list_a @ nil_list_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_append__Nil) ).
thf(684,plain,
! [A: list_list_a] :
( ( append_list_a @ nil_list_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(245,axiom,
! [A: ( a > list_a ) > list_a > list_list_a > $o,B: a > list_a,C: list_a,D: list_list_a] :
( ! [E: a > list_a,F: list_list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > list_a,F: a,G: list_a,H: list_list_a] :
( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_map__tailrec__rev_Oinduct) ).
thf(1444,plain,
! [A: ( a > list_a ) > list_a > list_list_a > $o,B: a > list_a,C: list_a,D: list_list_a] :
( ! [E: a > list_a,F: list_list_a] : ( A @ E @ nil_a @ F )
=> ( ! [E: a > list_a,F: a,G: list_a,H: list_list_a] :
( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons_a @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(244,axiom,
( ( butlast_a @ nil_a )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_butlast_Osimps_I1_J) ).
thf(1442,plain,
( ( butlast_a @ nil_a )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(107,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A = nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_last__appendL) ).
thf(752,plain,
! [A: list_list_a,B: list_list_a] :
( ( A = nil_list_a )
=> ( ( last_list_a @ ( append_list_a @ B @ A ) )
= ( last_list_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(262,axiom,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a > list_a > list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( ( size_size_list_a @ B )
= ( size_size_list_a @ C ) )
=> ( ( ( size_size_list_a @ C )
= ( size_size_list_a @ D ) )
=> ( ( E @ nil_a @ nil_a @ nil_a @ nil_a )
=> ( ! [F: a,G: list_a,H: a,I: list_a,J: a,K: list_a,L: a,M: list_a] :
( ( ( size_size_list_a @ G )
= ( size_size_list_a @ I ) )
=> ( ( ( size_size_list_a @ I )
= ( size_size_list_a @ K ) )
=> ( ( ( size_size_list_a @ K )
= ( size_size_list_a @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons_a @ F @ G ) @ ( cons_a @ H @ I ) @ ( cons_a @ J @ K ) @ ( cons_a @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_list__induct4) ).
thf(1512,plain,
! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a > list_a > list_a > list_a > $o] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ( ( size_size_list_a @ B )
= ( size_size_list_a @ C ) )
=> ( ( ( size_size_list_a @ C )
= ( size_size_list_a @ D ) )
=> ( ( E @ nil_a @ nil_a @ nil_a @ nil_a )
=> ( ! [F: a,G: list_a,H: a,I: list_a,J: a,K: list_a,L: a,M: list_a] :
( ( ( size_size_list_a @ G )
= ( size_size_list_a @ I ) )
=> ( ( ( size_size_list_a @ I )
= ( size_size_list_a @ K ) )
=> ( ( ( size_size_list_a @ K )
= ( size_size_list_a @ M ) )
=> ( ( E @ G @ I @ K @ M )
=> ( E @ ( cons_a @ F @ G ) @ ( cons_a @ H @ I ) @ ( cons_a @ J @ K ) @ ( cons_a @ L @ M ) ) ) ) ) )
=> ( E @ A @ B @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(39,axiom,
! [A: nat > list_a] :
( ( listIn1753026346list_a @ nil_list_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_i__append__Nil) ).
thf(432,plain,
! [A: nat > list_a] :
( ( listIn1753026346list_a @ nil_list_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(284,axiom,
! [A: list_a,B: a] :
( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_last__ConsR) ).
thf(1625,plain,
! [A: list_a,B: a] :
( ( A != nil_a )
=> ( ( last_a @ ( cons_a @ B @ A ) )
= ( last_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(264,axiom,
! [A: a,B: a,C: list_a] :
( ( ( A = B )
=> ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( remdups_adj_a @ ( cons_a @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( cons_a @ A @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_remdups__adj_Osimps_I3_J) ).
thf(1527,plain,
! [A: a,B: a,C: list_a] :
( ( ( A = B )
=> ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( remdups_adj_a @ ( cons_a @ A @ C ) ) ) )
& ( ( A != B )
=> ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
= ( cons_a @ A @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(36,axiom,
! [A: list_a,B: list_a] :
( ( if_list_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__List__Olist_Itf__a_J_T) ).
thf(422,plain,
! [A: list_a,B: list_a] :
( ( if_list_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(103,axiom,
! [A: list_list_a,B: list_a] :
( ( ( A = nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= B ) )
& ( ( A != nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_last_Osimps) ).
thf(735,plain,
! [A: list_list_a,B: list_a] :
( ( ( A = nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= B ) )
& ( ( A != nil_list_a )
=> ( ( last_list_a @ ( cons_list_a @ B @ A ) )
= ( last_list_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(156,axiom,
! [A: list_list_a,B: list_list_a > $o] :
( ( A != nil_list_a )
=> ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_list_a] :
( ( D != nil_list_a )
=> ( ( B @ D )
=> ( B @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_rev__nonempty__induct) ).
thf(999,plain,
! [A: list_list_a,B: list_list_a > $o] :
( ( A != nil_list_a )
=> ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
=> ( ! [C: list_a,D: list_list_a] :
( ( D != nil_list_a )
=> ( ( B @ D )
=> ( B @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(78,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_append__same__eq) ).
thf(620,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,axiom,
! [A: list_a,B: list_list_a] :
( ( tl_list_a @ ( cons_list_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_list_Osel_I3_J) ).
thf(373,plain,
! [A: list_a,B: list_list_a] :
( ( tl_list_a @ ( cons_list_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(74,axiom,
! [A: list_list_a,B: list_list_a] :
( ( A
= ( append_list_a @ B @ A ) )
= ( B = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_self__append__conv2) ).
thf(603,plain,
! [A: list_list_a,B: list_list_a] :
( ( A
= ( append_list_a @ B @ A ) )
= ( B = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(221,axiom,
! [A: a,B: list_a] :
( ( tl_a @ ( cons_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_list_Osel_I3_J) ).
thf(1314,plain,
! [A: a,B: list_a] :
( ( tl_a @ ( cons_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(290,axiom,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Cons__eq__appendI) ).
thf(1657,plain,
! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
( ( ( cons_a @ A @ B )
= C )
=> ( ( D
= ( append_a @ B @ E ) )
=> ( ( cons_a @ A @ D )
= ( append_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(58,axiom,
! [A: a,B: a > $o] :
( ( member_a2 @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mem__Collect__eq) ).
thf(506,plain,
! [A: a,B: a > $o] :
( ( member_a2 @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(11,axiom,
( ( concat_list_a @ nil_list_list_a )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_concat_Osimps_I1_J) ).
thf(358,plain,
( ( concat_list_a @ nil_list_list_a )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(133,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
= ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_append__assoc) ).
thf(897,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a] :
( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
= ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(87,axiom,
! [A: list_a] :
( ( insert_list_a @ A @ nil_list_a )
= ( cons_list_a @ A @ nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_insert__Nil) ).
thf(664,plain,
! [A: list_a] :
( ( insert_list_a @ A @ nil_list_a )
= ( cons_list_a @ A @ nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(303,axiom,
! [A: list_a > a > $o,B: list_a,C: a,D: list_list_a,E: list_a] :
( ( A @ B @ C )
=> ( ( listrelp_list_a_a @ A @ D @ E )
=> ( listrelp_list_a_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_listrelp_OCons) ).
thf(1710,plain,
! [A: list_a > a > $o,B: list_a,C: a,D: list_list_a,E: list_a] :
( ( A @ B @ C )
=> ( ( listrelp_list_a_a @ A @ D @ E )
=> ( listrelp_list_a_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(121,axiom,
! [A: list_a > list_a > $o,B: list_list_a,C: $o] :
( ( ( successively_list_a @ A @ B )
= C )
=> ( ( ( B = nil_list_a )
=> ~ C )
=> ( ( ? [D: list_a] :
( B
= ( cons_list_a @ D @ nil_list_a ) )
=> ~ C )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ ( cons_list_a @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively_list_a @ A @ ( cons_list_a @ E @ F ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_successively_Oelims_I1_J) ).
thf(828,plain,
! [A: list_a > list_a > $o,B: list_list_a,C: $o] :
( ( ( successively_list_a @ A @ B )
= C )
=> ( ( ( B = nil_list_a )
=> ~ C )
=> ( ( ? [D: list_a] :
( B
= ( cons_list_a @ D @ nil_list_a ) )
=> ~ C )
=> ~ ! [D: list_a,E: list_a,F: list_list_a] :
( ( B
= ( cons_list_a @ D @ ( cons_list_a @ E @ F ) ) )
=> ( C
= ( ~ ( ( A @ D @ E )
& ( successively_list_a @ A @ ( cons_list_a @ E @ F ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(253,axiom,
! [A: a > $o] :
~ ( list_ex1_a @ A @ nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list__ex1__simps_I1_J) ).
thf(1473,plain,
! [A: a > $o] :
~ ( list_ex1_a @ A @ nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(66,axiom,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ( A @ nil_list_a @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ nil_list_a @ ( cons_list_a @ D @ E ) )
=> ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_list__induct2_H) ).
thf(532,plain,
! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
( ( A @ nil_list_a @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_list_a )
=> ( ! [D: list_a,E: list_list_a] : ( A @ nil_list_a @ ( cons_list_a @ D @ E ) )
=> ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
( ( A @ E @ G )
=> ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(101,axiom,
! [A: list_a,B: list_list_a] :
( nil_list_a
!= ( cons_list_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_list_Odistinct_I1_J) ).
thf(728,plain,
! [A: list_a,B: list_list_a] :
( nil_list_a
!= ( cons_list_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(206,axiom,
! [A: list_a,B: list_a,C: list_a,D: a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ ( cons_a @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Cons__in__shuffles__leftI) ).
thf(1236,plain,
! [A: list_a,B: list_a,C: list_a,D: a] :
( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
=> ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ ( cons_a @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(210,axiom,
! [A: a,B: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ B ) )
= ( ( B = nil_a )
| ( ( A
!= ( hd_a @ B ) )
& ( distinct_adj_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_distinct__adj__Cons) ).
thf(1261,plain,
! [A: a,B: list_a] :
( ( distinct_adj_a @ ( cons_a @ A @ B ) )
= ( ( B = nil_a )
| ( ( A
!= ( hd_a @ B ) )
& ( distinct_adj_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(275,axiom,
! [A: a > list_a > $o] : ( listrelp_a_list_a @ A @ nil_a @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_listrelp_ONil) ).
thf(1582,plain,
! [A: a > list_a > $o] : ( listrelp_a_list_a @ A @ nil_a @ nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(278,axiom,
! [A: a > list_list_a] :
( ( bind_a_list_a @ nil_a @ A )
= nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_bind__simps_I1_J) ).
thf(1597,plain,
! [A: a > list_list_a] :
( ( bind_a_list_a @ nil_a @ A )
= nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(218,axiom,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
= ( B = nil_a ) )
=> ( ( ( A != nil_a )
=> ( ( B != nil_a )
=> ( ( ( hd_a @ A )
= ( hd_a @ B ) )
& ( ( tl_a @ A )
= ( tl_a @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_list_Oexpand) ).
thf(1299,plain,
! [A: list_a,B: list_a] :
( ( ( A = nil_a )
= ( B = nil_a ) )
=> ( ( ( A != nil_a )
=> ( ( B != nil_a )
=> ( ( ( hd_a @ A )
= ( hd_a @ B ) )
& ( ( tl_a @ A )
= ( tl_a @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(15,axiom,
! [A: list_a > list_a > $o] : ( listre1221556159list_a @ A @ nil_list_a @ nil_list_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_listrelp_ONil) ).
thf(369,plain,
! [A: list_a > list_a > $o] : ( listre1221556159list_a @ A @ nil_list_a @ nil_list_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(259,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Oexhaust) ).
thf(1500,plain,
! [A: list_a] :
( ( A != nil_a )
=> ~ ! [B: a,C: list_a] :
( A
!= ( cons_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(99,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= A )
= ( B = nil_list_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_append__self__conv) ).
thf(723,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( append_list_a @ A @ B )
= A )
= ( B = nil_list_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(123,axiom,
! [A: list_list_a,B: list_list_a,C: list_a,D: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( cons_list_a @ C @ D ) )
= ( ( ( A = nil_list_a )
& ( B
= ( cons_list_a @ C @ D ) ) )
| ? [E: list_list_a] :
( ( A
= ( cons_list_a @ C @ E ) )
& ( ( append_list_a @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_append__eq__Cons__conv) ).
thf(850,plain,
! [A: list_list_a,B: list_list_a,C: list_a,D: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( cons_list_a @ C @ D ) )
= ( ( ( A = nil_list_a )
& ( B
= ( cons_list_a @ C @ D ) ) )
| ? [E: list_list_a] :
( ( A
= ( cons_list_a @ C @ E ) )
& ( ( append_list_a @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(304,axiom,
! [A: list_a > list_a] :
( ( bind_list_a_a @ nil_list_a @ A )
= nil_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_bind__simps_I1_J) ).
thf(1713,plain,
! [A: list_a > list_a] :
( ( bind_list_a_a @ nil_list_a @ A )
= nil_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(52,axiom,
! [A: list_list_a,B: list_a] :
( ( butlast_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_butlast__snoc) ).
thf(486,plain,
! [A: list_list_a,B: list_a] :
( ( butlast_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(223,axiom,
( listrelp_a_a
= ( ^ [A: a > a > $o,B: list_a,C: list_a] :
( ( ( B = nil_a )
& ( C = nil_a ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_a_a @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_listrelp_Osimps) ).
thf(1320,plain,
( listrelp_a_a
= ( ^ [A: a > a > $o,B: list_a,C: list_a] :
( ( ( B = nil_a )
& ( C = nil_a ) )
| ? [D: a,E: a,F: list_a,G: list_a] :
( ( B
= ( cons_a @ D @ F ) )
& ( C
= ( cons_a @ E @ G ) )
& ( A @ D @ E )
& ( listrelp_a_a @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(4,axiom,
! [A: set_list_list_a,B: list_a,C: list_list_a] :
( ( bNF_Gr1046450207list_a @ ( bNF_Gr1972240547list_a @ A @ B ) @ C )
= ( bNF_Gr1046450207list_a @ A @ ( cons_list_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Succ__Shift) ).
thf(337,plain,
! [A: set_list_list_a,B: list_a,C: list_list_a] :
( ( bNF_Gr1046450207list_a @ ( bNF_Gr1972240547list_a @ A @ B ) @ C )
= ( bNF_Gr1046450207list_a @ A @ ( cons_list_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(139,axiom,
! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ C @ D ) )
= ( ? [E: list_list_a] :
( ( ( A
= ( append_list_a @ C @ E ) )
& ( ( append_list_a @ E @ B )
= D ) )
| ( ( ( append_list_a @ A @ E )
= C )
& ( B
= ( append_list_a @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_append__eq__append__conv2) ).
thf(923,plain,
! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
( ( ( append_list_a @ A @ B )
= ( append_list_a @ C @ D ) )
= ( ? [E: list_list_a] :
( ( ( A
= ( append_list_a @ C @ E ) )
& ( ( append_list_a @ E @ B )
= D ) )
| ( ( ( append_list_a @ A @ E )
= C )
& ( B
= ( append_list_a @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(272,axiom,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_rev__induct) ).
thf(1565,plain,
! [A: list_a > $o,B: list_a] :
( ( A @ nil_a )
=> ( ! [C: a,D: list_a] :
( ( A @ D )
=> ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(130,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
= ( B = nil_list_a ) )
=> ( ( ( A != nil_list_a )
=> ( ( B != nil_list_a )
=> ( ( ( hd_list_a @ A )
= ( hd_list_a @ B ) )
& ( ( tl_list_a @ A )
= ( tl_list_a @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_list_Oexpand) ).
thf(882,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( A = nil_list_a )
= ( B = nil_list_a ) )
=> ( ( ( A != nil_list_a )
=> ( ( B != nil_list_a )
=> ( ( ( hd_list_a @ A )
= ( hd_list_a @ B ) )
& ( ( tl_list_a @ A )
= ( tl_list_a @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(151,axiom,
! [A: list_a,B: list_list_a,C: list_a,D: list_list_a] :
( ( ( cons_list_a @ A @ B )
= ( cons_list_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_list_Oinject) ).
thf(972,plain,
! [A: list_a,B: list_list_a,C: list_a,D: list_list_a] :
( ( ( cons_list_a @ A @ B )
= ( cons_list_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(227,axiom,
! [A: list_a] :
( ( ( rotate1_a @ A )
= nil_a )
= ( A = nil_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_rotate1__is__Nil__conv) ).
thf(1331,plain,
! [A: list_a] :
( ( ( rotate1_a @ A )
= nil_a )
= ( A = nil_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(281,axiom,
! [A: list_a] :
( ( A != nil_a )
=> ( A
= ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_list_Oexhaust__sel) ).
thf(1606,plain,
! [A: list_a] :
( ( A != nil_a )
=> ( A
= ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(45,axiom,
! [A: list_a,B: list_list_a] :
( ( rotate1_list_a @ ( cons_list_a @ A @ B ) )
= ( append_list_a @ B @ ( cons_list_a @ A @ nil_list_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rotate1_Osimps_I2_J) ).
thf(454,plain,
! [A: list_a,B: list_list_a] :
( ( rotate1_list_a @ ( cons_list_a @ A @ B ) )
= ( append_list_a @ B @ ( cons_list_a @ A @ nil_list_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(176,axiom,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( listrelp_a_a @ A @ B @ C )
=> ( ( ( B = nil_a )
=> ( C != nil_a ) )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_a_a @ A @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_listrelp_Ocases) ).
thf(1069,plain,
! [A: a > a > $o,B: list_a,C: list_a] :
( ( listrelp_a_a @ A @ B @ C )
=> ( ( ( B = nil_a )
=> ( C != nil_a ) )
=> ~ ! [D: a,E: a,F: list_a] :
( ( B
= ( cons_a @ D @ F ) )
=> ! [G: list_a] :
( ( C
= ( cons_a @ E @ G ) )
=> ( ( A @ D @ E )
=> ~ ( listrelp_a_a @ A @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1906,plain,
$false,
inference(e,[status(thm)],[809,1337,1024,1168,1633,1559,941,481,1322,1665,333,628,1855,1211,1158,1406,1692,1486,1750,408,379,1269,1788,385,1756,500,1872,1233,698,1222,1063,340,1127,1095,404,1228,1482,389,1409,1287,1760,719,702,1577,934,1462,1860,1264,542,460,817,559,1704,606,416,1115,1875,638,853,1479,1609,1013,770,789,443,1109,376,623,1682,1828,353,492,1465,1334,646,1020,348,687,877,956,396,428,1600,1242,1215,634,411,1345,1863,678,529,1153,1470,366,1868,512,439,1047,1730,894,746,1355,820,392,1042,952,916,847,625,435,522,1210,1027,757,551,1291,519,1089,615,1328,1121,1111,1540,869,1118,1772,1259,1719,356,1584,489,1155,393,1451,1382,1429,779,371,503,1831,1231,1060,457,1857,360,1695,674,773,926,1086,938,1846,1054,1727,1764,425,1698,1219,1374,975,1007,732,1388,743,1535,1701,1124,875,826,545,1488,572,1707,1371,1312,1733,1058,1239,1092,335,919,681,419,1524,1349,996,1603,451,1722,900,406,509,880,1667,631,726,964,1556,1838,1325,462,932,983,399,1594,959,1643,1015,608,986,1775,922,1562,912,1171,1841,1396,636,1044,473,1034,1662,1166,944,1467,795,548,1134,749,516,342,823,1049,776,525,690,872,1225,414,1753,1267,1716,791,1188,1038,1317,1538,1679,1130,1285,1404,1849,1052,1427,1504,386,1670,446,1272,1617,465,1459,1553,671,1834,891,1448,363,556,495,1654,1010,1575,1646,1385,1476,1508,351,1629,401,1030,667,929,1308,383,684,1444,1442,752,1512,432,1625,1527,422,735,999,620,373,603,1314,1657,506,358,897,664,1710,828,1473,532,728,1236,1261,1582,1597,1299,369,1500,723,850,1713,486,1320,337,923,1565,882,972,1331,1606,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 18:07:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.86/1.12 % [INFO] Parsing done (270ms).
% 1.86/1.13 % [INFO] Running in sequential loop mode.
% 2.61/1.34 % [INFO] eprover registered as external prover.
% 2.61/1.34 % [INFO] cvc4 registered as external prover.
% 2.61/1.34 % [INFO] Scanning for conjecture ...
% 2.71/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ...
% 3.06/1.53 % [INFO] Axiom selection finished. Selected 330 axioms (removed 25 axioms).
% 3.77/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 4.08/1.75 % [INFO] Type checking passed.
% 4.08/1.75 % [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 ...
% 21.24/6.64 % External prover 'e' found a proof!
% 21.24/6.64 % [INFO] Killing All external provers ...
% 21.24/6.64 % Time passed: 6116ms (effective reasoning time: 5504ms)
% 21.24/6.64 % 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)>
% 21.24/6.64 % Axioms used in derivation (330): fact_277_distinct__adj__append__iff, fact_84_ord_Olexordp__eq_ONil, fact_57_listrelp_Oinducts, fact_180_Cons__eq__append__conv, fact_147_split__Nil__iff, fact_131_append_Oright__neutral, fact_3_list_Oinject, fact_162_Cons__eq__appendI, fact_279_rotate1__hd__tl, fact_182_rev__exhaust, fact_319_successively_Osimps_I2_J, fact_296_successively_Oelims_I3_J, fact_311_tl__Nil, fact_303_distinct__adj__appendD2, fact_83_ord_Olexordp__eq_OCons__eq, fact_322_successively_Oelims_I2_J, fact_264_hd__concat, fact_99_ord_Olexordp__eq_Ocases, fact_170_ord_Olexordp__eq__pref, fact_197_butlast__snoc, fact_10_list_Oinducts, fact_214_append__butlast__last__id, fact_20_induct__list012, fact_52_bind__simps_I1_J, fact_47_map__tailrec__rev_Oelims, fact_198_butlast__snoc, fact_299_successively_Osimps_I1_J, fact_137_self__append__conv2, fact_18_splice_Oinduct, fact_45_list__ex1__simps_I1_J, fact_95_map__tailrec__rev_Osimps_I2_J, fact_169_ord_Olexordp__eq__pref, fact_350_list__induct3, fact_50_ord_Olexordp__eq__simps_I3_J, fact_124_append__same__eq, fact_263_hd__concat, fact_250_concat__conv__foldr, fact_42_insert__Nil, fact_205_rotate1__is__Nil__conv, fact_71_ord_Olexordp__eq__simps_I2_J, fact_225_last__ConsR, fact_2_list_Oinject, fact_291_list_Osel_I3_J, fact_11_list_Oinducts, fact_305_distinct__adj__Nil, fact_139_append__self__conv2, fact_16_list__induct2_H, fact_43_insert__Nil, fact_344_remdups__adj_Osimps_I1_J, fact_163_append_Oleft__neutral, fact_246_empty__Shift, fact_72_ord_Olexordp__eq__simps_I1_J, fact_330_map2__Cons__not__empty, fact_130_append_Oright__neutral, fact_174_splice_Osimps_I1_J, fact_63_listrelp_Osimps, fact_181_rev__exhaust, fact_318_successively_Osimps_I2_J, fact_157_append__eq__appendI, fact_167_eq__Nil__appendI, fact_178_append__eq__Cons__conv, fact_240_maps__simps_I2_J, fact_226_last__ConsR, fact_101_ord_Olexordp__eq_Osimps, fact_314_list_Oexpand, fact_88_listrelp_OCons, fact_79_Collect__mem__eq, fact_64_listrelp_Ocases, fact_190_maps__simps_I1_J, fact_341_remdups__adj__Cons__alt, fact_21_induct__list012, fact_241_maps__simps_I2_J, fact_34_remdups__adj_Oinduct, fact_59_listrelp_Oinducts, fact_36_sorted__wrt_Oinduct, fact_128_append_Oassoc, fact_35_remdups__adj_Oinduct, fact_331_Nil__in__shuffles, fact_306_distinct__adj__Nil, help_If_3_1_If_001t__List__Olist_Itf__a_J_T, fact_96_map__tailrec__rev_Osimps_I2_J, fact_308_distinct__adj__ConsD, fact_237_butlast__append, fact_165_append__Nil, fact_74_ord_Olexordp__eq_Ocong, fact_230_longest__common__suffix, fact_202_SuccI, fact_340_remdups__adj__Nil__iff, fact_125_append__same__eq, fact_106_product__lists_Osimps_I1_J, fact_142_append__self__conv, fact_135_Nil__is__append__conv, fact_100_ord_Olexordp__eq_Ocases, fact_153_append1__eq__conv, fact_86_listrelp_OCons, fact_286_tl__append2, fact_313_Nil__tl, help_If_2_1_If_001t__List__Olist_Itf__a_J_T, fact_70_ord_Olexordp__eq__simps_I2_J, fact_65_listrelp_Ocases, fact_239_maps__simps_I2_J, fact_176_rev__nonempty__induct, fact_69_ord_Olexordp__eq__simps_I4_J, fact_349_list__induct2, fact_347_map2__snoc__snoc, fact_6_list_OdiscI, fact_134_Nil__is__append__conv, fact_60_listrelp_Osimps, fact_199_last__snoc, fact_323_successively_Oelims_I2_J, fact_191_maps__simps_I1_J, fact_27_map__tailrec__rev_Oinduct, fact_320_successively_Oelims_I1_J, fact_337_map2__Cons__if, fact_62_listrelp_Osimps, fact_229_longest__common__suffix, fact_13_neq__Nil__conv, fact_332_shufflesE, fact_112_member__rec_I2_J, fact_196_rotate1_Osimps_I2_J, fact_94_map__tailrec__rev_Osimps_I2_J, fact_56_listrelp_Oinducts, fact_259_hd__append2, fact_12_neq__Nil__conv, fact_175_rev__nonempty__induct, fact_342_remdups__adj_Oelims, fact_206_rotate1__is__Nil__conv, fact_23_shuffles_Oinduct, fact_194_concat__eq__append__conv, fact_268_longest__common__prefix, fact_192_maps__simps_I1_J, fact_97_map__tailrec__rev_Osimps_I2_J, fact_102_ord_Olexordp__eq_Osimps, fact_307_distinct__adj__ConsD, fact_9_list_Oexhaust, fact_129_append_Oassoc, fact_140_self__append__conv, fact_227_last__append, fact_338_remdups__adj__append_H, fact_251_foldr__append, fact_37_sorted__wrt_Oinduct, fact_315_list_Oexpand, help_If_1_1_If_001t__List__Olist_Itf__a_J_T, fact_5_list_Odistinct_I1_J, fact_108_subseqs_Osimps_I1_J, fact_127_append__assoc, fact_265_hd__append, fact_183_rev__induct, fact_81_ord_Olexordp__eq_OCons, fact_317_last__tl, fact_66_listrelp_Ocases, fact_151_i__append__assoc, fact_351_list__induct4, fact_204_SuccD, fact_288_hd__Cons__tl, fact_160_append__Cons, fact_123_same__append__eq, fact_25_not__Cons__self2, fact_266_hd__append, fact_328_distinct__adj__Cons, fact_30_list__nonempty__induct, fact_33_successively_Oinduct, fact_54_bind__simps_I1_J, fact_168_eq__Nil__appendI, fact_334_Cons__in__shuffles__leftI, fact_300_successively_Osimps_I1_J, fact_14_list__induct2_H, fact_98_map__tailrec__rev_Osimps_I1_J, fact_262_list_Osel_I1_J, fact_267_longest__common__prefix, fact_345_remdups__adj_Osimps_I3_J, fact_92_listrelp_ONil, fact_336_Nil__in__shufflesI, fact_224_last__ConsL, fact_171_splice_Osimps_I2_J, fact_143_append__self__conv, fact_41_transpose_Ocases, fact_210_last__appendR, fact_289_list_Ocollapse, fact_343_remdups__adj_Osimps_I2_J, fact_244_concat__eq__appendD, fact_177_append__eq__Cons__conv, fact_220_rotate1_Osimps_I1_J, fact_19_splice_Oinduct, fact_46_map__tailrec__rev_Oelims, fact_258_hd__append2, fact_213_append__butlast__last__id, fact_295_successively_Oelims_I3_J, fact_61_listrelp_Osimps, fact_132_append__is__Nil__conv, fact_179_Cons__eq__append__conv, fact_324_distinct__adj__singleton, fact_245_empty__Shift, fact_302_distinct__adj__appendD1, fact_242_maps__simps_I2_J, fact_310_tl__Nil, fact_346_remdups__adj__append__two, fact_116_splice_Oelims, fact_119_bind__simps_I2_J, fact_24_not__Cons__self2, fact_149_splice__Nil2, fact_285_tl__append2, fact_113_member__rec_I2_J, fact_212_concat__append, fact_133_append__is__Nil__conv, fact_321_successively_Oelims_I1_J, fact_78_Collect__mem__eq, fact_26_map__tailrec__rev_Oinduct, fact_80_ord_Olexordp__eq_OCons, fact_4_list_Odistinct_I1_J, fact_15_list__induct2_H, fact_145_append__Nil2, fact_7_list_OdiscI, fact_121_bind__simps_I2_J, fact_126_append__assoc, fact_215_butlast_Osimps_I1_J, fact_294_list_Osel_I2_J, fact_326_list_Oexhaust__sel, fact_207_last__appendL, fact_283_distinct__adj__Cons__Cons, fact_195_rotate1_Osimps_I2_J, fact_1_i__append__Nil, fact_185_append__eq__Cons, fact_218_snoc__eq__iff__butlast, fact_44_list__ex1__simps_I1_J, fact_152_append1__eq__conv, fact_327_successively__Cons, fact_232_butlast_Osimps_I2_J, fact_223_last__ConsL, fact_201_SuccI, fact_236_concat_Osimps_I2_J, fact_55_bind__simps_I1_J, fact_73_ord_Olexordp__eq__simps_I1_J, fact_155_append__eq__append__conv2, fact_254_list__strict__asc__def, fact_17_list__induct2_H, fact_38_remdups__adj_Ocases, fact_67_listrelp_Ocases, fact_233_concat_Osimps_I1_J, fact_217_snoc__eq__iff__butlast, fact_247_Succ__Shift, fact_91_listrelp_ONil, fact_120_bind__simps_I2_J, fact_280_rotate1__hd__tl, fact_141_self__append__conv, fact_76_mem__Collect__eq, fact_31_list__nonempty__induct, fact_203_SuccD, fact_118_bind__simps_I2_J, fact_103_ord_Olexordp__eq_Oinducts, fact_297_successively_Osimps_I3_J, fact_252_ShiftD, fact_216_butlast_Osimps_I1_J, fact_158_append__eq__appendI, fact_82_ord_Olexordp__eq_OCons__eq, fact_261_list_Osel_I1_J, fact_166_append__Nil, fact_173_splice_Osimps_I1_J, fact_348_length__greater__imp__not__empty, fact_222_last_Osimps, fact_156_append__eq__append__conv2, fact_298_successively_Osimps_I3_J, fact_172_splice_Osimps_I2_J, fact_228_last__append, fact_253_ShiftD, fact_144_append__Nil2, fact_312_Nil__tl, fact_39_remdups__adj_Ocases, fact_208_last__appendL, fact_249_concat__conv__foldr, fact_316_last__tl, fact_32_successively_Oinduct, fact_329_Cons__in__shuffles__iff, fact_29_map__tailrec__rev_Oinduct, fact_104_ord_Olexordp__eq_Oinducts, fact_28_map__tailrec__rev_Oinduct, fact_122_same__append__eq, fact_248_Succ__Shift, fact_209_last__appendR, fact_146_split__Nil__iff, fact_77_mem__Collect__eq, fact_117_splice_Oelims, fact_282_successively__append__iff, fact_184_rev__induct, fact_164_append_Oleft__neutral, fact_87_listrelp_OCons, fact_231_butlast_Osimps_I2_J, fact_304_distinct__adj__appendD2, fact_281_successively__append__iff, fact_8_list_Oexhaust, fact_234_concat_Osimps_I1_J, fact_325_distinct__adj__singleton, fact_219_rotate1_Osimps_I1_J, fact_278_distinct__adj__append__iff, fact_53_bind__simps_I1_J, fact_115_member__rec_I1_J, fact_309_butlast__tl, fact_221_last_Osimps, fact_238_butlast__append, fact_85_ord_Olexordp__eq_ONil, fact_75_ord_Olexordp__eq__refl, fact_58_listrelp_Oinducts, fact_150_i__append__assoc, fact_301_distinct__adj__appendD1, fact_51_ord_Olexordp__eq__simps_I3_J, fact_189_maps__simps_I1_J, fact_335_Cons__in__shuffles__rightI, fact_200_last__snoc, fact_49_map__tailrec__rev_Oelims, fact_68_ord_Olexordp__eq__simps_I4_J, fact_293_list_Osel_I2_J, fact_290_list_Ocollapse, fact_339_remdups__adj__append, fact_136_self__append__conv2, fact_148_splice__Nil2, fact_89_listrelp_OCons, fact_161_Cons__eq__appendI, fact_292_list_Osel_I3_J, fact_90_listrelp_ONil, fact_287_hd__Cons__tl, fact_186_append__eq__Cons, fact_138_append__self__conv2, fact_159_append__Cons, fact_93_listrelp_ONil, fact_48_map__tailrec__rev_Oelims, fact_22_shuffles_Oinduct, fact_333_map2__Cons__Cons, fact_0_i__append__Nil, fact_114_member__rec_I1_J, fact_284_distinct__adj__Cons__Cons
% 21.24/6.64 % No. of inferences in proof: 664
% 21.24/6.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6116 ms resp. 5504 ms w/o parsing
% 22.19/6.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.19/6.82 % [INFO] Killing All external provers ...
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