TSTP Solution File: DAT154^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT154^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:37 EDT 2024
% Result : Theorem 27.03s 10.12s
% Output : Refutation 27.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 313
% Syntax : Number of formulae : 576 ( 274 unt; 52 typ; 0 def)
% Number of atoms : 1618 ( 755 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 7865 ( 300 ~; 67 |; 152 &;6816 @)
% ( 0 <=>; 530 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 456 ( 456 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 55 usr; 7 con; 0-5 aty)
% Number of variables : 2135 ( 96 ^1856 !; 130 ?;2135 :)
% ( 53 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(ord_type,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(lattice_type,type,
lattice:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semilattice_inf_type,type,
semilattice_inf:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(bNF_Greatest_Shift_type,type,
bNF_Greatest_Shift:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > TA > ( set @ ( list @ TA ) ) ) ).
thf(bNF_Greatest_Succ_type,type,
bNF_Greatest_Succ:
!>[TA: $tType] : ( ( set @ ( list @ TA ) ) > ( list @ TA ) > ( set @ TA ) ) ).
thf(bNF_Greatest_shift_type,type,
bNF_Greatest_shift:
!>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).
thf(coindu1384447384of_aux_type,type,
coindu1384447384of_aux:
!>[TA: $tType] : ( ( list @ TA ) > ( coinductive_llist @ TA ) > ( list @ TA ) ) ).
thf(coinductive_LNil_type,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(coinductive_lnull_type,type,
coinductive_lnull:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > $o ) ).
thf(coinductive_lsorted_type,type,
coinductive_lsorted:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > $o ) ).
thf(hammin1328233080lmerge_type,type,
hammin1328233080lmerge:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(hammin1138290136lmerge_type,type,
hammin1138290136lmerge:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(bind_type,type,
bind:
!>[TA: $tType,TB: $tType] : ( ( list @ TB ) > ( TB > ( list @ TA ) ) > ( list @ TA ) ) ).
thf(butlast_type,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(hd_type,type,
hd:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(map_tailrec_type,type,
map_tailrec:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(map_tailrec_rev_type,type,
map_tailrec_rev:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(maps_type,type,
maps:
!>[TA: $tType,TB: $tType] : ( ( TB > ( list @ TA ) ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(lexordp_type,type,
lexordp:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(lexordp_eq_type,type,
lexordp_eq:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(product_lists_type,type,
product_lists:
!>[TA: $tType] : ( ( list @ ( list @ TA ) ) > ( list @ ( list @ TA ) ) ) ).
thf(rev_type,type,
rev:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(rotate1_type,type,
rotate1:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(sublists_type,type,
sublists:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(max_type,type,
max:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(min_type,type,
min:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > TA ) ).
thf(type2_type,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(set_atLeast_type,type,
set_atLeast:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_atLeastAtMost_type,type,
set_atLeastAtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atLeastLessThan_type,type,
set_atLeastLessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_atMost_type,type,
set_atMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_greaterThan_type,type,
set_greaterThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(set_gr323396891AtMost_type,type,
set_gr323396891AtMost:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_gr1161524159ssThan_type,type,
set_gr1161524159ssThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > TA > ( set @ TA ) ) ).
thf(set_lessThan_type,type,
set_lessThan:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > ( set @ TA ) ) ).
thf(prefixes_type,type,
prefixes:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ ( list @ TA ) ) ) ).
thf(strict_suffix_type,type,
strict_suffix:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(less_type,type,
less: a > a > $o ).
thf(less_eq_type,type,
less_eq: a > a > $o ).
thf(xs_type,type,
xs: coinductive_llist @ a ).
thf(ys_type,type,
ys: coinductive_llist @ a ).
thf(113,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_append__Nil2) ).
thf(645,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rev @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_rev__is__Nil__conv) ).
thf(333,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rev @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(187,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord_Olexordp_OCons) ).
thf(941,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(144,axiom,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_rotate1_Osimps_I1_J) ).
thf(777,plain,
! [TA: $tType] :
( ( rotate1 @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(28,axiom,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_rev__rev__ident) ).
thf(352,plain,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(65,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_list_Oexhaust) ).
thf(479,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(229,axiom,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp_eq @ a @ less @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_local_Olexordp__eq__simps_I4_J) ).
thf(1105,plain,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp_eq @ a @ less @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(45,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inf_Oleft__commute) ).
thf(408,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(139,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_rev__singleton__conv) ).
thf(762,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( A
= ( cons @ TA @ B @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(129,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inf__sup__aci_I2_J) ).
thf(730,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(202,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
= ( ( coinductive_lnull @ TA @ B )
| ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ord_Olmerge_Odisc__iff_I1_J) ).
thf(994,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) )
= ( ( coinductive_lnull @ TA @ B )
| ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(254,axiom,
! [A: a,B: a] :
( ( set_gr1161524159ssThan @ a @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_OgreaterThanLessThan__def) ).
thf(1205,plain,
! [A: a,B: a] :
( ( set_gr1161524159ssThan @ a @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(76,axiom,
! [TA: $tType] :
( ( set_gr1161524159ssThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ A @ B ) @ ( set_lessThan @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_ord_OgreaterThanLessThan__eq) ).
thf(511,plain,
! [TA: $tType] :
( ( set_gr1161524159ssThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ A @ B ) @ ( set_lessThan @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(208,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_lappend_Oexhaust) ).
thf(1041,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
=> ~ ( coinductive_lnull @ TA @ B ) )
=> ( ~ ( coinductive_lnull @ TA @ A )
| ~ ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(168,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_butlast__append) ).
thf(861,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
= ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(233,axiom,
! [A: a,B: a] :
( ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_local_OgreaterThanAtMost__def) ).
thf(1137,plain,
! [A: a,B: a] :
( ( set_gr323396891AtMost @ a @ less_eq @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(72,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_ord_Olexordp__eq__refl) ).
thf(500,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(241,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_local_Olexordp__eq__refl) ).
thf(1164,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(155,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_rev__induct) ).
thf(814,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(135,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_inf_Oleft__idem) ).
thf(747,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(182,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_remdups__adj_Ocases) ).
thf(930,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ! [B: TA] :
( A
!= ( cons @ TA @ B @ ( nil @ TA ) ) )
=> ~ ! [B: TA,C: TA,D: list @ TA] :
( A
!= ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_IntI) ).
thf(670,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(158,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_inf__sup__aci_I4_J) ).
thf(829,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(176,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ord_Olexordp__eq_Ocases) ).
thf(885,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: list @ TA] : ( C != D ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(115,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_last__ConsR) ).
thf(651,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_atLeastAtMost @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_ord_OatLeastAtMost__iff) ).
thf(841,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_atLeastAtMost @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rev @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_rev_Osimps_I2_J) ).
thf(417,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rev @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( ( prefixes @ TA @ A )
= B )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ( B
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( map @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ C ) @ ( prefixes @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_prefixes_Oelims) ).
thf(320,plain,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA )] :
( ( ( prefixes @ TA @ A )
= B )
=> ( ( ( A
= ( nil @ TA ) )
=> ( B
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ) )
=> ~ ! [C: TA,D: list @ TA] :
( ( A
= ( cons @ TA @ C @ D ) )
=> ( B
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( map @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ C ) @ ( prefixes @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_gr1161524159ssThan @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ord_OgreaterThanLessThan__iff) ).
thf(565,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA,D: TA] :
( ( member @ TA @ A @ ( set_gr1161524159ssThan @ TA @ B @ C @ D ) )
= ( ( B @ C @ A )
& ( B @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(41,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA > TA > $o,D: TA,E: TA] :
( ( member @ TA @ A @ ( set_gr323396891AtMost @ TA @ B @ C @ D @ E ) )
= ( ( C @ D @ A )
& ( B @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_ord_OgreaterThanAtMost__iff) ).
thf(389,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA > TA > $o,D: TA,E: TA] :
( ( member @ TA @ A @ ( set_gr323396891AtMost @ TA @ B @ C @ D @ E ) )
= ( ( C @ D @ A )
& ( B @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(212,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr323396891AtMost @ a @ less_eq @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_local_OgreaterThanAtMost__iff) ).
thf(1055,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr323396891AtMost @ a @ less_eq @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(125,axiom,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA ),C: list @ TA] :
( ( ( prefixes @ TA @ A )
= ( append @ ( list @ TA ) @ B @ ( cons @ ( list @ TA ) @ C @ ( nil @ ( list @ TA ) ) ) ) )
= ( ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ ( list @ TA ) ) ) )
| ? [D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
& ( B
= ( prefixes @ TA @ E ) ) ) )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_prefixes__eq__Snoc) ).
thf(719,plain,
! [TA: $tType,A: list @ TA,B: list @ ( list @ TA ),C: list @ TA] :
( ( ( prefixes @ TA @ A )
= ( append @ ( list @ TA ) @ B @ ( cons @ ( list @ TA ) @ C @ ( nil @ ( list @ TA ) ) ) ) )
= ( ( ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ ( list @ TA ) ) ) )
| ? [D: TA,E: list @ TA] :
( ( A
= ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
& ( B
= ( prefixes @ TA @ E ) ) ) )
& ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(104,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp @ TA @ A @ D @ E )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_ord_Olexordp_OCons__eq) ).
thf(619,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp @ TA @ A @ D @ E )
=> ( lexordp @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(177,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_last__snoc) ).
thf(917,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( last @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Int__iff) ).
thf(802,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(232,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_ord__class_Olmerge_Octr_I1_J) ).
thf(1132,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1138290136lmerge @ TA @ A @ B )
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(236,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ~ ( ~ ( coinductive_lnull @ a @ A )
=> ( coinductive_lnull @ a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lmerge_Oexhaust) ).
thf(1147,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ~ ( ~ ( coinductive_lnull @ a @ A )
=> ( coinductive_lnull @ a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(258,axiom,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Olexordp__eq__simps_I3_J) ).
thf(1247,plain,
! [A: a,B: list @ a] :
~ ( lexordp_eq @ a @ less @ ( cons @ a @ A @ B ) @ ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(170,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
~ ( lexordp @ TA @ A @ B @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_ord_Olexordp__simps_I2_J) ).
thf(870,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
~ ( lexordp @ TA @ A @ B @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(194,axiom,
! [A: a,B: a] :
( ( set_gr1161524159ssThan @ a @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_local_OgreaterThanLessThan__eq) ).
thf(969,plain,
! [A: a,B: a] :
( ( set_gr1161524159ssThan @ a @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_greaterThan @ a @ less @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( append @ TA @ B @ C ) )
= ( append @ TB @ ( map @ TA @ TB @ A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_map__append) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( append @ TA @ B @ C ) )
= ( append @ TB @ ( map @ TA @ TB @ A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(180,axiom,
! [TA: $tType,A: list @ TA] :
( ( coindu1384447384of_aux @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( rev @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_list__of__aux__code_I1_J) ).
thf(924,plain,
! [TA: $tType,A: list @ TA] :
( ( coindu1384447384of_aux @ TA @ A @ ( coinductive_LNil @ TA ) )
= ( rev @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(69,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Collect__mem__eq) ).
thf(492,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_maps__simps_I2_J) ).
thf(789,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( maps @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(95,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_local_Oord__eq__le__trans) ).
thf(591,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less_eq @ B @ C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(160,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rev__nonempty__induct) ).
thf(834,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(77,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_append__eq__Cons__conv) ).
thf(514,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( ( A
= ( nil @ TA ) )
& ( B
= ( cons @ TA @ C @ D ) ) )
| ? [E: list @ TA] :
( ( A
= ( cons @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_IntD2) ).
thf(937,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(91,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atLeast @ TA @ B @ C ) )
= ( B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_ord_OatLeast__iff) ).
thf(574,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atLeast @ TA @ B @ C ) )
= ( B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(193,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_list_Oinject) ).
thf(966,plain,
! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(198,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_llist_Ocollapse_I1_J) ).
thf(981,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ A )
=> ( A
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(217,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_ord_Olmerge_Odisc_I1_J) ).
thf(1072,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_list_Omap__disc__iff) ).
thf(265,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_list_Osimps_I8_J) ).
thf(312,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(243,axiom,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_local_Olexordp__irreflexive) ).
thf(1169,plain,
! [A: list @ a] :
( ! [B: a] :
~ ( less @ B @ B )
=> ~ ( lexordp @ a @ less @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(44,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ord_Olexordp__eq_Oinducts) ).
thf(397,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp_eq @ TA @ A @ B @ C )
=> ( ! [E: list @ TA] : ( D @ ( nil @ TA ) @ E )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp_eq @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(124,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: TA,E: list @ TA] :
( C
!= ( cons @ TA @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ord_Olexordp_Ocases) ).
thf(687,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ( ( B
= ( nil @ TA ) )
=> ! [D: TA,E: list @ TA] :
( C
!= ( cons @ TA @ D @ E ) ) )
=> ( ! [D: TA] :
( ? [E: list @ TA] :
( B
= ( cons @ TA @ D @ E ) )
=> ! [E: TA] :
( ? [F: list @ TA] :
( C
= ( cons @ TA @ E @ F ) )
=> ~ ( A @ D @ E ) ) )
=> ~ ! [D: TA,E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
=> ! [G: list @ TA] :
( ( C
= ( cons @ TA @ E @ G ) )
=> ( ~ ( A @ D @ E )
=> ( ~ ( A @ E @ D )
=> ~ ( lexordp @ TA @ A @ F @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(46,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_inf_Ocommute) ).
thf(411,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(200,axiom,
! [A: list @ a] :
( ( lexordp @ a @ less @ ( nil @ a ) @ A )
= ( A
!= ( nil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_local_Olexordp__simps_I1_J) ).
thf(988,plain,
! [A: list @ a] :
( ( lexordp @ a @ less @ ( nil @ a ) @ A )
= ( A
!= ( nil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(178,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ B ) @ ( append @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_ord_Olexordp__append__leftI) ).
thf(920,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ B ) @ ( append @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(38,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= ( rev @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_rev__is__rev__conv) ).
thf(380,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= ( rev @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(118,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_list_OdiscI) ).
thf(661,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(85,axiom,
! [TA: $tType] :
( ( set_atLeastAtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ B ) @ ( set_atMost @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord_OatLeastAtMost__def) ).
thf(546,plain,
! [TA: $tType] :
( ( set_atLeastAtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ B ) @ ( set_atMost @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(238,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_ord__class_Olmerge_Odisc__iff_I1_J) ).
thf(1153,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) )
= ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(81,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_snoc__eq__iff__butlast) ).
thf(534,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= C )
= ( ( C
!= ( nil @ TA ) )
& ( ( butlast @ TA @ C )
= A )
& ( ( last @ TA @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(215,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastLessThan @ a @ less_eq @ less @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_local_OatLeastLessThan__iff) ).
thf(1067,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastLessThan @ a @ less_eq @ less @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(225,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ( ( hammin1328233080lmerge @ a @ less @ A @ B )
= ( coinductive_LNil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_lmerge_Octr_I1_J) ).
thf(1091,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ( ( hammin1328233080lmerge @ a @ less @ A @ B )
= ( coinductive_LNil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(27,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( rev @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_rev__append) ).
thf(349,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( rev @ TA @ ( append @ TA @ A @ B ) )
= ( append @ TA @ ( rev @ TA @ B ) @ ( rev @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_eq__Nil__appendI) ).
thf(561,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A = B )
=> ( A
= ( append @ TA @ ( nil @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(42,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: set @ ( list @ TA )] :
( ( member @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ C )
=> ( member @ TA @ B @ ( bNF_Greatest_Succ @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_SuccI) ).
thf(392,plain,
! [TA: $tType,A: list @ TA,B: TA,C: set @ ( list @ TA )] :
( ( member @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ C )
=> ( member @ TA @ B @ ( bNF_Greatest_Succ @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_map__is__Nil__conv) ).
thf(297,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( map @ TA @ TB @ A @ B )
= ( nil @ TB ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(108,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_append__same__eq) ).
thf(630,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_greaterThan @ TA @ B @ C ) )
= ( B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ord_OgreaterThan__iff) ).
thf(429,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_greaterThan @ TA @ B @ C ) )
= ( B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(61,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_self__append__conv) ).
thf(467,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(163,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_append__butlast__last__id) ).
thf(847,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( append @ TA @ ( butlast @ TA @ A ) @ ( cons @ TA @ ( last @ TA @ A ) @ ( nil @ TA ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_hd__rev) ).
thf(361,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( rev @ TA @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_shift__def) ).
thf(879,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_shift @ TA @ TB )
= ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(246,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Olexordp__eq_ONil) ).
thf(1178,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Cons__eq__append__conv) ).
thf(665,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( cons @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ( ( C
= ( nil @ TA ) )
& ( ( cons @ TA @ A @ B )
= D ) )
| ? [E: list @ TA] :
( ( ( cons @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(220,axiom,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_llist_Odisc_I1_J) ).
thf(1079,plain,
! [TA: $tType] : ( coinductive_lnull @ TA @ ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(252,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_local_Omin__def) ).
thf(1195,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= A ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( min @ a @ less_eq @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(165,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_append__eq__append__conv2) ).
thf(852,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(54,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_prefixes_Ocases) ).
thf(435,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(133,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_inf__idem) ).
thf(742,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(874,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(189,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Int__left__commute) ).
thf(948,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(127,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_list__ex1__simps_I1_J) ).
thf(725,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(226,axiom,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ~ ( coinductive_lnull @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_ord_Olmerge_Odisc__iff_I2_J) ).
thf(1096,plain,
! [TA: $tType,A: TA > TA > $o,B: coinductive_llist @ TA,C: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ A @ B @ C ) ) )
= ( ~ ( coinductive_lnull @ TA @ B )
& ~ ( coinductive_lnull @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(206,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp @ a @ less @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_local_Olexordp_Ocases) ).
thf(1006,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: a,D: list @ a] :
( B
!= ( cons @ a @ C @ D ) ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp @ a @ less @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(101,axiom,
! [TA: $tType] :
( ( lexordp @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: TA,E: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ D @ E ) ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp @ TA @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ord_Olexordp_Osimps) ).
thf(610,plain,
! [TA: $tType] :
( ( lexordp @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: TA,E: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C
= ( cons @ TA @ D @ E ) ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp @ TA @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(262,axiom,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ ( nil @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_local_Olexordp__simps_I2_J) ).
thf(1259,plain,
! [A: list @ a] :
~ ( lexordp @ a @ less @ A @ ( nil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( rev @ TA @ A ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_Nil__is__rev__conv) ).
thf(317,plain,
! [TA: $tType,A: list @ TA] :
( ( ( nil @ TA )
= ( rev @ TA @ A ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(146,axiom,
! [TA: $tType] :
( ( set_gr323396891AtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ B @ C ) @ ( set_atMost @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_ord_OgreaterThanAtMost__def) ).
thf(783,plain,
! [TA: $tType] :
( ( set_gr323396891AtMost @ TA )
= ( ^ [A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ B @ C ) @ ( set_atMost @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(49,axiom,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_append__Nil) ).
thf(420,plain,
! [TA: $tType,A: list @ TA] :
( ( append @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(222,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr1161524159ssThan @ a @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_local_OgreaterThanLessThan__iff) ).
thf(1082,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_gr1161524159ssThan @ a @ less @ B @ C ) )
= ( ( less @ B @ A )
& ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__inf) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( semilattice_inf @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(183,axiom,
! [TA: $tType,A: list @ TA,B: set @ ( list @ TA ),C: TA] :
( ( member @ ( list @ TA ) @ A @ ( bNF_Greatest_Shift @ TA @ B @ C ) )
=> ( member @ ( list @ TA ) @ ( cons @ TA @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ShiftD) ).
thf(933,plain,
! [TA: $tType,A: list @ TA,B: set @ ( list @ TA ),C: TA] :
( ( member @ ( list @ TA ) @ A @ ( bNF_Greatest_Shift @ TA @ B @ C ) )
=> ( member @ ( list @ TA ) @ ( cons @ TA @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(137,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_last__append) ).
thf(753,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(248,axiom,
! [A: a,B: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_local_Olexordp_ONil) ).
thf(1182,plain,
! [A: a,B: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_append__eq__appendI) ).
thf(537,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(112,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_neq__Nil__conv) ).
thf(642,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
= ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(68,axiom,
! [TA: $tType] :
( ( set_gr1161524159ssThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ A @ B ) @ ( set_lessThan @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_ord_OgreaterThanLessThan__def) ).
thf(489,plain,
! [TA: $tType] :
( ( set_gr1161524159ssThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA,C: TA] : ( inf_inf @ ( set @ TA ) @ ( set_greaterThan @ TA @ A @ B ) @ ( set_lessThan @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(94,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_6) ).
thf(590,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(207,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_ord_Olmerge_Odisc_I2_J) ).
thf(1039,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1328233080lmerge @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(218,axiom,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LNil @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_local_Olsorted__code_I1_J) ).
thf(1075,plain,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_list_Odistinct_I1_J) ).
thf(476,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( nil @ TA )
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(203,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_local_Olexordp__eq_OCons) ).
thf(997,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(227,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_local_Olexordp_OCons) ).
thf(1099,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(237,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ~ ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ a @ A )
& ~ ( coinductive_lnull @ a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_lmerge_Osimps_I2_J) ).
thf(1150,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ~ ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ a @ A )
& ~ ( coinductive_lnull @ a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(116,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_same__append__eq) ).
thf(654,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(251,axiom,
! [A: a,B: a,C: list @ a,D: list @ a,E: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ ( cons @ a @ A @ D ) ) @ ( append @ a @ C @ ( cons @ a @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_local_Olexordp__append__left__rightI) ).
thf(1192,plain,
! [A: a,B: a,C: list @ a,D: list @ a,E: list @ a] :
( ( less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ ( cons @ a @ A @ D ) ) @ ( append @ a @ C @ ( cons @ a @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(214,axiom,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_local_Omax__def) ).
thf(1060,plain,
! [A: a,B: a] :
( ( ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= B ) )
& ( ~ ( less_eq @ A @ B )
=> ( ( max @ a @ less_eq @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(199,axiom,
! [A: list @ a,B: list @ a] :
( ( A
!= ( nil @ a ) )
=> ( lexordp @ a @ less @ B @ ( append @ a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_local_Olexordp__append__rightI) ).
thf(984,plain,
! [A: list @ a,B: list @ a] :
( ( A
!= ( nil @ a ) )
=> ( lexordp @ a @ less @ B @ ( append @ a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(256,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp_eq @ a @ less @ C @ D )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_local_Olexordp__eq_OCons__eq) ).
thf(1241,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp_eq @ a @ less @ C @ D )
=> ( lexordp_eq @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(109,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ C ) )
= ( A
= ( append @ TA @ ( rev @ TA @ C ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_rev__eq__Cons__iff) ).
thf(633,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
( ( ( rev @ TA @ A )
= ( cons @ TA @ B @ C ) )
= ( A
= ( append @ TA @ ( rev @ TA @ C ) @ ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_map__tailrec__rev_Oinduct) ).
thf(805,plain,
! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
=> ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
=> ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
=> ( A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(75,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Nil__is__append__conv) ).
thf(508,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( nil @ TA )
= ( append @ TA @ A @ B ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(83,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) )
=> ( ! [E: TA] :
~ ( A @ E @ E )
=> ( lexordp @ TA @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ord_Olexordp__append__leftD) ).
thf(541,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( lexordp @ TA @ A @ ( append @ TA @ B @ C ) @ ( append @ TA @ B @ D ) )
=> ( ! [E: TA] :
~ ( A @ E @ E )
=> ( lexordp @ TA @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Cons__eq__appendI) ).
thf(657,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( cons @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( cons @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(140,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_last__appendL) ).
thf(765,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(87,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_append__is__Nil__conv) ).
thf(558,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( nil @ TA ) )
= ( ( A
= ( nil @ TA ) )
& ( B
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: list @ TA,D: list @ TA] :
( ( ( map_tailrec_rev @ TB @ TA @ A @ B @ C )
= D )
=> ( ( ( B
= ( nil @ TB ) )
=> ( D != C ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
=> ( D
!= ( map_tailrec_rev @ TB @ TA @ A @ F @ ( cons @ TA @ ( A @ E ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_map__tailrec__rev_Oelims) ).
thf(674,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: list @ TA,D: list @ TA] :
( ( ( map_tailrec_rev @ TB @ TA @ A @ B @ C )
= D )
=> ( ( ( B
= ( nil @ TB ) )
=> ( D != C ) )
=> ~ ! [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
=> ( D
!= ( map_tailrec_rev @ TB @ TA @ A @ F @ ( cons @ TA @ ( A @ E ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(253,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ? [C: list @ a] :
( ( A
= ( nil @ a ) )
& ( B = C ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp_eq @ a @ less @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_local_Olexordp__eq_Osimps) ).
thf(1202,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
= ( ? [C: list @ a] :
( ( A
= ( nil @ a ) )
& ( B = C ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp_eq @ a @ less @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(149,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_longest__common__suffix) ).
thf(792,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
? [C: list @ TA,D: list @ TA,E: list @ TA] :
( ( A
= ( append @ TA @ D @ C ) )
& ( B
= ( append @ TA @ E @ C ) )
& ( ( D
= ( nil @ TA ) )
| ( E
= ( nil @ TA ) )
| ( ( last @ TA @ D )
!= ( last @ TA @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(136,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_append1__eq__conv) ).
thf(750,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
= ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(134,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ord_Olexordp__eq__simps_I3_J) ).
thf(745,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] :
~ ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(57,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_remdups__adj_Oinduct) ).
thf(444,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: TA,E: list @ TA] :
( ( ( C = D )
=> ( A @ ( cons @ TA @ C @ E ) ) )
=> ( ( ( C != D )
=> ( A @ ( cons @ TA @ D @ E ) ) )
=> ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(98,axiom,
! [TA: $tType] :
( ( set_atLeastLessThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ C ) @ ( set_lessThan @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ord_OatLeastLessThan__def) ).
thf(601,plain,
! [TA: $tType] :
( ( set_atLeastLessThan @ TA )
= ( ^ [A: TA > TA > $o,B: TA > TA > $o,C: TA,D: TA] : ( inf_inf @ ( set @ TA ) @ ( set_atLeast @ TA @ A @ C ) @ ( set_lessThan @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_map__tailrec__rev_Osimps_I1_J) ).
thf(375,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( nil @ TB ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA > TA > $o,D: TA,E: TA] :
( ( member @ TA @ A @ ( set_atLeastLessThan @ TA @ B @ C @ D @ E ) )
= ( ( B @ D @ A )
& ( C @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_ord_OatLeastLessThan__iff) ).
thf(733,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA > TA > $o,D: TA,E: TA] :
( ( member @ TA @ A @ ( set_atLeastLessThan @ TA @ B @ C @ D @ E ) )
= ( ( B @ D @ A )
& ( C @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(93,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_butlast_Osimps_I2_J) ).
thf(584,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( nil @ TA ) ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(196,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_local_OatLeast__iff) ).
thf(975,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atLeast @ a @ less_eq @ B ) )
= ( less_eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(50,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_inf__commute) ).
thf(423,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(142,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_inf__sup__aci_I3_J) ).
thf(772,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(92,axiom,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_list__nonempty__induct) ).
thf(577,plain,
! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
( ( A
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( B @ D )
=> ( B @ ( cons @ TA @ C @ D ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_last__map) ).
thf(281,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA > TB] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TB @ ( map @ TA @ TB @ B @ A ) )
= ( B @ ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(261,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) )
= ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_lmerge_Osimps_I1_J) ).
thf(1256,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) )
= ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(71,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_2) ).
thf(498,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(213,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_ord__class_Olmerge_Odisc_I2_J) ).
thf(1058,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( coinductive_lnull @ TA @ A )
=> ( ~ ( coinductive_lnull @ TA @ B )
=> ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(122,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] : ( lexordp @ TA @ A @ ( nil @ TA ) @ ( cons @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ord_Olexordp_ONil) ).
thf(672,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA] : ( lexordp @ TA @ A @ ( nil @ TA ) @ ( cons @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(99,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_rotate1__is__Nil__conv) ).
thf(604,plain,
! [TA: $tType,A: list @ TA] :
( ( ( rotate1 @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
=> ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Cons__eq__map__D) ).
thf(274,plain,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
=> ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(131,axiom,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_product__lists_Osimps_I1_J) ).
thf(736,plain,
! [TA: $tType] :
( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(235,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lmerge_Odisc_I1_J) ).
thf(1144,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ( ( coinductive_lnull @ a @ A )
| ( coinductive_lnull @ a @ B ) )
=> ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( rev @ TB @ ( map @ TA @ TB @ A @ B ) )
= ( map @ TA @ TB @ A @ ( rev @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_rev__map) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( rev @ TB @ ( map @ TA @ TB @ A @ B ) )
= ( map @ TA @ TB @ A @ ( rev @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA,F: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_ord_Olexordp__append__left__rightI) ).
thf(599,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA,F: list @ TA] :
( ( A @ B @ C )
=> ( lexordp @ TA @ A @ ( append @ TA @ D @ ( cons @ TA @ B @ E ) ) @ ( append @ TA @ D @ ( cons @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(245,axiom,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( coinductive_lnull @ a @ A )
=> ( ~ ( coinductive_lnull @ a @ B )
=> ~ ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lmerge_Odisc_I2_J) ).
thf(1175,plain,
! [A: coinductive_llist @ a,B: coinductive_llist @ a] :
( ~ ( coinductive_lnull @ a @ A )
=> ( ~ ( coinductive_lnull @ a @ B )
=> ~ ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(103,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inf__left__idem) ).
thf(616,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ A @ B ) )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Cons__eq__map__conv) ).
thf(303,plain,
! [TA: $tType,TB: $tType,A: TB,B: list @ TB,C: TA > TB,D: list @ TA] :
( ( ( cons @ TB @ A @ B )
= ( map @ TA @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( D
= ( cons @ TA @ E @ F ) )
& ( A
= ( C @ E ) )
& ( B
= ( map @ TA @ TB @ C @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(154,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_ord_Olexordp__eq__simps_I2_J) ).
thf(811,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp_eq @ TA @ A @ B @ ( nil @ TA ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( rev @ TA @ B ) )
= ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_singleton__rev__conv) ).
thf(799,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( ( cons @ TA @ A @ ( nil @ TA ) )
= ( rev @ TA @ B ) )
= ( B
= ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( prefixes @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( append @ ( list @ TA ) @ ( prefixes @ TA @ A ) @ ( cons @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( nil @ ( list @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_prefixes__snoc) ).
thf(621,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( prefixes @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= ( append @ ( list @ TA ) @ ( prefixes @ TA @ A ) @ ( cons @ ( list @ TA ) @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( nil @ ( list @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Int__absorb) ).
thf(769,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(188,axiom,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_local_Oord__le__eq__trans) ).
thf(943,plain,
! [A: a,B: a,C: a] :
( ( less_eq @ A @ B )
=> ( ( B = C )
=> ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(120,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_3) ).
thf(668,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(59,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ! [C: TA] :
~ ( A @ C @ C )
=> ~ ( lexordp @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_ord_Olexordp__irreflexive) ).
thf(462,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ! [C: TA] :
~ ( A @ C @ C )
=> ~ ( lexordp @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(25,axiom,
lattice @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_5) ).
thf(345,plain,
lattice @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(167,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_inf_Oidem) ).
thf(858,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( map_tailrec_rev @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( append @ TB @ ( rev @ TB @ ( map @ TA @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_map__tailrec__rev) ).
thf(367,plain,
! [TA: $tType,TB: $tType] :
( ( map_tailrec_rev @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( append @ TB @ ( rev @ TB @ ( map @ TA @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(157,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_ord_Olexordp__eq__simps_I1_J) ).
thf(827,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(145,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inf__left__commute) ).
thf(780,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) )
= ( inf_inf @ TA @ B @ ( inf_inf @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(204,axiom,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_local_Olexordp__eq__simps_I2_J) ).
thf(1000,plain,
! [A: list @ a] :
( ( lexordp_eq @ a @ less @ A @ ( nil @ a ) )
= ( A
= ( nil @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(259,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_OlessThan__iff) ).
thf(1250,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_lessThan @ a @ less @ B ) )
= ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(228,axiom,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp @ a @ less @ C @ D )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_local_Olexordp_OCons__eq) ).
thf(1102,plain,
! [A: a,B: a,C: list @ a,D: list @ a] :
( ~ ( less @ A @ B )
=> ( ~ ( less @ B @ A )
=> ( ( lexordp @ a @ less @ C @ D )
=> ( lexordp @ a @ less @ ( cons @ a @ A @ C ) @ ( cons @ a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(179,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_ord_Olexordp__eq_OCons) ).
thf(922,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ( A @ B @ C )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(110,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atMost @ TA @ B @ C ) )
= ( B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_ord_OatMost__iff) ).
thf(636,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_atMost @ TA @ B @ C ) )
= ( B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(209,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_local_Oord__eq__less__trans) ).
thf(1044,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(43,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_append__self__conv2) ).
thf(394,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= B )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_map__eq__map__tailrec) ).
thf(306,plain,
! [TA: $tType,TB: $tType] :
( ( map @ TA @ TB )
= ( map_tailrec @ TA @ TB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_ord_Olexordp__eq__simps_I4_J) ).
thf(505,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp_eq @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(55,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_inf_Oright__idem) ).
thf(438,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Int__left__absorb) ).
thf(722,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(255,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: list @ a] : ( B != C ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp_eq @ a @ less @ E @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_local_Olexordp__eq_Ocases) ).
thf(1208,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ( ( A
= ( nil @ a ) )
=> ! [C: list @ a] : ( B != C ) )
=> ( ! [C: a] :
( ? [D: list @ a] :
( A
= ( cons @ a @ C @ D ) )
=> ! [D: a] :
( ? [E: list @ a] :
( B
= ( cons @ a @ D @ E ) )
=> ~ ( less @ C @ D ) ) )
=> ~ ! [C: a,D: a,E: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
=> ! [F: list @ a] :
( ( B
= ( cons @ a @ D @ F ) )
=> ( ~ ( less @ C @ D )
=> ( ~ ( less @ D @ C )
=> ~ ( lexordp_eq @ a @ less @ E @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_bind__simps_I2_J) ).
thf(531,plain,
! [TA: $tType,TB: $tType,A: TA,B: list @ TA,C: TA > ( list @ TB )] :
( ( bind @ TA @ TB @ ( cons @ TA @ A @ B ) @ C )
= ( append @ TB @ ( C @ A ) @ ( bind @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_rotate1_Osimps_I2_J) ).
thf(927,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( rotate1 @ TA @ ( cons @ TA @ A @ B ) )
= ( append @ TA @ B @ ( cons @ TA @ A @ ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(114,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_rev__exhaust) ).
thf(648,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: list @ TA,C: TA] :
( A
!= ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(221,axiom,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LNil @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_local_Olsorted_OLNil) ).
thf(1081,plain,
coinductive_lsorted @ a @ less_eq @ ( coinductive_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_IntD1) ).
thf(939,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(24,axiom,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_butlast_Osimps_I1_J) ).
thf(342,plain,
! [TA: $tType] :
( ( butlast @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: list @ TB,D: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( map_tailrec_rev @ TB @ TA @ A @ C @ ( cons @ TA @ ( A @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_map__tailrec__rev_Osimps_I2_J) ).
thf(355,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: list @ TB,D: list @ TA] :
( ( map_tailrec_rev @ TB @ TA @ A @ ( cons @ TB @ B @ C ) @ D )
= ( map_tailrec_rev @ TB @ TA @ A @ C @ ( cons @ TA @ ( A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(156,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_longest__common__prefix_Oinduct) ).
thf(823,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( ( D = F )
=> ( A @ E @ G ) )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lzip_Oexhaust) ).
thf(1049,plain,
! [TA: $tType,TB: $tType,A: coinductive_llist @ TB,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TB @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TB @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(63,axiom,
! [TA: $tType] :
( ( strict_suffix @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
? [C: list @ TA] :
( ( B
= ( append @ TA @ C @ A ) )
& ( C
!= ( nil @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_strict__suffix__def) ).
thf(473,plain,
! [TA: $tType] :
( ( strict_suffix @ TA )
= ( ^ [A: list @ TA,B: list @ TA] :
? [C: list @ TA] :
( ( B
= ( append @ TA @ C @ A ) )
& ( C
!= ( nil @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(219,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ord__class_Olmerge_Odisc_I1_J) ).
thf(1076,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(51,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_last__appendR) ).
thf(426,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( append @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(242,axiom,
! [A: a,B: a] :
( ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_local_OatLeastLessThan__def) ).
thf(1166,plain,
! [A: a,B: a] :
( ( set_atLeastLessThan @ a @ less_eq @ less @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_lessThan @ a @ less @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(205,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_ord__class_Olmerge_Oexhaust) ).
thf(1003,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(166,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_inf__assoc) ).
thf(855,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(239,axiom,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_local_Oord__less__eq__trans) ).
thf(1156,plain,
! [A: a,B: a,C: a] :
( ( less @ A @ B )
=> ( ( B = C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(47,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_hd__append2) ).
thf(414,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( hd @ TA @ ( append @ TA @ A @ B ) )
= ( hd @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(132,axiom,
! [TA: $tType,A: list @ TA,B: TA > TA > $o,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( lexordp @ TA @ B @ C @ ( append @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_ord_Olexordp__append__rightI) ).
thf(739,plain,
! [TA: $tType,A: list @ TA,B: TA > TA > $o,C: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( lexordp @ TA @ B @ C @ ( append @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1,conjecture,
( ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ xs @ ys ) )
= ( ( coinductive_lnull @ a @ xs )
| ( coinductive_lnull @ a @ ys ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ xs @ ys ) )
!= ( ( coinductive_lnull @ a @ xs )
| ( coinductive_lnull @ a @ ys ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(263,plain,
( ( coinductive_lnull @ a @ ( hammin1328233080lmerge @ a @ less @ xs @ ys ) )
!= ( ( coinductive_lnull @ a @ xs )
| ( coinductive_lnull @ a @ ys ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(216,axiom,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_local_Olexordp__eq__simps_I1_J) ).
thf(1070,plain,
! [A: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(171,axiom,
! [TA: $tType,A: TA,B: set @ ( list @ TA ),C: list @ TA] :
( ( member @ TA @ A @ ( bNF_Greatest_Succ @ TA @ B @ C ) )
=> ( member @ ( list @ TA ) @ ( append @ TA @ C @ ( cons @ TA @ A @ ( nil @ TA ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_SuccD) ).
thf(872,plain,
! [TA: $tType,A: TA,B: set @ ( list @ TA ),C: list @ TA] :
( ( member @ TA @ A @ ( bNF_Greatest_Succ @ TA @ B @ C ) )
=> ( member @ ( list @ TA ) @ ( append @ TA @ C @ ( cons @ TA @ A @ ( nil @ TA ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_butlast__snoc) ).
thf(441,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [TA: $tType,A: set @ ( list @ TA ),B: TA,C: list @ TA] :
( ( bNF_Greatest_Succ @ TA @ ( bNF_Greatest_Shift @ TA @ A @ B ) @ C )
= ( bNF_Greatest_Succ @ TA @ A @ ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Succ__Shift) ).
thf(370,plain,
! [TA: $tType,A: set @ ( list @ TA ),B: TA,C: list @ TA] :
( ( bNF_Greatest_Succ @ TA @ ( bNF_Greatest_Shift @ TA @ A @ B ) @ C )
= ( bNF_Greatest_Succ @ TA @ A @ ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_IntE) ).
thf(502,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(223,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( ( A
= ( nil @ a ) )
& ( B
= ( cons @ a @ C @ D ) ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp @ a @ less @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_local_Olexordp_Osimps) ).
thf(1085,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
= ( ? [C: a,D: list @ a] :
( ( A
= ( nil @ a ) )
& ( B
= ( cons @ a @ C @ D ) ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ( less @ C @ D ) )
| ? [C: a,D: a,E: list @ a,F: list @ a] :
( ( A
= ( cons @ a @ C @ E ) )
& ( B
= ( cons @ a @ D @ F ) )
& ~ ( less @ C @ D )
& ~ ( less @ D @ C )
& ( lexordp @ a @ less @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(62,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__Nil) ).
thf(470,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(190,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_list_Oinducts) ).
thf(951,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(153,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_append__Cons) ).
thf(808,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
= ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(21,axiom,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_rev_Osimps_I1_J) ).
thf(336,plain,
! [TA: $tType] :
( ( rev @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(102,axiom,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_splice_Oinduct) ).
thf(613,plain,
! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(211,axiom,
! [A: a,B: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_local_OatLeastAtMost__def) ).
thf(1052,plain,
! [A: a,B: a] :
( ( set_atLeastAtMost @ a @ less_eq @ A @ B )
= ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ A ) @ ( set_atMost @ a @ less_eq @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(128,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inf_Oassoc) ).
thf(727,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ C )
= ( inf_inf @ TA @ A @ ( inf_inf @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_inf__apply) ).
thf(876,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(201,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_local_OatMost__iff) ).
thf(991,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_atMost @ a @ less_eq @ B ) )
= ( less_eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(40,axiom,
! [TA: $tType] :
( ( prefixes @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_prefixes_Osimps_I1_J) ).
thf(386,plain,
! [TA: $tType] :
( ( prefixes @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(197,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_ord__class_Olmerge_Odisc__iff_I2_J) ).
thf(978,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ( ~ ( coinductive_lnull @ TA @ ( hammin1138290136lmerge @ TA @ A @ B ) ) )
= ( ~ ( coinductive_lnull @ TA @ A )
& ~ ( coinductive_lnull @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(234,axiom,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_llist_OdiscI_I1_J) ).
thf(1140,plain,
! [TA: $tType,A: coinductive_llist @ TA] :
( ( A
= ( coinductive_LNil @ TA ) )
=> ( coinductive_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(107,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_mem__Collect__eq) ).
thf(627,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(247,axiom,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp_eq @ a @ less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_local_Olexordp__into__lexordp__eq) ).
thf(1180,plain,
! [A: list @ a,B: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp_eq @ a @ less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(66,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_last__ConsL) ).
thf(482,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(70,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Int__commute) ).
thf(495,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_inf__fun__def) ).
thf(759,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_inf @ TB @ ( type2 @ TB ) )
=> ( ( inf_inf @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( inf_inf @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(250,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_ord_Olmerge_Oexhaust) ).
thf(1189,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA] :
( ~ ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ~ ( ~ ( coinductive_lnull @ TA @ A )
=> ( coinductive_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(162,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Int__assoc) ).
thf(844,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(230,axiom,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp @ a @ less @ A @ B )
=> ( ! [D: a,E: list @ a] : ( C @ ( nil @ a ) @ ( cons @ a @ D @ E ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_local_Olexordp_Oinducts) ).
thf(1108,plain,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp @ a @ less @ A @ B )
=> ( ! [D: a,E: list @ a] : ( C @ ( nil @ a ) @ ( cons @ a @ D @ E ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(260,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ ( append @ a @ A @ B ) @ ( append @ a @ A @ C ) )
=> ( ! [D: a] :
~ ( less @ D @ D )
=> ( lexordp @ a @ less @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_local_Olexordp__append__leftD) ).
thf(1253,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ ( append @ a @ A @ B ) @ ( append @ a @ A @ C ) )
=> ( ! [D: a] :
~ ( less @ D @ D )
=> ( lexordp @ a @ less @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(257,axiom,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp @ a @ less @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_local_Olexordp__simps_I3_J) ).
thf(1244,plain,
! [A: a,B: list @ a,C: a,D: list @ a] :
( ( lexordp @ a @ less @ ( cons @ a @ A @ B ) @ ( cons @ a @ C @ D ) )
= ( ( less @ A @ C )
| ( ~ ( less @ C @ A )
& ( lexordp @ a @ less @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(147,axiom,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ord_Olexordp__eq_Osimps) ).
thf(786,plain,
! [TA: $tType] :
( ( lexordp_eq @ TA )
= ( ^ [A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ? [D: list @ TA] :
( ( B
= ( nil @ TA ) )
& ( C = D ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ( A @ D @ E ) )
| ? [D: TA,E: TA,F: list @ TA,G: list @ TA] :
( ( B
= ( cons @ TA @ D @ F ) )
& ( C
= ( cons @ TA @ E @ G ) )
& ~ ( A @ D @ E )
& ~ ( A @ E @ D )
& ( lexordp_eq @ TA @ A @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(192,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_append__assoc) ).
thf(963,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(78,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ! [E: TA,F: list @ TA] : ( D @ ( nil @ TA ) @ ( cons @ TA @ E @ F ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ord_Olexordp_Oinducts) ).
thf(517,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA,D: ( list @ TA ) > ( list @ TA ) > $o] :
( ( lexordp @ TA @ A @ B @ C )
=> ( ! [E: TA,F: list @ TA] : ( D @ ( nil @ TA ) @ ( cons @ TA @ E @ F ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ( A @ E @ F )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) )
=> ( ! [E: TA,F: TA,G: list @ TA,H: list @ TA] :
( ~ ( A @ E @ F )
=> ( ~ ( A @ F @ E )
=> ( ( lexordp @ TA @ A @ G @ H )
=> ( ( D @ G @ H )
=> ( D @ ( cons @ TA @ E @ G ) @ ( cons @ TA @ F @ H ) ) ) ) ) )
=> ( D @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(90,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_last_Osimps) ).
thf(568,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( ( A
= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= B ) )
& ( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ ( cons @ TA @ B @ A ) )
= ( last @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(378,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( lattice @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( prefixes @ TA @ ( cons @ TA @ A @ B ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( map @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A ) @ ( prefixes @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_prefixes_Osimps_I2_J) ).
thf(383,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( prefixes @ TA @ ( cons @ TA @ A @ B ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( map @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ A ) @ ( prefixes @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(159,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord_Olexordp__eq_OCons__eq) ).
thf(832,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: TA,D: list @ TA,E: list @ TA] :
( ~ ( A @ B @ C )
=> ( ~ ( A @ C @ B )
=> ( ( lexordp_eq @ TA @ A @ D @ E )
=> ( lexordp_eq @ TA @ A @ ( cons @ TA @ B @ D ) @ ( cons @ TA @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(26,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__cong) ).
thf(346,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(86,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_prefixes_Oinduct) ).
thf(549,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ( A @ ( nil @ TA ) )
=> ( ! [C: TA,D: list @ TA] :
( ( A @ D )
=> ( A @ ( cons @ TA @ C @ D ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(240,axiom,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_local_OgreaterThan__iff) ).
thf(1161,plain,
! [A: a,B: a] :
( ( member @ a @ A @ ( set_greaterThan @ a @ less @ B ) )
= ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: TA,D: list @ TA] :
( ( ( map @ TB @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ? [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TB @ TA @ A @ F )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_map__eq__Cons__D) ).
thf(287,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: list @ TB,C: TA,D: list @ TA] :
( ( ( map @ TB @ TA @ A @ B )
= ( cons @ TA @ C @ D ) )
=> ? [E: TB,F: list @ TB] :
( ( B
= ( cons @ TB @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TB @ TA @ A @ F )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TB @ ( A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_list_Osimps_I9_J) ).
thf(300,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: list @ TA] :
( ( map @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( cons @ TB @ ( A @ B ) @ ( map @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [TA: $tType,A: set @ ( list @ TA ),B: TA] :
( ( member @ ( list @ TA ) @ ( nil @ TA ) @ A )
=> ( ( member @ TA @ B @ ( bNF_Greatest_Succ @ TA @ A @ ( nil @ TA ) ) )
=> ( member @ ( list @ TA ) @ ( nil @ TA ) @ ( bNF_Greatest_Shift @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_empty__Shift) ).
thf(315,plain,
! [TA: $tType,A: set @ ( list @ TA ),B: TA] :
( ( member @ ( list @ TA ) @ ( nil @ TA ) @ A )
=> ( ( member @ TA @ B @ ( bNF_Greatest_Succ @ TA @ A @ ( nil @ TA ) ) )
=> ( member @ ( list @ TA ) @ ( nil @ TA ) @ ( bNF_Greatest_Shift @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_transpose_Ocases) ).
thf(432,plain,
! [TA: $tType,A: list @ ( list @ TA )] :
( ( A
!= ( nil @ ( list @ TA ) ) )
=> ( ! [B: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
=> ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
( A
!= ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bind__simps_I1_J) ).
thf(867,plain,
! [TA: $tType,TB: $tType,A: TB > ( list @ TA )] :
( ( bind @ TB @ TA @ ( nil @ TB ) @ A )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(35,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( strict_suffix @ TA @ A @ B )
=> ( ( strict_suffix @ TA @ B @ C )
=> ( strict_suffix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_strict__suffix__trans) ).
thf(373,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( strict_suffix @ TA @ A @ B )
=> ( ( strict_suffix @ TA @ B @ C )
=> ( strict_suffix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( butlast @ TA @ B ) )
= ( butlast @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_map__butlast) ).
thf(294,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( map @ TA @ TB @ A @ ( butlast @ TA @ B ) )
= ( butlast @ TB @ ( map @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
semilattice_inf @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__inf_4) ).
thf(341,plain,
semilattice_inf @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: TB,D: list @ TB] :
( ( ( map @ TA @ TB @ A @ B )
= ( cons @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TA @ TB @ A @ F )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_map__eq__Cons__conv) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA,C: TB,D: list @ TB] :
( ( ( map @ TA @ TB @ A @ B )
= ( cons @ TB @ C @ D ) )
= ( ? [E: TA,F: list @ TA] :
( ( B
= ( cons @ TA @ E @ F ) )
& ( ( A @ E )
= C )
& ( ( map @ TA @ TB @ A @ F )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= B )
= ( A
= ( rev @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rev__swap) ).
thf(358,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ A )
= B )
= ( A
= ( rev @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(244,axiom,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ A ) @ ( append @ a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_local_Olexordp__append__leftI) ).
thf(1172,plain,
! [A: list @ a,B: list @ a,C: list @ a] :
( ( lexordp @ a @ less @ A @ B )
=> ( lexordp @ a @ less @ ( append @ a @ C @ A ) @ ( append @ a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(191,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_not__Cons__self2) ).
thf(960,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( cons @ TA @ A @ B )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(106,axiom,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_inf__right__idem) ).
thf(624,plain,
! [TA: $tType] :
( ( semilattice_inf @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( inf_inf @ TA @ ( inf_inf @ TA @ A @ B ) @ B )
= ( inf_inf @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(60,axiom,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_sublists_Osimps_I1_J) ).
thf(464,plain,
! [TA: $tType] :
( ( sublists @ TA @ ( nil @ TA ) )
= ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_list__induct2_H) ).
thf(596,plain,
! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
=> ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
=> ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
=> ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
( ( A @ E @ G )
=> ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_lessThan @ TA @ B @ C ) )
= ( B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_ord_OlessThan__iff) ).
thf(528,plain,
! [TA: $tType,A: TA,B: TA > TA > $o,C: TA] :
( ( member @ TA @ A @ ( set_lessThan @ TA @ B @ C ) )
= ( B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(58,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_self__append__conv2) ).
thf(459,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( A
= ( append @ TA @ B @ A ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(164,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_ord_Olexordp__eq_ONil) ).
thf(850,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] : ( lexordp_eq @ TA @ A @ ( nil @ TA ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(231,axiom,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ! [D: list @ a] : ( C @ ( nil @ a ) @ D )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp_eq @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_Olexordp__eq_Oinducts) ).
thf(1120,plain,
! [A: list @ a,B: list @ a,C: ( list @ a ) > ( list @ a ) > $o] :
( ( lexordp_eq @ a @ less @ A @ B )
=> ( ! [D: list @ a] : ( C @ ( nil @ a ) @ D )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ( less @ D @ E )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) )
=> ( ! [D: a,E: a,F: list @ a,G: list @ a] :
( ~ ( less @ D @ E )
=> ( ~ ( less @ E @ D )
=> ( ( lexordp_eq @ a @ less @ F @ G )
=> ( ( C @ F @ G )
=> ( C @ ( cons @ a @ D @ F ) @ ( cons @ a @ E @ G ) ) ) ) ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_maps__simps_I1_J) ).
thf(607,plain,
! [TA: $tType,TB: $tType,A: TA > ( list @ TB ),B: TA,C: list @ TA] :
( ( maps @ TA @ TB @ A @ ( cons @ TA @ B @ C ) )
= ( append @ TB @ ( A @ B ) @ ( maps @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ord_Olexordp__simps_I3_J) ).
thf(486,plain,
! [TA: $tType,A: TA > TA > $o,B: TA,C: list @ TA,D: TA,E: list @ TA] :
( ( lexordp @ TA @ A @ ( cons @ TA @ B @ C ) @ ( cons @ TA @ D @ E ) )
= ( ( A @ B @ D )
| ( ~ ( A @ D @ B )
& ( lexordp @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(184,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp_eq @ TA @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_ord_Olexordp__into__lexordp__eq) ).
thf(935,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA,C: list @ TA] :
( ( lexordp @ TA @ A @ B @ C )
=> ( lexordp_eq @ TA @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(249,axiom,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1328233080lmerge @ TA @ C @ A @ B )
= ( coinductive_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_ord_Olmerge_Octr_I1_J) ).
thf(1184,plain,
! [TA: $tType,A: coinductive_llist @ TA,B: coinductive_llist @ TA,C: TA > TA > $o] :
( ( ( coinductive_lnull @ TA @ A )
| ( coinductive_lnull @ TA @ B ) )
=> ( ( hammin1328233080lmerge @ TA @ C @ A @ B )
= ( coinductive_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Nil__is__map__conv) ).
thf(309,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: list @ TA] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ A @ B ) )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_append__self__conv) ).
thf(543,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( append @ TA @ A @ B )
= A )
= ( B
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(143,axiom,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__inf_1) ).
thf(775,plain,
! [TA: $tType] : ( semilattice_inf @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(111,axiom,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp @ TA @ A @ ( nil @ TA ) @ B )
= ( B
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_ord_Olexordp__simps_I1_J) ).
thf(639,plain,
! [TA: $tType,A: TA > TA > $o,B: list @ TA] :
( ( lexordp @ TA @ A @ ( nil @ TA ) @ B )
= ( B
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(224,axiom,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lnull__def) ).
thf(1088,plain,
! [TA: $tType] :
( ( coinductive_lnull @ TA )
= ( ^ [A: coinductive_llist @ TA] :
( A
= ( coinductive_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( map_tailrec @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( rev @ TB @ ( map_tailrec_rev @ TA @ TB @ A @ B @ ( nil @ TB ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_map__tailrec__def) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( map_tailrec @ TA @ TB )
= ( ^ [A: TA > TB,B: list @ TA] : ( rev @ TB @ ( map_tailrec_rev @ TA @ TB @ A @ B @ ( nil @ TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(175,axiom,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_inf__sup__aci_I1_J) ).
thf(882,plain,
! [TA: $tType] :
( ( lattice @ TA @ ( type2 @ TA ) )
=> ( ( inf_inf @ TA )
= ( ^ [A: TA,B: TA] : ( inf_inf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(195,axiom,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_local_OatLeastAtMost__iff) ).
thf(972,plain,
! [A: a,B: a,C: a] :
( ( member @ a @ A @ ( set_atLeastAtMost @ a @ less_eq @ B @ C ) )
= ( ( less_eq @ B @ A )
& ( less_eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1265,plain,
$false,
inference(e,[status(thm)],[645,333,941,777,352,479,1105,408,762,730,994,1205,511,1041,861,1137,500,1164,814,747,930,670,829,885,651,841,417,320,565,389,1055,719,619,917,802,1132,1147,1247,870,969,284,924,492,789,591,834,514,937,574,966,981,1072,265,312,1169,397,687,411,988,920,380,661,546,1153,534,1067,1091,349,561,392,297,630,429,467,847,361,879,1178,665,1079,1195,852,435,742,874,948,725,1096,1006,610,1259,317,783,420,1082,339,933,753,1182,537,642,489,590,1039,1075,476,997,1099,1150,654,1192,1060,984,1241,633,805,508,541,657,765,558,674,1202,792,750,745,444,601,375,733,584,975,423,772,577,281,1256,498,1058,672,604,274,736,1144,271,599,1175,616,303,811,799,621,769,943,668,462,345,858,367,827,780,1000,1250,1102,922,636,1044,394,306,505,438,722,1208,531,927,648,1081,939,342,355,823,1049,473,1076,426,1166,1003,855,1156,414,739,263,1070,872,441,370,502,1085,470,951,808,336,613,1052,727,876,991,386,978,1140,627,1180,482,495,759,1189,844,1108,1253,1244,786,963,517,568,378,383,832,346,549,1161,287,300,315,432,867,373,294,341,268,358,1172,960,624,464,596,528,459,850,1120,607,486,935,1184,309,543,775,639,1088,364,882,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT154^1 : TPTP v8.1.2. Released v7.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 11:34:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.71/1.13 % [INFO] Parsing done (258ms).
% 1.71/1.14 % [INFO] Running in sequential loop mode.
% 2.66/1.36 % [INFO] eprover registered as external prover.
% 2.66/1.37 % [INFO] cvc4 registered as external prover.
% 2.66/1.37 % [INFO] Scanning for conjecture ...
% 3.02/1.48 % [INFO] Found a conjecture and 262 axioms. Running axiom selection ...
% 3.22/1.59 % [INFO] Axiom selection finished. Selected 260 axioms (removed 2 axioms).
% 4.21/1.82 % [INFO] Problem is higher-order (TPTP THF).
% 4.21/1.84 % [INFO] Type checking passed.
% 4.21/1.84 % [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 ...
% 27.03/10.12 % External prover 'e' found a proof!
% 27.03/10.12 % [INFO] Killing All external provers ...
% 27.03/10.12 % Time passed: 9592ms (effective reasoning time: 8979ms)
% 27.03/10.12 % 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)>
% 27.03/10.12 % Axioms used in derivation (260): fact_241_local_OatLeast__iff, fact_197_butlast_Osimps_I2_J, fact_207_map__tailrec__rev_Osimps_I2_J, fact_34_local_Olexordp__eq_ONil, fact_122_ord_Olexordp__eq__refl, fact_193_butlast_Osimps_I1_J, fact_81_ord_Olexordp_ONil, fact_95_Cons__eq__append__conv, fact_102_Cons__eq__appendI, fact_11_ord_Olmerge_Oexhaust, fact_18_local_OlessThan__iff, fact_196_last_Osimps, fact_215_ord_OgreaterThanAtMost__def, fact_176_map__eq__Cons__conv, fact_22_ord__class_Olmerge_Odisc_I2_J, fact_216_rev__rev__ident, fact_53_local_Olexordp_Osimps, fact_26_llist_OdiscI_I1_J, fact_116_ord_Olexordp_OCons__eq, fact_8_ord_Olmerge_Odisc_I1_J, fact_158_prefixes_Oinduct, fact_87_ord_Olexordp__eq_Oinducts, fact_124_ord_OgreaterThanLessThan__eq, fact_188_last__appendR, fact_167_maps__simps_I1_J, fact_111_rev__induct, fact_78_local_Olexordp__eq__simps_I2_J, fact_173_Cons__eq__map__D, fact_243_local_OatLeastLessThan__iff, tcon_Set_Oset___Lattices_Olattice_2, fact_132_inf_Oidem, fact_40_local_Olexordp__append__leftI, fact_66_ord_Olexordp__simps_I3_J, fact_185_map__eq__map__tailrec, fact_161_prefixes__eq__Snoc, fact_110_rev__exhaust, fact_170_list_Omap__disc__iff, fact_44_Collect__mem__eq, fact_71_ord_Olexordp__eq__simps_I2_J, fact_142_inf__commute, fact_220_rev__append, fact_228_rev__swap, fact_136_inf__sup__aci_I2_J, fact_250_hd__rev, fact_184_rotate1_Osimps_I1_J, fact_149_Int__absorb, fact_247_ord_OatLeastLessThan__def, fact_57_local_Olexordp__append__left__rightI, fact_63_self__append__conv, fact_112_list_OdiscI, tcon_fun___Orderings_Oord, fact_120_ord_Olexordp__eq_ONil, fact_86_ord_Olexordp__eq_Osimps, fact_119_ord_Olexordp__eq_OCons, fact_246_ord_OatLeastLessThan__iff, fact_166_prefixes_Oelims, fact_82_ord_Olexordp_Ocases, fact_210_shift__def, fact_131_inf__apply, fact_156_sublists_Osimps_I1_J, fact_183_rotate1__is__Nil__conv, fact_83_ord_Olexordp_Osimps, fact_129_inf__left__idem, fact_5_lmerge_Osimps_I2_J, fact_54_local_Olexordp__eq_Ocases, fact_68_ord_Olexordp__simps_I1_J, fact_30_ord__class_Olmerge_Odisc__iff_I2_J, fact_212_ShiftD, fact_126_IntI, fact_62_append__self__conv2, fact_199_longest__common__suffix, fact_4_lmerge_Odisc_I1_J, fact_147_IntD2, fact_164_prefixes_Osimps_I1_J, fact_226_ord_OgreaterThanAtMost__iff, fact_67_ord_Olexordp__eq__simps_I4_J, fact_0_lmerge_Oexhaust, fact_159_longest__common__prefix_Oinduct, fact_214_map__tailrec__def, fact_65_append__Nil2, fact_91_append__eq__append__conv2, fact_152_Int__left__commute, fact_43_mem__Collect__eq, fact_209_SuccI, fact_37_ord_Olexordp__into__lexordp__eq, fact_75_local_Olexordp__eq__simps_I4_J, fact_107_neq__Nil__conv, fact_128_inf_Oright__idem, fact_148_Int__assoc, fact_168_Nil__is__map__conv, fact_224_rev__map, fact_50_local_Olexordp_ONil, fact_182_rotate1_Osimps_I2_J, fact_179_prefixes_Osimps_I2_J, fact_205_map__tailrec__rev_Oelims, fact_27_llist_Odisc_I1_J, fact_108_list_Oinducts, fact_118_ord_Olexordp__eq_OCons__eq, fact_60_Nil__is__append__conv, fact_230_map__tailrec__rev, fact_104_eq__Nil__appendI, fact_194_last__ConsR, fact_10_ord_Olmerge_Odisc__iff_I1_J, fact_15_local_OgreaterThanLessThan__iff, fact_143_inf_Oleft__commute, fact_238_local_OgreaterThanAtMost__iff, fact_225_ord_OatMost__iff, fact_79_local_Olexordp__eq__simps_I1_J, fact_252_local_Olsorted__code_I1_J, fact_55_local_Olexordp__eq_Oinducts, fact_227_rev_Osimps_I1_J, tcon_Set_Oset___Lattices_Osemilattice__inf_1, fact_52_local_Olexordp_Oinducts, fact_251_hd__append2, fact_150_Int__commute, fact_7_ord_Olmerge_Odisc_I2_J, fact_39_local_Olexordp_OCons, fact_29_ord__class_Olmerge_Odisc__iff_I1_J, fact_41_local_Olexordp__append__leftD, fact_99_append__eq__appendI, fact_222_singleton__rev__conv, fact_172_list_Osimps_I9_J, fact_174_map__eq__Cons__D, fact_117_ord_Olexordp_OCons, fact_17_local_OgreaterThan__iff, fact_73_ord_Olexordp__eq__simps_I3_J, fact_49_append__assoc, fact_127_inf__right__idem, fact_248_ord_OatLeastAtMost__def, fact_100_append__Nil, tcon_fun___Lattices_Osemilattice__inf, fact_189_last__appendL, fact_13_lmerge_Octr_I1_J, fact_175_Cons__eq__map__conv, fact_211_empty__Shift, fact_61_self__append__conv2, fact_74_local_Olexordp__simps_I3_J, fact_115_ord_Olexordp__append__leftD, fact_177_list_Osimps_I8_J, fact_125_Int__iff, fact_141_inf_Ocommute, fact_213_Succ__Shift, fact_12_ord__class_Olmerge_Oexhaust, fact_134_inf__sup__aci_I4_J, fact_208_map__tailrec__rev_Osimps_I1_J, fact_2_local_Oord__less__eq__trans, fact_181_insert__Nil, fact_198_last__map, fact_138_inf__fun__def, fact_3_lmerge_Odisc_I2_J, fact_47_same__append__eq, fact_231_list__of__aux__code_I1_J, fact_221_rev__singleton__conv, fact_69_ord_Olexordp__simps_I2_J, fact_144_inf__left__commute, fact_171_map__append, fact_135_inf__sup__aci_I3_J, fact_6_lmerge_Osimps_I1_J, tcon_HOL_Obool___Lattices_Osemilattice__inf_4, fact_42_list_Oinject, fact_106_list__induct2_H, fact_154_ord_OgreaterThan__iff, fact_32_local_OgreaterThanLessThan__eq, fact_203_strict__suffix__def, fact_97_append__Cons, fact_56_local_Olexordp__eq_Osimps, fact_237_local_OatMost__iff, fact_139_inf_Oassoc, fact_236_local_Omin__def, fact_123_ord_OgreaterThanLessThan__def, fact_223_rev__eq__Cons__iff, fact_200_butlast__append, fact_218_Nil__is__rev__conv, fact_58_local_Olexordp__append__rightI, fact_133_inf__idem, fact_9_ord_Olmerge_Odisc__iff_I2_J, fact_233_local_Oord__eq__le__trans, fact_114_ord_Olexordp__append__leftI, fact_163_bind__simps_I1_J, fact_249_local_Olsorted_OLNil, fact_1_local_Oord__eq__less__trans, fact_162_bind__simps_I2_J, fact_21_ord_Olmerge_Octr_I1_J, fact_130_inf_Oleft__idem, fact_64_append__self__conv, fact_169_map__is__Nil__conv, fact_103_not__Cons__self2, fact_14_local_Olexordp__eq__refl, tcon_Set_Oset___Orderings_Oord_3, fact_36_local_Olexordp__eq_OCons, fact_51_local_Olexordp_Ocases, fact_190_append__butlast__last__id, fact_92_list__nonempty__induct, fact_235_local_Omax__def, fact_48_append__same__eq, fact_84_ord_Olexordp_Oinducts, fact_217_rev__is__rev__conv, fact_89_ord_Olexordp__append__left__rightI, fact_72_append1__eq__conv, fact_28_ord__class_Olmerge_Octr_I1_J, fact_90_map__tailrec__rev_Oinduct, fact_38_local_Olexordp_OCons__eq, fact_155_ord_OgreaterThanLessThan__iff, fact_94_append__eq__Cons__conv, fact_195_last__ConsL, fact_157_prefixes_Ocases, fact_76_local_Olexordp__simps_I2_J, fact_204_strict__suffix__trans, fact_85_ord_Olexordp__eq_Ocases, fact_101_transpose_Ocases, fact_109_list_Oexhaust, fact_24_lnull__def, fact_45_Collect__cong, fact_80_local_Olexordp__eq__simps_I3_J, fact_59_append__is__Nil__conv, fact_191_map__butlast, fact_240_local_OatLeastAtMost__def, fact_16_local_Olexordp__irreflexive, fact_35_local_Olexordp__eq_OCons__eq, fact_19_lzip_Oexhaust, fact_245_ord_OatLeastAtMost__iff, fact_151_Int__left__absorb, fact_187_butlast__snoc, fact_206_SuccD, fact_219_rev__is__Nil__conv, fact_146_IntD1, fact_234_local_Oord__le__eq__trans, fact_186_last__snoc, fact_20_lappend_Oexhaust, fact_242_local_OatLeastAtMost__iff, fact_165_product__lists_Osimps_I1_J, fact_244_ord_OatLeast__iff, fact_31_ord__class_Olmerge_Odisc_I1_J, fact_23_local_Olexordp__into__lexordp__eq, fact_239_local_OatLeastLessThan__def, fact_201_last__append, tcon_HOL_Obool___Orderings_Oord_6, fact_93_rev__nonempty__induct, fact_33_local_OgreaterThanLessThan__def, fact_140_inf__assoc, fact_96_remdups__adj_Oinduct, fact_137_inf__sup__aci_I1_J, fact_160_prefixes__snoc, fact_105_splice_Oinduct, tcon_HOL_Obool___Lattices_Olattice_5, fact_121_ord_Olexordp__irreflexive, fact_229_rev_Osimps_I2_J, fact_232_local_OgreaterThanAtMost__def, fact_145_IntE, fact_113_list_Odistinct_I1_J, fact_202_list__ex1__simps_I1_J, fact_25_llist_Ocollapse_I1_J, tcon_fun___Lattices_Olattice, fact_77_local_Olexordp__simps_I1_J, fact_192_snoc__eq__iff__butlast, fact_88_ord_Olexordp__append__rightI, fact_153_ord_OlessThan__iff, fact_178_maps__simps_I2_J, fact_70_ord_Olexordp__eq__simps_I1_J, fact_98_remdups__adj_Ocases
% 27.03/10.12 % No. of inferences in proof: 524
% 27.03/10.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9592 ms resp. 8979 ms w/o parsing
% 27.89/10.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.89/10.28 % [INFO] Killing All external provers ...
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