TSTP Solution File: ITP054^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP054^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:27 EDT 2024
% Result : Theorem 46.99s 16.47s
% Output : Refutation 47.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 320
% Syntax : Number of formulae : 593 ( 216 unt; 49 typ; 0 def)
% Number of atoms : 1479 ( 434 equ; 4 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 7080 ( 164 ~; 29 |; 88 &;6195 @)
% ( 0 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 294 ( 294 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 14 con; 0-7 aty)
% Number of variables : 1331 ( 38 ^1181 !; 70 ?;1331 :)
% ( 42 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(v_type,type,
v: $tType ).
thf(s_type,type,
s: $tType ).
thf(p_type,type,
p: $tType ).
thf(size_type,type,
size:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_type,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(msgs_type,type,
msgs:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( configuration_ext @ TD @ TC @ TB @ TA ) > ( message @ TD @ TC ) > nat ) ).
thf(enabled_type,type,
enabled:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( configuration_ext @ TC @ TB @ TA @ product_unit ) > ( message @ TC @ TB ) > $o ) ).
thf(firstOccurrence_type,type,
firstOccurrence:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( message @ TC @ TB ) > nat > $o ) ).
thf(minimalEnabled_type,type,
minimalEnabled:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( list @ ( configuration_ext @ TC @ TB @ TA @ product_unit ) ) > ( list @ ( message @ TC @ TB ) ) > ( message @ TC @ TB ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(prefixList_type,type,
prefixList:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > $o ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > TA ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(tl_type,type,
tl:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(list_ex_type,type,
list_ex:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(nth_type,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(remdups_adj_type,type,
remdups_adj:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(suc_type,type,
suc: nat > nat ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(consumedMsg_type,type,
consumedMsg: message @ p @ v ).
thf(fe_type,type,
fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
thf(firstOccSet_type,type,
firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
thf(ft_type,type,
ft: nat > ( list @ ( message @ p @ v ) ) ).
thf(index_type,type,
index: nat ).
thf(msg_type,type,
msg: message @ p @ v ).
thf(n0_type,type,
n0: nat ).
thf(n1_type,type,
n1: nat ).
thf(nMsg_type,type,
nMsg: nat ).
thf(n_type,type,
n: nat ).
thf(110,axiom,
! [A: nat,B: nat,C: nat,D: message @ p @ v] :
( ( ( ord_less_eq @ nat @ A @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ C ) ) )
& ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq @ nat @ A @ E )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ C ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ C ) @ E )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_MessageStaysOrConsumed) ).
thf(645,plain,
! [A: nat,B: nat,C: nat,D: message @ p @ v] :
( ( ( ord_less_eq @ nat @ A @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ C ) ) )
& ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ A ) @ D ) )
=> ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) @ B ) @ D )
| ? [E: nat] :
( ( ord_less_eq @ nat @ A @ E )
& ( ord_less @ nat @ E @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ C ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ C ) @ E )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(217,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_lift__Suc__mono__less) ).
thf(1036,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(142,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__Suc0) ).
thf(760,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(333,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_inc__induct) ).
thf(518,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ B )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(233,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_remdups__adj__length__ge1) ).
thf(1083,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(116,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_NotConsumedIntermediate) ).
thf(666,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A )
!= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(242,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(1110,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(48,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__le__mono) ).
thf(408,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_zero__less__diff) ).
thf(582,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(134,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_gr0__implies__Suc) ).
thf(730,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(205,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_infinite__descent__measure) ).
thf(994,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(229,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le0) ).
thf(1073,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(62,axiom,
wellorder @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Owellorder_5) ).
thf(449,plain,
wellorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(105,axiom,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( tl @ TA @ A ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_length__tl) ).
thf(614,plain,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( tl @ TA @ A ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(100,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Ex__less__Suc2) ).
thf(597,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(219,axiom,
! [TA: $tType,A: list @ TA] : ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ A ) ) @ ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_remdups__adj__length) ).
thf(1041,plain,
! [TA: $tType,A: list @ TA] : ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ A ) ) @ ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(261,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_le__refl) ).
thf(1173,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_PrefixListMonotonicity) ).
thf(440,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(83,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Skolem__list__nth) ).
thf(511,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(231,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_4) ).
thf(1078,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(91,axiom,
order @ product_unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_6) ).
thf(550,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_less__Suc__induct) ).
thf(698,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( ! [D: nat,E: nat,F: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ( ord_less @ nat @ E @ F )
=> ( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(189,axiom,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Suc__n__not__le__n) ).
thf(945,plain,
! [A: nat] :
~ ( ord_less_eq @ nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(185,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Nat_Oex__has__greatest__nat) ).
thf(930,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(258,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_diff__le__self) ).
thf(1164,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(150,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_less__zeroE) ).
thf(797,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(237,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Nat_Odiff__diff__eq) ).
thf(1095,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(246,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Suc__diff__diff) ).
thf(1127,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ A ) @ B ) @ ( suc @ C ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(51,axiom,
size @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(417,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_le__0__eq) ).
thf(885,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_le__iff__diff__le__0) ).
thf(301,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(224,axiom,
ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_LengthStep) ).
thf(1055,plain,
ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(95,axiom,
( ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) )
=> ? [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
& ? [B: nat] :
( ( ord_less_eq @ nat @ n0 @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Case2ImplThesis) ).
thf(570,plain,
( ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) )
=> ? [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
& ? [B: nat] :
( ( ord_less_eq @ nat @ n0 @ B )
& ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Suc__leD) ).
thf(719,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(39,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(372,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(80,axiom,
! [A: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_IPrefixListEx) ).
thf(504,plain,
! [A: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) @ ( fe @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Suc__le__D) ).
thf(802,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_old_Onat_Oinject) ).
thf(357,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(226,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_zero__induct__lemma) ).
thf(1059,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ ( suc @ D ) )
=> ( A @ D ) )
=> ( A @ ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(99,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_nat__induct) ).
thf(587,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(164,axiom,
( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_EnabledOrConsumedAtLast) ).
thf(838,plain,
( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__SucI) ).
thf(638,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(195,axiom,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zero__less__Suc) ).
thf(969,plain,
! [A: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_dec__induct) ).
thf(770,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( ord_less @ nat @ D @ B )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(289,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( suc @ B ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_diff__Suc__eq__diff__pred) ).
thf(475,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( suc @ B ) )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(147,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_less__irrefl__nat) ).
thf(789,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(20,axiom,
! [TA: $tType,A: list @ TA] :
( ( last @ TA @ ( remdups_adj @ TA @ A ) )
= ( last @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_last__remdups__adj) ).
thf(321,plain,
! [TA: $tType,A: list @ TA] :
( ( last @ TA @ ( remdups_adj @ TA @ A ) )
= ( last @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(249,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nat_Odistinct_I1_J) ).
thf(1136,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(84,axiom,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_list__ex__length) ).
thf(514,plain,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(254,axiom,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
& ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062) ).
thf(1151,plain,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
& ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(71,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lift__Suc__mono__less__iff) ).
thf(480,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less @ TA @ ( A @ B ) @ ( A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( minus_minus @ nat @ B @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Suc__diff__eq__diff__pred) ).
thf(766,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( minus_minus @ nat @ B @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(120,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_AssumptionFair_I3_J) ).
thf(687,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_diff__eq__diff__less__eq) ).
thf(280,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(170,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Ex__list__of__length) ).
thf(866,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(49,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq @ nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_le__Suc__eq) ).
thf(411,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq @ nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(240,axiom,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_length__greater__0__conv) ).
thf(1104,plain,
! [TA: $tType,A: list @ TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ TA ) @ A ) )
= ( A
!= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ ( suc @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_diff__Suc__less) ).
thf(428,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ ( suc @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(271,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_linorder__neqE__nat) ).
thf(1201,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(10,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_le__zero__eq) ).
thf(292,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(188,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_PrefixSameOnLow) ).
thf(942,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(270,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_less__eq__Suc__le) ).
thf(1199,plain,
( ( ord_less @ nat )
= ( ^ [A: nat] : ( ord_less_eq @ nat @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(37,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_diff__eq__diff__eq) ).
thf(366,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(129,axiom,
( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_EnabledOrConsumed) ).
thf(714,plain,
( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
| ? [A: nat] :
( ( ord_less_eq @ nat @ n0 @ A )
& ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
& ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ A )
= msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_less__Suc__eq__le) ).
thf(1047,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_le__SucI) ).
thf(910,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(176,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_neq0__conv) ).
thf(894,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(141,axiom,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_transitive__stepwise__le) ).
thf(746,plain,
! [A: nat,B: nat,C: nat > nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ! [D: nat] : ( C @ D @ D )
=> ( ! [D: nat,E: nat,F: nat] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( C @ D @ F ) ) )
=> ( ! [D: nat] : ( C @ D @ ( suc @ D ) )
=> ( C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(191,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_bot__nat__0_Oextremum__strict) ).
thf(952,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(30,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_list__ex__simps_I2_J) ).
thf(349,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(158,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_bot__nat__0_Oextremum__unique) ).
thf(820,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(4,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(275,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)],[4]) ).
thf(146,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(788,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(166,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).
thf(847,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_nat__induct__at__least) ).
thf(852,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( C @ A )
=> ( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( C @ D )
=> ( C @ ( suc @ D ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(268,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__SucE) ).
thf(1195,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( suc @ ( minus_minus @ nat @ B @ ( suc @ A ) ) )
= ( minus_minus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Suc__diff__Suc) ).
thf(551,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( suc @ ( minus_minus @ nat @ B @ ( suc @ A ) ) )
= ( minus_minus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_diff__ge__0__iff__ge) ).
thf(324,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(212,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_not__gr0) ).
thf(1012,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(23,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_n__not__Suc__n) ).
thf(329,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(263,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_not0__implies__Suc) ).
thf(1178,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(256,axiom,
! [A: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_IPrefixList) ).
thf(1159,plain,
! [A: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ A ) @ ( ft @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(64,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Suc__neq__Zero) ).
thf(461,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(235,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_diff__is__0__eq) ).
thf(1089,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(251,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_less__eq__nat_Osimps_I1_J) ).
thf(1143,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(214,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_nat__less__le) ).
thf(1017,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(243,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_full__nat__induct) ).
thf(1111,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ ( suc @ D ) @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(210,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_diff__gt__0__iff__gt) ).
thf(1006,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(44,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__nat__zero__code) ).
thf(388,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(171,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_diff__0__eq__0) ).
thf(869,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__or__eq__imp__le) ).
thf(420,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_bot__nat__0_Oextremum) ).
thf(499,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(111,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
= ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Suc__pred_H) ).
thf(650,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
= ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_gr__implies__not0) ).
thf(948,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(74,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
=> ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_EnabledIntermediate) ).
thf(488,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ A )
=> ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) @ msg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(93,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_ex__least__nat__less) ).
thf(554,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less_eq @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__lessE) ).
thf(669,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(230,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( one_one @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_diff__Suc__1) ).
thf(1075,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( one_one @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(255,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_gr__implies__not__zero) ).
thf(1155,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(107,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_infinite__descent0) ).
thf(622,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(206,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_bot__nat__0_Onot__eq__extremum) ).
thf(997,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_le__antisym) ).
thf(1099,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(137,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_le__eq__less__or__eq) ).
thf(738,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( enabled @ TA @ TB @ TC )
= ( ^ [A: configuration_ext @ TA @ TB @ TC @ product_unit,B: message @ TA @ TB] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_enabled__def) ).
thf(1192,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( enabled @ TA @ TB @ TC )
= ( ^ [A: configuration_ext @ TA @ TB @ TC @ product_unit,B: message @ TA @ TB] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ TA @ TB @ TC @ product_unit @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Suc__less__eq2) ).
thf(1050,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
= ( ? [C: nat] :
( ( B
= ( suc @ C ) )
& ( ord_less @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(131,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_lift__Suc__mono__le) ).
thf(721,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ D ) @ ( A @ ( suc @ D ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(208,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(1002,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(79,axiom,
member @ ( message @ p @ v ) @ consumedMsg @ ( firstOccSet @ index ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ConsumedInSet) ).
thf(503,plain,
member @ ( message @ p @ v ) @ consumedMsg @ ( firstOccSet @ index ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(28,axiom,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_remdups__adj_Osimps_I1_J) ).
thf(343,plain,
! [TA: $tType] :
( ( remdups_adj @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(148,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_diff__strict__left__mono) ).
thf(792,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(234,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ A )
= ( nth @ TA @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_last__conv__nth) ).
thf(1086,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ( ( last @ TA @ A )
= ( nth @ TA @ A @ ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(35,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_zero__diff) ).
thf(360,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(153,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_list_Osize_I3_J) ).
thf(805,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) @ ( nil @ TA ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_diff__le__mono2) ).
thf(508,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Suc__inject) ).
thf(311,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__diff__iff) ).
thf(541,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_diff__is__0__eq_H) ).
thf(1170,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(228,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_not__less__zero) ).
thf(1071,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(265,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Zero__neq__Suc) ).
thf(1185,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(149,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_minus__nat_Odiff__0) ).
thf(794,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(183,axiom,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062) ).
thf(926,plain,
enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_le__diff__iff_H) ).
thf(662,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq @ nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_le__SucE) ).
thf(888,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq @ nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(12,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_diff__right__commute) ).
thf(298,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Suc__diff__le) ).
thf(425,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( suc @ B ) @ A )
= ( suc @ ( minus_minus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(375,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(135,axiom,
! [A: nat,B: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ B @ ( firstOccSet @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(733,plain,
! [A: nat,B: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ B @ ( firstOccSet @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(123,axiom,
ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062) ).
thf(694,plain,
ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(165,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_less__mono__imp__le__mono) ).
thf(843,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(8,axiom,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_list_Osel_I2_J) ).
thf(286,plain,
! [TA: $tType] :
( ( tl @ TA @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(139,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_AssumptionFirstOccSetDecrOrConsumed_I1_J) ).
thf(743,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(160,axiom,
! [A: nat,B: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_diff__less__Suc) ).
thf(826,plain,
! [A: nat,B: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_diff__less__mono) ).
thf(579,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(193,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_EnabledInSuc) ).
thf(958,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_Nat_OlessE) ).
thf(545,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(45,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
=> ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ A )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_SameCfgOnLow) ).
thf(391,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
=> ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ A )
= ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(104,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_not__gr__zero) ).
thf(611,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_diff__diff__cancel) ).
thf(1107,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(88,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(540,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(61,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_size__neq__size__imp__neq) ).
thf(445,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(186,axiom,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( ^ [A: list @ TA] :
( if @ nat
@ ( A
= ( nil @ TA ) )
@ ( zero_zero @ nat )
@ ( suc @ ( size_size @ ( list @ TA ) @ ( tl @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Nitpick_Osize__list__simp_I2_J) ).
thf(936,plain,
! [TA: $tType] :
( ( size_size @ ( list @ TA ) )
= ( ^ [A: list @ TA] :
( if @ nat
@ ( A
= ( nil @ TA ) )
@ ( zero_zero @ nat )
@ ( suc @ ( size_size @ ( list @ TA ) @ ( tl @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_less__Suc__eq__0__disj) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( A
= ( zero_zero @ nat ) )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(236,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( tl @ TA @ B ) ) )
=> ( ( nth @ TA @ ( tl @ TA @ B ) @ A )
= ( nth @ TA @ B @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nth__tl) ).
thf(1092,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( tl @ TA @ B ) ) )
=> ( ( nth @ TA @ ( tl @ TA @ B ) @ A )
= ( nth @ TA @ B @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(178,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_less__not__refl) ).
thf(900,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(162,axiom,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_old_Onat_Odistinct_I2_J) ).
thf(831,plain,
! [A: nat] :
( ( suc @ A )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(274,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_measure__induct) ).
thf(567,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_nat_Oinject) ).
thf(318,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(262,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_AssumptionFairContr) ).
thf(1175,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ n @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ A ) ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ B )
=> ( msg
!= ( nth @ ( message @ p @ v ) @ ( ft @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_less__Suc__eq) ).
thf(979,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_measure__induct__rule) ).
thf(604,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( ( tl @ TA @ A )
!= ( nil @ TA ) ) )
=> ( ( last @ TA @ ( tl @ TA @ A ) )
= ( last @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_last__tl) ).
thf(377,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
= ( nil @ TA ) )
| ( ( tl @ TA @ A )
!= ( nil @ TA ) ) )
=> ( ( last @ TA @ ( tl @ TA @ A ) )
= ( last @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(203,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Suc__pred) ).
thf(990,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( suc @ ( zero_zero @ nat ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(220,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B
= ( zero_zero @ nat ) )
| ~ ( A @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_MinPredicate2) ).
thf(1043,plain,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ( ( B
= ( zero_zero @ nat ) )
| ~ ( A @ ( minus_minus @ nat @ B @ ( one_one @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_eq__imp__le) ).
thf(434,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(155,axiom,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_lessI) ).
thf(811,plain,
! [A: nat] : ( ord_less @ nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_not__less__less__Suc__eq) ).
thf(1080,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(157,axiom,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_KeepProperty) ).
thf(816,plain,
! [A: nat,B: nat > $o,C: nat > $o] :
( ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( ( B @ D )
=> ( ( B @ ( suc @ D ) )
& ( C @ D ) ) ) )
=> ( ( B @ A )
=> ! [D: nat] :
( ( ord_less_eq @ nat @ A @ D )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(72,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ ( suc @ A ) @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ B ) ) )
=> ( ( nth @ TA @ ( remdups_adj @ TA @ B ) @ A )
!= ( nth @ TA @ ( remdups_adj @ TA @ B ) @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_remdups__adj__adjacent) ).
thf(483,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ ( suc @ A ) @ ( size_size @ ( list @ TA ) @ ( remdups_adj @ TA @ B ) ) )
=> ( ( nth @ TA @ ( remdups_adj @ TA @ B ) @ A )
!= ( nth @ TA @ ( remdups_adj @ TA @ B ) @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(167,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_gr0__conv__Suc) ).
thf(848,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(182,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( one_one @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_nat__induct__non__zero) ).
thf(912,plain,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( one_one @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( B @ C )
=> ( B @ ( suc @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(269,axiom,
minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_ConsumedMsg_I1_J) ).
thf(1198,plain,
minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(194,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zero__induct) ).
thf(959,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(124,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Suc__diff__1) ).
thf(695,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( suc @ ( minus_minus @ nat @ A @ ( one_one @ nat ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(5,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( prefixList @ TA @ B @ C )
=> ( prefixList @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_PrefixListTransitive) ).
thf(278,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( prefixList @ TA @ A @ B )
=> ( ( prefixList @ TA @ B @ C )
=> ( prefixList @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(213,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_diff__strict__right__mono) ).
thf(1015,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(207,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_le__imp__less__Suc) ).
thf(1000,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Suc__lessD) ).
thf(438,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(56,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Suc__le__mono) ).
thf(431,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(112,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_All__less__Suc2) ).
thf(653,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ ( zero_zero @ nat ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(46,axiom,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J) ).
thf(394,plain,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( B @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(201,axiom,
ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_AssumptionFair_I2_J) ).
thf(986,plain,
ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(15,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_one__reorient) ).
thf(306,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(168,axiom,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_AssumpGreaterOccurrence_I2_J) ).
thf(851,plain,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(239,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_less__imp__le__nat) ).
thf(1102,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(75,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_infinite__descent0__measure) ).
thf(490,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_less__not__refl3) ).
thf(1166,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(184,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_diff__eq__diff__less) ).
thf(927,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(106,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_infinite__descent) ).
thf(617,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(187,axiom,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_MinPredicate) ).
thf(939,plain,
! [A: nat > $o] :
( ? [B: nat] : ( A @ B )
=> ? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(252,axiom,
! [A: message @ p @ v] :
( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ? [B: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A @ B )
& ! [C: message @ p @ v,D: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ C @ D )
=> ( ord_less_eq @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_MinImplAllBigger) ).
thf(1145,plain,
! [A: message @ p @ v] :
( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ? [B: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A @ B )
& ! [C: message @ p @ v,D: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ C @ D )
=> ( ord_less_eq @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_diff__mono) ).
thf(355,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(264,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_neq__if__length__neq) ).
thf(1181,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_less__trans__Suc) ).
thf(823,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ C )
=> ( ord_less @ nat @ ( suc @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(122,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_old_Onat_Oexhaust) ).
thf(690,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat_OdiscI) ).
thf(640,plain,
! [A: nat,B: nat] :
( ( A
= ( suc @ B ) )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(11,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_zero__reorient) ).
thf(295,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(172,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_ex__least__nat__le) ).
thf(872,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ~ ( A @ ( zero_zero @ nat ) )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Suc__leI) ).
thf(705,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(127,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_nth__equalityI) ).
thf(707,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(22,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_diff__right__mono) ).
thf(327,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(204,axiom,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_AssumptionCase1ImplThesis_H) ).
thf(993,plain,
enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(128,axiom,
! [A: message @ p @ v,B: nat,C: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062) ).
thf(712,plain,
! [A: message @ p @ v,B: nat,C: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ C ) @ ( ft @ C ) @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(209,axiom,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_All__less__Suc) ).
thf(1003,plain,
! [A: nat,B: nat > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
=> ( B @ C ) ) )
= ( ( B @ A )
& ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_diffs0__imp__equal) ).
thf(414,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(196,axiom,
wellorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(971,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(223,axiom,
! [A: message @ p @ v] :
( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_MinImplFirstOcc) ).
thf(1053,plain,
! [A: message @ p @ v] :
( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ A )
=> ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(118,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_length__induct) ).
thf(673,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(26,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_diff__0__right) ).
thf(338,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(68,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_nat__less__induct) ).
thf(470,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_le__less__Suc__eq) ).
thf(808,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(247,axiom,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_NotEmpty_I2_J) ).
thf(1130,plain,
( ( fe @ index )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(180,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_le__trans) ).
thf(907,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(218,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_not__less0) ).
thf(1038,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(98,axiom,
! [A: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_SmallIndex) ).
thf(585,plain,
! [A: nat] :
( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ A )
=> ( ord_less @ nat @ A @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Suc__le__lessD) ).
thf(744,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(25,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_zero__le) ).
thf(336,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(113,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_not__less__eq) ).
thf(656,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(101,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Zero__not__Suc) ).
thf(600,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Suc__le__eq) ).
thf(727,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ ( suc @ A ) @ B )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(76,axiom,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_One__nat__def) ).
thf(497,plain,
( ( one_one @ nat )
= ( suc @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(250,axiom,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_NotEmpty_I1_J) ).
thf(1140,plain,
( ( fe @ ( suc @ index ) )
!= ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(43,axiom,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_list__ex1__simps_I1_J) ).
thf(386,plain,
! [TA: $tType,A: TA > $o] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(65,axiom,
ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).
thf(465,plain,
ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_strict__inc__induct) ).
thf(450,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less @ nat @ A @ B )
=> ( ! [D: nat] :
( ( B
= ( suc @ D ) )
=> ( C @ D ) )
=> ( ! [D: nat] :
( ( ord_less @ nat @ D @ B )
=> ( ( C @ ( suc @ D ) )
=> ( C @ D ) ) )
=> ( C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(36,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_eq__iff__diff__eq__0) ).
thf(363,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(175,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_le__neq__implies__less) ).
thf(891,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(245,axiom,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_AssumpGreaterOccurrence_I3_J) ).
thf(1126,plain,
firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(266,axiom,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Ex__less__Suc) ).
thf(1189,plain,
! [A: nat,B: nat > $o] :
( ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( suc @ A ) )
& ( B @ C ) ) )
= ( ( B @ A )
| ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(198,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_diff__less__mono2) ).
thf(976,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Suc__less__SucD) ).
thf(688,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_less__not__refl2) ).
thf(903,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(156,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A )
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_SameMsgOnLow) ).
thf(813,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
=> ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ A )
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(85,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(517,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_diff__left__mono) ).
thf(304,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_remdups__adj__Nil__iff) ).
thf(351,plain,
! [TA: $tType,A: list @ TA] :
( ( ( remdups_adj @ TA @ A )
= ( nil @ TA ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
~ ( ord_less @ nat @ nMsg @ n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_AssumpGreaterOccurrence_I1_J) ).
thf(418,plain,
~ ( ord_less @ nat @ nMsg @ n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__mono) ).
thf(478,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(143,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_list__eq__iff__nth__eq) ).
thf(763,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(42,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_diff__self) ).
thf(383,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,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(346,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(87,axiom,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_old_Onat_Odistinct_I1_J) ).
thf(536,plain,
! [A: nat] :
( ( zero_zero @ nat )
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(257,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Suc__lessI) ).
thf(1161,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less @ nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_nat__le__linear) ).
thf(800,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(244,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_old_Onat_Oinducts) ).
thf(1116,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( A @ C )
=> ( A @ ( suc @ C ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_diff__Suc__Suc) ).
thf(1133,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( minus_minus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(18,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_diff__zero) ).
thf(315,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Suc__less__eq) ).
thf(835,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(47,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_less__one) ).
thf(405,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__iff__diff__less__0) ).
thf(1148,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1,conjecture,
ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(273,plain,
~ ( ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_nat__neq__iff) ).
thf(735,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_AsynchronousSystem_Omessage___Nat_Osize_7) ).
thf(341,plain,
! [TA: $tType,TB: $tType] : ( size @ ( message @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(81,axiom,
! [A: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ ( suc @ index ) ) )
=> ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Subset) ).
thf(506,plain,
! [A: message @ p @ v] :
( ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ ( suc @ index ) ) )
=> ( member @ ( message @ p @ v ) @ A @ ( firstOccSet @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(177,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_gr0I) ).
thf(897,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(225,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_diff__self__eq__0) ).
thf(1056,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(216,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_diff__commute) ).
thf(1033,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(161,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_bot__nat__0_Oextremum__uniqueI) ).
thf(828,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(192,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_gr__zeroI) ).
thf(955,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(7,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(283,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(138,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_length__0__conv) ).
thf(740,plain,
! [TA: $tType,A: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( zero_zero @ nat ) )
= ( A
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(202,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_zero__less__iff__neq__zero) ).
thf(987,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(215,axiom,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( zero_zero @ nat ) )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_NatPredicateTippingPoint) ).
thf(1019,plain,
! [A: nat,B: nat > $o] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( B @ ( zero_zero @ nat ) )
=> ( ~ ( B @ A )
=> ? [C: nat] :
( ( ord_less @ nat @ C @ A )
& ( B @ C )
& ~ ( B @ ( suc @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(132,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__diff__iff) ).
thf(723,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(200,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__induct) ).
thf(982,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat] : ( A @ D @ ( zero_zero @ nat ) )
=> ( ! [D: nat] : ( A @ ( zero_zero @ nat ) @ ( suc @ D ) )
=> ( ! [D: nat,E: nat] :
( ( A @ D @ E )
=> ( A @ ( suc @ D ) @ ( suc @ E ) ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_less__imp__diff__less) ).
thf(442,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(78,axiom,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_LastOfIndex) ).
thf(501,plain,
( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
= ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(38,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_diff__numeral__special_I9_J) ).
thf(369,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(103,axiom,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062) ).
thf(607,plain,
~ ? [A: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
& ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ A )
& ( msg
= ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(73,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_lift__Suc__antimono__le) ).
thf(486,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ! [D: nat] : ( ord_less_eq @ TA @ ( A @ ( suc @ D ) ) @ ( A @ D ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(67,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(469,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(32,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_3) ).
thf(354,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_diff__less) ).
thf(1009,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(119,axiom,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J) ).
thf(676,plain,
! [A: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,B: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,C: configuration_ext @ p @ v @ s @ product_unit,D: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),E: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),F: nat] :
( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( A @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( A @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( B @ G @ H @ I @ ( zero_zero @ nat ) )
=> ( ! [G: configuration_ext @ p @ v @ s @ product_unit,H: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),I: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),J: nat] :
( ( A @ G @ H @ I @ J )
=> ( ( B @ G @ H @ I @ J )
=> ( B @ G @ H @ I @ ( suc @ J ) ) ) )
=> ( A @ C @ D @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq @ nat @ A @ B ) )
= ( ord_less_eq @ nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_not__less__eq__eq) ).
thf(1204,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq @ nat @ A @ B ) )
= ( ord_less_eq @ nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(227,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_diff__strict__mono) ).
thf(1069,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_eq__diff__iff) ).
thf(972,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(16,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_2) ).
thf(309,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_less__antisym) ).
thf(659,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(1215,plain,
$false,
inference(e,[status(thm)],[645,1036,760,333,518,1083,666,1110,408,582,730,994,1073,449,614,597,1041,1173,440,511,1078,550,698,945,930,1164,797,1095,1127,417,885,301,1055,570,719,372,504,802,357,1059,587,838,638,969,770,289,475,789,321,1136,514,1151,480,766,687,280,866,411,1104,428,1201,292,942,1199,366,714,1047,910,894,746,952,349,820,275,788,847,852,1195,551,324,1012,329,1178,1159,461,1089,1143,1017,1111,1006,388,869,420,499,650,948,488,554,669,1075,1155,622,997,1099,738,1192,1050,721,1002,503,343,792,1086,360,805,508,311,541,1170,1071,1185,794,926,662,888,298,425,375,733,694,843,286,743,826,579,958,545,391,611,1107,540,445,936,466,1092,900,831,274,567,318,1175,979,604,377,990,1043,434,811,1080,816,483,848,912,1198,959,695,278,1015,1000,438,431,653,394,986,306,851,1102,490,1166,927,617,939,1145,355,1181,823,690,640,295,872,705,707,327,993,712,1003,414,971,1053,673,338,470,808,1130,907,1038,585,744,336,656,600,727,497,1140,386,465,450,363,891,1126,1189,976,688,903,813,517,304,351,418,478,763,383,346,536,1161,800,1116,1133,315,835,405,1148,273,735,341,506,897,1056,1033,828,955,283,740,987,1019,723,982,442,501,369,607,486,469,354,1009,676,1204,1069,972,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP054^2 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.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 14:33:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.13 % [INFO] Parsing done (268ms).
% 1.74/1.14 % [INFO] Running in sequential loop mode.
% 2.80/1.37 % [INFO] eprover registered as external prover.
% 2.80/1.38 % [INFO] cvc4 registered as external prover.
% 2.80/1.38 % [INFO] Scanning for conjecture ...
% 3.08/1.49 % [INFO] Found a conjecture and 270 axioms. Running axiom selection ...
% 3.39/1.58 % [INFO] Axiom selection finished. Selected 270 axioms (removed 0 axioms).
% 4.01/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 4.01/1.77 % [INFO] Type checking passed.
% 4.01/1.77 % [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 ...
% 46.99/16.46 % External prover 'e' found a proof!
% 46.99/16.46 % [INFO] Killing All external provers ...
% 46.99/16.46 % Time passed: 15930ms (effective reasoning time: 15316ms)
% 46.99/16.46 % 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)>
% 46.99/16.46 % Axioms used in derivation (270): fact_131_eq__imp__le, fact_197_diff__strict__left__mono, fact_48_measure__induct, fact_5_SameCfgOnLow, fact_42_lift__Suc__mono__less__iff, tcon_Product__Type_Ounit___Orderings_Owellorder_5, fact_51_infinite__descent, fact_129_nat__le__linear, fact_246_Suc__pred_H, fact_205_diff__le__mono2, fact_150_less__or__eq__imp__le, fact_19_lessI, fact_80_AssumptionCase1ImplThesis_H, fact_149_le__neq__implies__less, fact_239_length__tl, fact_241_one__reorient, fact_130_le__antisym, fact_189_diff__gt__0__iff__gt, fact_170_gr__implies__not__zero, fact_47_measure__induct__rule, fact_3_AssumptionFair_I2_J, fact_152_less__imp__le__nat, fact_118_bot__nat__0_Oextremum, fact_168_remdups__adj__length__ge1, fact_27_less__antisym, fact_62_length__greater__0__conv, tcon_Nat_Onat___Nat_Osize, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_125_zero__le, fact_237__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062, fact_52_nat__less__induct, fact_96_gr0I, fact_75_zero__less__Suc, fact_119_le0, fact_216_diff__less__mono2, fact_120_Suc__le__mono, fact_145_full__nat__induct, fact_44_Collect__mem__eq, fact_55_AssumptionFair_I3_J, fact_211_eq__diff__iff, fact_203_diff__eq__diff__less__eq, fact_15_old_Onat_Oinject, fact_242_One__nat__def, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_114__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, fact_135_bot__nat__0_Oextremum__unique, fact_77_length__0__conv, fact_196_diff__eq__diff__less, fact_227_MinPredicate, fact_111_Case2ImplThesis, fact_38_Nat_OlessE, fact_102_bot__nat__0_Oextremum__strict, fact_25_less__trans__Suc, fact_107_gr0__conv__Suc, fact_194_eq__iff__diff__eq__0, fact_117_le__zero__eq, fact_41_nth__equalityI, fact_248_last__conv__nth, fact_104_less__Suc__eq__0__disj, fact_14_nat_Oinject, fact_17_Suc__less__eq, fact_101_infinite__descent0, fact_69_less__nat__zero__code, fact_50_linorder__neqE__nat, fact_128_Nat_Oex__has__greatest__nat, fact_76_less__Suc0, fact_208_diff__le__mono, fact_191_diff__is__0__eq_H, fact_116_not__gr__zero, fact_53_Subset, fact_144_not__less__eq__eq, fact_113_NotConsumedIntermediate, fact_33_less__SucI, fact_94_old_Onat_Odistinct_I2_J, fact_195_diff__strict__mono, fact_57_AssumpGreaterOccurrence_I2_J, fact_142_le__Suc__eq, fact_207_diff__le__self, fact_123_last__remdups__adj, tcon_Nat_Onat___Groups_Oone, fact_43_mem__Collect__eq, fact_178_cancel__comm__monoid__add__class_Odiff__cancel, fact_90_diff__induct, fact_146_nat__induct__at__least, fact_158_inc__induct, fact_83_not0__implies__Suc, fact_126_lift__Suc__antimono__le, tcon_List_Olist___Nat_Osize_4, fact_82_list_Osel_I2_J, fact_231_PrefixListMonotonicity, fact_154_ex__least__nat__le, fact_31_less__Suc__eq, fact_204_diff__right__commute, fact_127_lift__Suc__mono__le, fact_224_less__diff__iff, fact_165_last__tl, fact_176_PrefixSameOnLow, fact_105_gr0__implies__Suc, fact_175__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_88_Suc__neq__Zero, fact_230_NatPredicateTippingPoint, fact_84_old_Onat_Oinducts, fact_134_bot__nat__0_Oextremum__uniqueI, fact_236_less__one, help_If_1_1_T, fact_160_le__less__Suc__eq, fact_85_old_Onat_Oexhaust, fact_97_not__gr0, fact_200_diff__mono, fact_73_list__ex__simps_I2_J, fact_72_remdups__adj__Nil__iff, fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062, fact_213_diffs0__imp__equal, fact_161_less__Suc__eq__le, fact_210_le__diff__iff, fact_93_old_Onat_Odistinct_I1_J, fact_112_MessageStaysOrConsumed, fact_215_less__imp__diff__less, fact_8_size__neq__size__imp__neq, fact_159_Suc__le__lessD, fact_143_Suc__n__not__le__n, fact_34_less__SucE, fact_163_le__imp__less__Suc, fact_66_ConsumedInSet, fact_59_LengthStep, tcon_Nat_Onat___Orderings_Owellorder, tcon_Nat_Onat___Groups_Ozero, fact_74_SmallIndex, fact_65_AssumpGreaterOccurrence_I3_J, fact_4_length__induct, fact_91_nat__induct, fact_190_zero__less__diff, fact_2_NotEmpty_I2_J, fact_11_less__not__refl2, fact_28_Suc__less__eq2, fact_21_n__not__Suc__n, fact_35_Suc__lessI, fact_54_IPrefixListEx, fact_225_diff__less__mono, fact_12_less__not__refl3, fact_153_nat__less__le, fact_185_Suc__diff__diff, fact_37_Suc__lessD, fact_87_Zero__neq__Suc, fact_222_Suc__diff__Suc, fact_243_MinPredicate2, fact_109_list_Osize_I3_J, fact_151_le__eq__less__or__eq, fact_173_LastOfIndex, fact_180_zero__diff, fact_206_le__diff__iff_H, fact_56_list__ex__length, fact_40_Skolem__list__nth, fact_247_Suc__diff__eq__diff__pred, tcon_AsynchronousSystem_Omessage___Nat_Osize_7, fact_221_diff__less__Suc, fact_13_less__irrefl__nat, fact_240_Suc__diff__1, fact_214_zero__induct__lemma, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_23_strict__inc__induct, fact_188_diff__ge__0__iff__ge, fact_132_le__trans, help_If_3_1_T, fact_232_EnabledOrConsumed, help_If_2_1_T, fact_100_gr__implies__not0, fact_223_Suc__diff__le, fact_39_list__eq__iff__nth__eq, fact_7_neq__if__length__neq, fact_98_not__less0, fact_244_diff__Suc__eq__diff__pred, fact_148_less__mono__imp__le__mono, fact_217_diff__commute, fact_199_diff__eq__diff__eq, fact_250_enabled__def, fact_10_less__not__refl, fact_229_KeepProperty, fact_220_diff__less, fact_147_transitive__stepwise__le, fact_219_less__iff__diff__less__0, fact_18_Suc__mono, fact_9_nat__neq__iff, fact_20_Suc__inject, fact_49_infinite__descent__measure, fact_245_nat__induct__non__zero, fact_212_minus__nat_Odiff__0, fact_183_diff__0__eq__0, fact_86_Zero__not__Suc, tcon_HOL_Obool___Orderings_Oorder_3, fact_155_Suc__leI, fact_89_zero__induct, fact_238_diff__Suc__1, fact_218_le__iff__diff__le__0, fact_115_Nitpick_Osize__list__simp_I2_J, fact_6_Ex__list__of__length, fact_198_diff__strict__right__mono, fact_67_SameMsgOnLow, fact_139_le__SucE, fact_182_diff__self, tcon_Set_Oset___Orderings_Oorder_2, fact_156_Suc__le__eq, fact_124_EnabledOrConsumedAtLast, fact_186_diff__Suc__Suc, fact_61_nth__tl, fact_108_Ex__less__Suc2, fact_60_remdups__adj__adjacent, fact_228_PrefixListTransitive, fact_95_nat_Odistinct_I1_J, fact_99_less__zeroE, fact_162_less__eq__Suc__le, fact_16_NotEmpty_I1_J, fact_110_MinImplFirstOcc, fact_192_diff__is__0__eq, fact_167_zero__reorient, fact_133_le__refl, fact_45_Collect__cong, fact_234_EnabledIntermediate, fact_36_Suc__lessE, fact_106_All__less__Suc2, fact_184_diff__self__eq__0, fact_138_Suc__leD, fact_79_AssumptionFirstOccSetDecrOrConsumed_I1_J, fact_0_AssumpGreaterOccurrence_I1_J, fact_174__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, fact_46_lift__Suc__mono__less, tcon_fun___Orderings_Oorder, fact_30_not__less__eq, fact_32_Ex__less__Suc, fact_201_diff__left__mono, fact_166_ex__least__nat__less, tcon_Nat_Onat___Orderings_Oorder_1, fact_181_diff__0__right, fact_187_diff__diff__cancel, fact_63_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, fact_136_le__0__eq, fact_157_dec__induct, fact_169_zero__less__iff__neq__zero, fact_209_Nat_Odiff__diff__eq, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_64_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, fact_171_not__less__zero, fact_22_not__less__less__Suc__eq, tcon_Product__Type_Ounit___Orderings_Oorder_6, fact_233__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, fact_137_less__eq__nat_Osimps_I1_J, fact_29_All__less__Suc, fact_164_remdups__adj__length, fact_141_Suc__le__D, fact_140_le__SucI, fact_249_diff__numeral__special_I9_J, fact_193_Suc__pred, fact_177_IPrefixList, fact_58_list__ex1__simps_I1_J, fact_24_less__Suc__induct, fact_70_bot__nat__0_Onot__eq__extremum, fact_226_diff__Suc__less, fact_68_neq0__conv, fact_179_diff__zero, fact_103_infinite__descent0__measure, fact_122_MinImplAllBigger, fact_235__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062, fact_26_Suc__less__SucD, fact_71_ConsumedMsg_I1_J, fact_92_nat_OdiscI, fact_121_EnabledInSuc, fact_81_remdups__adj_Osimps_I1_J, fact_172_gr__zeroI, fact_202_diff__right__mono, fact_78_AssumptionFairContr
% 46.99/16.46 % No. of inferences in proof: 544
% 46.99/16.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15930 ms resp. 15316 ms w/o parsing
% 47.63/16.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 47.63/16.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------