%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP055^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Wed Feb 25 08:55:11 AM UTC 2026
% Result : Theorem 2.98s 1.68s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 82 ( 10 ~; 3 |; 0 &; 66 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 209 ( 206 usr; 16 con; 0-4 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
p: $tType ).
thf(type_def_6,type,
s: $tType ).
thf(type_def_7,type,
messageValue_v: $tType ).
thf(type_def_9,type,
message_p_v: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(type_def_11,type,
config256849571t_unit: $tType ).
thf(type_def_12,type,
list_c1059388851t_unit: $tType ).
thf(type_def_13,type,
list_message_p_v: $tType ).
thf(type_def_14,type,
int: $tType ).
thf(type_def_15,type,
list_l611321411t_unit: $tType ).
thf(type_def_16,type,
list_l1619404459ge_p_v: $tType ).
thf(type_def_17,type,
list_l1584713811t_unit: $tType ).
thf(type_def_18,type,
list_l1341496881ge_p_v: $tType ).
thf(type_def_19,type,
set_nat: $tType ).
thf(func_def_0,type,
list_l1584713811t_unit: $tType ).
thf(func_def_1,type,
list_l611321411t_unit: $tType ).
thf(func_def_2,type,
list_c1059388851t_unit: $tType ).
thf(func_def_3,type,
config256849571t_unit: $tType ).
thf(func_def_4,type,
list_l1341496881ge_p_v: $tType ).
thf(func_def_5,type,
list_l1619404459ge_p_v: $tType ).
thf(func_def_6,type,
list_message_p_v: $tType ).
thf(func_def_7,type,
message_p_v: $tType ).
thf(func_def_8,type,
messageValue_v: $tType ).
thf(func_def_9,type,
set_nat: $tType ).
thf(func_def_10,type,
nat: $tType ).
thf(func_def_11,type,
int: $tType ).
thf(func_def_12,type,
s: $tType ).
thf(func_def_13,type,
p: $tType ).
thf(func_def_14,type,
fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
thf(func_def_15,type,
fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
thf(func_def_16,type,
fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
thf(func_def_17,type,
one_one_int: int ).
thf(func_def_18,type,
one_one_nat: nat ).
thf(func_def_19,type,
uminus_uminus_int: int > int ).
thf(func_def_20,type,
zero_zero_int: int ).
thf(func_def_21,type,
zero_zero_nat: nat ).
thf(func_def_22,type,
nat2: int > nat ).
thf(func_def_23,type,
ring_1_of_int_int: int > int ).
thf(func_def_24,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_25,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_26,type,
prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).
thf(func_def_27,type,
prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).
thf(func_def_28,type,
gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
thf(func_def_29,type,
gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
thf(func_def_30,type,
insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_31,type,
insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_32,type,
cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_33,type,
cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_34,type,
cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
thf(func_def_35,type,
cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(func_def_36,type,
cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).
thf(func_def_37,type,
cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).
thf(func_def_38,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_39,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_40,type,
nil_li307996205t_unit: list_l611321411t_unit ).
thf(func_def_41,type,
nil_list_message_p_v: list_l1619404459ge_p_v ).
thf(func_def_42,type,
nil_li2108369341t_unit: list_l1584713811t_unit ).
thf(func_def_43,type,
nil_li835338673ge_p_v: list_l1341496881ge_p_v ).
thf(func_def_44,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(func_def_45,type,
list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(func_def_46,type,
n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
thf(func_def_47,type,
n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
thf(func_def_48,type,
nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
thf(func_def_49,type,
nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
thf(func_def_50,type,
produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
thf(func_def_51,type,
produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(func_def_52,type,
subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
thf(func_def_53,type,
subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
thf(func_def_54,type,
suc: nat > nat ).
thf(func_def_55,type,
semiri2019852685at_int: nat > int ).
thf(func_def_56,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_57,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_58,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_59,type,
size_s503142615t_unit: list_l611321411t_unit > nat ).
thf(func_def_60,type,
size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).
thf(func_def_61,type,
ord_less_int: int > int > $o ).
thf(func_def_62,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_63,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_64,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_65,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_66,type,
member_nat: nat > set_nat > $o ).
thf(func_def_67,type,
cfg: config256849571t_unit ).
thf(func_def_68,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_69,type,
m: nat ).
thf(func_def_70,type,
n: nat ).
thf(func_def_71,type,
na: nat ).
thf(func_def_85,type,
sP0: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_86,type,
sP1: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_87,type,
sK2: ( nat > $o ) > nat > nat ).
thf(func_def_88,type,
sK3: ( nat > $o ) > nat > nat ).
thf(func_def_89,type,
sK4: nat > nat > nat ).
thf(func_def_90,type,
sK5: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_91,type,
sK6: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_92,type,
sK7: nat > nat ).
thf(func_def_93,type,
sK8: ( nat > $o ) > nat ).
thf(func_def_94,type,
sK9: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_95,type,
sK10: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_96,type,
sK11: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_97,type,
sK12: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_98,type,
sK13: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_99,type,
sK14: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_100,type,
sK15: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_101,type,
sK16: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_102,type,
sK17: ( nat > $o ) > nat > nat ).
thf(func_def_103,type,
sK18: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_104,type,
sK19: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_105,type,
sK20: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_106,type,
sK21: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_107,type,
sK22: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_108,type,
sK23: ( nat > nat > $o ) > nat ).
thf(func_def_109,type,
sK24: ( nat > nat > $o ) > nat ).
thf(func_def_110,type,
sK25: ( nat > nat > $o ) > nat ).
thf(func_def_111,type,
sK26: ( nat > nat > $o ) > nat ).
thf(func_def_112,type,
sK27: ( nat > $o ) > nat > nat ).
thf(func_def_113,type,
sK28: ( nat > $o ) > nat > nat ).
thf(func_def_114,type,
sK29: ( nat > $o ) > nat ).
thf(func_def_115,type,
sK30: ( nat > $o ) > nat ).
thf(func_def_116,type,
sK31: ( nat > nat > $o ) > nat ).
thf(func_def_117,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_118,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_119,type,
sK34: ( nat > nat > $o ) > nat ).
thf(func_def_120,type,
sK35: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_121,type,
sK36: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_122,type,
sK37: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_123,type,
sK38: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_124,type,
sK39: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_125,type,
sK40: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_126,type,
sK41: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_127,type,
sK42: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_128,type,
sK43: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_129,type,
sK44: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_130,type,
sK45: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_131,type,
sK46: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_132,type,
sK47: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_133,type,
sK48: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_134,type,
sK49: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_135,type,
sK50: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_136,type,
sK51: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_137,type,
sK52: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_138,type,
sK53: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_139,type,
sK54: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_140,type,
sK55: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_141,type,
sK56: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_142,type,
sK57: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_143,type,
sK58: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_144,type,
sK59: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_145,type,
sK60: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_146,type,
sK61: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_147,type,
sK62: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_148,type,
sK63: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_149,type,
sK64: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_150,type,
sK65: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_151,type,
sK66: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_152,type,
sK67: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_153,type,
sK68: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_154,type,
sK69: ( list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_155,type,
sK70: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_156,type,
sK71: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_157,type,
sK72: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit ).
thf(func_def_158,type,
sK73: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_159,type,
sK74: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_160,type,
sK75: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit ).
thf(func_def_161,type,
sK76: nat > ( nat > $o ) > nat ).
thf(func_def_162,type,
sK77: nat > ( nat > $o ) > nat ).
thf(func_def_163,type,
sK78: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_164,type,
sK79: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_165,type,
sK80: list_c1059388851t_unit > list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_166,type,
sK81: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_167,type,
sK82: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_168,type,
sK83: nat > nat > nat ).
thf(func_def_169,type,
sK84: nat > nat > nat ).
thf(func_def_170,type,
sK85: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_171,type,
sK86: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_172,type,
sK87: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_173,type,
sK88: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_174,type,
sK89: ( nat > $o ) > nat > nat ).
thf(func_def_175,type,
sK90: ( nat > $o ) > nat > nat ).
thf(func_def_176,type,
sK91: ( nat > $o ) > nat ).
thf(func_def_177,type,
sK92: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_178,type,
sK93: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_179,type,
sK94: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_180,type,
sK95: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_181,type,
sK96: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_182,type,
sK97: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_183,type,
sK98: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_184,type,
sK99: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_185,type,
sK100: list_c1059388851t_unit > nat > list_c1059388851t_unit ).
thf(func_def_186,type,
sK101: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_187,type,
sK102: nat > nat ).
thf(func_def_188,type,
sK103: ( nat > nat ) > nat ).
thf(func_def_189,type,
sK104: ( nat > $o ) > nat ).
thf(func_def_190,type,
sK105: ( nat > nat ) > nat ).
thf(func_def_191,type,
sK106: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_192,type,
sK107: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_193,type,
sK108: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_194,type,
sK109: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_195,type,
sK110: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_196,type,
sK111: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_197,type,
sK112: nat > ( nat > $o ) > nat ).
thf(func_def_198,type,
sK113: nat > ( nat > $o ) > nat ).
thf(func_def_199,type,
sK114: nat > list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_200,type,
sK115: nat > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_201,type,
sK116: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_202,type,
sK117: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_203,type,
sK118: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_204,type,
sK119: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_205,type,
sK120: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_206,type,
sK121: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_207,type,
sK122: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_208,type,
sK123: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_209,type,
sK124: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_210,type,
sK125: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_211,type,
sK126: nat > nat > nat ).
thf(func_def_212,type,
sK127: nat > list_c1059388851t_unit ).
thf(func_def_213,type,
sK128: nat > nat ).
thf(func_def_214,type,
sK129: nat > nat ).
thf(func_def_215,type,
sK130: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_216,type,
sK131: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_217,type,
sK132: ( nat > $o ) > nat ).
thf(func_def_218,type,
sK133: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_219,type,
sK134: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_220,type,
sK135: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_221,type,
sK136: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_222,type,
sK137: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_223,type,
sK138: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_224,type,
sK139: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_225,type,
sK140: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_226,type,
sK141: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_227,type,
sK142: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_228,type,
sK143: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_229,type,
sK144: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_230,type,
sK145: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_231,type,
sK146: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_233,type,
ph148:
!>[X0: $tType] : X0 ).
thf(f1472,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1471,f1347]) ).
thf(f1347,plain,
( ( ord_less_nat @ m @ na )
= $true ),
inference(cnf_transformation,[status(thm)],[f618]) ).
thf(f618,plain,
( ( ord_less_nat @ m @ na )
= $true ),
inference(fool_elimination,[status(thm)],[f617]) ).
thf(f617,plain,
ord_less_nat @ m @ na,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_less_nat @ m @ na,
file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',fact_0__092_060open_062m_A_060_An_092_060close_062) ).
thf(f1471,plain,
( ( ord_less_nat @ m @ na )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1468]) ).
thf(f1468,plain,
( ( ( ord_less_nat @ m @ na )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1175,f1351]) ).
thf(f1351,plain,
( ( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
= $true )
| ( ( ord_less_nat @ m @ na )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f869]) ).
thf(f869,plain,
( ( ( ord_less_nat @ m @ na )
!= $true )
| ( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f550]) ).
thf(f550,plain,
( ( ( ord_less_nat @ m @ na )
= $true )
=> ( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f549]) ).
thf(f549,plain,
( ( ord_less_nat @ m @ na )
=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ord_less_nat @ m @ na )
=> ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',fact_2_IA_I1_J) ).
thf(f1175,plain,
( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f819]) ).
thf(f819,plain,
( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
!= $true ),
inference(flattening,[status(thm)],[f364]) ).
thf(f364,plain,
( ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f363]) ).
thf(f363,plain,
~ ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ),
inference(rectify,[status(thm)],[f343]) ).
thf(f343,negated_conjecture,
~ ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ),
inference(negated_conjecture,[status(cth)],[f342]) ).
thf(f342,conjecture,
prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ),
file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP055^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n011.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:32 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : ITP055^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.46 % Domain : Interactive Theorem Proving
% 0.27/0.46 % Problem : Sledgehammer FLPTheorem problem prob_1231__3305662_1
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Des21]
% 0.27/0.46 % Names : FLPTheorem/prob_1231__3305662_1 [Des21]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.27/0.46 % Syntax : Number of formulae : 414 ( 186 unt; 72 typ; 0 def)
% 0.27/0.46 % Number of atoms : 741 ( 451 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.27/0.46 % Number of connectives : 3000 ( 179 ~; 10 |; 38 &;2297 @)
% 0.27/0.46 % ( 0 <=>; 476 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 23 ( 7 avg)
% 0.27/0.46 % Number of types : 15 ( 14 usr)
% 0.27/0.46 % Number of type conns : 520 ( 520 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 59 ( 58 usr; 14 con; 0-4 aty)
% 0.27/0.46 % Number of variables : 1101 ( 11 ^;1046 !; 44 ?;1101 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:18.186
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % Could-be-implicit typings (14)
% 0.27/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J_J,type,
% 0.27/0.46 list_l1584713811t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.27/0.46 list_l611321411t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.27/0.46 list_c1059388851t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 config256849571t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J_J,type,
% 0.27/0.46 list_l1341496881ge_p_v: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.27/0.46 list_l1619404459ge_p_v: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.27/0.46 list_message_p_v: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 message_p_v: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 0.27/0.46 messageValue_v: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.27/0.46 set_nat: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.27/0.46 nat: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Int__Oint,type,
% 0.27/0.46 int: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_tf__s,type,
% 0.27/0.46 s: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_tf__p,type,
% 0.27/0.46 p: $tType ).
% 0.27/0.46
% 0.27/0.46 % Explicit typings (58)
% 0.27/0.46 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 0.27/0.46 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 0.27/0.46 fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 0.27/0.46 fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.27/0.46 one_one_int: int ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.27/0.46 one_one_nat: nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 0.27/0.46 uminus_uminus_int: int > int ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.27/0.46 zero_zero_int: int ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.27/0.46 zero_zero_nat: nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Int_Onat,type,
% 0.27/0.46 nat2: int > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 0.27/0.46 ring_1_of_int_int: int > int ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.27/0.46 prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.27/0.46 prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.27/0.46 cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.27/0.46 cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.27/0.46 cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.27/0.46 cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 nil_message_p_v: list_message_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.27/0.46 nil_li307996205t_unit: list_l611321411t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.27/0.46 nil_list_message_p_v: list_l1619404459ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.27/0.46 nil_li2108369341t_unit: list_l1584713811t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.27/0.46 nil_li835338673ge_p_v: list_l1341496881ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.27/0.46 subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_OSuc,type,
% 0.27/0.46 suc: nat > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.27/0.46 semiri2019852685at_int: nat > int ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.27/0.46 semiri1382578993at_nat: nat > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.27/0.46 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.27/0.46 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.27/0.46 size_s503142615t_unit: list_l611321411t_unit > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.27/0.46 size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.27/0.46 ord_less_int: int > int > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.27/0.46 ord_less_nat: nat > nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.27/0.46 ord_less_eq_int: int > int > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.27/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.27/0.46 collect_nat: ( nat > $o ) > set_nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_member_001t__Nat__Onat,type,
% 0.27/0.46 member_nat: nat > set_nat > $o ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_cfg____,type,
% 0.27/0.46 cfg: config256849571t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_fe____,type,
% 0.27/0.46 fe: nat > list_c1059388851t_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_m____,type,
% 0.27/0.46 m: nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_n____,type,
% 0.27/0.46 n: nat ).
% 0.27/0.46
% 0.27/0.46 thf(sy_v_na____,type,
% 0.27/0.46 na: nat ).
% 0.27/0.46
% 0.27/0.46 % Relevant facts (341)
% 0.27/0.46 thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
% 0.27/0.46 ord_less_nat @ m @ na ).
% 0.27/0.46
% 0.27/0.46 % \<open>m < n\<close>
% 0.27/0.46 thf(fact_1_MLessN,axiom,
% 0.27/0.46 ord_less_nat @ m @ n ).
% 0.27/0.46
% 0.27/0.46 % MLessN
% 0.27/0.46 thf(fact_2_IA_I1_J,axiom,
% 0.27/0.46 ( ( ord_less_nat @ m @ na )
% 0.27/0.46 => ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % IA(1)
% 0.27/0.46 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
% 0.27/0.46 ( ( m = na )
% 0.27/0.46 | ( ord_less_nat @ m @ na ) ) ).
% 0.27/0.46
% 0.27/0.46 % \<open>m = n \<or> m < n\<close>
% 0.27/0.46 thf(fact_4_IA_I2_J,axiom,
% 0.27/0.46 ord_less_nat @ m @ ( suc @ na ) ).
% 0.27/0.46
% 0.27/0.46 % IA(2)
% 0.27/0.46 thf(fact_5_PrefixListTransitive,axiom,
% 0.27/0.46 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.27/0.46 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.27/0.46 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.27/0.46 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % PrefixListTransitive
% 0.27/0.46 thf(fact_6_PrefixListTransitive,axiom,
% 0.27/0.46 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.27/0.46 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.27/0.46 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.27/0.46 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % PrefixListTransitive
% 0.27/0.46 thf(fact_7_FE_I1_J,axiom,
% 0.27/0.46 ( ( fe @ zero_zero_nat )
% 0.27/0.46 = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% 0.27/0.46
% 0.27/0.46 % FE(1)
% 0.27/0.46 thf(fact_8_prefixList_Ointros_I2_J,axiom,
% 0.27/0.46 ! [Xa: list_l611321411t_unit,Xb: list_l611321411t_unit,X: list_c1059388851t_unit] :
% 0.27/0.46 ( ( prefix747844452t_unit @ Xa @ Xb )
% 0.27/0.46 => ( prefix747844452t_unit @ ( cons_l1083444861t_unit @ X @ Xa ) @ ( cons_l1083444861t_unit @ X @ Xb ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(2)
% 0.27/0.46 thf(fact_9_prefixList_Ointros_I2_J,axiom,
% 0.27/0.46 ! [Xa: list_l1619404459ge_p_v,Xb: list_l1619404459ge_p_v,X: list_message_p_v] :
% 0.27/0.46 ( ( prefix1465223476ge_p_v @ Xa @ Xb )
% 0.27/0.46 => ( prefix1465223476ge_p_v @ ( cons_l233104475ge_p_v @ X @ Xa ) @ ( cons_l233104475ge_p_v @ X @ Xb ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(2)
% 0.27/0.46 thf(fact_10_prefixList_Ointros_I2_J,axiom,
% 0.27/0.46 ! [Xa: list_message_p_v,Xb: list_message_p_v,X: message_p_v] :
% 0.27/0.46 ( ( prefix47729710ge_p_v @ Xa @ Xb )
% 0.27/0.46 => ( prefix47729710ge_p_v @ ( cons_message_p_v @ X @ Xa ) @ ( cons_message_p_v @ X @ Xb ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(2)
% 0.27/0.46 thf(fact_11_prefixList_Ointros_I2_J,axiom,
% 0.27/0.46 ! [Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,X: config256849571t_unit] :
% 0.27/0.46 ( ( prefix1615116500t_unit @ Xa @ Xb )
% 0.27/0.46 => ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ X @ Xa ) @ ( cons_c1162654829t_unit @ X @ Xb ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(2)
% 0.27/0.46 thf(fact_12_PrefixListMonotonicity,axiom,
% 0.27/0.46 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.27/0.46 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.27/0.46 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % PrefixListMonotonicity
% 0.27/0.46 thf(fact_13_PrefixListMonotonicity,axiom,
% 0.27/0.46 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.27/0.46 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.27/0.46 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % PrefixListMonotonicity
% 0.27/0.46 thf(fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.27/0.46 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
% 0.27/0.46 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.27/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.27/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.27/0.46 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.27/0.46 thf(fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.27/0.46 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 0.27/0.46 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.27/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.27/0.46 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.27/0.46 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.27/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.27/0.46 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.27/0.46 thf(fact_16_prefixList_Ointros_I1_J,axiom,
% 0.27/0.46 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] : ( prefix747844452t_unit @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X @ Xs ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(1)
% 0.27/0.46 thf(fact_17_prefixList_Ointros_I1_J,axiom,
% 0.27/0.46 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] : ( prefix1465223476ge_p_v @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X @ Xs ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(1)
% 0.27/0.46 thf(fact_18_prefixList_Ointros_I1_J,axiom,
% 0.27/0.46 ! [X: message_p_v,Xs: list_message_p_v] : ( prefix47729710ge_p_v @ nil_message_p_v @ ( cons_message_p_v @ X @ Xs ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(1)
% 0.27/0.46 thf(fact_19_prefixList_Ointros_I1_J,axiom,
% 0.27/0.46 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) ) ).
% 0.27/0.46
% 0.27/0.46 % prefixList.intros(1)
% 0.27/0.46 thf(fact_20_prefixList_Ocases,axiom,
% 0.27/0.46 ! [A1: list_l611321411t_unit,A2: list_l611321411t_unit] :
% 0.27/0.46 ( ( prefix747844452t_unit @ A1 @ A2 )
% 0.27/0.46 => ( ( ( A1 = nil_li307996205t_unit )
% 0.27/0.47 => ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.27/0.47 ( A2
% 0.27/0.47 != ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ~ ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( A1
% 0.27/0.47 = ( cons_l1083444861t_unit @ X2 @ Xa2 ) )
% 0.27/0.47 => ( ( A2
% 0.27/0.47 = ( cons_l1083444861t_unit @ X2 @ Xb2 ) )
% 0.27/0.47 => ~ ( prefix747844452t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.cases
% 0.27/0.47 thf(fact_21_prefixList_Ocases,axiom,
% 0.27/0.47 ! [A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( prefix1465223476ge_p_v @ A1 @ A2 )
% 0.27/0.47 => ( ( ( A1 = nil_list_message_p_v )
% 0.27/0.47 => ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( A2
% 0.27/0.47 != ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ~ ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 0.27/0.47 ( ( A1
% 0.27/0.47 = ( cons_l233104475ge_p_v @ X2 @ Xa2 ) )
% 0.27/0.47 => ( ( A2
% 0.27/0.47 = ( cons_l233104475ge_p_v @ X2 @ Xb2 ) )
% 0.27/0.47 => ~ ( prefix1465223476ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.cases
% 0.27/0.47 thf(fact_22_prefixList_Ocases,axiom,
% 0.27/0.47 ! [A1: list_message_p_v,A2: list_message_p_v] :
% 0.27/0.47 ( ( prefix47729710ge_p_v @ A1 @ A2 )
% 0.27/0.47 => ( ( ( A1 = nil_message_p_v )
% 0.27/0.47 => ! [X2: message_p_v,Xs2: list_message_p_v] :
% 0.27/0.47 ( A2
% 0.27/0.47 != ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ~ ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 0.27/0.47 ( ( A1
% 0.27/0.47 = ( cons_message_p_v @ X2 @ Xa2 ) )
% 0.27/0.47 => ( ( A2
% 0.27/0.47 = ( cons_message_p_v @ X2 @ Xb2 ) )
% 0.27/0.47 => ~ ( prefix47729710ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.cases
% 0.27/0.47 thf(fact_23_prefixList_Ocases,axiom,
% 0.27/0.47 ! [A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( prefix1615116500t_unit @ A1 @ A2 )
% 0.27/0.47 => ( ( ( A1 = nil_co1338500125t_unit )
% 0.27/0.47 => ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( A2
% 0.27/0.47 != ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ~ ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 0.27/0.47 ( ( A1
% 0.27/0.47 = ( cons_c1162654829t_unit @ X2 @ Xa2 ) )
% 0.27/0.47 => ( ( A2
% 0.27/0.47 = ( cons_c1162654829t_unit @ X2 @ Xb2 ) )
% 0.27/0.47 => ~ ( prefix1615116500t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.cases
% 0.27/0.47 thf(fact_24_prefixList_Osimps,axiom,
% 0.27/0.47 ( prefix747844452t_unit
% 0.27/0.47 = ( ^ [A12: list_l611321411t_unit,A22: list_l611321411t_unit] :
% 0.27/0.47 ( ? [X3: list_c1059388851t_unit,Xs3: list_l611321411t_unit] :
% 0.27/0.47 ( ( A12 = nil_li307996205t_unit )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_l1083444861t_unit @ X3 @ Xs3 ) ) )
% 0.27/0.47 | ? [Xa3: list_l611321411t_unit,Xb3: list_l611321411t_unit,X3: list_c1059388851t_unit] :
% 0.27/0.47 ( ( A12
% 0.27/0.47 = ( cons_l1083444861t_unit @ X3 @ Xa3 ) )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_l1083444861t_unit @ X3 @ Xb3 ) )
% 0.27/0.47 & ( prefix747844452t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.simps
% 0.27/0.47 thf(fact_25_prefixList_Osimps,axiom,
% 0.27/0.47 ( prefix1465223476ge_p_v
% 0.27/0.47 = ( ^ [A12: list_l1619404459ge_p_v,A22: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ? [X3: list_message_p_v,Xs3: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( A12 = nil_list_message_p_v )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_l233104475ge_p_v @ X3 @ Xs3 ) ) )
% 0.27/0.47 | ? [Xa3: list_l1619404459ge_p_v,Xb3: list_l1619404459ge_p_v,X3: list_message_p_v] :
% 0.27/0.47 ( ( A12
% 0.27/0.47 = ( cons_l233104475ge_p_v @ X3 @ Xa3 ) )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_l233104475ge_p_v @ X3 @ Xb3 ) )
% 0.27/0.47 & ( prefix1465223476ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.simps
% 0.27/0.47 thf(fact_26_prefixList_Osimps,axiom,
% 0.27/0.47 ( prefix47729710ge_p_v
% 0.27/0.47 = ( ^ [A12: list_message_p_v,A22: list_message_p_v] :
% 0.27/0.47 ( ? [X3: message_p_v,Xs3: list_message_p_v] :
% 0.27/0.47 ( ( A12 = nil_message_p_v )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_message_p_v @ X3 @ Xs3 ) ) )
% 0.27/0.47 | ? [Xa3: list_message_p_v,Xb3: list_message_p_v,X3: message_p_v] :
% 0.27/0.47 ( ( A12
% 0.27/0.47 = ( cons_message_p_v @ X3 @ Xa3 ) )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_message_p_v @ X3 @ Xb3 ) )
% 0.27/0.47 & ( prefix47729710ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.simps
% 0.27/0.47 thf(fact_27_prefixList_Osimps,axiom,
% 0.27/0.47 ( prefix1615116500t_unit
% 0.27/0.47 = ( ^ [A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 0.27/0.47 ( ? [X3: config256849571t_unit,Xs3: list_c1059388851t_unit] :
% 0.27/0.47 ( ( A12 = nil_co1338500125t_unit )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_c1162654829t_unit @ X3 @ Xs3 ) ) )
% 0.27/0.47 | ? [Xa3: list_c1059388851t_unit,Xb3: list_c1059388851t_unit,X3: config256849571t_unit] :
% 0.27/0.47 ( ( A12
% 0.27/0.47 = ( cons_c1162654829t_unit @ X3 @ Xa3 ) )
% 0.27/0.47 & ( A22
% 0.27/0.47 = ( cons_c1162654829t_unit @ X3 @ Xb3 ) )
% 0.27/0.47 & ( prefix1615116500t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.simps
% 0.27/0.47 thf(fact_28_prefixList_Oinducts,axiom,
% 0.27/0.47 ! [X1: list_l611321411t_unit,X22: list_l611321411t_unit,P: list_l611321411t_unit > list_l611321411t_unit > $o] :
% 0.27/0.47 ( ( prefix747844452t_unit @ X1 @ X22 )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) )
% 0.27/0.47 => ( ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( prefix747844452t_unit @ Xa2 @ Xb2 )
% 0.27/0.47 => ( ( P @ Xa2 @ Xb2 )
% 0.27/0.47 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xa2 ) @ ( cons_l1083444861t_unit @ X2 @ Xb2 ) ) ) )
% 0.27/0.47 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.inducts
% 0.27/0.47 thf(fact_29_prefixList_Oinducts,axiom,
% 0.27/0.47 ! [X1: list_l1619404459ge_p_v,X22: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o] :
% 0.27/0.47 ( ( prefix1465223476ge_p_v @ X1 @ X22 )
% 0.27/0.47 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) )
% 0.27/0.47 => ( ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 0.27/0.47 ( ( prefix1465223476ge_p_v @ Xa2 @ Xb2 )
% 0.27/0.47 => ( ( P @ Xa2 @ Xb2 )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xa2 ) @ ( cons_l233104475ge_p_v @ X2 @ Xb2 ) ) ) )
% 0.27/0.47 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.inducts
% 0.27/0.47 thf(fact_30_prefixList_Oinducts,axiom,
% 0.27/0.47 ! [X1: list_message_p_v,X22: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.27/0.47 ( ( prefix47729710ge_p_v @ X1 @ X22 )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) )
% 0.27/0.47 => ( ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 0.27/0.47 ( ( prefix47729710ge_p_v @ Xa2 @ Xb2 )
% 0.27/0.47 => ( ( P @ Xa2 @ Xb2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xa2 ) @ ( cons_message_p_v @ X2 @ Xb2 ) ) ) )
% 0.27/0.47 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.inducts
% 0.27/0.47 thf(fact_31_prefixList_Oinducts,axiom,
% 0.27/0.47 ! [X1: list_c1059388851t_unit,X22: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( prefix1615116500t_unit @ X1 @ X22 )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) )
% 0.27/0.47 => ( ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 0.27/0.47 ( ( prefix1615116500t_unit @ Xa2 @ Xb2 )
% 0.27/0.47 => ( ( P @ Xa2 @ Xb2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xa2 ) @ ( cons_c1162654829t_unit @ X2 @ Xb2 ) ) ) )
% 0.27/0.47 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % prefixList.inducts
% 0.27/0.47 thf(fact_32_NatPredicateTippingPoint,axiom,
% 0.27/0.47 ! [N2: nat,Pr: nat > $o] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.27/0.47 => ( ( Pr @ zero_zero_nat )
% 0.27/0.47 => ( ~ ( Pr @ N2 )
% 0.27/0.47 => ? [N: nat] :
% 0.27/0.47 ( ( ord_less_nat @ N @ N2 )
% 0.27/0.47 & ( Pr @ N )
% 0.27/0.47 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % NatPredicateTippingPoint
% 0.27/0.47 thf(fact_33_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.27/0.47 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.27/0.47 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionCfg.simps(1)
% 0.27/0.47 thf(fact_34_length__greater__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_l611321411t_unit] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ Xs ) )
% 0.27/0.47 = ( Xs != nil_li307996205t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_greater_0_conv
% 0.27/0.47 thf(fact_35_length__greater__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ Xs ) )
% 0.27/0.47 = ( Xs != nil_list_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_greater_0_conv
% 0.27/0.47 thf(fact_36_length__greater__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.27/0.47 = ( Xs != nil_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_greater_0_conv
% 0.27/0.47 thf(fact_37_length__greater__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.27/0.47 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_greater_0_conv
% 0.27/0.47 thf(fact_38_length__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_l611321411t_unit] :
% 0.27/0.47 ( ( ( size_s503142615t_unit @ Xs )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( Xs = nil_li307996205t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_0_conv
% 0.27/0.47 thf(fact_39_length__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( ( size_s1809856791ge_p_v @ Xs )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( Xs = nil_list_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_0_conv
% 0.27/0.47 thf(fact_40_length__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( Xs = nil_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_0_conv
% 0.27/0.47 thf(fact_41_length__0__conv,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_0_conv
% 0.27/0.47 thf(fact_42_less__Suc0,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 0.27/0.47 = ( N3 = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_Suc0
% 0.27/0.47 thf(fact_43_zero__less__Suc,axiom,
% 0.27/0.47 ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_less_Suc
% 0.27/0.47 thf(fact_44_lessI,axiom,
% 0.27/0.47 ! [N3: nat] : ( ord_less_nat @ N3 @ ( suc @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % lessI
% 0.27/0.47 thf(fact_45_Suc__mono,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_mono
% 0.27/0.47 thf(fact_46_Suc__less__eq,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_less_eq
% 0.27/0.47 thf(fact_47_neq0__conv,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( N3 != zero_zero_nat )
% 0.27/0.47 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq0_conv
% 0.27/0.47 thf(fact_48_less__nat__zero__code,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % less_nat_zero_code
% 0.27/0.47 thf(fact_49_bot__nat__0_Onot__eq__extremum,axiom,
% 0.27/0.47 ! [A: nat] :
% 0.27/0.47 ( ( A != zero_zero_nat )
% 0.27/0.47 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % bot_nat_0.not_eq_extremum
% 0.27/0.47 thf(fact_50_list_Oinject,axiom,
% 0.27/0.47 ! [X21: message_p_v,X222: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
% 0.27/0.47 ( ( ( cons_message_p_v @ X21 @ X222 )
% 0.27/0.47 = ( cons_message_p_v @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inject
% 0.27/0.47 thf(fact_51_list_Oinject,axiom,
% 0.27/0.47 ! [X21: list_c1059388851t_unit,X222: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
% 0.27/0.47 ( ( ( cons_l1083444861t_unit @ X21 @ X222 )
% 0.27/0.47 = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inject
% 0.27/0.47 thf(fact_52_list_Oinject,axiom,
% 0.27/0.47 ! [X21: list_message_p_v,X222: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( ( cons_l233104475ge_p_v @ X21 @ X222 )
% 0.27/0.47 = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inject
% 0.27/0.47 thf(fact_53_list_Oinject,axiom,
% 0.27/0.47 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( cons_c1162654829t_unit @ X21 @ X222 )
% 0.27/0.47 = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inject
% 0.27/0.47 thf(fact_54_old_Onat_Oinject,axiom,
% 0.27/0.47 ! [Nat: nat,Nat2: nat] :
% 0.27/0.47 ( ( ( suc @ Nat )
% 0.27/0.47 = ( suc @ Nat2 ) )
% 0.27/0.47 = ( Nat = Nat2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.nat.inject
% 0.27/0.47 thf(fact_55_nat_Oinject,axiom,
% 0.27/0.47 ! [X22: nat,Y2: nat] :
% 0.27/0.47 ( ( ( suc @ X22 )
% 0.27/0.47 = ( suc @ Y2 ) )
% 0.27/0.47 = ( X22 = Y2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat.inject
% 0.27/0.47 thf(fact_56_not__Cons__self2,axiom,
% 0.27/0.47 ! [X: message_p_v,Xs: list_message_p_v] :
% 0.27/0.47 ( ( cons_message_p_v @ X @ Xs )
% 0.27/0.47 != Xs ) ).
% 0.27/0.47
% 0.27/0.47 % not_Cons_self2
% 0.27/0.47 thf(fact_57_not__Cons__self2,axiom,
% 0.27/0.47 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
% 0.27/0.47 ( ( cons_l1083444861t_unit @ X @ Xs )
% 0.27/0.47 != Xs ) ).
% 0.27/0.47
% 0.27/0.47 % not_Cons_self2
% 0.27/0.47 thf(fact_58_not__Cons__self2,axiom,
% 0.27/0.47 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( cons_l233104475ge_p_v @ X @ Xs )
% 0.27/0.47 != Xs ) ).
% 0.27/0.47
% 0.27/0.47 % not_Cons_self2
% 0.27/0.47 thf(fact_59_not__Cons__self2,axiom,
% 0.27/0.47 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( cons_c1162654829t_unit @ X @ Xs )
% 0.27/0.47 != Xs ) ).
% 0.27/0.47
% 0.27/0.47 % not_Cons_self2
% 0.27/0.47 thf(fact_60_n__not__Suc__n,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( N3
% 0.27/0.47 != ( suc @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % n_not_Suc_n
% 0.27/0.47 thf(fact_61_Suc__inject,axiom,
% 0.27/0.47 ! [X: nat,Y: nat] :
% 0.27/0.47 ( ( ( suc @ X )
% 0.27/0.47 = ( suc @ Y ) )
% 0.27/0.47 => ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_inject
% 0.27/0.47 thf(fact_62_linorder__neqE__nat,axiom,
% 0.27/0.47 ! [X: nat,Y: nat] :
% 0.27/0.47 ( ( X != Y )
% 0.27/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.27/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % linorder_neqE_nat
% 0.27/0.47 thf(fact_63_infinite__descent,axiom,
% 0.27/0.47 ! [P: nat > $o,N3: nat] :
% 0.27/0.47 ( ! [N: nat] :
% 0.27/0.47 ( ~ ( P @ N )
% 0.27/0.47 => ? [M2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.27/0.47 & ~ ( P @ M2 ) ) )
% 0.27/0.47 => ( P @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % infinite_descent
% 0.27/0.47 thf(fact_64_nat__less__induct,axiom,
% 0.27/0.47 ! [P: nat > $o,N3: nat] :
% 0.27/0.47 ( ! [N: nat] :
% 0.27/0.47 ( ! [M2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.27/0.47 => ( P @ M2 ) )
% 0.27/0.47 => ( P @ N ) )
% 0.27/0.47 => ( P @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_less_induct
% 0.27/0.47 thf(fact_65_less__irrefl__nat,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 0.27/0.47
% 0.27/0.47 % less_irrefl_nat
% 0.27/0.47 thf(fact_66_less__not__refl3,axiom,
% 0.27/0.47 ! [S: nat,T: nat] :
% 0.27/0.47 ( ( ord_less_nat @ S @ T )
% 0.27/0.47 => ( S != T ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_refl3
% 0.27/0.47 thf(fact_67_less__not__refl2,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] :
% 0.27/0.47 ( ( ord_less_nat @ N3 @ M )
% 0.27/0.47 => ( M != N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_refl2
% 0.27/0.47 thf(fact_68_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A: nat,P: nat > $o] :
% 0.27/0.47 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.27/0.47 = ( P @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_69_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A8: set_nat] :
% 0.27/0.47 ( ( collect_nat
% 0.27/0.47 @ ^ [X3: nat] : ( member_nat @ X3 @ A8 ) )
% 0.27/0.47 = A8 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_70_less__not__refl,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 0.27/0.47
% 0.27/0.47 % less_not_refl
% 0.27/0.47 thf(fact_71_nat__neq__iff,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( M != N3 )
% 0.27/0.47 = ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 | ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_neq_iff
% 0.27/0.47 thf(fact_72_size__neq__size__imp__neq,axiom,
% 0.27/0.47 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ X )
% 0.27/0.47 != ( size_s1168481041ge_p_v @ Y ) )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % size_neq_size_imp_neq
% 0.27/0.47 thf(fact_73_size__neq__size__imp__neq,axiom,
% 0.27/0.47 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ X )
% 0.27/0.47 != ( size_s1406904903t_unit @ Y ) )
% 0.27/0.47 => ( X != Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % size_neq_size_imp_neq
% 0.27/0.47 thf(fact_74_neq__if__length__neq,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( Xs != Ys ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq_if_length_neq
% 0.27/0.47 thf(fact_75_neq__if__length__neq,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 != ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( Xs != Ys ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq_if_length_neq
% 0.27/0.47 thf(fact_76_Ex__list__of__length,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ? [Xs2: list_message_p_v] :
% 0.27/0.47 ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = N3 ) ).
% 0.27/0.47
% 0.27/0.47 % Ex_list_of_length
% 0.27/0.47 thf(fact_77_Ex__list__of__length,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ? [Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = N3 ) ).
% 0.27/0.47
% 0.27/0.47 % Ex_list_of_length
% 0.27/0.47 thf(fact_78_not0__implies__Suc,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( N3 != zero_zero_nat )
% 0.27/0.47 => ? [M3: nat] :
% 0.27/0.47 ( N3
% 0.27/0.47 = ( suc @ M3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not0_implies_Suc
% 0.27/0.47 thf(fact_79_old_Onat_Oinducts,axiom,
% 0.27/0.47 ! [P: nat > $o,Nat: nat] :
% 0.27/0.47 ( ( P @ zero_zero_nat )
% 0.27/0.47 => ( ! [Nat3: nat] :
% 0.27/0.47 ( ( P @ Nat3 )
% 0.27/0.47 => ( P @ ( suc @ Nat3 ) ) )
% 0.27/0.47 => ( P @ Nat ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.nat.inducts
% 0.27/0.47 thf(fact_80_old_Onat_Oexhaust,axiom,
% 0.27/0.47 ! [Y: nat] :
% 0.27/0.47 ( ( Y != zero_zero_nat )
% 0.27/0.47 => ~ ! [Nat3: nat] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( suc @ Nat3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.nat.exhaust
% 0.27/0.47 thf(fact_81_Zero__not__Suc,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( zero_zero_nat
% 0.27/0.47 != ( suc @ M ) ) ).
% 0.27/0.47
% 0.27/0.47 % Zero_not_Suc
% 0.27/0.47 thf(fact_82_Zero__neq__Suc,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( zero_zero_nat
% 0.27/0.47 != ( suc @ M ) ) ).
% 0.27/0.47
% 0.27/0.47 % Zero_neq_Suc
% 0.27/0.47 thf(fact_83_Suc__neq__Zero,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( ( suc @ M )
% 0.27/0.47 != zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_neq_Zero
% 0.27/0.47 thf(fact_84_zero__induct,axiom,
% 0.27/0.47 ! [P: nat > $o,K: nat] :
% 0.27/0.47 ( ( P @ K )
% 0.27/0.47 => ( ! [N: nat] :
% 0.27/0.47 ( ( P @ ( suc @ N ) )
% 0.27/0.47 => ( P @ N ) )
% 0.27/0.47 => ( P @ zero_zero_nat ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_induct
% 0.27/0.47 thf(fact_85_diff__induct,axiom,
% 0.27/0.47 ! [P: nat > nat > $o,M: nat,N3: nat] :
% 0.27/0.47 ( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
% 0.27/0.47 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.27/0.47 => ( ! [X2: nat,Y3: nat] :
% 0.27/0.47 ( ( P @ X2 @ Y3 )
% 0.27/0.47 => ( P @ ( suc @ X2 ) @ ( suc @ Y3 ) ) )
% 0.27/0.47 => ( P @ M @ N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % diff_induct
% 0.27/0.47 thf(fact_86_nat__induct,axiom,
% 0.27/0.47 ! [P: nat > $o,N3: nat] :
% 0.27/0.47 ( ( P @ zero_zero_nat )
% 0.27/0.47 => ( ! [N: nat] :
% 0.27/0.47 ( ( P @ N )
% 0.27/0.47 => ( P @ ( suc @ N ) ) )
% 0.27/0.47 => ( P @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_induct
% 0.27/0.47 thf(fact_87_nat_OdiscI,axiom,
% 0.27/0.47 ! [Nat: nat,X22: nat] :
% 0.27/0.47 ( ( Nat
% 0.27/0.47 = ( suc @ X22 ) )
% 0.27/0.47 => ( Nat != zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat.discI
% 0.27/0.47 thf(fact_88_old_Onat_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Nat2: nat] :
% 0.27/0.47 ( zero_zero_nat
% 0.27/0.47 != ( suc @ Nat2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.nat.distinct(1)
% 0.27/0.47 thf(fact_89_old_Onat_Odistinct_I2_J,axiom,
% 0.27/0.47 ! [Nat2: nat] :
% 0.27/0.47 ( ( suc @ Nat2 )
% 0.27/0.47 != zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % old.nat.distinct(2)
% 0.27/0.47 thf(fact_90_nat_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X22: nat] :
% 0.27/0.47 ( zero_zero_nat
% 0.27/0.47 != ( suc @ X22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat.distinct(1)
% 0.27/0.47 thf(fact_91_bot__nat__0_Oextremum__strict,axiom,
% 0.27/0.47 ! [A: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % bot_nat_0.extremum_strict
% 0.27/0.47 thf(fact_92_infinite__descent0,axiom,
% 0.27/0.47 ! [P: nat > $o,N3: nat] :
% 0.27/0.47 ( ( P @ zero_zero_nat )
% 0.27/0.47 => ( ! [N: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.27/0.47 => ( ~ ( P @ N )
% 0.27/0.47 => ? [M2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M2 @ N )
% 0.27/0.47 & ~ ( P @ M2 ) ) ) )
% 0.27/0.47 => ( P @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % infinite_descent0
% 0.27/0.47 thf(fact_93_gr__implies__not0,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( N3 != zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr_implies_not0
% 0.27/0.47 thf(fact_94_less__zeroE,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % less_zeroE
% 0.27/0.47 thf(fact_95_not__less0,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % not_less0
% 0.27/0.47 thf(fact_96_not__gr0,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.27/0.47 = ( N3 = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_gr0
% 0.27/0.47 thf(fact_97_gr0I,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( N3 != zero_zero_nat )
% 0.27/0.47 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr0I
% 0.27/0.47 thf(fact_98_not__less__less__Suc__eq,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] :
% 0.27/0.47 ( ~ ( ord_less_nat @ N3 @ M )
% 0.27/0.47 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 0.27/0.47 = ( N3 = M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_less_less_Suc_eq
% 0.27/0.47 thf(fact_99_strict__inc__induct,axiom,
% 0.27/0.47 ! [I: nat,J: nat,P: nat > $o] :
% 0.27/0.47 ( ( ord_less_nat @ I @ J )
% 0.27/0.47 => ( ! [I2: nat] :
% 0.27/0.47 ( ( J
% 0.27/0.47 = ( suc @ I2 ) )
% 0.27/0.47 => ( P @ I2 ) )
% 0.27/0.47 => ( ! [I2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.27/0.47 => ( ( P @ ( suc @ I2 ) )
% 0.27/0.47 => ( P @ I2 ) ) )
% 0.27/0.47 => ( P @ I ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % strict_inc_induct
% 0.27/0.47 thf(fact_100_less__Suc__induct,axiom,
% 0.27/0.47 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.27/0.47 ( ( ord_less_nat @ I @ J )
% 0.27/0.47 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.27/0.47 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I2 @ J2 )
% 0.27/0.47 => ( ( ord_less_nat @ J2 @ K2 )
% 0.27/0.47 => ( ( P @ I2 @ J2 )
% 0.27/0.47 => ( ( P @ J2 @ K2 )
% 0.27/0.47 => ( P @ I2 @ K2 ) ) ) ) )
% 0.27/0.47 => ( P @ I @ J ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_Suc_induct
% 0.27/0.47 thf(fact_101_less__trans__Suc,axiom,
% 0.27/0.47 ! [I: nat,J: nat,K: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I @ J )
% 0.27/0.47 => ( ( ord_less_nat @ J @ K )
% 0.27/0.47 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_trans_Suc
% 0.27/0.47 thf(fact_102_Suc__less__SucD,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.27/0.47 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_less_SucD
% 0.27/0.47 thf(fact_103_less__antisym,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] :
% 0.27/0.47 ( ~ ( ord_less_nat @ N3 @ M )
% 0.27/0.47 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 0.27/0.47 => ( M = N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_antisym
% 0.27/0.47 thf(fact_104_Suc__less__eq2,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ N3 ) @ M )
% 0.27/0.47 = ( ? [M4: nat] :
% 0.27/0.47 ( ( M
% 0.27/0.47 = ( suc @ M4 ) )
% 0.27/0.47 & ( ord_less_nat @ N3 @ M4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_less_eq2
% 0.27/0.47 thf(fact_105_All__less__Suc,axiom,
% 0.27/0.47 ! [N3: nat,P: nat > $o] :
% 0.27/0.47 ( ( ! [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.27/0.47 => ( P @ I3 ) ) )
% 0.27/0.47 = ( ( P @ N3 )
% 0.27/0.47 & ! [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ N3 )
% 0.27/0.47 => ( P @ I3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % All_less_Suc
% 0.27/0.47 thf(fact_106_not__less__eq,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ~ ( ord_less_nat @ M @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ N3 @ ( suc @ M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_less_eq
% 0.27/0.47 thf(fact_107_less__Suc__eq,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.27/0.47 = ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 | ( M = N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_Suc_eq
% 0.27/0.47 thf(fact_108_Ex__less__Suc,axiom,
% 0.27/0.47 ! [N3: nat,P: nat > $o] :
% 0.27/0.47 ( ( ? [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.27/0.47 & ( P @ I3 ) ) )
% 0.27/0.47 = ( ( P @ N3 )
% 0.27/0.47 | ? [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ N3 )
% 0.27/0.47 & ( P @ I3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Ex_less_Suc
% 0.27/0.47 thf(fact_109_less__SucI,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( ord_less_nat @ M @ ( suc @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_SucI
% 0.27/0.47 thf(fact_110_less__SucE,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.27/0.47 => ( ~ ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( M = N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_SucE
% 0.27/0.47 thf(fact_111_Suc__lessI,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( ( ( suc @ M )
% 0.27/0.47 != N3 )
% 0.27/0.47 => ( ord_less_nat @ ( suc @ M ) @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_lessI
% 0.27/0.47 thf(fact_112_Suc__lessE,axiom,
% 0.27/0.47 ! [I: nat,K: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.27/0.47 => ~ ! [J2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.27/0.47 => ( K
% 0.27/0.47 != ( suc @ J2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_lessE
% 0.27/0.47 thf(fact_113_Suc__lessD,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ M ) @ N3 )
% 0.27/0.47 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_lessD
% 0.27/0.47 thf(fact_114_Nat_OlessE,axiom,
% 0.27/0.47 ! [I: nat,K: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I @ K )
% 0.27/0.47 => ( ( K
% 0.27/0.47 != ( suc @ I ) )
% 0.27/0.47 => ~ ! [J2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.27/0.47 => ( K
% 0.27/0.47 != ( suc @ J2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Nat.lessE
% 0.27/0.47 thf(fact_115_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,A0: message_p_v > config256849571t_unit,A1: list_message_p_v,A2: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: message_p_v > config256849571t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_116_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.27/0.47 => ( ! [F: config256849571t_unit > config256849571t_unit,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_117_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,A0: message_p_v > message_p_v,A1: list_message_p_v,A2: list_message_p_v] :
% 0.27/0.47 ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: message_p_v > message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_118_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_message_p_v > message_p_v ) > list_l1619404459ge_p_v > list_message_p_v > $o,A0: list_message_p_v > message_p_v,A1: list_l1619404459ge_p_v,A2: list_message_p_v] :
% 0.27/0.47 ( ! [F: list_message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: list_message_p_v > message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_message_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_119_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > list_message_p_v ) > list_message_p_v > list_l1619404459ge_p_v > $o,A0: message_p_v > list_message_p_v,A1: list_message_p_v,A2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ! [F: message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: message_p_v > list_message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_120_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,A0: config256849571t_unit > message_p_v,A1: list_c1059388851t_unit,A2: list_message_p_v] :
% 0.27/0.47 ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.27/0.47 => ( ! [F: config256849571t_unit > message_p_v,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_121_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_message_p_v > list_message_p_v ) > list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v,A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ! [F: list_message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: list_message_p_v > list_message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_122_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_message_p_v > config256849571t_unit ) > list_l1619404459ge_p_v > list_c1059388851t_unit > $o,A0: list_message_p_v > config256849571t_unit,A1: list_l1619404459ge_p_v,A2: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [F: list_message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: list_message_p_v > config256849571t_unit,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_123_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_c1059388851t_unit > message_p_v ) > list_l611321411t_unit > list_message_p_v > $o,A0: list_c1059388851t_unit > message_p_v,A1: list_l611321411t_unit,A2: list_message_p_v] :
% 0.27/0.47 ( ! [F: list_c1059388851t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_li307996205t_unit @ X_1 )
% 0.27/0.47 => ( ! [F: list_c1059388851t_unit > message_p_v,A9: list_c1059388851t_unit,As: list_l611321411t_unit,Bs: list_message_p_v] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_l1083444861t_unit @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_124_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > list_c1059388851t_unit ) > list_message_p_v > list_l611321411t_unit > $o,A0: message_p_v > list_c1059388851t_unit,A1: list_message_p_v,A2: list_l611321411t_unit] :
% 0.27/0.47 ( ! [F: message_p_v > list_c1059388851t_unit,X_1: list_l611321411t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [F: message_p_v > list_c1059388851t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_l611321411t_unit] :
% 0.27/0.47 ( ( P @ F @ As @ ( cons_l1083444861t_unit @ ( F @ A9 ) @ Bs ) )
% 0.27/0.47 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.27/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % map_tailrec_rev.induct
% 0.27/0.47 thf(fact_125_list__nonempty__induct,axiom,
% 0.27/0.47 ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
% 0.27/0.47 ( ( Xs != nil_li307996205t_unit )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.27/0.47 ( ( Xs2 != nil_li307996205t_unit )
% 0.27/0.47 => ( ( P @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_nonempty_induct
% 0.27/0.47 thf(fact_126_list__nonempty__induct,axiom,
% 0.27/0.47 ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
% 0.27/0.47 ( ( Xs != nil_list_message_p_v )
% 0.27/0.47 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.27/0.47 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( Xs2 != nil_list_message_p_v )
% 0.27/0.47 => ( ( P @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_nonempty_induct
% 0.27/0.47 thf(fact_127_list__nonempty__induct,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
% 0.27/0.47 ( ( Xs != nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v] :
% 0.27/0.47 ( ( Xs2 != nil_message_p_v )
% 0.27/0.47 => ( ( P @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_nonempty_induct
% 0.27/0.47 thf(fact_128_list__nonempty__induct,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( Xs != nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( Xs2 != nil_co1338500125t_unit )
% 0.27/0.47 => ( ( P @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_nonempty_induct
% 0.27/0.47 thf(fact_129_successively_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.27/0.47 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.27/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.27/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.27/0.47 ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
% 0.27/0.47 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % successively.induct
% 0.27/0.47 thf(fact_130_successively_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.27/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.27/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
% 0.27/0.47 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % successively.induct
% 0.27/0.47 thf(fact_131_successively_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 0.27/0.47 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.27/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.27/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.27/0.47 ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
% 0.27/0.47 => ( P @ P2 @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % successively.induct
% 0.27/0.47 thf(fact_132_successively_Oinduct,axiom,
% 0.27/0.47 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.27/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
% 0.27/0.47 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % successively.induct
% 0.27/0.47 thf(fact_133_remdups__adj_Oinduct,axiom,
% 0.27/0.47 ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
% 0.27/0.47 ( ( P @ nil_li307996205t_unit )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.27/0.47 ( ( ( X2 = Y3 )
% 0.27/0.47 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ( ( ( X2 != Y3 )
% 0.27/0.47 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
% 0.27/0.47 => ( P @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.27/0.47 => ( P @ A0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.induct
% 0.27/0.47 thf(fact_134_remdups__adj_Oinduct,axiom,
% 0.27/0.47 ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ nil_list_message_p_v )
% 0.27/0.47 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.27/0.47 => ( ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( ( X2 = Y3 )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ( ( ( X2 != Y3 )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.27/0.47 => ( P @ A0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.induct
% 0.27/0.47 thf(fact_135_remdups__adj_Oinduct,axiom,
% 0.27/0.47 ! [P: list_message_p_v > $o,A0: list_message_p_v] :
% 0.27/0.47 ( ( P @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.27/0.47 => ( ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.27/0.47 ( ( ( X2 = Y3 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ( ( ( X2 != Y3 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.27/0.47 => ( P @ A0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.induct
% 0.27/0.47 thf(fact_136_remdups__adj_Oinduct,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( X2 = Y3 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 0.27/0.47 => ( ( ( X2 != Y3 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.27/0.47 => ( P @ A0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.induct
% 0.27/0.47 thf(fact_137_sorted__wrt_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.27/0.47 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.27/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Ys2: list_l611321411t_unit] :
% 0.27/0.47 ( ( P @ P2 @ Ys2 )
% 0.27/0.47 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_wrt.induct
% 0.27/0.47 thf(fact_138_sorted__wrt_Oinduct,axiom,
% 0.27/0.47 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.27/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ P2 @ Ys2 )
% 0.27/0.47 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_wrt.induct
% 0.27/0.47 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 0.27/0.47 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 0.27/0.47 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.27/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( P @ P2 @ Ys2 )
% 0.27/0.47 => ( P @ P2 @ ( cons_message_p_v @ X2 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_wrt.induct
% 0.27/0.47 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 0.27/0.47 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ P2 @ Ys2 )
% 0.27/0.47 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % sorted_wrt.induct
% 0.27/0.47 thf(fact_141_remdups__adj_Ocases,axiom,
% 0.27/0.47 ! [X: list_l611321411t_unit] :
% 0.27/0.47 ( ( X != nil_li307996205t_unit )
% 0.27/0.47 => ( ! [X2: list_c1059388851t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.27/0.47 => ~ ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.cases
% 0.27/0.47 thf(fact_142_remdups__adj_Ocases,axiom,
% 0.27/0.47 ! [X: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( X != nil_list_message_p_v )
% 0.27/0.47 => ( ! [X2: list_message_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.27/0.47 => ~ ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.cases
% 0.27/0.47 thf(fact_143_remdups__adj_Ocases,axiom,
% 0.27/0.47 ! [X: list_message_p_v] :
% 0.27/0.47 ( ( X != nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.27/0.47 => ~ ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.cases
% 0.27/0.47 thf(fact_144_remdups__adj_Ocases,axiom,
% 0.27/0.47 ! [X: list_c1059388851t_unit] :
% 0.27/0.47 ( ( X != nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.27/0.47 => ~ ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % remdups_adj.cases
% 0.27/0.47 thf(fact_145_transpose_Ocases,axiom,
% 0.27/0.47 ! [X: list_l1584713811t_unit] :
% 0.27/0.47 ( ( X != nil_li2108369341t_unit )
% 0.27/0.47 => ( ! [Xss: list_l1584713811t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1777019405t_unit @ nil_li307996205t_unit @ Xss ) )
% 0.27/0.47 => ~ ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Xss: list_l1584713811t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1777019405t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transpose.cases
% 0.27/0.47 thf(fact_146_transpose_Ocases,axiom,
% 0.27/0.47 ! [X: list_l1341496881ge_p_v] :
% 0.27/0.47 ( ( X != nil_li835338673ge_p_v )
% 0.27/0.47 => ( ! [Xss: list_l1341496881ge_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1383421281ge_p_v @ nil_list_message_p_v @ Xss ) )
% 0.27/0.47 => ~ ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Xss: list_l1341496881ge_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1383421281ge_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transpose.cases
% 0.27/0.47 thf(fact_147_transpose_Ocases,axiom,
% 0.27/0.47 ! [X: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( X != nil_list_message_p_v )
% 0.27/0.47 => ( ! [Xss: list_l1619404459ge_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
% 0.27/0.47 => ~ ! [X2: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transpose.cases
% 0.27/0.47 thf(fact_148_transpose_Ocases,axiom,
% 0.27/0.47 ! [X: list_l611321411t_unit] :
% 0.27/0.47 ( ( X != nil_li307996205t_unit )
% 0.27/0.47 => ( ! [Xss: list_l611321411t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
% 0.27/0.47 => ~ ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
% 0.27/0.47 ( X
% 0.27/0.47 != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transpose.cases
% 0.27/0.47 thf(fact_149_shuffles_Oinduct,axiom,
% 0.27/0.47 ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [Xs2: list_l1619404459ge_p_v] : ( P @ Xs2 @ nil_list_message_p_v )
% 0.27/0.47 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 0.27/0.47 ( ( P @ Xs2 @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % shuffles.induct
% 0.27/0.47 thf(fact_150_shuffles_Oinduct,axiom,
% 0.27/0.47 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.27/0.47 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % shuffles.induct
% 0.27/0.47 thf(fact_151_shuffles_Oinduct,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.27/0.47 => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % shuffles.induct
% 0.27/0.47 thf(fact_152_induct__list012,axiom,
% 0.27/0.47 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.27/0.47 ( ( P @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.27/0.47 => ( ! [X2: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
% 0.27/0.47 ( ( P @ Zs )
% 0.27/0.47 => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % induct_list012
% 0.27/0.47 thf(fact_153_induct__list012,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ Zs )
% 0.27/0.47 => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % induct_list012
% 0.27/0.47 thf(fact_154_splice_Oinduct,axiom,
% 0.27/0.47 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.27/0.47 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( P @ Ys2 @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % splice.induct
% 0.27/0.47 thf(fact_155_splice_Oinduct,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ Ys2 @ Xs2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 ) )
% 0.27/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % splice.induct
% 0.27/0.47 thf(fact_156_list__induct2_H,axiom,
% 0.27/0.47 ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.27/0.47 ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_message_p_v )
% 0.27/0.47 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2'
% 0.27/0.47 thf(fact_157_list__induct2_H,axiom,
% 0.27/0.47 ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2'
% 0.27/0.47 thf(fact_158_list__induct2_H,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys: list_message_p_v] :
% 0.27/0.47 ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_message_p_v )
% 0.27/0.47 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2'
% 0.27/0.47 thf(fact_159_list__induct2_H,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2'
% 0.27/0.47 thf(fact_160_neq__Nil__conv,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v] :
% 0.27/0.47 ( ( Xs != nil_message_p_v )
% 0.27/0.47 = ( ? [Y4: message_p_v,Ys3: list_message_p_v] :
% 0.27/0.47 ( Xs
% 0.27/0.47 = ( cons_message_p_v @ Y4 @ Ys3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq_Nil_conv
% 0.27/0.47 thf(fact_161_neq__Nil__conv,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( Xs != nil_co1338500125t_unit )
% 0.27/0.47 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.27/0.47 ( Xs
% 0.27/0.47 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % neq_Nil_conv
% 0.27/0.47 thf(fact_162_list_Oinducts,axiom,
% 0.27/0.47 ! [P: list_message_p_v > $o,List: list_message_p_v] :
% 0.27/0.47 ( ( P @ nil_message_p_v )
% 0.27/0.47 => ( ! [X12: message_p_v,X23: list_message_p_v] :
% 0.27/0.47 ( ( P @ X23 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X12 @ X23 ) ) )
% 0.27/0.47 => ( P @ List ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inducts
% 0.27/0.47 thf(fact_163_list_Oinducts,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X12: config256849571t_unit,X23: list_c1059388851t_unit] :
% 0.27/0.47 ( ( P @ X23 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X12 @ X23 ) ) )
% 0.27/0.47 => ( P @ List ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inducts
% 0.27/0.47 thf(fact_164_list_Oexhaust,axiom,
% 0.27/0.47 ! [Y: list_message_p_v] :
% 0.27/0.47 ( ( Y != nil_message_p_v )
% 0.27/0.47 => ~ ! [X212: message_p_v,X223: list_message_p_v] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( cons_message_p_v @ X212 @ X223 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.exhaust
% 0.27/0.47 thf(fact_165_list_Oexhaust,axiom,
% 0.27/0.47 ! [Y: list_c1059388851t_unit] :
% 0.27/0.47 ( ( Y != nil_co1338500125t_unit )
% 0.27/0.47 => ~ ! [X212: config256849571t_unit,X223: list_c1059388851t_unit] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( cons_c1162654829t_unit @ X212 @ X223 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.exhaust
% 0.27/0.47 thf(fact_166_list_OdiscI,axiom,
% 0.27/0.47 ! [List: list_message_p_v,X21: message_p_v,X222: list_message_p_v] :
% 0.27/0.47 ( ( List
% 0.27/0.47 = ( cons_message_p_v @ X21 @ X222 ) )
% 0.27/0.47 => ( List != nil_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.discI
% 0.27/0.47 thf(fact_167_list_OdiscI,axiom,
% 0.27/0.47 ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 0.27/0.47 ( ( List
% 0.27/0.47 = ( cons_c1162654829t_unit @ X21 @ X222 ) )
% 0.27/0.47 => ( List != nil_co1338500125t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.discI
% 0.27/0.47 thf(fact_168_list_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X21: message_p_v,X222: list_message_p_v] :
% 0.27/0.47 ( nil_message_p_v
% 0.27/0.47 != ( cons_message_p_v @ X21 @ X222 ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.distinct(1)
% 0.27/0.47 thf(fact_169_list_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 0.27/0.47 ( nil_co1338500125t_unit
% 0.27/0.47 != ( cons_c1162654829t_unit @ X21 @ X222 ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.distinct(1)
% 0.27/0.47 thf(fact_170_length__induct,axiom,
% 0.27/0.47 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [Xs2: list_c1059388851t_unit] :
% 0.27/0.47 ( ! [Ys4: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys4 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.27/0.47 => ( P @ Ys4 ) )
% 0.27/0.47 => ( P @ Xs2 ) )
% 0.27/0.47 => ( P @ Xs ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_induct
% 0.27/0.47 thf(fact_171_lift__Suc__mono__less__iff,axiom,
% 0.27/0.47 ! [F2: nat > nat,N3: nat,M: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.27/0.47 => ( ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 0.27/0.47 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_mono_less_iff
% 0.27/0.47 thf(fact_172_lift__Suc__mono__less__iff,axiom,
% 0.27/0.47 ! [F2: nat > int,N3: nat,M: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.27/0.47 => ( ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 0.27/0.47 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_mono_less_iff
% 0.27/0.47 thf(fact_173_lift__Suc__mono__less,axiom,
% 0.27/0.47 ! [F2: nat > nat,N3: nat,N4: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.27/0.47 => ( ( ord_less_nat @ N3 @ N4 )
% 0.27/0.47 => ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_mono_less
% 0.27/0.47 thf(fact_174_lift__Suc__mono__less,axiom,
% 0.27/0.47 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.27/0.47 => ( ( ord_less_nat @ N3 @ N4 )
% 0.27/0.47 => ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_mono_less
% 0.27/0.47 thf(fact_175_less__Suc__eq__0__disj,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.27/0.47 = ( ( M = zero_zero_nat )
% 0.27/0.47 | ? [J3: nat] :
% 0.27/0.47 ( ( M
% 0.27/0.47 = ( suc @ J3 ) )
% 0.27/0.47 & ( ord_less_nat @ J3 @ N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_Suc_eq_0_disj
% 0.27/0.47 thf(fact_176_gr0__implies__Suc,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.27/0.47 => ? [M3: nat] :
% 0.27/0.47 ( N3
% 0.27/0.47 = ( suc @ M3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr0_implies_Suc
% 0.27/0.47 thf(fact_177_All__less__Suc2,axiom,
% 0.27/0.47 ! [N3: nat,P: nat > $o] :
% 0.27/0.47 ( ( ! [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.27/0.47 => ( P @ I3 ) ) )
% 0.27/0.47 = ( ( P @ zero_zero_nat )
% 0.27/0.47 & ! [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ N3 )
% 0.27/0.47 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % All_less_Suc2
% 0.27/0.47 thf(fact_178_gr0__conv__Suc,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.27/0.47 = ( ? [M5: nat] :
% 0.27/0.47 ( N3
% 0.27/0.47 = ( suc @ M5 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr0_conv_Suc
% 0.27/0.47 thf(fact_179_Ex__less__Suc2,axiom,
% 0.27/0.47 ! [N3: nat,P: nat > $o] :
% 0.27/0.47 ( ( ? [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.27/0.47 & ( P @ I3 ) ) )
% 0.27/0.47 = ( ( P @ zero_zero_nat )
% 0.27/0.47 | ? [I3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I3 @ N3 )
% 0.27/0.47 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Ex_less_Suc2
% 0.27/0.47 thf(fact_180_length__Suc__conv,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,N3: nat] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( suc @ N3 ) )
% 0.27/0.47 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.27/0.47 ( ( Xs
% 0.27/0.47 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 0.27/0.47 & ( ( size_s1406904903t_unit @ Ys3 )
% 0.27/0.47 = N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_Suc_conv
% 0.27/0.47 thf(fact_181_Suc__length__conv,axiom,
% 0.27/0.47 ! [N3: nat,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( suc @ N3 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Xs ) )
% 0.27/0.47 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.27/0.47 ( ( Xs
% 0.27/0.47 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 0.27/0.47 & ( ( size_s1406904903t_unit @ Ys3 )
% 0.27/0.47 = N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Suc_length_conv
% 0.27/0.47 thf(fact_182_list_Osize_I3_J,axiom,
% 0.27/0.47 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.27/0.47 = zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % list.size(3)
% 0.27/0.47 thf(fact_183_list_Osize_I3_J,axiom,
% 0.27/0.47 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 = zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % list.size(3)
% 0.27/0.47 thf(fact_184_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_185_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_186_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_187_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_188_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_189_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_190_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_191_list__induct3,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Zs ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct3
% 0.27/0.47 thf(fact_192_list__induct2,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2
% 0.27/0.47 thf(fact_193_list__induct2,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2
% 0.27/0.47 thf(fact_194_list__induct2,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2
% 0.27/0.47 thf(fact_195_list__induct2,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys ) )
% 0.27/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.27/0.47 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.27/0.47 => ( ( P @ Xs2 @ Ys2 )
% 0.27/0.47 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.27/0.47 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list_induct2
% 0.27/0.47 thf(fact_196_infiniteExecutionCfg_Oelims,axiom,
% 0.27/0.47 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 0.27/0.47 ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.27/0.47 = Y )
% 0.27/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( Xc
% 0.27/0.47 = ( suc @ N ) )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionCfg.elims
% 0.27/0.47 thf(fact_197_infiniteExecutionMsg_Oelims,axiom,
% 0.27/0.47 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 0.27/0.47 ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.27/0.47 = Y )
% 0.27/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.27/0.47 => ( Y != nil_message_p_v ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( Xc
% 0.27/0.47 = ( suc @ N ) )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionMsg.elims
% 0.27/0.47 thf(fact_198_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.27/0.47 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.27/0.47 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.27/0.47 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionMsg.simps(2)
% 0.27/0.47 thf(fact_199_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.27/0.47 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.27/0.47 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.27/0.47 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionCfg.simps(2)
% 0.27/0.47 thf(fact_200_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.27/0.47 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.27/0.47 = nil_message_p_v ) ).
% 0.27/0.47
% 0.27/0.47 % infiniteExecutionMsg.simps(1)
% 0.27/0.47 thf(fact_201_not__gr__zero,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.27/0.47 = ( N3 = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % not_gr_zero
% 0.27/0.47 thf(fact_202_length__Cons,axiom,
% 0.27/0.47 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 0.27/0.47 = ( suc @ ( size_s1406904903t_unit @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_Cons
% 0.27/0.47 thf(fact_203_zero__reorient,axiom,
% 0.27/0.47 ! [X: nat] :
% 0.27/0.47 ( ( zero_zero_nat = X )
% 0.27/0.47 = ( X = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_reorient
% 0.27/0.47 thf(fact_204_zero__reorient,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ( ( zero_zero_int = X )
% 0.27/0.47 = ( X = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_reorient
% 0.27/0.47 thf(fact_205_gr__zeroI,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( N3 != zero_zero_nat )
% 0.27/0.47 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr_zeroI
% 0.27/0.47 thf(fact_206_not__less__zero,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % not_less_zero
% 0.27/0.47 thf(fact_207_gr__implies__not__zero,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( N3 != zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % gr_implies_not_zero
% 0.27/0.47 thf(fact_208_zero__less__iff__neq__zero,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.27/0.47 = ( N3 != zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_less_iff_neq_zero
% 0.27/0.47 thf(fact_209_n__lists__Nil,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ( N3 = zero_zero_nat )
% 0.27/0.47 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 0.27/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
% 0.27/0.47 & ( ( N3 != zero_zero_nat )
% 0.27/0.47 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 0.27/0.47 = nil_li307996205t_unit ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % n_lists_Nil
% 0.27/0.47 thf(fact_210_n__lists__Nil,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ( N3 = zero_zero_nat )
% 0.27/0.47 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 0.27/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
% 0.27/0.47 & ( ( N3 != zero_zero_nat )
% 0.27/0.47 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 0.27/0.47 = nil_list_message_p_v ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % n_lists_Nil
% 0.27/0.47 thf(fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.27/0.47 = Y )
% 0.27/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( Xc
% 0.27/0.47 = ( suc @ N ) )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionCfg.elims
% 0.27/0.47 thf(fact_212_n__lists_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
% 0.27/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % n_lists.simps(1)
% 0.27/0.47 thf(fact_213_n__lists_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Xs: list_message_p_v] :
% 0.27/0.47 ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
% 0.27/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % n_lists.simps(1)
% 0.27/0.47 thf(fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.27/0.47 = Y )
% 0.27/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.27/0.47 => ( Y != nil_message_p_v ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( Xc
% 0.27/0.47 = ( suc @ N ) )
% 0.27/0.47 => ( Y
% 0.27/0.47 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionMsg.elims
% 0.27/0.47 thf(fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.27/0.47 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(2)
% 0.27/0.47 thf(fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.27/0.47 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(2)
% 0.27/0.47 thf(fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.27/0.47 = nil_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(1)
% 0.27/0.47 thf(fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.27/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.27/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.27/0.47 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.27/0.47 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(1)
% 0.27/0.47 thf(fact_219_less__numeral__extra_I3_J,axiom,
% 0.27/0.47 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % less_numeral_extra(3)
% 0.27/0.47 thf(fact_220_less__numeral__extra_I3_J,axiom,
% 0.27/0.47 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % less_numeral_extra(3)
% 0.27/0.47 thf(fact_221_product__lists_Osimps_I1_J,axiom,
% 0.27/0.47 ( ( produc663212148t_unit @ nil_li307996205t_unit )
% 0.27/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % product_lists.simps(1)
% 0.27/0.47 thf(fact_222_product__lists_Osimps_I1_J,axiom,
% 0.27/0.47 ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
% 0.27/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % product_lists.simps(1)
% 0.27/0.47 thf(fact_223_subseqs_Osimps_I1_J,axiom,
% 0.27/0.47 ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
% 0.27/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % subseqs.simps(1)
% 0.27/0.47 thf(fact_224_subseqs_Osimps_I1_J,axiom,
% 0.27/0.47 ( ( subseqs_message_p_v @ nil_message_p_v )
% 0.27/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % subseqs.simps(1)
% 0.27/0.47 thf(fact_225_length__code,axiom,
% 0.27/0.47 ( size_s1406904903t_unit
% 0.27/0.47 = ( gen_le193291088t_unit @ zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % length_code
% 0.27/0.47 thf(fact_226_gen__length__code_I2_J,axiom,
% 0.27/0.47 ! [N3: nat,X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.27/0.47 ( ( gen_le193291088t_unit @ N3 @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 0.27/0.47 = ( gen_le193291088t_unit @ ( suc @ N3 ) @ Xs ) ) ).
% 0.27/0.47
% 0.27/0.47 % gen_length_code(2)
% 0.27/0.47 thf(fact_227_gen__length__code_I1_J,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( gen_le193291088t_unit @ N3 @ nil_co1338500125t_unit )
% 0.27/0.47 = N3 ) ).
% 0.27/0.47
% 0.27/0.47 % gen_length_code(1)
% 0.27/0.47 thf(fact_228_gen__length__code_I1_J,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( gen_le697204914ge_p_v @ N3 @ nil_message_p_v )
% 0.27/0.47 = N3 ) ).
% 0.27/0.47
% 0.27/0.47 % gen_length_code(1)
% 0.27/0.47 thf(fact_229_insert__Nil,axiom,
% 0.27/0.47 ! [X: message_p_v] :
% 0.27/0.47 ( ( insert_message_p_v @ X @ nil_message_p_v )
% 0.27/0.47 = ( cons_message_p_v @ X @ nil_message_p_v ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_Nil
% 0.27/0.47 thf(fact_230_insert__Nil,axiom,
% 0.27/0.47 ! [X: config256849571t_unit] :
% 0.27/0.47 ( ( insert1308755079t_unit @ X @ nil_co1338500125t_unit )
% 0.27/0.47 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % insert_Nil
% 0.27/0.47 thf(fact_231_nths__singleton,axiom,
% 0.27/0.47 ! [A8: set_nat,X: message_p_v] :
% 0.27/0.47 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 0.27/0.47 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 0.27/0.47 = ( cons_message_p_v @ X @ nil_message_p_v ) ) )
% 0.27/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 0.27/0.47 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 0.27/0.47 = nil_message_p_v ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nths_singleton
% 0.27/0.47 thf(fact_232_nths__singleton,axiom,
% 0.27/0.47 ! [A8: set_nat,X: config256849571t_unit] :
% 0.27/0.47 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 0.27/0.47 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 0.27/0.47 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.27/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 0.27/0.47 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 0.27/0.47 = nil_co1338500125t_unit ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nths_singleton
% 0.27/0.47 thf(fact_233_of__nat__0__less__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0_less_iff
% 0.27/0.47 thf(fact_234_of__nat__0__less__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0_less_iff
% 0.27/0.47 thf(fact_235_of__nat__eq__iff,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ( semiri2019852685at_int @ M )
% 0.27/0.47 = ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( M = N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_eq_iff
% 0.27/0.47 thf(fact_236_nths__nil,axiom,
% 0.27/0.47 ! [A8: set_nat] :
% 0.27/0.47 ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A8 )
% 0.27/0.47 = nil_co1338500125t_unit ) ).
% 0.27/0.47
% 0.27/0.47 % nths_nil
% 0.27/0.47 thf(fact_237_nths__nil,axiom,
% 0.27/0.47 ! [A8: set_nat] :
% 0.27/0.47 ( ( nths_message_p_v @ nil_message_p_v @ A8 )
% 0.27/0.47 = nil_message_p_v ) ).
% 0.27/0.47
% 0.27/0.47 % nths_nil
% 0.27/0.47 thf(fact_238_of__nat__0,axiom,
% 0.27/0.47 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.27/0.47 = zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0
% 0.27/0.47 thf(fact_239_of__nat__0,axiom,
% 0.27/0.47 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.27/0.47 = zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0
% 0.27/0.47 thf(fact_240_of__nat__0__eq__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( zero_zero_nat
% 0.27/0.47 = ( semiri1382578993at_nat @ N3 ) )
% 0.27/0.47 = ( zero_zero_nat = N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0_eq_iff
% 0.27/0.47 thf(fact_241_of__nat__0__eq__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( zero_zero_int
% 0.27/0.47 = ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( zero_zero_nat = N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_0_eq_iff
% 0.27/0.47 thf(fact_242_of__nat__eq__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( ( ( semiri1382578993at_nat @ M )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( M = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_eq_0_iff
% 0.27/0.47 thf(fact_243_of__nat__eq__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( ( ( semiri2019852685at_int @ M )
% 0.27/0.47 = zero_zero_int )
% 0.27/0.47 = ( M = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_eq_0_iff
% 0.27/0.47 thf(fact_244_of__nat__less__iff,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_iff
% 0.27/0.47 thf(fact_245_of__nat__less__iff,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_iff
% 0.27/0.47 thf(fact_246_of__nat__less__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_0_iff
% 0.27/0.47 thf(fact_247_of__nat__less__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_0_iff
% 0.27/0.47 thf(fact_248_of__nat__neq__0,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( semiri1382578993at_nat @ ( suc @ N3 ) )
% 0.27/0.47 != zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_neq_0
% 0.27/0.47 thf(fact_249_of__nat__neq__0,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( semiri2019852685at_int @ ( suc @ N3 ) )
% 0.27/0.47 != zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_neq_0
% 0.27/0.47 thf(fact_250_less__imp__of__nat__less,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_of_nat_less
% 0.27/0.47 thf(fact_251_less__imp__of__nat__less,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ M @ N3 )
% 0.27/0.47 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_imp_of_nat_less
% 0.27/0.47 thf(fact_252_of__nat__less__imp__less,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 0.27/0.47 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_imp_less
% 0.27/0.47 thf(fact_253_of__nat__less__imp__less,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_imp_less
% 0.27/0.47 thf(fact_254_nths__all,axiom,
% 0.27/0.47 ! [Xs: list_c1059388851t_unit,I4: set_nat] :
% 0.27/0.47 ( ! [I2: nat] :
% 0.27/0.47 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
% 0.27/0.47 => ( member_nat @ I2 @ I4 ) )
% 0.27/0.47 => ( ( nths_c890550943t_unit @ Xs @ I4 )
% 0.27/0.47 = Xs ) ) ).
% 0.27/0.47
% 0.27/0.47 % nths_all
% 0.27/0.47 thf(fact_255_pos__int__cases,axiom,
% 0.27/0.47 ! [K: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ K )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( K
% 0.27/0.47 = ( semiri2019852685at_int @ N ) )
% 0.27/0.47 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pos_int_cases
% 0.27/0.47 thf(fact_256_zero__less__imp__eq__int,axiom,
% 0.27/0.47 ! [K: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ K )
% 0.27/0.47 => ? [N: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.27/0.47 & ( K
% 0.27/0.47 = ( semiri2019852685at_int @ N ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_less_imp_eq_int
% 0.27/0.47 thf(fact_257_list__ex1__simps_I1_J,axiom,
% 0.27/0.47 ! [P: config256849571t_unit > $o] :
% 0.27/0.47 ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% 0.27/0.47
% 0.27/0.47 % list_ex1_simps(1)
% 0.27/0.47 thf(fact_258_list__ex1__simps_I1_J,axiom,
% 0.27/0.47 ! [P: message_p_v > $o] :
% 0.27/0.47 ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% 0.27/0.47
% 0.27/0.47 % list_ex1_simps(1)
% 0.27/0.47 thf(fact_259_nat__int__comparison_I2_J,axiom,
% 0.27/0.47 ( ord_less_nat
% 0.27/0.47 = ( ^ [A10: nat,B: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A10 ) @ ( semiri2019852685at_int @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_int_comparison(2)
% 0.27/0.47 thf(fact_260_int__ops_I1_J,axiom,
% 0.27/0.47 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.27/0.47 = zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % int_ops(1)
% 0.27/0.47 thf(fact_261_neg__int__cases,axiom,
% 0.27/0.47 ! [K: int] :
% 0.27/0.47 ( ( ord_less_int @ K @ zero_zero_int )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( K
% 0.27/0.47 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 0.27/0.47 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_int_cases
% 0.27/0.47 thf(fact_262_neg__equal__iff__equal,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( ( uminus_uminus_int @ A )
% 0.27/0.47 = ( uminus_uminus_int @ B2 ) )
% 0.27/0.47 = ( A = B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_equal_iff_equal
% 0.27/0.47 thf(fact_263_add_Oinverse__inverse,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % add.inverse_inverse
% 0.27/0.47 thf(fact_264_add_Oinverse__neutral,axiom,
% 0.27/0.47 ( ( uminus_uminus_int @ zero_zero_int )
% 0.27/0.47 = zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % add.inverse_neutral
% 0.27/0.47 thf(fact_265_neg__0__equal__iff__equal,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( zero_zero_int
% 0.27/0.47 = ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( zero_zero_int = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_0_equal_iff_equal
% 0.27/0.47 thf(fact_266_neg__equal__0__iff__equal,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ( uminus_uminus_int @ A )
% 0.27/0.47 = zero_zero_int )
% 0.27/0.47 = ( A = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_equal_0_iff_equal
% 0.27/0.47 thf(fact_267_equal__neg__zero,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( A = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % equal_neg_zero
% 0.27/0.47 thf(fact_268_neg__equal__zero,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ( uminus_uminus_int @ A )
% 0.27/0.47 = A )
% 0.27/0.47 = ( A = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_equal_zero
% 0.27/0.47 thf(fact_269_neg__less__iff__less,axiom,
% 0.27/0.47 ! [B2: int,A: int] :
% 0.27/0.47 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_int @ A @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_less_iff_less
% 0.27/0.47 thf(fact_270_less__neg__neg,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_neg_neg
% 0.27/0.47 thf(fact_271_neg__less__pos,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.27/0.47 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_less_pos
% 0.27/0.47 thf(fact_272_neg__0__less__iff__less,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_0_less_iff_less
% 0.27/0.47 thf(fact_273_neg__less__0__iff__less,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.27/0.47 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_less_0_iff_less
% 0.27/0.47 thf(fact_274_negative__eq__positive,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] :
% 0.27/0.47 ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( semiri2019852685at_int @ M ) )
% 0.27/0.47 = ( ( N3 = zero_zero_nat )
% 0.27/0.47 & ( M = zero_zero_nat ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % negative_eq_positive
% 0.27/0.47 thf(fact_275_negative__zless,axiom,
% 0.27/0.47 ! [N3: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ ( semiri2019852685at_int @ M ) ) ).
% 0.27/0.47
% 0.27/0.47 % negative_zless
% 0.27/0.47 thf(fact_276_minus__less__iff,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
% 0.27/0.47 = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % minus_less_iff
% 0.27/0.47 thf(fact_277_less__minus__iff,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
% 0.27/0.47 = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_minus_iff
% 0.27/0.47 thf(fact_278_verit__negate__coefficient_I2_J,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( ord_less_int @ A @ B2 )
% 0.27/0.47 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % verit_negate_coefficient(2)
% 0.27/0.47 thf(fact_279_minus__equation__iff,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( ( uminus_uminus_int @ A )
% 0.27/0.47 = B2 )
% 0.27/0.47 = ( ( uminus_uminus_int @ B2 )
% 0.27/0.47 = A ) ) ).
% 0.27/0.47
% 0.27/0.47 % minus_equation_iff
% 0.27/0.47 thf(fact_280_equation__minus__iff,axiom,
% 0.27/0.47 ! [A: int,B2: int] :
% 0.27/0.47 ( ( A
% 0.27/0.47 = ( uminus_uminus_int @ B2 ) )
% 0.27/0.47 = ( B2
% 0.27/0.47 = ( uminus_uminus_int @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % equation_minus_iff
% 0.27/0.47 thf(fact_281_int__cases,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ! [N: nat] :
% 0.27/0.47 ( Z2
% 0.27/0.47 != ( semiri2019852685at_int @ N ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( Z2
% 0.27/0.47 != ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % int_cases
% 0.27/0.47 thf(fact_282_int__of__nat__induct,axiom,
% 0.27/0.47 ! [P: int > $o,Z2: int] :
% 0.27/0.47 ( ! [N: nat] : ( P @ ( semiri2019852685at_int @ N ) )
% 0.27/0.47 => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) )
% 0.27/0.47 => ( P @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % int_of_nat_induct
% 0.27/0.47 thf(fact_283_int__cases4,axiom,
% 0.27/0.47 ! [M: int] :
% 0.27/0.47 ( ! [N: nat] :
% 0.27/0.47 ( M
% 0.27/0.47 != ( semiri2019852685at_int @ N ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.27/0.47 => ( M
% 0.27/0.47 != ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % int_cases4
% 0.27/0.47 thf(fact_284_verit__comp__simplify1_I1_J,axiom,
% 0.27/0.47 ! [A: nat] :
% 0.27/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.27/0.47
% 0.27/0.47 % verit_comp_simplify1(1)
% 0.27/0.47 thf(fact_285_verit__comp__simplify1_I1_J,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ~ ( ord_less_int @ A @ A ) ).
% 0.27/0.47
% 0.27/0.47 % verit_comp_simplify1(1)
% 0.27/0.47 thf(fact_286_int__cases3,axiom,
% 0.27/0.47 ! [K: int] :
% 0.27/0.47 ( ( K != zero_zero_int )
% 0.27/0.47 => ( ! [N: nat] :
% 0.27/0.47 ( ( K
% 0.27/0.47 = ( semiri2019852685at_int @ N ) )
% 0.27/0.47 => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.27/0.47 => ~ ! [N: nat] :
% 0.27/0.47 ( ( K
% 0.27/0.47 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 0.27/0.47 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % int_cases3
% 0.27/0.47 thf(fact_287_negative__zless__0,axiom,
% 0.27/0.47 ! [N3: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % negative_zless_0
% 0.27/0.47 thf(fact_288_negD,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ( ( ord_less_int @ X @ zero_zero_int )
% 0.27/0.47 => ? [N: nat] :
% 0.27/0.47 ( X
% 0.27/0.47 = ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % negD
% 0.27/0.47 thf(fact_289_zero__less__nat__eq,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_less_nat_eq
% 0.27/0.47 thf(fact_290_of__int__0__less__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_0_less_iff
% 0.27/0.47 thf(fact_291_of__int__0,axiom,
% 0.27/0.47 ( ( ring_1_of_int_int @ zero_zero_int )
% 0.27/0.47 = zero_zero_int ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_0
% 0.27/0.47 thf(fact_292_of__int__0__eq__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( zero_zero_int
% 0.27/0.47 = ( ring_1_of_int_int @ Z2 ) )
% 0.27/0.47 = ( Z2 = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_0_eq_iff
% 0.27/0.47 thf(fact_293_of__int__eq__0__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ( ring_1_of_int_int @ Z2 )
% 0.27/0.47 = zero_zero_int )
% 0.27/0.47 = ( Z2 = zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_eq_0_iff
% 0.27/0.47 thf(fact_294_of__int__less__iff,axiom,
% 0.27/0.47 ! [W: int,Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ W @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_less_iff
% 0.27/0.47 thf(fact_295_zless__nat__conj,axiom,
% 0.27/0.47 ! [W: int,Z2: int] :
% 0.27/0.47 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.27/0.47 = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.27/0.47 & ( ord_less_int @ W @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % zless_nat_conj
% 0.27/0.47 thf(fact_296_nat__zminus__int,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) ) )
% 0.27/0.47 = zero_zero_nat ) ).
% 0.27/0.47
% 0.27/0.47 % nat_zminus_int
% 0.27/0.47 thf(fact_297_of__int__less__0__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.27/0.47 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_less_0_iff
% 0.27/0.47 thf(fact_298_nat__zero__as__int,axiom,
% 0.27/0.47 ( zero_zero_nat
% 0.27/0.47 = ( nat2 @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_zero_as_int
% 0.27/0.47 thf(fact_299_nat__mono__iff,axiom,
% 0.27/0.47 ! [Z2: int,W: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.27/0.47 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ W @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_mono_iff
% 0.27/0.47 thf(fact_300_zless__nat__eq__int__zless,axiom,
% 0.27/0.47 ! [M: nat,Z2: int] :
% 0.27/0.47 ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ ( semiri2019852685at_int @ M ) @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % zless_nat_eq_int_zless
% 0.27/0.47 thf(fact_301_of__int__pos,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.27/0.47 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_pos
% 0.27/0.47 thf(fact_302_of__nat__less__of__int__iff,axiom,
% 0.27/0.47 ! [N3: nat,X: int] :
% 0.27/0.47 ( ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ ( ring_1_of_int_int @ X ) )
% 0.27/0.47 = ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_less_of_int_iff
% 0.27/0.47 thf(fact_303_split__nat,axiom,
% 0.27/0.47 ! [P: nat > $o,I: int] :
% 0.27/0.47 ( ( P @ ( nat2 @ I ) )
% 0.27/0.47 = ( ! [N5: nat] :
% 0.27/0.47 ( ( I
% 0.27/0.47 = ( semiri2019852685at_int @ N5 ) )
% 0.27/0.47 => ( P @ N5 ) )
% 0.27/0.47 & ( ( ord_less_int @ I @ zero_zero_int )
% 0.27/0.47 => ( P @ zero_zero_nat ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % split_nat
% 0.27/0.47 thf(fact_304_one__less__nat__eq,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % one_less_nat_eq
% 0.27/0.47 thf(fact_305_nat__less__iff,axiom,
% 0.27/0.47 ! [W: int,M: nat] :
% 0.27/0.47 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.27/0.47 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.27/0.47 = ( ord_less_int @ W @ ( semiri2019852685at_int @ M ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_less_iff
% 0.27/0.47 thf(fact_306_le__zero__eq,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
% 0.27/0.47 = ( N3 = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % le_zero_eq
% 0.27/0.47 thf(fact_307_neg__le__iff__le,axiom,
% 0.27/0.47 ! [B2: int,A: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_le_iff_le
% 0.27/0.47 thf(fact_308_of__nat__le__iff,axiom,
% 0.27/0.47 ! [M: nat,N3: nat] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( ord_less_eq_nat @ M @ N3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_le_iff
% 0.27/0.47 thf(fact_309_of__nat__1,axiom,
% 0.27/0.47 ( ( semiri2019852685at_int @ one_one_nat )
% 0.27/0.47 = one_one_int ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_1
% 0.27/0.47 thf(fact_310_of__nat__1__eq__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( one_one_int
% 0.27/0.47 = ( semiri2019852685at_int @ N3 ) )
% 0.27/0.47 = ( N3 = one_one_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_1_eq_iff
% 0.27/0.47 thf(fact_311_of__nat__eq__1__iff,axiom,
% 0.27/0.47 ! [N3: nat] :
% 0.27/0.47 ( ( ( semiri2019852685at_int @ N3 )
% 0.27/0.47 = one_one_int )
% 0.27/0.47 = ( N3 = one_one_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_eq_1_iff
% 0.27/0.47 thf(fact_312_neg__0__le__iff__le,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_0_le_iff_le
% 0.27/0.47 thf(fact_313_neg__le__0__iff__le,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.27/0.47 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_le_0_iff_le
% 0.27/0.47 thf(fact_314_less__eq__neg__nonpos,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.27/0.47 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_eq_neg_nonpos
% 0.27/0.47 thf(fact_315_neg__less__eq__nonneg,axiom,
% 0.27/0.47 ! [A: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.27/0.47 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % neg_less_eq_nonneg
% 0.27/0.47 thf(fact_316_of__nat__le__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 0.27/0.47 = ( M = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_le_0_iff
% 0.27/0.47 thf(fact_317_of__nat__le__0__iff,axiom,
% 0.27/0.47 ! [M: nat] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
% 0.27/0.47 = ( M = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_le_0_iff
% 0.27/0.47 thf(fact_318_nat__1,axiom,
% 0.27/0.47 ( ( nat2 @ one_one_int )
% 0.27/0.47 = ( suc @ zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_1
% 0.27/0.47 thf(fact_319_nat__le__0,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.27/0.47 => ( ( nat2 @ Z2 )
% 0.27/0.47 = zero_zero_nat ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_le_0
% 0.27/0.47 thf(fact_320_nat__0__iff,axiom,
% 0.27/0.47 ! [I: int] :
% 0.27/0.47 ( ( ( nat2 @ I )
% 0.27/0.47 = zero_zero_nat )
% 0.27/0.47 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % nat_0_iff
% 0.27/0.47 thf(fact_321_of__int__le__0__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.27/0.47 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_le_0_iff
% 0.27/0.47 thf(fact_322_of__int__0__le__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.27/0.47 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_0_le_iff
% 0.27/0.47 thf(fact_323_of__int__less__1__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.27/0.47 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_less_1_iff
% 0.27/0.47 thf(fact_324_of__int__1__less__iff,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.27/0.47 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_1_less_iff
% 0.27/0.47 thf(fact_325_of__int__nonneg,axiom,
% 0.27/0.47 ! [Z2: int] :
% 0.27/0.47 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.27/0.47 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_int_nonneg
% 0.27/0.47 thf(fact_326_verit__comp__simplify1_I3_J,axiom,
% 0.27/0.47 ! [B3: nat,A11: nat] :
% 0.27/0.47 ( ( ~ ( ord_less_eq_nat @ B3 @ A11 ) )
% 0.27/0.47 = ( ord_less_nat @ A11 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % verit_comp_simplify1(3)
% 0.27/0.47 thf(fact_327_verit__comp__simplify1_I3_J,axiom,
% 0.27/0.47 ! [B3: int,A11: int] :
% 0.27/0.47 ( ( ~ ( ord_less_eq_int @ B3 @ A11 ) )
% 0.27/0.47 = ( ord_less_int @ A11 @ B3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % verit_comp_simplify1(3)
% 0.27/0.47 thf(fact_328_le__numeral__extra_I4_J,axiom,
% 0.27/0.47 ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.27/0.47
% 0.27/0.47 % le_numeral_extra(4)
% 0.27/0.47 thf(fact_329_one__reorient,axiom,
% 0.27/0.47 ! [X: int] :
% 0.27/0.47 ( ( one_one_int = X )
% 0.27/0.47 = ( X = one_one_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % one_reorient
% 0.27/0.47 thf(fact_330_lift__Suc__antimono__le,axiom,
% 0.27/0.47 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ N ) )
% 0.27/0.47 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F2 @ N4 ) @ ( F2 @ N3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_antimono_le
% 0.27/0.47 thf(fact_331_lift__Suc__mono__le,axiom,
% 0.27/0.47 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.27/0.47 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.27/0.47 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 0.27/0.47 => ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % lift_Suc_mono_le
% 0.27/0.47 thf(fact_332_zero__le,axiom,
% 0.27/0.47 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.27/0.47
% 0.27/0.47 % zero_le
% 0.27/0.47 thf(fact_333_le__numeral__extra_I3_J,axiom,
% 0.27/0.47 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.27/0.47
% 0.27/0.47 % le_numeral_extra(3)
% 0.27/0.47 thf(fact_334_le__numeral__extra_I3_J,axiom,
% 0.27/0.47 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.27/0.47
% 0.27/0.47 % le_numeral_extra(3)
% 0.27/0.47 thf(fact_335_less__numeral__extra_I4_J,axiom,
% 0.27/0.47 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.27/0.47
% 0.27/0.47 % less_numeral_extra(4)
% 0.27/0.47 thf(fact_336_less__numeral__extra_I4_J,axiom,
% 0.27/0.47 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.27/0.47
% 0.27/0.47 % less_numeral_extra(4)
% 0.27/0.47 thf(fact_337_of__nat__mono,axiom,
% 0.27/0.47 ! [I: nat,J: nat] :
% 0.27/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.27/0.47 => ( ord_less_eq_int @ ( semiri2019852685at_int @ I ) @ ( semiri2019852685at_int @ J ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % of_nat_mono
% 0.27/0.47 thf(fact_338_less__minus__one__simps_I4_J,axiom,
% 0.27/0.47 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % less_minus_one_simps(4)
% 0.27/0.47 thf(fact_339_less__minus__one__simps_I2_J,axiom,
% 0.27/0.47 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.27/0.47
% 0.27/0.47 % less_minus_one_simps(2)
% 0.27/0.47 thf(fact_340_zero__neq__neg__one,axiom,
% 0.27/0.47 ( zero_zero_int
% 0.27/0.47 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.27/0.47
% 0.27/0.47 % zero_neq_neg_one
% 0.27/0.47
% 0.27/0.47 % Conjectures (1)
% 0.27/0.47 thf(conj_0,conjecture,
% 0.27/0.47 prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.87/1.55 ---- Embedded in THF ---
% 2.87/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.87/1.55 %%% Generated on Tue Feb 24 08:24:33 EST 2026
% 2.87/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.87/1.55 %%% Logic specification used:
% 2.87/1.55 %%% thf(spec, logic, $$dhol).
% 2.87/1.55
% 2.87/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2DTF20758.p
% See solution above
% 2.87/1.55 ------------------------
% 2.98/1.61 ---- Cleaned THF ---
% 2.98/1.61 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J_J,type,
% 2.98/1.61 list_l1584713811t_unit: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 2.98/1.61 list_l611321411t_unit: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.98/1.61 list_c1059388851t_unit: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 config256849571t_unit: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J_J,type,
% 2.98/1.61 list_l1341496881ge_p_v: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 2.98/1.61 list_l1619404459ge_p_v: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.98/1.61 list_message_p_v: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 message_p_v: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 2.98/1.61 messageValue_v: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.98/1.61 set_nat: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__Nat__Onat,type,
% 2.98/1.61 nat: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_t__Int__Oint,type,
% 2.98/1.61 int: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_tf__s,type,
% 2.98/1.61 s: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(ty_n_tf__p,type,
% 2.98/1.61 p: $tType ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 2.98/1.61 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 2.98/1.61 fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 2.98/1.61 fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 2.98/1.61 one_one_int: int ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.98/1.61 one_one_nat: nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 2.98/1.61 uminus_uminus_int: int > int ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 2.98/1.61 zero_zero_int: int ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.98/1.61 zero_zero_nat: nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Int_Onat,type,
% 2.98/1.61 nat2: int > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 2.98/1.61 ring_1_of_int_int: int > int ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.98/1.61 prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.98/1.61 prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.98/1.61 cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.98/1.61 cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 2.98/1.61 cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 2.98/1.61 cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 nil_message_p_v: list_message_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.98/1.61 nil_li307996205t_unit: list_l611321411t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.98/1.61 nil_list_message_p_v: list_l1619404459ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 2.98/1.61 nil_li2108369341t_unit: list_l1584713811t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 2.98/1.61 nil_li835338673ge_p_v: list_l1341496881ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 2.98/1.61 subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 2.98/1.61 subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_OSuc,type,
% 2.98/1.61 suc: nat > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 2.98/1.61 semiri2019852685at_int: nat > int ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 2.98/1.61 semiri1382578993at_nat: nat > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 2.98/1.61 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 2.98/1.61 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 2.98/1.61 size_s503142615t_unit: list_l611321411t_unit > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 2.98/1.61 size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 2.98/1.61 ord_less_int: int > int > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 2.98/1.61 ord_less_nat: nat > nat > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 2.98/1.61 ord_less_eq_int: int > int > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.98/1.61 ord_less_eq_nat: nat > nat > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.98/1.61 collect_nat: ( nat > $o ) > set_nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_c_member_001t__Nat__Onat,type,
% 2.98/1.61 member_nat: nat > set_nat > $o ).
% 2.98/1.61
% 2.98/1.61 thf(sy_v_cfg____,type,
% 2.98/1.61 cfg: config256849571t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_v_fe____,type,
% 2.98/1.61 fe: nat > list_c1059388851t_unit ).
% 2.98/1.61
% 2.98/1.61 thf(sy_v_m____,type,
% 2.98/1.61 m: nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_v_n____,type,
% 2.98/1.61 n: nat ).
% 2.98/1.61
% 2.98/1.61 thf(sy_v_na____,type,
% 2.98/1.61 na: nat ).
% 2.98/1.61
% 2.98/1.61 thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
% 2.98/1.61 ord_less_nat @ m @ na ).
% 2.98/1.61
% 2.98/1.61 thf(fact_1_MLessN,axiom,
% 2.98/1.61 ord_less_nat @ m @ n ).
% 2.98/1.61
% 2.98/1.61 thf(fact_2_IA_I1_J,axiom,
% 2.98/1.61 ( ( ord_less_nat @ m @ na )
% 2.98/1.61 => ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
% 2.98/1.61 ( ( m = na )
% 2.98/1.61 | ( ord_less_nat @ m @ na ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_4_IA_I2_J,axiom,
% 2.98/1.61 ord_less_nat @ m @ ( suc @ na ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_5_PrefixListTransitive,axiom,
% 2.98/1.61 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 2.98/1.61 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 2.98/1.61 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_6_PrefixListTransitive,axiom,
% 2.98/1.61 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 2.98/1.61 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 2.98/1.61 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_7_FE_I1_J,axiom,
% 2.98/1.61 ( ( fe @ zero_zero_nat )
% 2.98/1.61 = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_8_prefixList_Ointros_I2_J,axiom,
% 2.98/1.61 ! [Xa: list_l611321411t_unit,Xb: list_l611321411t_unit,X: list_c1059388851t_unit] :
% 2.98/1.61 ( ( prefix747844452t_unit @ Xa @ Xb )
% 2.98/1.61 => ( prefix747844452t_unit @ ( cons_l1083444861t_unit @ X @ Xa ) @ ( cons_l1083444861t_unit @ X @ Xb ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_9_prefixList_Ointros_I2_J,axiom,
% 2.98/1.61 ! [Xa: list_l1619404459ge_p_v,Xb: list_l1619404459ge_p_v,X: list_message_p_v] :
% 2.98/1.61 ( ( prefix1465223476ge_p_v @ Xa @ Xb )
% 2.98/1.61 => ( prefix1465223476ge_p_v @ ( cons_l233104475ge_p_v @ X @ Xa ) @ ( cons_l233104475ge_p_v @ X @ Xb ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_10_prefixList_Ointros_I2_J,axiom,
% 2.98/1.61 ! [Xa: list_message_p_v,Xb: list_message_p_v,X: message_p_v] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ Xa @ Xb )
% 2.98/1.61 => ( prefix47729710ge_p_v @ ( cons_message_p_v @ X @ Xa ) @ ( cons_message_p_v @ X @ Xb ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_11_prefixList_Ointros_I2_J,axiom,
% 2.98/1.61 ! [Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,X: config256849571t_unit] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ Xa @ Xb )
% 2.98/1.61 => ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ X @ Xa ) @ ( cons_c1162654829t_unit @ X @ Xb ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_12_PrefixListMonotonicity,axiom,
% 2.98/1.61 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 2.98/1.61 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_13_PrefixListMonotonicity,axiom,
% 2.98/1.61 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 2.98/1.61 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 2.98/1.61 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
% 2.98/1.61 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 2.98/1.61 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 2.98/1.61 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.98/1.61 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 2.98/1.61 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 2.98/1.61 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 2.98/1.61 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 2.98/1.61 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 2.98/1.61 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.98/1.61 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_16_prefixList_Ointros_I1_J,axiom,
% 2.98/1.61 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] : ( prefix747844452t_unit @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_17_prefixList_Ointros_I1_J,axiom,
% 2.98/1.61 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] : ( prefix1465223476ge_p_v @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_18_prefixList_Ointros_I1_J,axiom,
% 2.98/1.61 ! [X: message_p_v,Xs: list_message_p_v] : ( prefix47729710ge_p_v @ nil_message_p_v @ ( cons_message_p_v @ X @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_19_prefixList_Ointros_I1_J,axiom,
% 2.98/1.61 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_20_prefixList_Ocases,axiom,
% 2.98/1.61 ! [A1: list_l611321411t_unit,A2: list_l611321411t_unit] :
% 2.98/1.61 ( ( prefix747844452t_unit @ A1 @ A2 )
% 2.98/1.61 => ( ( ( A1 = nil_li307996205t_unit )
% 2.98/1.61 => ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 2.98/1.61 ( A2
% 2.98/1.61 != ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ~ ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( A1
% 2.98/1.61 = ( cons_l1083444861t_unit @ X2 @ Xa2 ) )
% 2.98/1.61 => ( ( A2
% 2.98/1.61 = ( cons_l1083444861t_unit @ X2 @ Xb2 ) )
% 2.98/1.61 => ~ ( prefix747844452t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_21_prefixList_Ocases,axiom,
% 2.98/1.61 ! [A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( prefix1465223476ge_p_v @ A1 @ A2 )
% 2.98/1.61 => ( ( ( A1 = nil_list_message_p_v )
% 2.98/1.61 => ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( A2
% 2.98/1.61 != ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ~ ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 2.98/1.61 ( ( A1
% 2.98/1.61 = ( cons_l233104475ge_p_v @ X2 @ Xa2 ) )
% 2.98/1.61 => ( ( A2
% 2.98/1.61 = ( cons_l233104475ge_p_v @ X2 @ Xb2 ) )
% 2.98/1.61 => ~ ( prefix1465223476ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_22_prefixList_Ocases,axiom,
% 2.98/1.61 ! [A1: list_message_p_v,A2: list_message_p_v] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ A1 @ A2 )
% 2.98/1.61 => ( ( ( A1 = nil_message_p_v )
% 2.98/1.61 => ! [X2: message_p_v,Xs2: list_message_p_v] :
% 2.98/1.61 ( A2
% 2.98/1.61 != ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ~ ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 2.98/1.61 ( ( A1
% 2.98/1.61 = ( cons_message_p_v @ X2 @ Xa2 ) )
% 2.98/1.61 => ( ( A2
% 2.98/1.61 = ( cons_message_p_v @ X2 @ Xb2 ) )
% 2.98/1.61 => ~ ( prefix47729710ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_23_prefixList_Ocases,axiom,
% 2.98/1.61 ! [A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ A1 @ A2 )
% 2.98/1.61 => ( ( ( A1 = nil_co1338500125t_unit )
% 2.98/1.61 => ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( A2
% 2.98/1.61 != ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ~ ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 2.98/1.61 ( ( A1
% 2.98/1.61 = ( cons_c1162654829t_unit @ X2 @ Xa2 ) )
% 2.98/1.61 => ( ( A2
% 2.98/1.61 = ( cons_c1162654829t_unit @ X2 @ Xb2 ) )
% 2.98/1.61 => ~ ( prefix1615116500t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_24_prefixList_Osimps,axiom,
% 2.98/1.61 ( prefix747844452t_unit
% 2.98/1.61 = ( ^ [A12: list_l611321411t_unit,A22: list_l611321411t_unit] :
% 2.98/1.61 ( ? [X3: list_c1059388851t_unit,Xs3: list_l611321411t_unit] :
% 2.98/1.61 ( ( A12 = nil_li307996205t_unit )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_l1083444861t_unit @ X3 @ Xs3 ) ) )
% 2.98/1.61 | ? [Xa3: list_l611321411t_unit,Xb3: list_l611321411t_unit,X3: list_c1059388851t_unit] :
% 2.98/1.61 ( ( A12
% 2.98/1.61 = ( cons_l1083444861t_unit @ X3 @ Xa3 ) )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_l1083444861t_unit @ X3 @ Xb3 ) )
% 2.98/1.61 & ( prefix747844452t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_25_prefixList_Osimps,axiom,
% 2.98/1.61 ( prefix1465223476ge_p_v
% 2.98/1.61 = ( ^ [A12: list_l1619404459ge_p_v,A22: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ? [X3: list_message_p_v,Xs3: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( A12 = nil_list_message_p_v )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_l233104475ge_p_v @ X3 @ Xs3 ) ) )
% 2.98/1.61 | ? [Xa3: list_l1619404459ge_p_v,Xb3: list_l1619404459ge_p_v,X3: list_message_p_v] :
% 2.98/1.61 ( ( A12
% 2.98/1.61 = ( cons_l233104475ge_p_v @ X3 @ Xa3 ) )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_l233104475ge_p_v @ X3 @ Xb3 ) )
% 2.98/1.61 & ( prefix1465223476ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_26_prefixList_Osimps,axiom,
% 2.98/1.61 ( prefix47729710ge_p_v
% 2.98/1.61 = ( ^ [A12: list_message_p_v,A22: list_message_p_v] :
% 2.98/1.61 ( ? [X3: message_p_v,Xs3: list_message_p_v] :
% 2.98/1.61 ( ( A12 = nil_message_p_v )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_message_p_v @ X3 @ Xs3 ) ) )
% 2.98/1.61 | ? [Xa3: list_message_p_v,Xb3: list_message_p_v,X3: message_p_v] :
% 2.98/1.61 ( ( A12
% 2.98/1.61 = ( cons_message_p_v @ X3 @ Xa3 ) )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_message_p_v @ X3 @ Xb3 ) )
% 2.98/1.61 & ( prefix47729710ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_27_prefixList_Osimps,axiom,
% 2.98/1.61 ( prefix1615116500t_unit
% 2.98/1.61 = ( ^ [A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 2.98/1.61 ( ? [X3: config256849571t_unit,Xs3: list_c1059388851t_unit] :
% 2.98/1.61 ( ( A12 = nil_co1338500125t_unit )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_c1162654829t_unit @ X3 @ Xs3 ) ) )
% 2.98/1.61 | ? [Xa3: list_c1059388851t_unit,Xb3: list_c1059388851t_unit,X3: config256849571t_unit] :
% 2.98/1.61 ( ( A12
% 2.98/1.61 = ( cons_c1162654829t_unit @ X3 @ Xa3 ) )
% 2.98/1.61 & ( A22
% 2.98/1.61 = ( cons_c1162654829t_unit @ X3 @ Xb3 ) )
% 2.98/1.61 & ( prefix1615116500t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_28_prefixList_Oinducts,axiom,
% 2.98/1.61 ! [X1: list_l611321411t_unit,X22: list_l611321411t_unit,P: list_l611321411t_unit > list_l611321411t_unit > $o] :
% 2.98/1.61 ( ( prefix747844452t_unit @ X1 @ X22 )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) )
% 2.98/1.61 => ( ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( prefix747844452t_unit @ Xa2 @ Xb2 )
% 2.98/1.61 => ( ( P @ Xa2 @ Xb2 )
% 2.98/1.61 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xa2 ) @ ( cons_l1083444861t_unit @ X2 @ Xb2 ) ) ) )
% 2.98/1.61 => ( P @ X1 @ X22 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_29_prefixList_Oinducts,axiom,
% 2.98/1.61 ! [X1: list_l1619404459ge_p_v,X22: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o] :
% 2.98/1.61 ( ( prefix1465223476ge_p_v @ X1 @ X22 )
% 2.98/1.61 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) )
% 2.98/1.61 => ( ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 2.98/1.61 ( ( prefix1465223476ge_p_v @ Xa2 @ Xb2 )
% 2.98/1.61 => ( ( P @ Xa2 @ Xb2 )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xa2 ) @ ( cons_l233104475ge_p_v @ X2 @ Xb2 ) ) ) )
% 2.98/1.61 => ( P @ X1 @ X22 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_30_prefixList_Oinducts,axiom,
% 2.98/1.61 ! [X1: list_message_p_v,X22: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ X1 @ X22 )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) )
% 2.98/1.61 => ( ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 2.98/1.61 ( ( prefix47729710ge_p_v @ Xa2 @ Xb2 )
% 2.98/1.61 => ( ( P @ Xa2 @ Xb2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xa2 ) @ ( cons_message_p_v @ X2 @ Xb2 ) ) ) )
% 2.98/1.61 => ( P @ X1 @ X22 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_31_prefixList_Oinducts,axiom,
% 2.98/1.61 ! [X1: list_c1059388851t_unit,X22: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ X1 @ X22 )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) )
% 2.98/1.61 => ( ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 2.98/1.61 ( ( prefix1615116500t_unit @ Xa2 @ Xb2 )
% 2.98/1.61 => ( ( P @ Xa2 @ Xb2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xa2 ) @ ( cons_c1162654829t_unit @ X2 @ Xb2 ) ) ) )
% 2.98/1.61 => ( P @ X1 @ X22 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_32_NatPredicateTippingPoint,axiom,
% 2.98/1.61 ! [N2: nat,Pr: nat > $o] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 2.98/1.61 => ( ( Pr @ zero_zero_nat )
% 2.98/1.61 => ( ~ ( Pr @ N2 )
% 2.98/1.61 => ? [N: nat] :
% 2.98/1.61 ( ( ord_less_nat @ N @ N2 )
% 2.98/1.61 & ( Pr @ N )
% 2.98/1.61 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_33_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 2.98/1.61 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 2.98/1.61 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_34_length__greater__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_l611321411t_unit] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ Xs ) )
% 2.98/1.61 = ( Xs != nil_li307996205t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_35_length__greater__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ Xs ) )
% 2.98/1.61 = ( Xs != nil_list_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_36_length__greater__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 2.98/1.61 = ( Xs != nil_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_37_length__greater__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 2.98/1.61 = ( Xs != nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_38_length__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_l611321411t_unit] :
% 2.98/1.61 ( ( ( size_s503142615t_unit @ Xs )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( Xs = nil_li307996205t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_39_length__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( ( size_s1809856791ge_p_v @ Xs )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( Xs = nil_list_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_40_length__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( Xs = nil_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_41_length__0__conv,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( Xs = nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_42_less__Suc0,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 2.98/1.61 = ( N3 = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_43_zero__less__Suc,axiom,
% 2.98/1.61 ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_44_lessI,axiom,
% 2.98/1.61 ! [N3: nat] : ( ord_less_nat @ N3 @ ( suc @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_45_Suc__mono,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_46_Suc__less__eq,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_47_neq0__conv,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( N3 != zero_zero_nat )
% 2.98/1.61 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_48_less__nat__zero__code,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_49_bot__nat__0_Onot__eq__extremum,axiom,
% 2.98/1.61 ! [A: nat] :
% 2.98/1.61 ( ( A != zero_zero_nat )
% 2.98/1.61 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_50_list_Oinject,axiom,
% 2.98/1.61 ! [X21: message_p_v,X222: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
% 2.98/1.61 ( ( ( cons_message_p_v @ X21 @ X222 )
% 2.98/1.61 = ( cons_message_p_v @ Y21 @ Y22 ) )
% 2.98/1.61 = ( ( X21 = Y21 )
% 2.98/1.61 & ( X222 = Y22 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_51_list_Oinject,axiom,
% 2.98/1.61 ! [X21: list_c1059388851t_unit,X222: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
% 2.98/1.61 ( ( ( cons_l1083444861t_unit @ X21 @ X222 )
% 2.98/1.61 = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
% 2.98/1.61 = ( ( X21 = Y21 )
% 2.98/1.61 & ( X222 = Y22 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_52_list_Oinject,axiom,
% 2.98/1.61 ! [X21: list_message_p_v,X222: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( ( cons_l233104475ge_p_v @ X21 @ X222 )
% 2.98/1.61 = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
% 2.98/1.61 = ( ( X21 = Y21 )
% 2.98/1.61 & ( X222 = Y22 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_53_list_Oinject,axiom,
% 2.98/1.61 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( cons_c1162654829t_unit @ X21 @ X222 )
% 2.98/1.61 = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
% 2.98/1.61 = ( ( X21 = Y21 )
% 2.98/1.61 & ( X222 = Y22 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_54_old_Onat_Oinject,axiom,
% 2.98/1.61 ! [Nat: nat,Nat2: nat] :
% 2.98/1.61 ( ( ( suc @ Nat )
% 2.98/1.61 = ( suc @ Nat2 ) )
% 2.98/1.61 = ( Nat = Nat2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_55_nat_Oinject,axiom,
% 2.98/1.61 ! [X22: nat,Y2: nat] :
% 2.98/1.61 ( ( ( suc @ X22 )
% 2.98/1.61 = ( suc @ Y2 ) )
% 2.98/1.61 = ( X22 = Y2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_56_not__Cons__self2,axiom,
% 2.98/1.61 ! [X: message_p_v,Xs: list_message_p_v] :
% 2.98/1.61 ( ( cons_message_p_v @ X @ Xs )
% 2.98/1.61 != Xs ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_57_not__Cons__self2,axiom,
% 2.98/1.61 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
% 2.98/1.61 ( ( cons_l1083444861t_unit @ X @ Xs )
% 2.98/1.61 != Xs ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_58_not__Cons__self2,axiom,
% 2.98/1.61 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( cons_l233104475ge_p_v @ X @ Xs )
% 2.98/1.61 != Xs ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_59_not__Cons__self2,axiom,
% 2.98/1.61 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( cons_c1162654829t_unit @ X @ Xs )
% 2.98/1.61 != Xs ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_60_n__not__Suc__n,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( N3
% 2.98/1.61 != ( suc @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_61_Suc__inject,axiom,
% 2.98/1.61 ! [X: nat,Y: nat] :
% 2.98/1.61 ( ( ( suc @ X )
% 2.98/1.61 = ( suc @ Y ) )
% 2.98/1.61 => ( X = Y ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_62_linorder__neqE__nat,axiom,
% 2.98/1.61 ! [X: nat,Y: nat] :
% 2.98/1.61 ( ( X != Y )
% 2.98/1.61 => ( ~ ( ord_less_nat @ X @ Y )
% 2.98/1.61 => ( ord_less_nat @ Y @ X ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_63_infinite__descent,axiom,
% 2.98/1.61 ! [P: nat > $o,N3: nat] :
% 2.98/1.61 ( ! [N: nat] :
% 2.98/1.61 ( ~ ( P @ N )
% 2.98/1.61 => ? [M2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M2 @ N )
% 2.98/1.61 & ~ ( P @ M2 ) ) )
% 2.98/1.61 => ( P @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_64_nat__less__induct,axiom,
% 2.98/1.61 ! [P: nat > $o,N3: nat] :
% 2.98/1.61 ( ! [N: nat] :
% 2.98/1.61 ( ! [M2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M2 @ N )
% 2.98/1.61 => ( P @ M2 ) )
% 2.98/1.61 => ( P @ N ) )
% 2.98/1.61 => ( P @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_65_less__irrefl__nat,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_66_less__not__refl3,axiom,
% 2.98/1.61 ! [S: nat,T: nat] :
% 2.98/1.61 ( ( ord_less_nat @ S @ T )
% 2.98/1.61 => ( S != T ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_67_less__not__refl2,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] :
% 2.98/1.61 ( ( ord_less_nat @ N3 @ M )
% 2.98/1.61 => ( M != N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_68_mem__Collect__eq,axiom,
% 2.98/1.61 ! [A: nat,P: nat > $o] :
% 2.98/1.61 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 2.98/1.61 = ( P @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_69_Collect__mem__eq,axiom,
% 2.98/1.61 ! [A8: set_nat] :
% 2.98/1.61 ( ( collect_nat
% 2.98/1.61 @ ^ [X3: nat] : ( member_nat @ X3 @ A8 ) )
% 2.98/1.61 = A8 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_70_less__not__refl,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_71_nat__neq__iff,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( M != N3 )
% 2.98/1.61 = ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 | ( ord_less_nat @ N3 @ M ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_72_size__neq__size__imp__neq,axiom,
% 2.98/1.61 ! [X: list_message_p_v,Y: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ X )
% 2.98/1.61 != ( size_s1168481041ge_p_v @ Y ) )
% 2.98/1.61 => ( X != Y ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_73_size__neq__size__imp__neq,axiom,
% 2.98/1.61 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ X )
% 2.98/1.61 != ( size_s1406904903t_unit @ Y ) )
% 2.98/1.61 => ( X != Y ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_74_neq__if__length__neq,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 != ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( Xs != Ys ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_75_neq__if__length__neq,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 != ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( Xs != Ys ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_76_Ex__list__of__length,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ? [Xs2: list_message_p_v] :
% 2.98/1.61 ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_77_Ex__list__of__length,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ? [Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_78_not0__implies__Suc,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( N3 != zero_zero_nat )
% 2.98/1.61 => ? [M3: nat] :
% 2.98/1.61 ( N3
% 2.98/1.61 = ( suc @ M3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_79_old_Onat_Oinducts,axiom,
% 2.98/1.61 ! [P: nat > $o,Nat: nat] :
% 2.98/1.61 ( ( P @ zero_zero_nat )
% 2.98/1.61 => ( ! [Nat3: nat] :
% 2.98/1.61 ( ( P @ Nat3 )
% 2.98/1.61 => ( P @ ( suc @ Nat3 ) ) )
% 2.98/1.61 => ( P @ Nat ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_80_old_Onat_Oexhaust,axiom,
% 2.98/1.61 ! [Y: nat] :
% 2.98/1.61 ( ( Y != zero_zero_nat )
% 2.98/1.61 => ~ ! [Nat3: nat] :
% 2.98/1.61 ( Y
% 2.98/1.61 != ( suc @ Nat3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_81_Zero__not__Suc,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( zero_zero_nat
% 2.98/1.61 != ( suc @ M ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_82_Zero__neq__Suc,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( zero_zero_nat
% 2.98/1.61 != ( suc @ M ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_83_Suc__neq__Zero,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( ( suc @ M )
% 2.98/1.61 != zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_84_zero__induct,axiom,
% 2.98/1.61 ! [P: nat > $o,K: nat] :
% 2.98/1.61 ( ( P @ K )
% 2.98/1.61 => ( ! [N: nat] :
% 2.98/1.61 ( ( P @ ( suc @ N ) )
% 2.98/1.61 => ( P @ N ) )
% 2.98/1.61 => ( P @ zero_zero_nat ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_85_diff__induct,axiom,
% 2.98/1.61 ! [P: nat > nat > $o,M: nat,N3: nat] :
% 2.98/1.61 ( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
% 2.98/1.61 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 2.98/1.61 => ( ! [X2: nat,Y3: nat] :
% 2.98/1.61 ( ( P @ X2 @ Y3 )
% 2.98/1.61 => ( P @ ( suc @ X2 ) @ ( suc @ Y3 ) ) )
% 2.98/1.61 => ( P @ M @ N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_86_nat__induct,axiom,
% 2.98/1.61 ! [P: nat > $o,N3: nat] :
% 2.98/1.61 ( ( P @ zero_zero_nat )
% 2.98/1.61 => ( ! [N: nat] :
% 2.98/1.61 ( ( P @ N )
% 2.98/1.61 => ( P @ ( suc @ N ) ) )
% 2.98/1.61 => ( P @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_87_nat_OdiscI,axiom,
% 2.98/1.61 ! [Nat: nat,X22: nat] :
% 2.98/1.61 ( ( Nat
% 2.98/1.61 = ( suc @ X22 ) )
% 2.98/1.61 => ( Nat != zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_88_old_Onat_Odistinct_I1_J,axiom,
% 2.98/1.61 ! [Nat2: nat] :
% 2.98/1.61 ( zero_zero_nat
% 2.98/1.61 != ( suc @ Nat2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_89_old_Onat_Odistinct_I2_J,axiom,
% 2.98/1.61 ! [Nat2: nat] :
% 2.98/1.61 ( ( suc @ Nat2 )
% 2.98/1.61 != zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_90_nat_Odistinct_I1_J,axiom,
% 2.98/1.61 ! [X22: nat] :
% 2.98/1.61 ( zero_zero_nat
% 2.98/1.61 != ( suc @ X22 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_91_bot__nat__0_Oextremum__strict,axiom,
% 2.98/1.61 ! [A: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_92_infinite__descent0,axiom,
% 2.98/1.61 ! [P: nat > $o,N3: nat] :
% 2.98/1.61 ( ( P @ zero_zero_nat )
% 2.98/1.61 => ( ! [N: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.98/1.61 => ( ~ ( P @ N )
% 2.98/1.61 => ? [M2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M2 @ N )
% 2.98/1.61 & ~ ( P @ M2 ) ) ) )
% 2.98/1.61 => ( P @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_93_gr__implies__not0,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( N3 != zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_94_less__zeroE,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_95_not__less0,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_96_not__gr0,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 2.98/1.61 = ( N3 = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_97_gr0I,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( N3 != zero_zero_nat )
% 2.98/1.61 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_98_not__less__less__Suc__eq,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] :
% 2.98/1.61 ( ~ ( ord_less_nat @ N3 @ M )
% 2.98/1.61 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 2.98/1.61 = ( N3 = M ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_99_strict__inc__induct,axiom,
% 2.98/1.61 ! [I: nat,J: nat,P: nat > $o] :
% 2.98/1.61 ( ( ord_less_nat @ I @ J )
% 2.98/1.61 => ( ! [I2: nat] :
% 2.98/1.61 ( ( J
% 2.98/1.61 = ( suc @ I2 ) )
% 2.98/1.61 => ( P @ I2 ) )
% 2.98/1.61 => ( ! [I2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I2 @ J )
% 2.98/1.61 => ( ( P @ ( suc @ I2 ) )
% 2.98/1.61 => ( P @ I2 ) ) )
% 2.98/1.61 => ( P @ I ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_100_less__Suc__induct,axiom,
% 2.98/1.61 ! [I: nat,J: nat,P: nat > nat > $o] :
% 2.98/1.61 ( ( ord_less_nat @ I @ J )
% 2.98/1.61 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 2.98/1.61 => ( ! [I2: nat,J2: nat,K2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I2 @ J2 )
% 2.98/1.61 => ( ( ord_less_nat @ J2 @ K2 )
% 2.98/1.61 => ( ( P @ I2 @ J2 )
% 2.98/1.61 => ( ( P @ J2 @ K2 )
% 2.98/1.61 => ( P @ I2 @ K2 ) ) ) ) )
% 2.98/1.61 => ( P @ I @ J ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_101_less__trans__Suc,axiom,
% 2.98/1.61 ! [I: nat,J: nat,K: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I @ J )
% 2.98/1.61 => ( ( ord_less_nat @ J @ K )
% 2.98/1.61 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_102_Suc__less__SucD,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 2.98/1.61 => ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_103_less__antisym,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] :
% 2.98/1.61 ( ~ ( ord_less_nat @ N3 @ M )
% 2.98/1.61 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 2.98/1.61 => ( M = N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_104_Suc__less__eq2,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ N3 ) @ M )
% 2.98/1.61 = ( ? [M4: nat] :
% 2.98/1.61 ( ( M
% 2.98/1.61 = ( suc @ M4 ) )
% 2.98/1.61 & ( ord_less_nat @ N3 @ M4 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_105_All__less__Suc,axiom,
% 2.98/1.61 ! [N3: nat,P: nat > $o] :
% 2.98/1.61 ( ( ! [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 2.98/1.61 => ( P @ I3 ) ) )
% 2.98/1.61 = ( ( P @ N3 )
% 2.98/1.61 & ! [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ N3 )
% 2.98/1.61 => ( P @ I3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_106_not__less__eq,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ~ ( ord_less_nat @ M @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ N3 @ ( suc @ M ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_107_less__Suc__eq,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 2.98/1.61 = ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 | ( M = N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_108_Ex__less__Suc,axiom,
% 2.98/1.61 ! [N3: nat,P: nat > $o] :
% 2.98/1.61 ( ( ? [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 2.98/1.61 & ( P @ I3 ) ) )
% 2.98/1.61 = ( ( P @ N3 )
% 2.98/1.61 | ? [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ N3 )
% 2.98/1.61 & ( P @ I3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_109_less__SucI,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( ord_less_nat @ M @ ( suc @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_110_less__SucE,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 2.98/1.61 => ( ~ ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( M = N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_111_Suc__lessI,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( ( ( suc @ M )
% 2.98/1.61 != N3 )
% 2.98/1.61 => ( ord_less_nat @ ( suc @ M ) @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_112_Suc__lessE,axiom,
% 2.98/1.61 ! [I: nat,K: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 2.98/1.61 => ~ ! [J2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I @ J2 )
% 2.98/1.61 => ( K
% 2.98/1.61 != ( suc @ J2 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_113_Suc__lessD,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ M ) @ N3 )
% 2.98/1.61 => ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_114_Nat_OlessE,axiom,
% 2.98/1.61 ! [I: nat,K: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I @ K )
% 2.98/1.61 => ( ( K
% 2.98/1.61 != ( suc @ I ) )
% 2.98/1.61 => ~ ! [J2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I @ J2 )
% 2.98/1.61 => ( K
% 2.98/1.61 != ( suc @ J2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_115_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,A0: message_p_v > config256849571t_unit,A1: list_message_p_v,A2: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: message_p_v > config256849571t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_116_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 2.98/1.61 => ( ! [F: config256849571t_unit > config256849571t_unit,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_117_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,A0: message_p_v > message_p_v,A1: list_message_p_v,A2: list_message_p_v] :
% 2.98/1.61 ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: message_p_v > message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_118_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_message_p_v > message_p_v ) > list_l1619404459ge_p_v > list_message_p_v > $o,A0: list_message_p_v > message_p_v,A1: list_l1619404459ge_p_v,A2: list_message_p_v] :
% 2.98/1.61 ( ! [F: list_message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: list_message_p_v > message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_message_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_119_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > list_message_p_v ) > list_message_p_v > list_l1619404459ge_p_v > $o,A0: message_p_v > list_message_p_v,A1: list_message_p_v,A2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ! [F: message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: message_p_v > list_message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_120_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,A0: config256849571t_unit > message_p_v,A1: list_c1059388851t_unit,A2: list_message_p_v] :
% 2.98/1.61 ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 2.98/1.61 => ( ! [F: config256849571t_unit > message_p_v,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_121_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_message_p_v > list_message_p_v ) > list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v,A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ! [F: list_message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: list_message_p_v > list_message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_122_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_message_p_v > config256849571t_unit ) > list_l1619404459ge_p_v > list_c1059388851t_unit > $o,A0: list_message_p_v > config256849571t_unit,A1: list_l1619404459ge_p_v,A2: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [F: list_message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: list_message_p_v > config256849571t_unit,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_123_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_c1059388851t_unit > message_p_v ) > list_l611321411t_unit > list_message_p_v > $o,A0: list_c1059388851t_unit > message_p_v,A1: list_l611321411t_unit,A2: list_message_p_v] :
% 2.98/1.61 ( ! [F: list_c1059388851t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_li307996205t_unit @ X_1 )
% 2.98/1.61 => ( ! [F: list_c1059388851t_unit > message_p_v,A9: list_c1059388851t_unit,As: list_l611321411t_unit,Bs: list_message_p_v] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_l1083444861t_unit @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_124_map__tailrec__rev_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > list_c1059388851t_unit ) > list_message_p_v > list_l611321411t_unit > $o,A0: message_p_v > list_c1059388851t_unit,A1: list_message_p_v,A2: list_l611321411t_unit] :
% 2.98/1.61 ( ! [F: message_p_v > list_c1059388851t_unit,X_1: list_l611321411t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [F: message_p_v > list_c1059388851t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_l611321411t_unit] :
% 2.98/1.61 ( ( P @ F @ As @ ( cons_l1083444861t_unit @ ( F @ A9 ) @ Bs ) )
% 2.98/1.61 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 2.98/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_125_list__nonempty__induct,axiom,
% 2.98/1.61 ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
% 2.98/1.61 ( ( Xs != nil_li307996205t_unit )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 2.98/1.61 ( ( Xs2 != nil_li307996205t_unit )
% 2.98/1.61 => ( ( P @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_126_list__nonempty__induct,axiom,
% 2.98/1.61 ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
% 2.98/1.61 ( ( Xs != nil_list_message_p_v )
% 2.98/1.61 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 2.98/1.61 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( Xs2 != nil_list_message_p_v )
% 2.98/1.61 => ( ( P @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_127_list__nonempty__induct,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
% 2.98/1.61 ( ( Xs != nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v] :
% 2.98/1.61 ( ( Xs2 != nil_message_p_v )
% 2.98/1.61 => ( ( P @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_128_list__nonempty__induct,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( Xs != nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( Xs2 != nil_co1338500125t_unit )
% 2.98/1.61 => ( ( P @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_129_successively_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 2.98/1.61 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 2.98/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 2.98/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 2.98/1.61 ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
% 2.98/1.61 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_130_successively_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 2.98/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 2.98/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
% 2.98/1.61 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_131_successively_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 2.98/1.61 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 2.98/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 2.98/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 2.98/1.61 ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
% 2.98/1.61 => ( P @ P2 @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_132_successively_Oinduct,axiom,
% 2.98/1.61 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 2.98/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
% 2.98/1.61 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_133_remdups__adj_Oinduct,axiom,
% 2.98/1.61 ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
% 2.98/1.61 ( ( P @ nil_li307996205t_unit )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 2.98/1.61 ( ( ( X2 = Y3 )
% 2.98/1.61 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ( ( ( X2 != Y3 )
% 2.98/1.61 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
% 2.98/1.61 => ( P @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
% 2.98/1.61 => ( P @ A0 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_134_remdups__adj_Oinduct,axiom,
% 2.98/1.61 ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ nil_list_message_p_v )
% 2.98/1.61 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 2.98/1.61 => ( ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( ( X2 = Y3 )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ( ( ( X2 != Y3 )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
% 2.98/1.61 => ( P @ A0 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_135_remdups__adj_Oinduct,axiom,
% 2.98/1.61 ! [P: list_message_p_v > $o,A0: list_message_p_v] :
% 2.98/1.61 ( ( P @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 2.98/1.61 => ( ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 2.98/1.61 ( ( ( X2 = Y3 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ( ( ( X2 != Y3 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
% 2.98/1.61 => ( P @ A0 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_136_remdups__adj_Oinduct,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( X2 = Y3 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 2.98/1.61 => ( ( ( X2 != Y3 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
% 2.98/1.61 => ( P @ A0 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_137_sorted__wrt_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 2.98/1.61 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 2.98/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Ys2: list_l611321411t_unit] :
% 2.98/1.61 ( ( P @ P2 @ Ys2 )
% 2.98/1.61 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_138_sorted__wrt_Oinduct,axiom,
% 2.98/1.61 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 2.98/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ P2 @ Ys2 )
% 2.98/1.61 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 2.98/1.61 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 2.98/1.61 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 2.98/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( P @ P2 @ Ys2 )
% 2.98/1.61 => ( P @ P2 @ ( cons_message_p_v @ X2 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 2.98/1.61 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ P2 @ Ys2 )
% 2.98/1.61 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_141_remdups__adj_Ocases,axiom,
% 2.98/1.61 ! [X: list_l611321411t_unit] :
% 2.98/1.61 ( ( X != nil_li307996205t_unit )
% 2.98/1.61 => ( ! [X2: list_c1059388851t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 2.98/1.61 => ~ ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_142_remdups__adj_Ocases,axiom,
% 2.98/1.61 ! [X: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( X != nil_list_message_p_v )
% 2.98/1.61 => ( ! [X2: list_message_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 2.98/1.61 => ~ ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_143_remdups__adj_Ocases,axiom,
% 2.98/1.61 ! [X: list_message_p_v] :
% 2.98/1.61 ( ( X != nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 2.98/1.61 => ~ ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_144_remdups__adj_Ocases,axiom,
% 2.98/1.61 ! [X: list_c1059388851t_unit] :
% 2.98/1.61 ( ( X != nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 2.98/1.61 => ~ ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_145_transpose_Ocases,axiom,
% 2.98/1.61 ! [X: list_l1584713811t_unit] :
% 2.98/1.61 ( ( X != nil_li2108369341t_unit )
% 2.98/1.61 => ( ! [Xss: list_l1584713811t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1777019405t_unit @ nil_li307996205t_unit @ Xss ) )
% 2.98/1.61 => ~ ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Xss: list_l1584713811t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1777019405t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_146_transpose_Ocases,axiom,
% 2.98/1.61 ! [X: list_l1341496881ge_p_v] :
% 2.98/1.61 ( ( X != nil_li835338673ge_p_v )
% 2.98/1.61 => ( ! [Xss: list_l1341496881ge_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1383421281ge_p_v @ nil_list_message_p_v @ Xss ) )
% 2.98/1.61 => ~ ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Xss: list_l1341496881ge_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1383421281ge_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_147_transpose_Ocases,axiom,
% 2.98/1.61 ! [X: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( X != nil_list_message_p_v )
% 2.98/1.61 => ( ! [Xss: list_l1619404459ge_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
% 2.98/1.61 => ~ ! [X2: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_148_transpose_Ocases,axiom,
% 2.98/1.61 ! [X: list_l611321411t_unit] :
% 2.98/1.61 ( ( X != nil_li307996205t_unit )
% 2.98/1.61 => ( ! [Xss: list_l611321411t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
% 2.98/1.61 => ~ ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
% 2.98/1.61 ( X
% 2.98/1.61 != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_149_shuffles_Oinduct,axiom,
% 2.98/1.61 ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [Xs2: list_l1619404459ge_p_v] : ( P @ Xs2 @ nil_list_message_p_v )
% 2.98/1.61 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 2.98/1.61 ( ( P @ Xs2 @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_150_shuffles_Oinduct,axiom,
% 2.98/1.61 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 2.98/1.61 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_151_shuffles_Oinduct,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 2.98/1.61 => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_152_induct__list012,axiom,
% 2.98/1.61 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 2.98/1.61 ( ( P @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 2.98/1.61 => ( ! [X2: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
% 2.98/1.61 ( ( P @ Zs )
% 2.98/1.61 => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_153_induct__list012,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ Zs )
% 2.98/1.61 => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_154_splice_Oinduct,axiom,
% 2.98/1.61 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 2.98/1.61 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( P @ Ys2 @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_155_splice_Oinduct,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ Ys2 @ Xs2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 ) )
% 2.98/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_156_list__induct2_H,axiom,
% 2.98/1.61 ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys: list_message_p_v] :
% 2.98/1.61 ( ( P @ nil_message_p_v @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_message_p_v )
% 2.98/1.61 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_157_list__induct2_H,axiom,
% 2.98/1.61 ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_158_list__induct2_H,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys: list_message_p_v] :
% 2.98/1.61 ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_message_p_v )
% 2.98/1.61 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_159_list__induct2_H,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_160_neq__Nil__conv,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v] :
% 2.98/1.61 ( ( Xs != nil_message_p_v )
% 2.98/1.61 = ( ? [Y4: message_p_v,Ys3: list_message_p_v] :
% 2.98/1.61 ( Xs
% 2.98/1.61 = ( cons_message_p_v @ Y4 @ Ys3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_161_neq__Nil__conv,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( Xs != nil_co1338500125t_unit )
% 2.98/1.61 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 2.98/1.61 ( Xs
% 2.98/1.61 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_162_list_Oinducts,axiom,
% 2.98/1.61 ! [P: list_message_p_v > $o,List: list_message_p_v] :
% 2.98/1.61 ( ( P @ nil_message_p_v )
% 2.98/1.61 => ( ! [X12: message_p_v,X23: list_message_p_v] :
% 2.98/1.61 ( ( P @ X23 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X12 @ X23 ) ) )
% 2.98/1.61 => ( P @ List ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_163_list_Oinducts,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X12: config256849571t_unit,X23: list_c1059388851t_unit] :
% 2.98/1.61 ( ( P @ X23 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X12 @ X23 ) ) )
% 2.98/1.61 => ( P @ List ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_164_list_Oexhaust,axiom,
% 2.98/1.61 ! [Y: list_message_p_v] :
% 2.98/1.61 ( ( Y != nil_message_p_v )
% 2.98/1.61 => ~ ! [X212: message_p_v,X223: list_message_p_v] :
% 2.98/1.61 ( Y
% 2.98/1.61 != ( cons_message_p_v @ X212 @ X223 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_165_list_Oexhaust,axiom,
% 2.98/1.61 ! [Y: list_c1059388851t_unit] :
% 2.98/1.61 ( ( Y != nil_co1338500125t_unit )
% 2.98/1.61 => ~ ! [X212: config256849571t_unit,X223: list_c1059388851t_unit] :
% 2.98/1.61 ( Y
% 2.98/1.61 != ( cons_c1162654829t_unit @ X212 @ X223 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_166_list_OdiscI,axiom,
% 2.98/1.61 ! [List: list_message_p_v,X21: message_p_v,X222: list_message_p_v] :
% 2.98/1.61 ( ( List
% 2.98/1.61 = ( cons_message_p_v @ X21 @ X222 ) )
% 2.98/1.61 => ( List != nil_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_167_list_OdiscI,axiom,
% 2.98/1.61 ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 2.98/1.61 ( ( List
% 2.98/1.61 = ( cons_c1162654829t_unit @ X21 @ X222 ) )
% 2.98/1.61 => ( List != nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_168_list_Odistinct_I1_J,axiom,
% 2.98/1.61 ! [X21: message_p_v,X222: list_message_p_v] :
% 2.98/1.61 ( nil_message_p_v
% 2.98/1.61 != ( cons_message_p_v @ X21 @ X222 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_169_list_Odistinct_I1_J,axiom,
% 2.98/1.61 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 2.98/1.61 ( nil_co1338500125t_unit
% 2.98/1.61 != ( cons_c1162654829t_unit @ X21 @ X222 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_170_length__induct,axiom,
% 2.98/1.61 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [Xs2: list_c1059388851t_unit] :
% 2.98/1.61 ( ! [Ys4: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys4 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 2.98/1.61 => ( P @ Ys4 ) )
% 2.98/1.61 => ( P @ Xs2 ) )
% 2.98/1.61 => ( P @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_171_lift__Suc__mono__less__iff,axiom,
% 2.98/1.61 ! [F2: nat > nat,N3: nat,M: nat] :
% 2.98/1.61 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 2.98/1.61 => ( ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 2.98/1.61 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_172_lift__Suc__mono__less__iff,axiom,
% 2.98/1.61 ! [F2: nat > int,N3: nat,M: nat] :
% 2.98/1.61 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 2.98/1.61 => ( ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 2.98/1.61 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_173_lift__Suc__mono__less,axiom,
% 2.98/1.61 ! [F2: nat > nat,N3: nat,N4: nat] :
% 2.98/1.61 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 2.98/1.61 => ( ( ord_less_nat @ N3 @ N4 )
% 2.98/1.61 => ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_174_lift__Suc__mono__less,axiom,
% 2.98/1.61 ! [F2: nat > int,N3: nat,N4: nat] :
% 2.98/1.61 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 2.98/1.61 => ( ( ord_less_nat @ N3 @ N4 )
% 2.98/1.61 => ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_175_less__Suc__eq__0__disj,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 2.98/1.61 = ( ( M = zero_zero_nat )
% 2.98/1.61 | ? [J3: nat] :
% 2.98/1.61 ( ( M
% 2.98/1.61 = ( suc @ J3 ) )
% 2.98/1.61 & ( ord_less_nat @ J3 @ N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_176_gr0__implies__Suc,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 2.98/1.61 => ? [M3: nat] :
% 2.98/1.61 ( N3
% 2.98/1.61 = ( suc @ M3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_177_All__less__Suc2,axiom,
% 2.98/1.61 ! [N3: nat,P: nat > $o] :
% 2.98/1.61 ( ( ! [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 2.98/1.61 => ( P @ I3 ) ) )
% 2.98/1.61 = ( ( P @ zero_zero_nat )
% 2.98/1.61 & ! [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ N3 )
% 2.98/1.61 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_178_gr0__conv__Suc,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 2.98/1.61 = ( ? [M5: nat] :
% 2.98/1.61 ( N3
% 2.98/1.61 = ( suc @ M5 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_179_Ex__less__Suc2,axiom,
% 2.98/1.61 ! [N3: nat,P: nat > $o] :
% 2.98/1.61 ( ( ? [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 2.98/1.61 & ( P @ I3 ) ) )
% 2.98/1.61 = ( ( P @ zero_zero_nat )
% 2.98/1.61 | ? [I3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I3 @ N3 )
% 2.98/1.61 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_180_length__Suc__conv,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,N3: nat] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( suc @ N3 ) )
% 2.98/1.61 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 2.98/1.61 ( ( Xs
% 2.98/1.61 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 2.98/1.61 & ( ( size_s1406904903t_unit @ Ys3 )
% 2.98/1.61 = N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_181_Suc__length__conv,axiom,
% 2.98/1.61 ! [N3: nat,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( suc @ N3 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Xs ) )
% 2.98/1.61 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 2.98/1.61 ( ( Xs
% 2.98/1.61 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 2.98/1.61 & ( ( size_s1406904903t_unit @ Ys3 )
% 2.98/1.61 = N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_182_list_Osize_I3_J,axiom,
% 2.98/1.61 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 2.98/1.61 = zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_183_list_Osize_I3_J,axiom,
% 2.98/1.61 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 = zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_184_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_185_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_186_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_187_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_188_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_189_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_190_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_191_list__induct3,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_192_list__induct2,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_193_list__induct2,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_194_list__induct2,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_195_list__induct2,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys ) )
% 2.98/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 2.98/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 2.98/1.61 => ( ( P @ Xs2 @ Ys2 )
% 2.98/1.61 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 2.98/1.61 => ( P @ Xs @ Ys ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_196_infiniteExecutionCfg_Oelims,axiom,
% 2.98/1.61 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 2.98/1.61 ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 2.98/1.61 = Y )
% 2.98/1.61 => ( ( ( Xc = zero_zero_nat )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( Xc
% 2.98/1.61 = ( suc @ N ) )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_197_infiniteExecutionMsg_Oelims,axiom,
% 2.98/1.61 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 2.98/1.61 ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 2.98/1.61 = Y )
% 2.98/1.61 => ( ( ( Xc = zero_zero_nat )
% 2.98/1.61 => ( Y != nil_message_p_v ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( Xc
% 2.98/1.61 = ( suc @ N ) )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_198_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 2.98/1.61 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 2.98/1.61 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.98/1.61 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_199_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 2.98/1.61 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 2.98/1.61 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.98/1.61 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_200_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 2.98/1.61 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 2.98/1.61 = nil_message_p_v ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_201_not__gr__zero,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 2.98/1.61 = ( N3 = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_202_length__Cons,axiom,
% 2.98/1.61 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 2.98/1.61 = ( suc @ ( size_s1406904903t_unit @ Xs ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_203_zero__reorient,axiom,
% 2.98/1.61 ! [X: nat] :
% 2.98/1.61 ( ( zero_zero_nat = X )
% 2.98/1.61 = ( X = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_204_zero__reorient,axiom,
% 2.98/1.61 ! [X: int] :
% 2.98/1.61 ( ( zero_zero_int = X )
% 2.98/1.61 = ( X = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_205_gr__zeroI,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( N3 != zero_zero_nat )
% 2.98/1.61 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_206_not__less__zero,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_207_gr__implies__not__zero,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( N3 != zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_208_zero__less__iff__neq__zero,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 2.98/1.61 = ( N3 != zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_209_n__lists__Nil,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ( N3 = zero_zero_nat )
% 2.98/1.61 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 2.98/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
% 2.98/1.61 & ( ( N3 != zero_zero_nat )
% 2.98/1.61 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 2.98/1.61 = nil_li307996205t_unit ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_210_n__lists__Nil,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ( N3 = zero_zero_nat )
% 2.98/1.61 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 2.98/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
% 2.98/1.61 & ( ( N3 != zero_zero_nat )
% 2.98/1.61 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 2.98/1.61 = nil_list_message_p_v ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 2.98/1.61 = Y )
% 2.98/1.61 => ( ( ( Xc = zero_zero_nat )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( Xc
% 2.98/1.61 = ( suc @ N ) )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_212_n__lists_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
% 2.98/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_213_n__lists_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Xs: list_message_p_v] :
% 2.98/1.61 ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
% 2.98/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 2.98/1.61 = Y )
% 2.98/1.61 => ( ( ( Xc = zero_zero_nat )
% 2.98/1.61 => ( Y != nil_message_p_v ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( Xc
% 2.98/1.61 = ( suc @ N ) )
% 2.98/1.61 => ( Y
% 2.98/1.61 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.98/1.61 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.98/1.61 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 2.98/1.61 = nil_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 2.98/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 2.98/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 2.98/1.61 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 2.98/1.61 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_219_less__numeral__extra_I3_J,axiom,
% 2.98/1.61 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_220_less__numeral__extra_I3_J,axiom,
% 2.98/1.61 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_221_product__lists_Osimps_I1_J,axiom,
% 2.98/1.61 ( ( produc663212148t_unit @ nil_li307996205t_unit )
% 2.98/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_222_product__lists_Osimps_I1_J,axiom,
% 2.98/1.61 ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
% 2.98/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_223_subseqs_Osimps_I1_J,axiom,
% 2.98/1.61 ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
% 2.98/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_224_subseqs_Osimps_I1_J,axiom,
% 2.98/1.61 ( ( subseqs_message_p_v @ nil_message_p_v )
% 2.98/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_225_length__code,axiom,
% 2.98/1.61 ( size_s1406904903t_unit
% 2.98/1.61 = ( gen_le193291088t_unit @ zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_226_gen__length__code_I2_J,axiom,
% 2.98/1.61 ! [N3: nat,X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 2.98/1.61 ( ( gen_le193291088t_unit @ N3 @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 2.98/1.61 = ( gen_le193291088t_unit @ ( suc @ N3 ) @ Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_227_gen__length__code_I1_J,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( gen_le193291088t_unit @ N3 @ nil_co1338500125t_unit )
% 2.98/1.61 = N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_228_gen__length__code_I1_J,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( gen_le697204914ge_p_v @ N3 @ nil_message_p_v )
% 2.98/1.61 = N3 ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_229_insert__Nil,axiom,
% 2.98/1.61 ! [X: message_p_v] :
% 2.98/1.61 ( ( insert_message_p_v @ X @ nil_message_p_v )
% 2.98/1.61 = ( cons_message_p_v @ X @ nil_message_p_v ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_230_insert__Nil,axiom,
% 2.98/1.61 ! [X: config256849571t_unit] :
% 2.98/1.61 ( ( insert1308755079t_unit @ X @ nil_co1338500125t_unit )
% 2.98/1.61 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_231_nths__singleton,axiom,
% 2.98/1.61 ! [A8: set_nat,X: message_p_v] :
% 2.98/1.61 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 2.98/1.61 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 2.98/1.61 = ( cons_message_p_v @ X @ nil_message_p_v ) ) )
% 2.98/1.61 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 2.98/1.61 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 2.98/1.61 = nil_message_p_v ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_232_nths__singleton,axiom,
% 2.98/1.61 ! [A8: set_nat,X: config256849571t_unit] :
% 2.98/1.61 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 2.98/1.61 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 2.98/1.61 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 2.98/1.61 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 2.98/1.61 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 2.98/1.61 = nil_co1338500125t_unit ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_233_of__nat__0__less__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_234_of__nat__0__less__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_235_of__nat__eq__iff,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ( semiri2019852685at_int @ M )
% 2.98/1.61 = ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( M = N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_236_nths__nil,axiom,
% 2.98/1.61 ! [A8: set_nat] :
% 2.98/1.61 ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A8 )
% 2.98/1.61 = nil_co1338500125t_unit ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_237_nths__nil,axiom,
% 2.98/1.61 ! [A8: set_nat] :
% 2.98/1.61 ( ( nths_message_p_v @ nil_message_p_v @ A8 )
% 2.98/1.61 = nil_message_p_v ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_238_of__nat__0,axiom,
% 2.98/1.61 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 2.98/1.61 = zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_239_of__nat__0,axiom,
% 2.98/1.61 ( ( semiri2019852685at_int @ zero_zero_nat )
% 2.98/1.61 = zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_240_of__nat__0__eq__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( zero_zero_nat
% 2.98/1.61 = ( semiri1382578993at_nat @ N3 ) )
% 2.98/1.61 = ( zero_zero_nat = N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_241_of__nat__0__eq__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( zero_zero_int
% 2.98/1.61 = ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( zero_zero_nat = N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_242_of__nat__eq__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( ( ( semiri1382578993at_nat @ M )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( M = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_243_of__nat__eq__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( ( ( semiri2019852685at_int @ M )
% 2.98/1.61 = zero_zero_int )
% 2.98/1.61 = ( M = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_244_of__nat__less__iff,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_245_of__nat__less__iff,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_246_of__nat__less__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_247_of__nat__less__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_248_of__nat__neq__0,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( semiri1382578993at_nat @ ( suc @ N3 ) )
% 2.98/1.61 != zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_249_of__nat__neq__0,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( semiri2019852685at_int @ ( suc @ N3 ) )
% 2.98/1.61 != zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_250_less__imp__of__nat__less,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_251_less__imp__of__nat__less,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ M @ N3 )
% 2.98/1.61 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_252_of__nat__less__imp__less,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 2.98/1.61 => ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_253_of__nat__less__imp__less,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 => ( ord_less_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_254_nths__all,axiom,
% 2.98/1.61 ! [Xs: list_c1059388851t_unit,I4: set_nat] :
% 2.98/1.61 ( ! [I2: nat] :
% 2.98/1.61 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
% 2.98/1.61 => ( member_nat @ I2 @ I4 ) )
% 2.98/1.61 => ( ( nths_c890550943t_unit @ Xs @ I4 )
% 2.98/1.61 = Xs ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_255_pos__int__cases,axiom,
% 2.98/1.61 ! [K: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ K )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( K
% 2.98/1.61 = ( semiri2019852685at_int @ N ) )
% 2.98/1.61 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_256_zero__less__imp__eq__int,axiom,
% 2.98/1.61 ! [K: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ K )
% 2.98/1.61 => ? [N: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.98/1.61 & ( K
% 2.98/1.61 = ( semiri2019852685at_int @ N ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_257_list__ex1__simps_I1_J,axiom,
% 2.98/1.61 ! [P: config256849571t_unit > $o] :
% 2.98/1.61 ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_258_list__ex1__simps_I1_J,axiom,
% 2.98/1.61 ! [P: message_p_v > $o] :
% 2.98/1.61 ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_259_nat__int__comparison_I2_J,axiom,
% 2.98/1.61 ( ord_less_nat
% 2.98/1.61 = ( ^ [A10: nat,B: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A10 ) @ ( semiri2019852685at_int @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_260_int__ops_I1_J,axiom,
% 2.98/1.61 ( ( semiri2019852685at_int @ zero_zero_nat )
% 2.98/1.61 = zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_261_neg__int__cases,axiom,
% 2.98/1.61 ! [K: int] :
% 2.98/1.61 ( ( ord_less_int @ K @ zero_zero_int )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( K
% 2.98/1.61 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 2.98/1.61 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_262_neg__equal__iff__equal,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( ( uminus_uminus_int @ A )
% 2.98/1.61 = ( uminus_uminus_int @ B2 ) )
% 2.98/1.61 = ( A = B2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_263_add_Oinverse__inverse,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = A ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_264_add_Oinverse__neutral,axiom,
% 2.98/1.61 ( ( uminus_uminus_int @ zero_zero_int )
% 2.98/1.61 = zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_265_neg__0__equal__iff__equal,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( zero_zero_int
% 2.98/1.61 = ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( zero_zero_int = A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_266_neg__equal__0__iff__equal,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ( uminus_uminus_int @ A )
% 2.98/1.61 = zero_zero_int )
% 2.98/1.61 = ( A = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_267_equal__neg__zero,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( A
% 2.98/1.61 = ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( A = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_268_neg__equal__zero,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ( uminus_uminus_int @ A )
% 2.98/1.61 = A )
% 2.98/1.61 = ( A = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_269_neg__less__iff__less,axiom,
% 2.98/1.61 ! [B2: int,A: int] :
% 2.98/1.61 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_int @ A @ B2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_270_less__neg__neg,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_271_neg__less__pos,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 2.98/1.61 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_272_neg__0__less__iff__less,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_273_neg__less__0__iff__less,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 2.98/1.61 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_274_negative__eq__positive,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] :
% 2.98/1.61 ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( semiri2019852685at_int @ M ) )
% 2.98/1.61 = ( ( N3 = zero_zero_nat )
% 2.98/1.61 & ( M = zero_zero_nat ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_275_negative__zless,axiom,
% 2.98/1.61 ! [N3: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ ( semiri2019852685at_int @ M ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_276_minus__less__iff,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
% 2.98/1.61 = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_277_less__minus__iff,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
% 2.98/1.61 = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_278_verit__negate__coefficient_I2_J,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( ord_less_int @ A @ B2 )
% 2.98/1.61 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_279_minus__equation__iff,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( ( uminus_uminus_int @ A )
% 2.98/1.61 = B2 )
% 2.98/1.61 = ( ( uminus_uminus_int @ B2 )
% 2.98/1.61 = A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_280_equation__minus__iff,axiom,
% 2.98/1.61 ! [A: int,B2: int] :
% 2.98/1.61 ( ( A
% 2.98/1.61 = ( uminus_uminus_int @ B2 ) )
% 2.98/1.61 = ( B2
% 2.98/1.61 = ( uminus_uminus_int @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_281_int__cases,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ! [N: nat] :
% 2.98/1.61 ( Z2
% 2.98/1.61 != ( semiri2019852685at_int @ N ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( Z2
% 2.98/1.61 != ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_282_int__of__nat__induct,axiom,
% 2.98/1.61 ! [P: int > $o,Z2: int] :
% 2.98/1.61 ( ! [N: nat] : ( P @ ( semiri2019852685at_int @ N ) )
% 2.98/1.61 => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) )
% 2.98/1.61 => ( P @ Z2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_283_int__cases4,axiom,
% 2.98/1.61 ! [M: int] :
% 2.98/1.61 ( ! [N: nat] :
% 2.98/1.61 ( M
% 2.98/1.61 != ( semiri2019852685at_int @ N ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.98/1.61 => ( M
% 2.98/1.61 != ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_284_verit__comp__simplify1_I1_J,axiom,
% 2.98/1.61 ! [A: nat] :
% 2.98/1.61 ~ ( ord_less_nat @ A @ A ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_285_verit__comp__simplify1_I1_J,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ~ ( ord_less_int @ A @ A ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_286_int__cases3,axiom,
% 2.98/1.61 ! [K: int] :
% 2.98/1.61 ( ( K != zero_zero_int )
% 2.98/1.61 => ( ! [N: nat] :
% 2.98/1.61 ( ( K
% 2.98/1.61 = ( semiri2019852685at_int @ N ) )
% 2.98/1.61 => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.98/1.61 => ~ ! [N: nat] :
% 2.98/1.61 ( ( K
% 2.98/1.61 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 2.98/1.61 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_287_negative__zless__0,axiom,
% 2.98/1.61 ! [N3: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_288_negD,axiom,
% 2.98/1.61 ! [X: int] :
% 2.98/1.61 ( ( ord_less_int @ X @ zero_zero_int )
% 2.98/1.61 => ? [N: nat] :
% 2.98/1.61 ( X
% 2.98/1.61 = ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_289_zero__less__nat__eq,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_290_of__int__0__less__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_291_of__int__0,axiom,
% 2.98/1.61 ( ( ring_1_of_int_int @ zero_zero_int )
% 2.98/1.61 = zero_zero_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_292_of__int__0__eq__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( zero_zero_int
% 2.98/1.61 = ( ring_1_of_int_int @ Z2 ) )
% 2.98/1.61 = ( Z2 = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_293_of__int__eq__0__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ( ring_1_of_int_int @ Z2 )
% 2.98/1.61 = zero_zero_int )
% 2.98/1.61 = ( Z2 = zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_294_of__int__less__iff,axiom,
% 2.98/1.61 ! [W: int,Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ W @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_295_zless__nat__conj,axiom,
% 2.98/1.61 ! [W: int,Z2: int] :
% 2.98/1.61 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 2.98/1.61 = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 2.98/1.61 & ( ord_less_int @ W @ Z2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_296_nat__zminus__int,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) ) )
% 2.98/1.61 = zero_zero_nat ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_297_of__int__less__0__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 2.98/1.61 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_298_nat__zero__as__int,axiom,
% 2.98/1.61 ( zero_zero_nat
% 2.98/1.61 = ( nat2 @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_299_nat__mono__iff,axiom,
% 2.98/1.61 ! [Z2: int,W: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 2.98/1.61 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ W @ Z2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_300_zless__nat__eq__int__zless,axiom,
% 2.98/1.61 ! [M: nat,Z2: int] :
% 2.98/1.61 ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ ( semiri2019852685at_int @ M ) @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_301_of__int__pos,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 2.98/1.61 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_302_of__nat__less__of__int__iff,axiom,
% 2.98/1.61 ! [N3: nat,X: int] :
% 2.98/1.61 ( ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ ( ring_1_of_int_int @ X ) )
% 2.98/1.61 = ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ X ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_303_split__nat,axiom,
% 2.98/1.61 ! [P: nat > $o,I: int] :
% 2.98/1.61 ( ( P @ ( nat2 @ I ) )
% 2.98/1.61 = ( ! [N5: nat] :
% 2.98/1.61 ( ( I
% 2.98/1.61 = ( semiri2019852685at_int @ N5 ) )
% 2.98/1.61 => ( P @ N5 ) )
% 2.98/1.61 & ( ( ord_less_int @ I @ zero_zero_int )
% 2.98/1.61 => ( P @ zero_zero_nat ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_304_one__less__nat__eq,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_305_nat__less__iff,axiom,
% 2.98/1.61 ! [W: int,M: nat] :
% 2.98/1.61 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 2.98/1.61 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 2.98/1.61 = ( ord_less_int @ W @ ( semiri2019852685at_int @ M ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_306_le__zero__eq,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
% 2.98/1.61 = ( N3 = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_307_neg__le__iff__le,axiom,
% 2.98/1.61 ! [B2: int,A: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_308_of__nat__le__iff,axiom,
% 2.98/1.61 ! [M: nat,N3: nat] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( ord_less_eq_nat @ M @ N3 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_309_of__nat__1,axiom,
% 2.98/1.61 ( ( semiri2019852685at_int @ one_one_nat )
% 2.98/1.61 = one_one_int ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_310_of__nat__1__eq__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( one_one_int
% 2.98/1.61 = ( semiri2019852685at_int @ N3 ) )
% 2.98/1.61 = ( N3 = one_one_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_311_of__nat__eq__1__iff,axiom,
% 2.98/1.61 ! [N3: nat] :
% 2.98/1.61 ( ( ( semiri2019852685at_int @ N3 )
% 2.98/1.61 = one_one_int )
% 2.98/1.61 = ( N3 = one_one_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_312_neg__0__le__iff__le,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_313_neg__le__0__iff__le,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 2.98/1.61 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_314_less__eq__neg__nonpos,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 2.98/1.61 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_315_neg__less__eq__nonneg,axiom,
% 2.98/1.61 ! [A: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 2.98/1.61 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_316_of__nat__le__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 2.98/1.61 = ( M = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_317_of__nat__le__0__iff,axiom,
% 2.98/1.61 ! [M: nat] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
% 2.98/1.61 = ( M = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_318_nat__1,axiom,
% 2.98/1.61 ( ( nat2 @ one_one_int )
% 2.98/1.61 = ( suc @ zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_319_nat__le__0,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 2.98/1.61 => ( ( nat2 @ Z2 )
% 2.98/1.61 = zero_zero_nat ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_320_nat__0__iff,axiom,
% 2.98/1.61 ! [I: int] :
% 2.98/1.61 ( ( ( nat2 @ I )
% 2.98/1.61 = zero_zero_nat )
% 2.98/1.61 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_321_of__int__le__0__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 2.98/1.61 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_322_of__int__0__le__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 2.98/1.61 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_323_of__int__less__1__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 2.98/1.61 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_324_of__int__1__less__iff,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 2.98/1.61 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(fact_325_of__int__nonneg,axiom,
% 2.98/1.61 ! [Z2: int] :
% 2.98/1.61 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 2.98/1.62 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_326_verit__comp__simplify1_I3_J,axiom,
% 2.98/1.62 ! [B3: nat,A11: nat] :
% 2.98/1.62 ( ( ~ ( ord_less_eq_nat @ B3 @ A11 ) )
% 2.98/1.62 = ( ord_less_nat @ A11 @ B3 ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_327_verit__comp__simplify1_I3_J,axiom,
% 2.98/1.62 ! [B3: int,A11: int] :
% 2.98/1.62 ( ( ~ ( ord_less_eq_int @ B3 @ A11 ) )
% 2.98/1.62 = ( ord_less_int @ A11 @ B3 ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_328_le__numeral__extra_I4_J,axiom,
% 2.98/1.62 ord_less_eq_int @ one_one_int @ one_one_int ).
% 2.98/1.62
% 2.98/1.62 thf(fact_329_one__reorient,axiom,
% 2.98/1.62 ! [X: int] :
% 2.98/1.62 ( ( one_one_int = X )
% 2.98/1.62 = ( X = one_one_int ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_330_lift__Suc__antimono__le,axiom,
% 2.98/1.62 ! [F2: nat > int,N3: nat,N4: nat] :
% 2.98/1.62 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ N ) )
% 2.98/1.62 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 2.98/1.62 => ( ord_less_eq_int @ ( F2 @ N4 ) @ ( F2 @ N3 ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_331_lift__Suc__mono__le,axiom,
% 2.98/1.62 ! [F2: nat > int,N3: nat,N4: nat] :
% 2.98/1.62 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 2.98/1.62 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 2.98/1.62 => ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_332_zero__le,axiom,
% 2.98/1.62 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_333_le__numeral__extra_I3_J,axiom,
% 2.98/1.62 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 2.98/1.62
% 2.98/1.62 thf(fact_334_le__numeral__extra_I3_J,axiom,
% 2.98/1.62 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 2.98/1.62
% 2.98/1.62 thf(fact_335_less__numeral__extra_I4_J,axiom,
% 2.98/1.62 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_336_less__numeral__extra_I4_J,axiom,
% 2.98/1.62 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_337_of__nat__mono,axiom,
% 2.98/1.62 ! [I: nat,J: nat] :
% 2.98/1.62 ( ( ord_less_eq_nat @ I @ J )
% 2.98/1.62 => ( ord_less_eq_int @ ( semiri2019852685at_int @ I ) @ ( semiri2019852685at_int @ J ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_338_less__minus__one__simps_I4_J,axiom,
% 2.98/1.62 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(fact_339_less__minus__one__simps_I2_J,axiom,
% 2.98/1.62 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 2.98/1.62
% 2.98/1.62 thf(fact_340_zero__neq__neg__one,axiom,
% 2.98/1.62 ( zero_zero_int
% 2.98/1.62 != ( uminus_uminus_int @ one_one_int ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(conj_0,conjecture,
% 2.98/1.62 prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ).
% 2.98/1.62 ------------------------
% 2.98/1.65 % (21036)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/275Mi)
% 2.98/1.65 % (21037)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/18Mi)
% 2.98/1.66 % (21032)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/4Mi)
% 2.98/1.66 % (21031)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/183Mi)
% 2.98/1.66 % (21037)Instruction limit reached!
% 2.98/1.66 % (21037)------------------------------
% 2.98/1.66 % (21037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (21037)Termination reason: Unknown
% 2.98/1.66 % (21037)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (21037)Memory used [KB]: 1791
% 2.98/1.66 % (21037)Time elapsed: 0.008 s
% 2.98/1.66 % (21037)Instructions burned: 19 (million)
% 2.98/1.66 % (21037)------------------------------
% 2.98/1.66 % (21037)------------------------------
% 2.98/1.66 % (21033)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/27Mi)
% 2.98/1.66 % (21034)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/2Mi)
% 2.98/1.66 % (21035)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/2Mi)
% 2.98/1.66 % (21034)Instruction limit reached!
% 2.98/1.66 % (21034)------------------------------
% 2.98/1.66 % (21034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (21034)Termination reason: Unknown
% 2.98/1.66 % (21034)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (21034)Memory used [KB]: 1407
% 2.98/1.66 % (21034)Time elapsed: 0.004 s
% 2.98/1.66 % (21034)Instructions burned: 2 (million)
% 2.98/1.66 % (21034)------------------------------
% 2.98/1.66 % (21034)------------------------------
% 2.98/1.66 % (21035)Instruction limit reached!
% 2.98/1.66 % (21035)------------------------------
% 2.98/1.66 % (21035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (21035)Termination reason: Unknown
% 2.98/1.66 % (21035)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (21035)Memory used [KB]: 1407
% 2.98/1.66 % (21035)Time elapsed: 0.004 s
% 2.98/1.66 % (21035)Instructions burned: 3 (million)
% 2.98/1.66 % (21035)------------------------------
% 2.98/1.66 % (21035)------------------------------
% 2.98/1.66 % (21032)Instruction limit reached!
% 2.98/1.66 % (21032)------------------------------
% 2.98/1.66 % (21032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (21032)Termination reason: Unknown
% 2.98/1.66 % (21032)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (21032)Memory used [KB]: 1407
% 2.98/1.66 % (21032)Time elapsed: 0.005 s
% 2.98/1.66 % (21032)Instructions burned: 5 (million)
% 2.98/1.66 % (21032)------------------------------
% 2.98/1.66 % (21032)------------------------------
% 2.98/1.67 % (21038)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/3Mi)
% 2.98/1.67 % (21038)Instruction limit reached!
% 2.98/1.67 % (21038)------------------------------
% 2.98/1.67 % (21038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.67 % (21038)Termination reason: Unknown
% 2.98/1.67 % (21038)Termination phase: shuffling
% 2.98/1.67
% 2.98/1.67 % (21038)Memory used [KB]: 1407
% 2.98/1.67 % (21038)Time elapsed: 0.003 s
% 2.98/1.67 % (21038)Instructions burned: 3 (million)
% 2.98/1.67 % (21038)------------------------------
% 2.98/1.67 % (21038)------------------------------
% 2.98/1.67 % (21033)Instruction limit reached!
% 2.98/1.67 % (21033)------------------------------
% 2.98/1.67 % (21033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.67 % (21033)Termination reason: Unknown
% 2.98/1.67 % (21033)Termination phase: shuffling
% 2.98/1.67
% 2.98/1.67 % (21033)Memory used [KB]: 1918
% 2.98/1.67 % (21033)Time elapsed: 0.019 s
% 2.98/1.67 % (21033)Instructions burned: 27 (million)
% 2.98/1.67 % (21033)------------------------------
% 2.98/1.67 % (21033)------------------------------
% 2.98/1.68 % (21040)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/15Mi)
% 2.98/1.68 % (21039)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/37Mi)
% 2.98/1.68 % (21041)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/3Mi)
% 2.98/1.68 % (21042)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_20758 for (2999ds/1041Mi)
% 2.98/1.68 % (21041)Instruction limit reached!
% 2.98/1.68 % (21041)------------------------------
% 2.98/1.68 % (21041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.68 % (21041)Termination reason: Unknown
% 2.98/1.68 % (21041)Termination phase: shuffling
% 2.98/1.68
% 2.98/1.68 % (21041)Memory used [KB]: 1407
% 2.98/1.68 % (21041)Time elapsed: 0.004 s
% 2.98/1.68 % (21041)Instructions burned: 3 (million)
% 2.98/1.68 % (21041)------------------------------
% 2.98/1.68 % (21041)------------------------------
% 2.98/1.68 % (21036)First to succeed.
% 2.98/1.68 % (21036)Refutation found. Thanks to Tanya!
% 2.98/1.68 % SZS status Theorem for DTF2THF_20758
% 2.98/1.68 % SZS output start Proof for DTF2THF_20758
% 2.98/1.68 thf(type_def_5, type, p: $tType).
% 2.98/1.68 thf(type_def_6, type, s: $tType).
% 2.98/1.68 thf(type_def_7, type, messageValue_v: $tType).
% 2.98/1.68 thf(type_def_9, type, message_p_v: $tType).
% 2.98/1.68 thf(type_def_10, type, nat: $tType).
% 2.98/1.68 thf(type_def_11, type, config256849571t_unit: $tType).
% 2.98/1.68 thf(type_def_12, type, list_c1059388851t_unit: $tType).
% 2.98/1.68 thf(type_def_13, type, list_message_p_v: $tType).
% 2.98/1.68 thf(type_def_14, type, int: $tType).
% 2.98/1.68 thf(type_def_15, type, list_l611321411t_unit: $tType).
% 2.98/1.68 thf(type_def_16, type, list_l1619404459ge_p_v: $tType).
% 2.98/1.68 thf(type_def_17, type, list_l1584713811t_unit: $tType).
% 2.98/1.68 thf(type_def_18, type, list_l1341496881ge_p_v: $tType).
% 2.98/1.68 thf(type_def_19, type, set_nat: $tType).
% 2.98/1.68 thf(func_def_0, type, list_l1584713811t_unit: $tType).
% 2.98/1.68 thf(func_def_1, type, list_l611321411t_unit: $tType).
% 2.98/1.68 thf(func_def_2, type, list_c1059388851t_unit: $tType).
% 2.98/1.68 thf(func_def_3, type, config256849571t_unit: $tType).
% 2.98/1.68 thf(func_def_4, type, list_l1341496881ge_p_v: $tType).
% 2.98/1.68 thf(func_def_5, type, list_l1619404459ge_p_v: $tType).
% 2.98/1.68 thf(func_def_6, type, list_message_p_v: $tType).
% 2.98/1.68 thf(func_def_7, type, message_p_v: $tType).
% 2.98/1.68 thf(func_def_8, type, messageValue_v: $tType).
% 2.98/1.68 thf(func_def_9, type, set_nat: $tType).
% 2.98/1.68 thf(func_def_10, type, nat: $tType).
% 2.98/1.68 thf(func_def_11, type, int: $tType).
% 2.98/1.68 thf(func_def_12, type, s: $tType).
% 2.98/1.68 thf(func_def_13, type, p: $tType).
% 2.98/1.68 thf(func_def_14, type, fLPThe9398366_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > $o).
% 2.98/1.68 thf(func_def_15, type, fLPThe1519354920_p_v_s: config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_16, type, fLPThe536531371_p_v_s: config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > list_message_p_v).
% 2.98/1.68 thf(func_def_17, type, one_one_int: int).
% 2.98/1.68 thf(func_def_18, type, one_one_nat: nat).
% 2.98/1.68 thf(func_def_19, type, uminus_uminus_int: int > int).
% 2.98/1.68 thf(func_def_20, type, zero_zero_int: int).
% 2.98/1.68 thf(func_def_21, type, zero_zero_nat: nat).
% 2.98/1.68 thf(func_def_22, type, nat2: int > nat).
% 2.98/1.68 thf(func_def_23, type, ring_1_of_int_int: int > int).
% 2.98/1.68 thf(func_def_24, type, prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 2.98/1.68 thf(func_def_25, type, prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o).
% 2.98/1.68 thf(func_def_26, type, prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o).
% 2.98/1.68 thf(func_def_27, type, prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o).
% 2.98/1.68 thf(func_def_28, type, gen_le193291088t_unit: nat > list_c1059388851t_unit > nat).
% 2.98/1.68 thf(func_def_29, type, gen_le697204914ge_p_v: nat > list_message_p_v > nat).
% 2.98/1.68 thf(func_def_30, type, insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_31, type, insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_32, type, cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_33, type, cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_34, type, cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit).
% 2.98/1.68 thf(func_def_35, type, cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v).
% 2.98/1.68 thf(func_def_36, type, cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit).
% 2.98/1.68 thf(func_def_37, type, cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v).
% 2.98/1.68 thf(func_def_38, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_39, type, nil_message_p_v: list_message_p_v).
% 2.98/1.68 thf(func_def_40, type, nil_li307996205t_unit: list_l611321411t_unit).
% 2.98/1.68 thf(func_def_41, type, nil_list_message_p_v: list_l1619404459ge_p_v).
% 2.98/1.68 thf(func_def_42, type, nil_li2108369341t_unit: list_l1584713811t_unit).
% 2.98/1.68 thf(func_def_43, type, nil_li835338673ge_p_v: list_l1341496881ge_p_v).
% 2.98/1.68 thf(func_def_44, type, list_e1598815642t_unit: (config256849571t_unit > $o) > list_c1059388851t_unit > $o).
% 2.98/1.68 thf(func_def_45, type, list_ex1_message_p_v: (message_p_v > $o) > list_message_p_v > $o).
% 2.98/1.68 thf(func_def_46, type, n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit).
% 2.98/1.68 thf(func_def_47, type, n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v).
% 2.98/1.68 thf(func_def_48, type, nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_49, type, nths_message_p_v: list_message_p_v > set_nat > list_message_p_v).
% 2.98/1.68 thf(func_def_50, type, produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit).
% 2.98/1.68 thf(func_def_51, type, produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v).
% 2.98/1.68 thf(func_def_52, type, subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit).
% 2.98/1.68 thf(func_def_53, type, subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v).
% 2.98/1.68 thf(func_def_54, type, suc: nat > nat).
% 2.98/1.68 thf(func_def_55, type, semiri2019852685at_int: nat > int).
% 2.98/1.68 thf(func_def_56, type, semiri1382578993at_nat: nat > nat).
% 2.98/1.68 thf(func_def_57, type, size_s1406904903t_unit: list_c1059388851t_unit > nat).
% 2.98/1.68 thf(func_def_58, type, size_s1168481041ge_p_v: list_message_p_v > nat).
% 2.98/1.68 thf(func_def_59, type, size_s503142615t_unit: list_l611321411t_unit > nat).
% 2.98/1.68 thf(func_def_60, type, size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat).
% 2.98/1.68 thf(func_def_61, type, ord_less_int: int > int > $o).
% 2.98/1.68 thf(func_def_62, type, ord_less_nat: nat > nat > $o).
% 2.98/1.68 thf(func_def_63, type, ord_less_eq_int: int > int > $o).
% 2.98/1.68 thf(func_def_64, type, ord_less_eq_nat: nat > nat > $o).
% 2.98/1.68 thf(func_def_65, type, collect_nat: (nat > $o) > set_nat).
% 2.98/1.68 thf(func_def_66, type, member_nat: nat > set_nat > $o).
% 2.98/1.68 thf(func_def_67, type, cfg: config256849571t_unit).
% 2.98/1.68 thf(func_def_68, type, fe: nat > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_69, type, m: nat).
% 2.98/1.68 thf(func_def_70, type, n: nat).
% 2.98/1.68 thf(func_def_71, type, na: nat).
% 2.98/1.68 thf(func_def_85, type, sP0: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o).
% 2.98/1.68 thf(func_def_86, type, sP1: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o).
% 2.98/1.68 thf(func_def_87, type, sK2: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_88, type, sK3: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_89, type, sK4: nat > nat > nat).
% 2.98/1.68 thf(func_def_90, type, sK5: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_91, type, sK6: list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_92, type, sK7: nat > nat).
% 2.98/1.68 thf(func_def_93, type, sK8: (nat > $o) > nat).
% 2.98/1.68 thf(func_def_94, type, sK9: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_95, type, sK10: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_96, type, sK11: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_97, type, sK12: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_98, type, sK13: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_99, type, sK14: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_100, type, sK15: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_101, type, sK16: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_102, type, sK17: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_103, type, sK18: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_104, type, sK19: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_105, type, sK20: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_106, type, sK21: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_107, type, sK22: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_108, type, sK23: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_109, type, sK24: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_110, type, sK25: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_111, type, sK26: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_112, type, sK27: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_113, type, sK28: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_114, type, sK29: (nat > $o) > nat).
% 2.98/1.68 thf(func_def_115, type, sK30: (nat > $o) > nat).
% 2.98/1.68 thf(func_def_116, type, sK31: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_117, type, sK32: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_118, type, sK33: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_119, type, sK34: (nat > nat > $o) > nat).
% 2.98/1.68 thf(func_def_120, type, sK35: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_121, type, sK36: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 2.98/1.68 thf(func_def_122, type, sK37: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_123, type, sK38: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_124, type, sK39: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_125, type, sK40: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_126, type, sK41: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_127, type, sK42: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_128, type, sK43: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 2.98/1.68 thf(func_def_129, type, sK44: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_130, type, sK45: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_131, type, sK46: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_132, type, sK47: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.68 thf(func_def_133, type, sK48: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_134, type, sK49: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_135, type, sK50: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 2.98/1.68 thf(func_def_136, type, sK51: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_137, type, sK52: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_138, type, sK53: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 2.98/1.68 thf(func_def_139, type, sK54: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_140, type, sK55: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 2.98/1.68 thf(func_def_141, type, sK56: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_142, type, sK57: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_143, type, sK58: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_144, type, sK59: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_145, type, sK60: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 2.98/1.68 thf(func_def_146, type, sK61: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_147, type, sK62: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 2.98/1.68 thf(func_def_148, type, sK63: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_149, type, sK64: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_150, type, sK65: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_151, type, sK66: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_152, type, sK67: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_153, type, sK68: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_154, type, sK69: (list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_155, type, sK70: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_156, type, sK71: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_157, type, sK72: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_158, type, sK73: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_159, type, sK74: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_160, type, sK75: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_161, type, sK76: nat > (nat > $o) > nat).
% 2.98/1.68 thf(func_def_162, type, sK77: nat > (nat > $o) > nat).
% 2.98/1.68 thf(func_def_163, type, sK78: list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_164, type, sK79: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_165, type, sK80: list_c1059388851t_unit > list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_166, type, sK81: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_167, type, sK82: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_168, type, sK83: nat > nat > nat).
% 2.98/1.68 thf(func_def_169, type, sK84: nat > nat > nat).
% 2.98/1.68 thf(func_def_170, type, sK85: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_171, type, sK86: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_172, type, sK87: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_173, type, sK88: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_174, type, sK89: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_175, type, sK90: (nat > $o) > nat > nat).
% 2.98/1.68 thf(func_def_176, type, sK91: (nat > $o) > nat).
% 2.98/1.68 thf(func_def_177, type, sK92: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_178, type, sK93: list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_179, type, sK94: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_180, type, sK95: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_181, type, sK96: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_182, type, sK97: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_183, type, sK98: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_184, type, sK99: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_185, type, sK100: list_c1059388851t_unit > nat > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_186, type, sK101: list_c1059388851t_unit > nat > config256849571t_unit).
% 2.98/1.68 thf(func_def_187, type, sK102: nat > nat).
% 2.98/1.68 thf(func_def_188, type, sK103: (nat > nat) > nat).
% 2.98/1.68 thf(func_def_189, type, sK104: (nat > $o) > nat).
% 2.98/1.68 thf(func_def_190, type, sK105: (nat > nat) > nat).
% 2.98/1.68 thf(func_def_191, type, sK106: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_192, type, sK107: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_193, type, sK108: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_194, type, sK109: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.68 thf(func_def_195, type, sK110: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_196, type, sK111: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.68 thf(func_def_197, type, sK112: nat > (nat > $o) > nat).
% 2.98/1.68 thf(func_def_198, type, sK113: nat > (nat > $o) > nat).
% 2.98/1.68 thf(func_def_199, type, sK114: nat > list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.68 thf(func_def_200, type, sK115: nat > list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_201, type, sK116: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_202, type, sK117: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_203, type, sK118: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_204, type, sK119: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_205, type, sK120: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_206, type, sK121: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_207, type, sK122: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_208, type, sK123: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_209, type, sK124: list_c1059388851t_unit > config256849571t_unit).
% 2.98/1.69 thf(func_def_210, type, sK125: list_c1059388851t_unit > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_211, type, sK126: nat > nat > nat).
% 2.98/1.69 thf(func_def_212, type, sK127: nat > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_213, type, sK128: nat > nat).
% 2.98/1.69 thf(func_def_214, type, sK129: nat > nat).
% 2.98/1.69 thf(func_def_215, type, sK130: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_216, type, sK131: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_217, type, sK132: (nat > $o) > nat).
% 2.98/1.69 thf(func_def_218, type, sK133: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 2.98/1.69 thf(func_def_219, type, sK134: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.69 thf(func_def_220, type, sK135: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_221, type, sK136: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_222, type, sK137: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_223, type, sK138: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.69 thf(func_def_224, type, sK139: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_225, type, sK140: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_226, type, sK141: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.69 thf(func_def_227, type, sK142: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_228, type, sK143: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 2.98/1.69 thf(func_def_229, type, sK144: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 2.98/1.69 thf(func_def_230, type, sK145: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 2.98/1.69 thf(func_def_231, type, sK146: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 2.98/1.69 thf(func_def_233, type, ph148: !>[X0: $tType]:(X0)).
% 2.98/1.69 thf(f1472,plain,(
% 2.98/1.69 $false),
% 2.98/1.69 inference(subsumption_resolution,[status(thm)],[f1471,f1347])).
% 2.98/1.69 thf(f1347,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) = $true)),
% 2.98/1.69 inference(cnf_transformation,[status(thm)],[f618])).
% 2.98/1.69 thf(f618,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) = $true)),
% 2.98/1.69 inference(fool_elimination,[status(thm)],[f617])).
% 2.98/1.69 thf(f617,plain,(
% 2.98/1.69 (ord_less_nat @ m @ na)),
% 2.98/1.69 inference(rectify,[status(thm)],[f1])).
% 2.98/1.69 thf(f1,axiom,(
% 2.98/1.69 (ord_less_nat @ m @ na)),
% 2.98/1.69 file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',fact_0__092_060open_062m_A_060_An_092_060close_062)).
% 2.98/1.69 thf(f1471,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) != $true)),
% 2.98/1.69 inference(trivial_inequality_removal,[status(thm)],[f1468])).
% 2.98/1.69 thf(f1468,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) != $true) | ($true != $true)),
% 2.98/1.69 inference(superposition,[status(thm)],[f1175,f1351])).
% 2.98/1.69 thf(f1351,plain,(
% 2.98/1.69 ((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) = $true) | ((ord_less_nat @ m @ na) != $true)),
% 2.98/1.69 inference(cnf_transformation,[status(thm)],[f869])).
% 2.98/1.69 thf(f869,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) != $true) | ((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) = $true)),
% 2.98/1.69 inference(ennf_transformation,[status(thm)],[f550])).
% 2.98/1.69 thf(f550,plain,(
% 2.98/1.69 ((ord_less_nat @ m @ na) = $true) => ((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) = $true)),
% 2.98/1.69 inference(fool_elimination,[status(thm)],[f549])).
% 2.98/1.69 thf(f549,plain,(
% 2.98/1.69 (ord_less_nat @ m @ na) => (prefix1615116500t_unit @ (fe @ m) @ (fe @ na))),
% 2.98/1.69 inference(rectify,[status(thm)],[f3])).
% 2.98/1.69 thf(f3,axiom,(
% 2.98/1.69 (ord_less_nat @ m @ na) => (prefix1615116500t_unit @ (fe @ m) @ (fe @ na))),
% 2.98/1.69 file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',fact_2_IA_I1_J)).
% 2.98/1.69 thf(f1175,plain,(
% 2.98/1.69 ((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) != $true)),
% 2.98/1.69 inference(cnf_transformation,[status(thm)],[f819])).
% 2.98/1.69 thf(f819,plain,(
% 2.98/1.69 ((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) != $true)),
% 2.98/1.69 inference(flattening,[status(thm)],[f364])).
% 2.98/1.69 thf(f364,plain,(
% 2.98/1.69 ~((prefix1615116500t_unit @ (fe @ m) @ (fe @ na)) = $true)),
% 2.98/1.69 inference(fool_elimination,[status(thm)],[f363])).
% 2.98/1.69 thf(f363,plain,(
% 2.98/1.69 ~(prefix1615116500t_unit @ (fe @ m) @ (fe @ na))),
% 2.98/1.69 inference(rectify,[status(thm)],[f343])).
% 2.98/1.69 thf(f343,negated_conjecture,(
% 2.98/1.69 ~(prefix1615116500t_unit @ (fe @ m) @ (fe @ na))),
% 2.98/1.69 inference(negated_conjecture,[status(cth)],[f342])).
% 2.98/1.69 thf(f342,conjecture,(
% 2.98/1.69 (prefix1615116500t_unit @ (fe @ m) @ (fe @ na))),
% 2.98/1.69 file('/export/starexec/sandbox2/tmp/tmp.dO3cIqbV2J/DTF2THF_20758.p',conj_0)).
% 2.98/1.69 % SZS output end Proof for DTF2THF_20758
% 2.98/1.69 % (21036)------------------------------
% 2.98/1.69 % (21036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.69 % (21036)Termination reason: Refutation
% 2.98/1.69
% 2.98/1.69 % (21036)Memory used [KB]: 7164
% 2.98/1.69 % (21036)Time elapsed: 0.034 s
% 2.98/1.69 % (21036)Instructions burned: 95 (million)
% 2.98/1.69 % (21036)------------------------------
% 2.98/1.69 % (21036)------------------------------
% 2.98/1.69 % (21030)Success in time 0.066 s
%------------------------------------------------------------------------------