%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP058^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 08:55:12 AM UTC 2026
% Result : Theorem 3.10s 1.68s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 40 ( 4 ~; 0 |; 0 &; 36 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 126 usr; 9 con; 0-5 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 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,
list_l611321411t_unit: $tType ).
thf(type_def_15,type,
list_l1619404459ge_p_v: $tType ).
thf(type_def_16,type,
list_nat: $tType ).
thf(type_def_17,type,
list_list_nat: $tType ).
thf(type_def_18,type,
set_nat: $tType ).
thf(func_def_0,type,
list_l611321411t_unit: $tType ).
thf(func_def_1,type,
list_c1059388851t_unit: $tType ).
thf(func_def_2,type,
config256849571t_unit: $tType ).
thf(func_def_3,type,
list_l1619404459ge_p_v: $tType ).
thf(func_def_4,type,
list_message_p_v: $tType ).
thf(func_def_5,type,
list_list_nat: $tType ).
thf(func_def_6,type,
message_p_v: $tType ).
thf(func_def_7,type,
messageValue_v: $tType ).
thf(func_def_8,type,
list_nat: $tType ).
thf(func_def_9,type,
set_nat: $tType ).
thf(func_def_10,type,
nat: $tType ).
thf(func_def_11,type,
s: $tType ).
thf(func_def_12,type,
p: $tType ).
thf(func_def_13,type,
fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
thf(func_def_14,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_15,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_16,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_17,type,
zero_zero_nat: nat ).
thf(func_def_18,type,
bind_c1439720399t_unit: list_c1059388851t_unit > ( config256849571t_unit > list_c1059388851t_unit ) > list_c1059388851t_unit ).
thf(func_def_19,type,
bind_c246984691ge_p_v: list_c1059388851t_unit > ( config256849571t_unit > list_message_p_v ) > list_message_p_v ).
thf(func_def_20,type,
bind_m595590011t_unit: list_message_p_v > ( message_p_v > list_c1059388851t_unit ) > list_c1059388851t_unit ).
thf(func_def_21,type,
bind_m729301831ge_p_v: list_message_p_v > ( message_p_v > list_message_p_v ) > list_message_p_v ).
thf(func_def_22,type,
count_1396868135t_unit: list_c1059388851t_unit > config256849571t_unit > nat ).
thf(func_def_23,type,
count_1322329499ge_p_v: list_message_p_v > message_p_v > nat ).
thf(func_def_24,type,
gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
thf(func_def_25,type,
gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
thf(func_def_26,type,
insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_27,type,
insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_28,type,
cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_29,type,
cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_30,type,
cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
thf(func_def_31,type,
cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(func_def_32,type,
cons_list_nat: list_nat > list_list_nat > list_list_nat ).
thf(func_def_33,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_34,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_35,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_36,type,
nil_li307996205t_unit: list_l611321411t_unit ).
thf(func_def_37,type,
nil_list_message_p_v: list_l1619404459ge_p_v ).
thf(func_def_38,type,
nil_list_nat: list_list_nat ).
thf(func_def_39,type,
nil_nat: list_nat ).
thf(func_def_40,type,
list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
thf(func_def_41,type,
list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
thf(func_def_42,type,
listre990624391t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_43,type,
listre823101243ge_p_v: ( config256849571t_unit > message_p_v > $o ) > list_c1059388851t_unit > list_message_p_v > $o ).
thf(func_def_44,type,
listre1171706563t_unit: ( message_p_v > config256849571t_unit > $o ) > list_message_p_v > list_c1059388851t_unit > $o ).
thf(func_def_45,type,
listre1295695359ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
thf(func_def_46,type,
map_ta91747645t_unit: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_47,type,
map_ta782801413ge_p_v: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_48,type,
map_ta1131406733t_unit: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_49,type,
map_ta1016577461ge_p_v: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_50,type,
member1087090632t_unit: list_c1059388851t_unit > config256849571t_unit > $o ).
thf(func_def_51,type,
member_message_p_v: list_message_p_v > message_p_v > $o ).
thf(func_def_52,type,
n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
thf(func_def_53,type,
n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
thf(func_def_54,type,
nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
thf(func_def_55,type,
nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
thf(func_def_56,type,
lexord1758866263t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_57,type,
lexord2101627499ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
thf(func_def_58,type,
ord_lexordp_nat: list_nat > list_nat > $o ).
thf(func_def_59,type,
ord_lexordp_eq_nat: list_nat > list_nat > $o ).
thf(func_def_60,type,
produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
thf(func_def_61,type,
produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
thf(func_def_62,type,
splice888123018t_unit: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_63,type,
splice_message_p_v: list_message_p_v > list_message_p_v > list_message_p_v ).
thf(func_def_64,type,
subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
thf(func_def_65,type,
subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
thf(func_def_66,type,
suc: nat > nat ).
thf(func_def_67,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_68,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_69,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_70,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_71,type,
member_nat: nat > set_nat > $o ).
thf(func_def_72,type,
cfg: config256849571t_unit ).
thf(func_def_73,type,
fStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_74,type,
fStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_75,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_76,type,
ft: nat > list_message_p_v ).
thf(func_def_93,type,
sK0: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_94,type,
sK1: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_95,type,
sK2: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_96,type,
sK3: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_97,type,
sK4: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_98,type,
sK5: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_99,type,
sK6: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_100,type,
sK7: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_101,type,
sK8: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_102,type,
sK9: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_103,type,
sK10: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_104,type,
sK11: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_105,type,
sK12: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_106,type,
sK13: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_107,type,
sK14: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit ).
thf(func_def_108,type,
sK15: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit ).
thf(func_def_109,type,
sK16: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_110,type,
sK17: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_111,type,
sK18: ( ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_112,type,
sK19: list_c1059388851t_unit > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > nat > nat ).
thf(func_def_113,type,
sK20: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_114,type,
sK21: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_115,type,
sK22: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_116,type,
sK23: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_117,type,
sK24: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_118,type,
sK25: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_119,type,
sK26: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_120,type,
sK27: ( nat > $o ) > nat ).
thf(func_def_121,type,
sK28: ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > config256849571t_unit > nat ).
thf(func_def_122,type,
sK29: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_123,type,
sK30: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_124,type,
sK31: ( list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_125,type,
sK32: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_126,type,
sK33: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_127,type,
sK34: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_128,type,
sK35: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_129,type,
sK36: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_130,type,
sK37: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_131,type,
sK38: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_132,type,
sK39: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_133,type,
sK40: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_134,type,
sK41: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_135,type,
sK42: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_136,type,
sK43: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_137,type,
sK44: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_138,type,
sK45: ( nat > $o ) > nat ).
thf(func_def_139,type,
sK46: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_140,type,
sK47: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit > config256849571t_unit > $o ).
thf(func_def_141,type,
sK48: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_142,type,
sK49: ( ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_143,type,
sK50: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_144,type,
sK51: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_145,type,
sK52: list_c1059388851t_unit > list_c1059388851t_unit ).
thf(func_def_146,type,
sK53: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_147,type,
sK54: ( nat > $o ) > nat ).
thf(func_def_148,type,
sK55: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_149,type,
sK56: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_150,type,
sK57: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > config256849571t_unit ).
thf(func_def_151,type,
sK58: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_152,type,
sK59: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_153,type,
sK60: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_155,type,
ph62:
!>[X0: $tType] : X0 ).
thf(f1053,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1027,f1003]) ).
thf(f1003,plain,
! [X2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,X0: config256849571t_unit,X1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit] :
( ( fLPThe1519354920_p_v_s @ X0 @ X1 @ X2 @ zero_zero_nat )
= ( cons_c1162654829t_unit @ X0 @ nil_co1338500125t_unit ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: config256849571t_unit,X1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,X2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
( ( fLPThe1519354920_p_v_s @ X0 @ X1 @ X2 @ zero_zero_nat )
= ( cons_c1162654829t_unit @ X0 @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',fact_2_infiniteExecutionCfg_Osimps_I1_J) ).
thf(f1027,plain,
( ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit )
!= ( fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg @ zero_zero_nat ) ),
inference(definition_unfolding,[status(thm)],[f956,f946]) ).
thf(f946,plain,
( fe
= ( fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( fe
= ( fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ),
file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',fact_1_fe__def) ).
thf(f956,plain,
( ( fe @ zero_zero_nat )
!= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
inference(cnf_transformation,[status(thm)],[f813]) ).
thf(f813,plain,
( ( fe @ zero_zero_nat )
!= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
inference(flattening,[status(thm)],[f343]) ).
thf(f343,negated_conjecture,
( ( fe @ zero_zero_nat )
!= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
inference(negated_conjecture,[status(cth)],[f342]) ).
thf(f342,conjecture,
( ( fe @ zero_zero_nat )
= ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ),
file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP058^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.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 08:24:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : ITP058^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.47 % Domain : Interactive Theorem Proving
% 0.19/0.47 % Problem : Sledgehammer FLPTheorem problem prob_419__3294834_1
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Des21]
% 0.19/0.47 % Names : FLPTheorem/prob_419__3294834_1 [Des21]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.19/0.47 % Syntax : Number of formulae : 419 ( 161 unt; 77 typ; 0 def)
% 0.19/0.47 % Number of atoms : 746 ( 494 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 11 ( 2 avg)
% 0.19/0.47 % Number of connectives : 3919 ( 250 ~; 23 |; 75 &;2899 @)
% 0.19/0.47 % ( 0 <=>; 672 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 23 ( 8 avg)
% 0.19/0.47 % Number of types : 14 ( 13 usr)
% 0.19/0.47 % Number of type conns : 722 ( 722 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 65 ( 64 usr; 8 con; 0-4 aty)
% 0.19/0.47 % Number of variables : 1489 ( 22 ^;1374 !; 93 ?;1489 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:48.868
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % Could-be-implicit typings (13)
% 0.19/0.47 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,
% 0.19/0.47 list_l611321411t_unit: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.19/0.47 list_c1059388851t_unit: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 config256849571t_unit: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.19/0.47 list_l1619404459ge_p_v: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.19/0.47 list_message_p_v: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.19/0.47 list_list_nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 message_p_v: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 0.19/0.47 messageValue_v: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.47 list_nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.19/0.47 set_nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.19/0.47 nat: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_tf__s,type,
% 0.19/0.47 s: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(ty_n_tf__p,type,
% 0.19/0.47 p: $tType ).
% 0.19/0.47
% 0.19/0.47 % Explicit typings (64)
% 0.19/0.47 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 0.19/0.47 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 0.19/0.47 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 ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 0.19/0.47 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 ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.19/0.47 minus_minus_nat: nat > nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.19/0.47 zero_zero_nat: nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Obind_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 bind_c1439720399t_unit: list_c1059388851t_unit > ( config256849571t_unit > list_c1059388851t_unit ) > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Obind_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 bind_c246984691ge_p_v: list_c1059388851t_unit > ( config256849571t_unit > list_message_p_v ) > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Obind_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 bind_m595590011t_unit: list_message_p_v > ( message_p_v > list_c1059388851t_unit ) > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Obind_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 bind_m729301831ge_p_v: list_message_p_v > ( message_p_v > list_message_p_v ) > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Ocount__list_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 count_1396868135t_unit: list_c1059388851t_unit > config256849571t_unit > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Ocount__list_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 count_1322329499ge_p_v: list_message_p_v > message_p_v > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 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,
% 0.19/0.47 cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.19/0.47 cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.47 cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.19/0.47 cons_nat: nat > list_nat > list_nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 nil_message_p_v: list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 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,
% 0.19/0.47 nil_li307996205t_unit: list_l611321411t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.19/0.47 nil_list_message_p_v: list_l1619404459ge_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 0.19/0.47 nil_list_nat: list_list_nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.19/0.47 nil_nat: list_nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 listre990624391t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 listre823101243ge_p_v: ( config256849571t_unit > message_p_v > $o ) > list_c1059388851t_unit > list_message_p_v > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 listre1171706563t_unit: ( message_p_v > config256849571t_unit > $o ) > list_message_p_v > list_c1059388851t_unit > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 listre1295695359ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 map_ta91747645t_unit: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 map_ta782801413ge_p_v: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 map_ta1131406733t_unit: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 map_ta1016577461ge_p_v: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omember_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 member1087090632t_unit: list_c1059388851t_unit > config256849571t_unit > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Omember_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 member_message_p_v: list_message_p_v > message_p_v > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oord_Olexordp__eq_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 lexord1758866263t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oord_Olexordp__eq_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 lexord2101627499ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oord__class_Olexordp_001t__Nat__Onat,type,
% 0.19/0.47 ord_lexordp_nat: list_nat > list_nat > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Nat__Onat,type,
% 0.19/0.47 ord_lexordp_eq_nat: list_nat > list_nat > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Osplice_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 splice888123018t_unit: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Osplice_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 splice_message_p_v: list_message_p_v > list_message_p_v > list_message_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.19/0.47 subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.19/0.47 subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Nat_OSuc,type,
% 0.19/0.47 suc: nat > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.19/0.47 semiri1382578993at_nat: nat > nat ).
% 0.19/0.47
% 0.19/0.47 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,
% 0.19/0.47 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.19/0.47 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.19/0.47 ord_less_nat: nat > nat > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.19/0.47 member_nat: nat > set_nat > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_cfg,type,
% 0.19/0.47 cfg: config256849571t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_fStepCfg____,type,
% 0.19/0.47 fStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_fStepMsg____,type,
% 0.19/0.47 fStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_fe____,type,
% 0.31/0.47 fe: nat > list_c1059388851t_unit ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_ft____,type,
% 0.31/0.47 ft: nat > list_message_p_v ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (341)
% 0.31/0.47 thf(fact_0_ft__def,axiom,
% 0.31/0.47 ( ft
% 0.31/0.47 = ( fLPThe536531371_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ) ).
% 0.31/0.47
% 0.31/0.47 % ft_def
% 0.31/0.47 thf(fact_1_fe__def,axiom,
% 0.31/0.47 ( fe
% 0.31/0.47 = ( fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ) ).
% 0.31/0.47
% 0.31/0.47 % fe_def
% 0.31/0.47 thf(fact_2_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.31/0.47 = ( cons_c1162654829t_unit @ Cfg @ nil_co1338500125t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionCfg.simps(1)
% 0.31/0.47 thf(fact_3_list_Oinject,axiom,
% 0.31/0.47 ! [X21: list_message_p_v,X22: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( ( cons_l233104475ge_p_v @ X21 @ X22 )
% 0.31/0.47 = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inject
% 0.31/0.47 thf(fact_4_list_Oinject,axiom,
% 0.31/0.47 ! [X21: list_c1059388851t_unit,X22: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
% 0.31/0.47 ( ( ( cons_l1083444861t_unit @ X21 @ X22 )
% 0.31/0.47 = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inject
% 0.31/0.47 thf(fact_5_list_Oinject,axiom,
% 0.31/0.47 ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 0.31/0.47 ( ( ( cons_nat @ X21 @ X22 )
% 0.31/0.47 = ( cons_nat @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inject
% 0.31/0.47 thf(fact_6_list_Oinject,axiom,
% 0.31/0.47 ! [X21: message_p_v,X22: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
% 0.31/0.47 ( ( ( cons_message_p_v @ X21 @ X22 )
% 0.31/0.47 = ( cons_message_p_v @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inject
% 0.31/0.47 thf(fact_7_list_Oinject,axiom,
% 0.31/0.47 ! [X21: config256849571t_unit,X22: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( cons_c1162654829t_unit @ X21 @ X22 )
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
% 0.31/0.47 = ( ( X21 = Y21 )
% 0.31/0.47 & ( X22 = Y22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inject
% 0.31/0.47 thf(fact_8_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: list_message_p_v,X22: list_l1619404459ge_p_v] :
% 0.31/0.47 ( nil_list_message_p_v
% 0.31/0.47 != ( cons_l233104475ge_p_v @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_9_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: list_c1059388851t_unit,X22: list_l611321411t_unit] :
% 0.31/0.47 ( nil_li307996205t_unit
% 0.31/0.47 != ( cons_l1083444861t_unit @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_10_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: nat,X22: list_nat] :
% 0.31/0.47 ( nil_nat
% 0.31/0.47 != ( cons_nat @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_11_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: message_p_v,X22: list_message_p_v] :
% 0.31/0.47 ( nil_message_p_v
% 0.31/0.47 != ( cons_message_p_v @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_12_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: config256849571t_unit,X22: list_c1059388851t_unit] :
% 0.31/0.47 ( nil_co1338500125t_unit
% 0.31/0.47 != ( cons_c1162654829t_unit @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_13_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_l1619404459ge_p_v,X21: list_message_p_v,X22: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_l233104475ge_p_v @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_list_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_14_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_l611321411t_unit,X21: list_c1059388851t_unit,X22: list_l611321411t_unit] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_l1083444861t_unit @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_li307996205t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_15_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_nat,X21: nat,X22: list_nat] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_nat @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_16_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_message_p_v,X21: message_p_v,X22: list_message_p_v] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_message_p_v @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_17_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X22: list_c1059388851t_unit] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_c1162654829t_unit @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_co1338500125t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_18_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( Y != nil_list_message_p_v )
% 0.31/0.47 => ~ ! [X212: list_message_p_v,X222: list_l1619404459ge_p_v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_l233104475ge_p_v @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_19_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_l611321411t_unit] :
% 0.31/0.47 ( ( Y != nil_li307996205t_unit )
% 0.31/0.47 => ~ ! [X212: list_c1059388851t_unit,X222: list_l611321411t_unit] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_l1083444861t_unit @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_20_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_nat] :
% 0.31/0.47 ( ( Y != nil_nat )
% 0.31/0.47 => ~ ! [X212: nat,X222: list_nat] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_nat @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_21_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_message_p_v] :
% 0.31/0.47 ( ( Y != nil_message_p_v )
% 0.31/0.47 => ~ ! [X212: message_p_v,X222: list_message_p_v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_message_p_v @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_22_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Y != nil_co1338500125t_unit )
% 0.31/0.47 => ~ ! [X212: config256849571t_unit,X222: list_c1059388851t_unit] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( cons_c1162654829t_unit @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_23_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_l1619404459ge_p_v > $o,List: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [X1: list_message_p_v,X2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X1 @ X2 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_24_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_l611321411t_unit > $o,List: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ nil_li307996205t_unit )
% 0.31/0.47 => ( ! [X1: list_c1059388851t_unit,X2: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X1 @ X2 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_25_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_nat > $o,List: list_nat] :
% 0.31/0.47 ( ( P @ nil_nat )
% 0.31/0.47 => ( ! [X1: nat,X2: list_nat] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( cons_nat @ X1 @ X2 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_26_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_message_p_v > $o,List: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_message_p_v )
% 0.31/0.47 => ( ! [X1: message_p_v,X2: list_message_p_v] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X1 @ X2 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_27_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X1: config256849571t_unit,X2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ X2 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X1 @ X2 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_28_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( Xs != nil_list_message_p_v )
% 0.31/0.47 = ( ? [Y2: list_message_p_v,Ys: list_l1619404459ge_p_v] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_l233104475ge_p_v @ Y2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_29_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_l611321411t_unit] :
% 0.31/0.47 ( ( Xs != nil_li307996205t_unit )
% 0.31/0.47 = ( ? [Y2: list_c1059388851t_unit,Ys: list_l611321411t_unit] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_l1083444861t_unit @ Y2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_30_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_nat] :
% 0.31/0.47 ( ( Xs != nil_nat )
% 0.31/0.47 = ( ? [Y2: nat,Ys: list_nat] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_nat @ Y2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_31_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_message_p_v] :
% 0.31/0.47 ( ( Xs != nil_message_p_v )
% 0.31/0.47 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_message_p_v @ Y2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_32_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Xs != nil_co1338500125t_unit )
% 0.31/0.47 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_33_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_message_p_v )
% 0.31/0.47 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_34_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_message_p_v )
% 0.31/0.47 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_35_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_36_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_37_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys2: list_nat] :
% 0.31/0.47 ( ( P @ nil_nat @ nil_nat )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_nat )
% 0.31/0.47 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_38_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_message_p_v > list_nat > $o,Xs: list_message_p_v,Ys2: list_nat] :
% 0.31/0.47 ( ( P @ nil_message_p_v @ nil_nat )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_nat )
% 0.31/0.47 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_message_p_v @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_39_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_nat > list_message_p_v > $o,Xs: list_nat,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_nat @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_message_p_v )
% 0.31/0.47 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_nat @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_40_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_l1619404459ge_p_v > list_nat > $o,Xs: list_l1619404459ge_p_v,Ys2: list_nat] :
% 0.31/0.47 ( ( P @ nil_list_message_p_v @ nil_nat )
% 0.31/0.47 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ nil_nat )
% 0.31/0.47 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_list_message_p_v @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_41_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_nat > list_l1619404459ge_p_v > $o,Xs: list_nat,Ys2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ nil_nat @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [Y3: list_message_p_v,Ys3: list_l1619404459ge_p_v] : ( P @ nil_nat @ ( cons_l233104475ge_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat,Y3: list_message_p_v,Ys3: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_42_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > list_nat > $o,Xs: list_c1059388851t_unit,Ys2: list_nat] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit @ nil_nat )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_nat )
% 0.31/0.47 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_co1338500125t_unit @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_43_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v,Ys3: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_44_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_l611321411t_unit > list_l611321411t_unit > $o,A0: list_l611321411t_unit,A1: list_l611321411t_unit] :
% 0.31/0.47 ( ! [X_1: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ X_1 )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Ys3: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_45_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 0.31/0.47 ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_46_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_47_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.31/0.47 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_48_induct__list012,axiom,
% 0.31/0.47 ! [P: list_l1619404459ge_p_v > $o,Xs: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 0.31/0.47 => ( ! [X: list_message_p_v,Y3: list_message_p_v,Zs: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_l233104475ge_p_v @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_49_induct__list012,axiom,
% 0.31/0.47 ! [P: list_l611321411t_unit > $o,Xs: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ nil_li307996205t_unit )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Zs: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_l1083444861t_unit @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_50_induct__list012,axiom,
% 0.31/0.47 ! [P: list_nat > $o,Xs: list_nat] :
% 0.31/0.47 ( ( P @ nil_nat )
% 0.31/0.47 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.31/0.47 => ( ! [X: nat,Y3: nat,Zs: list_nat] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_nat @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_51_induct__list012,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_52_induct__list012,axiom,
% 0.31/0.47 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
% 0.31/0.47 ( ( P @ Zs )
% 0.31/0.47 => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_53_min__list_Ocases,axiom,
% 0.31/0.47 ! [X3: list_nat] :
% 0.31/0.47 ( ! [X: nat,Xs2: list_nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_nat @ X @ Xs2 ) )
% 0.31/0.47 => ( X3 = nil_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_list.cases
% 0.31/0.47 thf(fact_54_min__list_Oinduct,axiom,
% 0.31/0.47 ! [P: list_nat > $o,A0: list_nat] :
% 0.31/0.47 ( ! [X: nat,Xs2: list_nat] :
% 0.31/0.47 ( ! [X213: nat,X223: list_nat] :
% 0.31/0.47 ( ( Xs2
% 0.31/0.47 = ( cons_nat @ X213 @ X223 ) )
% 0.31/0.47 => ( P @ Xs2 ) )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( P @ nil_nat )
% 0.31/0.47 => ( P @ A0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_list.induct
% 0.31/0.47 thf(fact_55_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.31/0.47 = nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionMsg.simps(1)
% 0.31/0.47 thf(fact_56_zero__reorient,axiom,
% 0.31/0.47 ! [X3: nat] :
% 0.31/0.47 ( ( zero_zero_nat = X3 )
% 0.31/0.47 = ( X3 = zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % zero_reorient
% 0.31/0.47 thf(fact_57_not__Cons__self2,axiom,
% 0.31/0.47 ! [X3: list_message_p_v,Xs: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( cons_l233104475ge_p_v @ X3 @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_58_not__Cons__self2,axiom,
% 0.31/0.47 ! [X3: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
% 0.31/0.47 ( ( cons_l1083444861t_unit @ X3 @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_59_not__Cons__self2,axiom,
% 0.31/0.47 ! [X3: nat,Xs: list_nat] :
% 0.31/0.47 ( ( cons_nat @ X3 @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_60_not__Cons__self2,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( cons_c1162654829t_unit @ X3 @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_61_not__Cons__self2,axiom,
% 0.31/0.47 ! [X3: message_p_v,Xs: list_message_p_v] :
% 0.31/0.47 ( ( cons_message_p_v @ X3 @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_62_strict__sorted_Oinduct,axiom,
% 0.31/0.47 ! [P: list_nat > $o,A0: list_nat] :
% 0.31/0.47 ( ( P @ nil_nat )
% 0.31/0.47 => ( ! [X: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % strict_sorted.induct
% 0.31/0.47 thf(fact_63_strict__sorted_Ocases,axiom,
% 0.31/0.47 ! [X3: list_nat] :
% 0.31/0.47 ( ( X3 != nil_nat )
% 0.31/0.47 => ~ ! [X: nat,Ys3: list_nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_nat @ X @ Ys3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % strict_sorted.cases
% 0.31/0.47 thf(fact_64_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [F: message_p_v > message_p_v,A: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_65_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [F: message_p_v > config256849571t_unit,A: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_66_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.31/0.47 => ( ! [F: config256849571t_unit > message_p_v,A: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_c1162654829t_unit @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_67_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.31/0.47 => ( ! [F: config256849571t_unit > config256849571t_unit,A: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_c1162654829t_unit @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_68_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > nat ) > list_nat > list_nat > $o,A0: nat > nat,A1: list_nat,A2: list_nat] :
% 0.31/0.47 ( ! [F: nat > nat,X_1: list_nat] : ( P @ F @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [F: nat > nat,A: nat,As: list_nat,Bs: list_nat] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_69_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > message_p_v ) > list_nat > list_message_p_v > $o,A0: nat > message_p_v,A1: list_nat,A2: list_message_p_v] :
% 0.31/0.47 ( ! [F: nat > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [F: nat > message_p_v,A: nat,As: list_nat,Bs: list_message_p_v] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( message_p_v > nat ) > list_message_p_v > list_nat > $o,A0: message_p_v > nat,A1: list_message_p_v,A2: list_nat] :
% 0.31/0.47 ( ! [F: message_p_v > nat,X_1: list_nat] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [F: message_p_v > nat,A: message_p_v,As: list_message_p_v,Bs: list_nat] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_71_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > list_message_p_v ) > list_nat > list_l1619404459ge_p_v > $o,A0: nat > list_message_p_v,A1: list_nat,A2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ! [F: nat > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [F: nat > list_message_p_v,A: nat,As: list_nat,Bs: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_72_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( list_message_p_v > nat ) > list_l1619404459ge_p_v > list_nat > $o,A0: list_message_p_v > nat,A1: list_l1619404459ge_p_v,A2: list_nat] :
% 0.31/0.47 ( ! [F: list_message_p_v > nat,X_1: list_nat] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [F: list_message_p_v > nat,A: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_nat] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_l233104475ge_p_v @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_73_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > config256849571t_unit ) > list_nat > list_c1059388851t_unit > $o,A0: nat > config256849571t_unit,A1: list_nat,A2: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [F: nat > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [F: nat > config256849571t_unit,A: nat,As: list_nat,Bs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_74_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
% 0.31/0.47 ( ( Xs != nil_list_message_p_v )
% 0.31/0.47 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 0.31/0.47 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( Xs2 != nil_list_message_p_v )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_75_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
% 0.31/0.47 ( ( Xs != nil_li307996205t_unit )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.31/0.47 ( ( Xs2 != nil_li307996205t_unit )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_76_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_nat,P: list_nat > $o] :
% 0.31/0.47 ( ( Xs != nil_nat )
% 0.31/0.47 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.31/0.47 => ( ! [X: nat,Xs2: list_nat] :
% 0.31/0.47 ( ( Xs2 != nil_nat )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_77_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
% 0.31/0.47 ( ( Xs != nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Xs2 != nil_co1338500125t_unit )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_78_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
% 0.31/0.47 ( ( Xs != nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( Xs2 != nil_message_p_v )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_79_successively_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 0.31/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_80_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.31/0.47 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.31/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 0.31/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_81_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.31/0.47 ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.31/0.47 => ( ! [P2: nat > nat > $o,X: nat] : ( P @ P2 @ ( cons_nat @ X @ nil_nat ) )
% 0.31/0.47 => ( ! [P2: nat > nat > $o,X: nat,Y3: nat,Xs2: list_nat] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_nat @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_82_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 0.31/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_83_successively_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.31/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 0.31/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_84_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 0.31/0.47 => ( ! [X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( ( X = Y3 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_85_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ nil_li307996205t_unit )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.31/0.47 ( ( ( X = Y3 )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_86_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_nat > $o,A0: list_nat] :
% 0.31/0.47 ( ( P @ nil_nat )
% 0.31/0.47 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.31/0.47 => ( ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.31/0.47 ( ( ( X = Y3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ( P @ ( cons_nat @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_87_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( X = Y3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_88_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_message_p_v > $o,A0: list_message_p_v] :
% 0.31/0.47 ( ( P @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( ( X = Y3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_89_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.31/0.47 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v,Ys3: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_90_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.31/0.47 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.31/0.47 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit,Ys3: list_l611321411t_unit] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_l1083444861t_unit @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_91_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.31/0.47 ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.31/0.47 => ( ! [P2: nat > nat > $o,X: nat,Ys3: list_nat] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_nat @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_92_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_c1162654829t_unit @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_93_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.31/0.47 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_message_p_v @ X @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_94_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X3: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( X3 != nil_list_message_p_v )
% 0.31/0.47 => ( ! [X: list_message_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 0.31/0.47 => ~ ! [X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_95_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X3: list_l611321411t_unit] :
% 0.31/0.47 ( ( X3 != nil_li307996205t_unit )
% 0.31/0.47 => ( ! [X: list_c1059388851t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 0.31/0.47 => ~ ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_96_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X3: list_nat] :
% 0.31/0.47 ( ( X3 != nil_nat )
% 0.31/0.47 => ( ! [X: nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_nat @ X @ nil_nat ) )
% 0.31/0.47 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_97_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( X3 != nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_98_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X3: list_message_p_v] :
% 0.31/0.47 ( ( X3 != nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_message_p_v @ X @ nil_message_p_v ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_99_transpose_Ocases,axiom,
% 0.31/0.47 ! [X3: list_list_nat] :
% 0.31/0.47 ( ( X3 != nil_list_nat )
% 0.31/0.47 => ( ! [Xss: list_list_nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_list_nat @ nil_nat @ Xss ) )
% 0.31/0.47 => ~ ! [X: nat,Xs2: list_nat,Xss: list_list_nat] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_list_nat @ ( cons_nat @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_100_transpose_Ocases,axiom,
% 0.31/0.47 ! [X3: list_l611321411t_unit] :
% 0.31/0.47 ( ( X3 != nil_li307996205t_unit )
% 0.31/0.47 => ( ! [Xss: list_l611321411t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_101_transpose_Ocases,axiom,
% 0.31/0.47 ! [X3: list_l1619404459ge_p_v] :
% 0.31/0.47 ( ( X3 != nil_list_message_p_v )
% 0.31/0.47 => ( ! [Xss: list_l1619404459ge_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
% 0.31/0.47 ( X3
% 0.31/0.47 != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_102_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.31/0.47 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.31/0.47 => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_103_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.31/0.47 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_message_p_v @ X @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_104_infiniteExecutionCfg_Oelims,axiom,
% 0.31/0.47 ! [X3: 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] :
% 0.31/0.47 ( ( ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 0.31/0.47 => ~ ! [N: nat] :
% 0.31/0.47 ( ( Xc
% 0.31/0.47 = ( suc @ N ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( Xa @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionCfg.elims
% 0.31/0.47 thf(fact_105_infiniteExecutionMsg_Oelims,axiom,
% 0.31/0.47 ! [X3: 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] :
% 0.31/0.47 ( ( ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.31/0.47 => ( Y != nil_message_p_v ) )
% 0.31/0.47 => ~ ! [N: nat] :
% 0.31/0.47 ( ( Xc
% 0.31/0.47 = ( suc @ N ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( Xb @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionMsg.elims
% 0.31/0.47 thf(fact_106_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.31/0.47 ! [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,N2: nat] :
% 0.31/0.47 ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 0.31/0.47 = ( FStepCfg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionCfg.simps(2)
% 0.31/0.47 thf(fact_107_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.31/0.47 ! [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,N2: nat] :
% 0.31/0.47 ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 0.31/0.47 = ( FStepMsg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionMsg.simps(2)
% 0.31/0.47 thf(fact_108_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.31/0.47 = ( cons_c1162654829t_unit @ Cfg @ nil_co1338500125t_unit ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(1)
% 0.31/0.47 thf(fact_109_n__lists__Nil,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ( N2 = zero_zero_nat )
% 0.31/0.47 => ( ( n_list1987762709t_unit @ N2 @ nil_co1338500125t_unit )
% 0.31/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
% 0.31/0.47 & ( ( N2 != zero_zero_nat )
% 0.31/0.47 => ( ( n_list1987762709t_unit @ N2 @ nil_co1338500125t_unit )
% 0.31/0.47 = nil_li307996205t_unit ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists_Nil
% 0.31/0.47 thf(fact_110_n__lists__Nil,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ( N2 = zero_zero_nat )
% 0.31/0.47 => ( ( n_lists_message_p_v @ N2 @ nil_message_p_v )
% 0.31/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
% 0.31/0.47 & ( ( N2 != zero_zero_nat )
% 0.31/0.47 => ( ( n_lists_message_p_v @ N2 @ nil_message_p_v )
% 0.31/0.47 = nil_list_message_p_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists_Nil
% 0.31/0.47 thf(fact_111_insert__Nil,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit] :
% 0.31/0.47 ( ( insert1308755079t_unit @ X3 @ nil_co1338500125t_unit )
% 0.31/0.47 = ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_Nil
% 0.31/0.47 thf(fact_112_insert__Nil,axiom,
% 0.31/0.47 ! [X3: message_p_v] :
% 0.31/0.47 ( ( insert_message_p_v @ X3 @ nil_message_p_v )
% 0.31/0.47 = ( cons_message_p_v @ X3 @ nil_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_Nil
% 0.31/0.47 thf(fact_113_nths__singleton,axiom,
% 0.31/0.47 ! [A3: set_nat,X3: config256849571t_unit] :
% 0.31/0.47 ( ( ( member_nat @ zero_zero_nat @ A3 )
% 0.31/0.47 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) @ A3 )
% 0.31/0.47 = ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 0.31/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 0.31/0.47 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) @ A3 )
% 0.31/0.47 = nil_co1338500125t_unit ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nths_singleton
% 0.31/0.47 thf(fact_114_nths__singleton,axiom,
% 0.31/0.47 ! [A3: set_nat,X3: message_p_v] :
% 0.31/0.47 ( ( ( member_nat @ zero_zero_nat @ A3 )
% 0.31/0.47 => ( ( nths_message_p_v @ ( cons_message_p_v @ X3 @ nil_message_p_v ) @ A3 )
% 0.31/0.47 = ( cons_message_p_v @ X3 @ nil_message_p_v ) ) )
% 0.31/0.47 & ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 0.31/0.47 => ( ( nths_message_p_v @ ( cons_message_p_v @ X3 @ nil_message_p_v ) @ A3 )
% 0.31/0.47 = nil_message_p_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nths_singleton
% 0.31/0.47 thf(fact_115_list__ex1__simps_I1_J,axiom,
% 0.31/0.47 ! [P: config256849571t_unit > $o] :
% 0.31/0.47 ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % list_ex1_simps(1)
% 0.31/0.47 thf(fact_116_list__ex1__simps_I1_J,axiom,
% 0.31/0.47 ! [P: message_p_v > $o] :
% 0.31/0.47 ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % list_ex1_simps(1)
% 0.31/0.47 thf(fact_117_n__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
% 0.31/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists.simps(1)
% 0.31/0.47 thf(fact_118_n__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Xs: list_message_p_v] :
% 0.31/0.47 ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
% 0.31/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_lists.simps(1)
% 0.31/0.47 thf(fact_119_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.31/0.47 ! [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] :
% 0.31/0.47 ( ! [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] : ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.31/0.47 => ( ! [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,N: nat] :
% 0.31/0.47 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 0.31/0.47 => ( ! [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] : ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.31/0.47 => ( ! [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,N: nat] :
% 0.31/0.47 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 0.31/0.47 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.31/0.47 thf(fact_120_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.31/0.47 ! [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,A32: nat] :
% 0.31/0.47 ( ! [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] : ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.31/0.47 => ( ! [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,N: nat] :
% 0.31/0.47 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 0.31/0.47 => ( ! [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] : ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.31/0.47 => ( ! [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,N: nat] :
% 0.31/0.47 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 0.31/0.47 => ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A2 @ A32 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.31/0.47 thf(fact_121_nths__nil,axiom,
% 0.31/0.47 ! [A3: set_nat] :
% 0.31/0.47 ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A3 )
% 0.31/0.47 = nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % nths_nil
% 0.31/0.47 thf(fact_122_nths__nil,axiom,
% 0.31/0.47 ! [A3: set_nat] :
% 0.31/0.47 ( ( nths_message_p_v @ nil_message_p_v @ A3 )
% 0.31/0.47 = nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % nths_nil
% 0.31/0.47 thf(fact_123_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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,N2: nat] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 0.31/0.47 = ( FStepMsg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(2)
% 0.31/0.47 thf(fact_124_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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,N2: nat] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 0.31/0.47 = ( FStepCfg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(2)
% 0.31/0.47 thf(fact_125_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X3: 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] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.31/0.47 => ( Y != nil_message_p_v ) )
% 0.31/0.47 => ~ ! [N: nat] :
% 0.31/0.47 ( ( Xc
% 0.31/0.47 = ( suc @ N ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( Xb @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionMsg.elims
% 0.31/0.47 thf(fact_126_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.31/0.47 = nil_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(1)
% 0.31/0.47 thf(fact_127_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 0.31/0.47 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X3: 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] :
% 0.31/0.47 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.31/0.47 => ( ( ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xc = zero_zero_nat )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 0.31/0.47 => ~ ! [N: nat] :
% 0.31/0.47 ( ( Xc
% 0.31/0.47 = ( suc @ N ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( Xa @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % flpPseudoConsensus.infiniteExecutionCfg.elims
% 0.31/0.47 thf(fact_128_old_Onat_Oinject,axiom,
% 0.31/0.47 ! [Nat: nat,Nat2: nat] :
% 0.31/0.47 ( ( ( suc @ Nat )
% 0.31/0.47 = ( suc @ Nat2 ) )
% 0.31/0.47 = ( Nat = Nat2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.nat.inject
% 0.31/0.47 thf(fact_129_nat_Oinject,axiom,
% 0.31/0.47 ! [X23: nat,Y23: nat] :
% 0.31/0.47 ( ( ( suc @ X23 )
% 0.31/0.47 = ( suc @ Y23 ) )
% 0.31/0.47 = ( X23 = Y23 ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat.inject
% 0.31/0.47 thf(fact_130_nat_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X23: nat] :
% 0.31/0.47 ( zero_zero_nat
% 0.31/0.47 != ( suc @ X23 ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat.distinct(1)
% 0.31/0.47 thf(fact_131_old_Onat_Odistinct_I2_J,axiom,
% 0.31/0.47 ! [Nat2: nat] :
% 0.31/0.47 ( ( suc @ Nat2 )
% 0.31/0.47 != zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % old.nat.distinct(2)
% 0.31/0.47 thf(fact_132_old_Onat_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [Nat2: nat] :
% 0.31/0.47 ( zero_zero_nat
% 0.31/0.47 != ( suc @ Nat2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.nat.distinct(1)
% 0.31/0.47 thf(fact_133_nat_OdiscI,axiom,
% 0.31/0.47 ! [Nat: nat,X23: nat] :
% 0.31/0.47 ( ( Nat
% 0.31/0.47 = ( suc @ X23 ) )
% 0.31/0.47 => ( Nat != zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat.discI
% 0.31/0.47 thf(fact_134_nat__induct,axiom,
% 0.31/0.47 ! [P: nat > $o,N2: nat] :
% 0.31/0.47 ( ( P @ zero_zero_nat )
% 0.31/0.47 => ( ! [N: nat] :
% 0.31/0.47 ( ( P @ N )
% 0.31/0.47 => ( P @ ( suc @ N ) ) )
% 0.31/0.47 => ( P @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_induct
% 0.31/0.47 thf(fact_135_Suc__inject,axiom,
% 0.31/0.47 ! [X3: nat,Y: nat] :
% 0.31/0.47 ( ( ( suc @ X3 )
% 0.31/0.47 = ( suc @ Y ) )
% 0.31/0.47 => ( X3 = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_inject
% 0.31/0.47 thf(fact_136_n__not__Suc__n,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( N2
% 0.31/0.47 != ( suc @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % n_not_Suc_n
% 0.31/0.47 thf(fact_137_not0__implies__Suc,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( N2 != zero_zero_nat )
% 0.31/0.47 => ? [M: nat] :
% 0.31/0.47 ( N2
% 0.31/0.47 = ( suc @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not0_implies_Suc
% 0.31/0.47 thf(fact_138_old_Onat_Oinducts,axiom,
% 0.31/0.47 ! [P: nat > $o,Nat: nat] :
% 0.31/0.47 ( ( P @ zero_zero_nat )
% 0.31/0.47 => ( ! [Nat3: nat] :
% 0.31/0.47 ( ( P @ Nat3 )
% 0.31/0.47 => ( P @ ( suc @ Nat3 ) ) )
% 0.31/0.47 => ( P @ Nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.nat.inducts
% 0.31/0.47 thf(fact_139_old_Onat_Oexhaust,axiom,
% 0.31/0.47 ! [Y: nat] :
% 0.31/0.47 ( ( Y != zero_zero_nat )
% 0.31/0.47 => ~ ! [Nat3: nat] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( suc @ Nat3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.nat.exhaust
% 0.31/0.47 thf(fact_140_Zero__not__Suc,axiom,
% 0.31/0.47 ! [M2: nat] :
% 0.31/0.47 ( zero_zero_nat
% 0.31/0.47 != ( suc @ M2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Zero_not_Suc
% 0.31/0.47 thf(fact_141_Zero__neq__Suc,axiom,
% 0.31/0.47 ! [M2: nat] :
% 0.31/0.47 ( zero_zero_nat
% 0.31/0.47 != ( suc @ M2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Zero_neq_Suc
% 0.31/0.47 thf(fact_142_Suc__neq__Zero,axiom,
% 0.31/0.47 ! [M2: nat] :
% 0.31/0.47 ( ( suc @ M2 )
% 0.31/0.47 != zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_neq_Zero
% 0.31/0.47 thf(fact_143_zero__induct,axiom,
% 0.31/0.47 ! [P: nat > $o,K: nat] :
% 0.31/0.47 ( ( P @ K )
% 0.31/0.47 => ( ! [N: nat] :
% 0.31/0.47 ( ( P @ ( suc @ N ) )
% 0.31/0.47 => ( P @ N ) )
% 0.31/0.47 => ( P @ zero_zero_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % zero_induct
% 0.31/0.47 thf(fact_144_diff__induct,axiom,
% 0.31/0.47 ! [P: nat > nat > $o,M2: nat,N2: nat] :
% 0.31/0.47 ( ! [X: nat] : ( P @ X @ zero_zero_nat )
% 0.31/0.47 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.31/0.47 => ( ! [X: nat,Y3: nat] :
% 0.31/0.47 ( ( P @ X @ Y3 )
% 0.31/0.47 => ( P @ ( suc @ X ) @ ( suc @ Y3 ) ) )
% 0.31/0.47 => ( P @ M2 @ N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_induct
% 0.31/0.47 thf(fact_145_product__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( produc663212148t_unit @ nil_li307996205t_unit )
% 0.31/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % product_lists.simps(1)
% 0.31/0.47 thf(fact_146_product__lists_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
% 0.31/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % product_lists.simps(1)
% 0.31/0.47 thf(fact_147_subseqs_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
% 0.31/0.47 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % subseqs.simps(1)
% 0.31/0.47 thf(fact_148_subseqs_Osimps_I1_J,axiom,
% 0.31/0.47 ( ( subseqs_message_p_v @ nil_message_p_v )
% 0.31/0.47 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % subseqs.simps(1)
% 0.31/0.47 thf(fact_149_gen__length__code_I2_J,axiom,
% 0.31/0.47 ! [N2: nat,X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( gen_le193291088t_unit @ N2 @ ( cons_c1162654829t_unit @ X3 @ Xs ) )
% 0.31/0.47 = ( gen_le193291088t_unit @ ( suc @ N2 ) @ Xs ) ) ).
% 0.31/0.47
% 0.31/0.47 % gen_length_code(2)
% 0.31/0.47 thf(fact_150_gen__length__code_I2_J,axiom,
% 0.31/0.47 ! [N2: nat,X3: message_p_v,Xs: list_message_p_v] :
% 0.31/0.47 ( ( gen_le697204914ge_p_v @ N2 @ ( cons_message_p_v @ X3 @ Xs ) )
% 0.31/0.47 = ( gen_le697204914ge_p_v @ ( suc @ N2 ) @ Xs ) ) ).
% 0.31/0.47
% 0.31/0.47 % gen_length_code(2)
% 0.31/0.47 thf(fact_151_count__list_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Y: config256849571t_unit] :
% 0.31/0.47 ( ( count_1396868135t_unit @ nil_co1338500125t_unit @ Y )
% 0.31/0.47 = zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % count_list.simps(1)
% 0.31/0.47 thf(fact_152_count__list_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Y: message_p_v] :
% 0.31/0.47 ( ( count_1322329499ge_p_v @ nil_message_p_v @ Y )
% 0.31/0.47 = zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % count_list.simps(1)
% 0.31/0.47 thf(fact_153_map__tailrec__rev_Oelims,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit > config256849571t_unit,Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( map_ta91747645t_unit @ X3 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xa = nil_co1338500125t_unit )
% 0.31/0.47 => ( Y != Xb ) )
% 0.31/0.47 => ~ ! [A: config256849571t_unit,As: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( cons_c1162654829t_unit @ A @ As ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( map_ta91747645t_unit @ X3 @ As @ ( cons_c1162654829t_unit @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.elims
% 0.31/0.47 thf(fact_154_map__tailrec__rev_Oelims,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit > message_p_v,Xa: list_c1059388851t_unit,Xb: list_message_p_v,Y: list_message_p_v] :
% 0.31/0.47 ( ( ( map_ta782801413ge_p_v @ X3 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xa = nil_co1338500125t_unit )
% 0.31/0.47 => ( Y != Xb ) )
% 0.31/0.47 => ~ ! [A: config256849571t_unit,As: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( cons_c1162654829t_unit @ A @ As ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( map_ta782801413ge_p_v @ X3 @ As @ ( cons_message_p_v @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.elims
% 0.31/0.47 thf(fact_155_map__tailrec__rev_Oelims,axiom,
% 0.31/0.47 ! [X3: message_p_v > config256849571t_unit,Xa: list_message_p_v,Xb: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( map_ta1131406733t_unit @ X3 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xa = nil_message_p_v )
% 0.31/0.47 => ( Y != Xb ) )
% 0.31/0.47 => ~ ! [A: message_p_v,As: list_message_p_v] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( cons_message_p_v @ A @ As ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( map_ta1131406733t_unit @ X3 @ As @ ( cons_c1162654829t_unit @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.elims
% 0.31/0.47 thf(fact_156_map__tailrec__rev_Oelims,axiom,
% 0.31/0.47 ! [X3: message_p_v > message_p_v,Xa: list_message_p_v,Xb: list_message_p_v,Y: list_message_p_v] :
% 0.31/0.47 ( ( ( map_ta1016577461ge_p_v @ X3 @ Xa @ Xb )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( Xa = nil_message_p_v )
% 0.31/0.47 => ( Y != Xb ) )
% 0.31/0.47 => ~ ! [A: message_p_v,As: list_message_p_v] :
% 0.31/0.47 ( ( Xa
% 0.31/0.47 = ( cons_message_p_v @ A @ As ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( map_ta1016577461ge_p_v @ X3 @ As @ ( cons_message_p_v @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.elims
% 0.31/0.47 thf(fact_157_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.31/0.47 ! [F2: config256849571t_unit > config256849571t_unit,A8: config256849571t_unit,As2: list_c1059388851t_unit,Bs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( map_ta91747645t_unit @ F2 @ ( cons_c1162654829t_unit @ A8 @ As2 ) @ Bs2 )
% 0.31/0.47 = ( map_ta91747645t_unit @ F2 @ As2 @ ( cons_c1162654829t_unit @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.simps(2)
% 0.31/0.47 thf(fact_158_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.31/0.47 ! [F2: config256849571t_unit > message_p_v,A8: config256849571t_unit,As2: list_c1059388851t_unit,Bs2: list_message_p_v] :
% 0.31/0.47 ( ( map_ta782801413ge_p_v @ F2 @ ( cons_c1162654829t_unit @ A8 @ As2 ) @ Bs2 )
% 0.31/0.47 = ( map_ta782801413ge_p_v @ F2 @ As2 @ ( cons_message_p_v @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.simps(2)
% 0.31/0.47 thf(fact_159_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.31/0.47 ! [F2: message_p_v > config256849571t_unit,A8: message_p_v,As2: list_message_p_v,Bs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( map_ta1131406733t_unit @ F2 @ ( cons_message_p_v @ A8 @ As2 ) @ Bs2 )
% 0.31/0.47 = ( map_ta1131406733t_unit @ F2 @ As2 @ ( cons_c1162654829t_unit @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.simps(2)
% 0.31/0.47 thf(fact_160_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.31/0.47 ! [F2: message_p_v > message_p_v,A8: message_p_v,As2: list_message_p_v,Bs2: list_message_p_v] :
% 0.31/0.47 ( ( map_ta1016577461ge_p_v @ F2 @ ( cons_message_p_v @ A8 @ As2 ) @ Bs2 )
% 0.31/0.47 = ( map_ta1016577461ge_p_v @ F2 @ As2 @ ( cons_message_p_v @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.simps(2)
% 0.31/0.47 thf(fact_161_gen__length__code_I1_J,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( gen_le193291088t_unit @ N2 @ nil_co1338500125t_unit )
% 0.31/0.47 = N2 ) ).
% 0.31/0.47
% 0.31/0.47 % gen_length_code(1)
% 0.31/0.47 thf(fact_162_gen__length__code_I1_J,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( gen_le697204914ge_p_v @ N2 @ nil_message_p_v )
% 0.31/0.47 = N2 ) ).
% 0.31/0.47
% 0.31/0.47 % gen_length_code(1)
% 0.31/0.47 thf(fact_163_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.31/0.47 ~ ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(3)
% 0.31/0.47 thf(fact_164_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Xs: list_message_p_v] :
% 0.31/0.47 ~ ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(3)
% 0.31/0.47 thf(fact_165_bind__simps_I1_J,axiom,
% 0.31/0.47 ! [F2: config256849571t_unit > list_c1059388851t_unit] :
% 0.31/0.47 ( ( bind_c1439720399t_unit @ nil_co1338500125t_unit @ F2 )
% 0.31/0.47 = nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % bind_simps(1)
% 0.31/0.47 thf(fact_166_bind__simps_I1_J,axiom,
% 0.31/0.47 ! [F2: config256849571t_unit > list_message_p_v] :
% 0.31/0.47 ( ( bind_c246984691ge_p_v @ nil_co1338500125t_unit @ F2 )
% 0.31/0.47 = nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % bind_simps(1)
% 0.31/0.47 thf(fact_167_bind__simps_I1_J,axiom,
% 0.31/0.47 ! [F2: message_p_v > list_c1059388851t_unit] :
% 0.31/0.47 ( ( bind_m595590011t_unit @ nil_message_p_v @ F2 )
% 0.31/0.47 = nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % bind_simps(1)
% 0.31/0.47 thf(fact_168_bind__simps_I1_J,axiom,
% 0.31/0.47 ! [F2: message_p_v > list_message_p_v] :
% 0.31/0.47 ( ( bind_m729301831ge_p_v @ nil_message_p_v @ F2 )
% 0.31/0.47 = nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % bind_simps(1)
% 0.31/0.47 thf(fact_169_listrelp_Ocases,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( listre990624391t_unit @ R @ A1 @ A2 )
% 0.31/0.47 => ( ( ( A1 = nil_co1338500125t_unit )
% 0.31/0.47 => ( A2 != nil_co1338500125t_unit ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( R @ X @ Y3 )
% 0.31/0.47 => ~ ( listre990624391t_unit @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.cases
% 0.31/0.47 thf(fact_170_listrelp_Ocases,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > message_p_v > $o,A1: list_c1059388851t_unit,A2: list_message_p_v] :
% 0.31/0.47 ( ( listre823101243ge_p_v @ R @ A1 @ A2 )
% 0.31/0.47 => ( ( ( A1 = nil_co1338500125t_unit )
% 0.31/0.47 => ( A2 != nil_message_p_v ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Y3: message_p_v,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_message_p_v] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( R @ X @ Y3 )
% 0.31/0.47 => ~ ( listre823101243ge_p_v @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.cases
% 0.31/0.47 thf(fact_171_listrelp_Ocases,axiom,
% 0.31/0.47 ! [R: message_p_v > config256849571t_unit > $o,A1: list_message_p_v,A2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( listre1171706563t_unit @ R @ A1 @ A2 )
% 0.31/0.47 => ( ( ( A1 = nil_message_p_v )
% 0.31/0.47 => ( A2 != nil_co1338500125t_unit ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Y3: config256849571t_unit,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_message_p_v @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( R @ X @ Y3 )
% 0.31/0.47 => ~ ( listre1171706563t_unit @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.cases
% 0.31/0.47 thf(fact_172_listrelp_Ocases,axiom,
% 0.31/0.47 ! [R: message_p_v > message_p_v > $o,A1: list_message_p_v,A2: list_message_p_v] :
% 0.31/0.47 ( ( listre1295695359ge_p_v @ R @ A1 @ A2 )
% 0.31/0.47 => ( ( ( A1 = nil_message_p_v )
% 0.31/0.47 => ( A2 != nil_message_p_v ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_message_p_v @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_message_p_v] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ( R @ X @ Y3 )
% 0.31/0.47 => ~ ( listre1295695359ge_p_v @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.cases
% 0.31/0.47 thf(fact_173_listrelp_Osimps,axiom,
% 0.31/0.47 ( listre990624391t_unit
% 0.31/0.47 = ( ^ [R2: config256849571t_unit > config256849571t_unit > $o,A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( A12 = nil_co1338500125t_unit )
% 0.31/0.47 & ( A22 = nil_co1338500125t_unit ) )
% 0.31/0.47 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.47 & ( R2 @ X4 @ Y2 )
% 0.31/0.47 & ( listre990624391t_unit @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.simps
% 0.31/0.47 thf(fact_174_listrelp_Osimps,axiom,
% 0.31/0.47 ( listre823101243ge_p_v
% 0.31/0.47 = ( ^ [R2: config256849571t_unit > message_p_v > $o,A12: list_c1059388851t_unit,A22: list_message_p_v] :
% 0.31/0.47 ( ( ( A12 = nil_co1338500125t_unit )
% 0.31/0.47 & ( A22 = nil_message_p_v ) )
% 0.31/0.47 | ? [X4: config256849571t_unit,Y2: message_p_v,Xs3: list_c1059388851t_unit,Ys: list_message_p_v] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.47 & ( R2 @ X4 @ Y2 )
% 0.31/0.47 & ( listre823101243ge_p_v @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.simps
% 0.31/0.47 thf(fact_175_listrelp_Osimps,axiom,
% 0.31/0.47 ( listre1171706563t_unit
% 0.31/0.47 = ( ^ [R2: message_p_v > config256849571t_unit > $o,A12: list_message_p_v,A22: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( A12 = nil_message_p_v )
% 0.31/0.47 & ( A22 = nil_co1338500125t_unit ) )
% 0.31/0.47 | ? [X4: message_p_v,Y2: config256849571t_unit,Xs3: list_message_p_v,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.47 & ( R2 @ X4 @ Y2 )
% 0.31/0.47 & ( listre1171706563t_unit @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.simps
% 0.31/0.47 thf(fact_176_listrelp_Osimps,axiom,
% 0.31/0.47 ( listre1295695359ge_p_v
% 0.31/0.47 = ( ^ [R2: message_p_v > message_p_v > $o,A12: list_message_p_v,A22: list_message_p_v] :
% 0.31/0.47 ( ( ( A12 = nil_message_p_v )
% 0.31/0.47 & ( A22 = nil_message_p_v ) )
% 0.31/0.47 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.47 & ( R2 @ X4 @ Y2 )
% 0.31/0.47 & ( listre1295695359ge_p_v @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.simps
% 0.31/0.47 thf(fact_177_listrelp_Oinducts,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > config256849571t_unit > $o,X12: list_c1059388851t_unit,X23: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.31/0.47 ( ( listre990624391t_unit @ R @ X12 @ X23 )
% 0.31/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( R @ X @ Y3 )
% 0.31/0.47 => ( ( listre990624391t_unit @ R @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.inducts
% 0.31/0.47 thf(fact_178_listrelp_Oinducts,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > message_p_v > $o,X12: list_c1059388851t_unit,X23: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 0.31/0.47 ( ( listre823101243ge_p_v @ R @ X12 @ X23 )
% 0.31/0.47 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: message_p_v,Xs2: list_c1059388851t_unit,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( R @ X @ Y3 )
% 0.31/0.47 => ( ( listre823101243ge_p_v @ R @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.inducts
% 0.31/0.47 thf(fact_179_listrelp_Oinducts,axiom,
% 0.31/0.47 ! [R: message_p_v > config256849571t_unit > $o,X12: list_message_p_v,X23: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 0.31/0.47 ( ( listre1171706563t_unit @ R @ X12 @ X23 )
% 0.31/0.47 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: config256849571t_unit,Xs2: list_message_p_v,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( R @ X @ Y3 )
% 0.31/0.47 => ( ( listre1171706563t_unit @ R @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.inducts
% 0.31/0.47 thf(fact_180_listrelp_Oinducts,axiom,
% 0.31/0.47 ! [R: message_p_v > message_p_v > $o,X12: list_message_p_v,X23: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.31/0.47 ( ( listre1295695359ge_p_v @ R @ X12 @ X23 )
% 0.31/0.47 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( R @ X @ Y3 )
% 0.31/0.47 => ( ( listre1295695359ge_p_v @ R @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.inducts
% 0.31/0.47 thf(fact_181_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Xs: list_c1059388851t_unit,Y: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) )
% 0.31/0.47 = ( ( Less @ X3 @ Y )
% 0.31/0.47 | ( ~ ( Less @ Y @ X3 )
% 0.31/0.47 & ( lexord1758866263t_unit @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(4)
% 0.31/0.47 thf(fact_182_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Xs: list_message_p_v,Y: message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) )
% 0.31/0.47 = ( ( Less @ X3 @ Y )
% 0.31/0.47 | ( ~ ( Less @ Y @ X3 )
% 0.31/0.47 & ( lexord2101627499ge_p_v @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(4)
% 0.31/0.47 thf(fact_183_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,Ys2: list_c1059388851t_unit] : ( lexord1758866263t_unit @ Less @ nil_co1338500125t_unit @ Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(1)
% 0.31/0.47 thf(fact_184_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,Ys2: list_message_p_v] : ( lexord2101627499ge_p_v @ Less @ nil_message_p_v @ Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(1)
% 0.31/0.47 thf(fact_185_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( lexord1758866263t_unit @ Less @ Xs @ nil_co1338500125t_unit )
% 0.31/0.47 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(2)
% 0.31/0.47 thf(fact_186_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,Xs: list_message_p_v] :
% 0.31/0.47 ( ( lexord2101627499ge_p_v @ Less @ Xs @ nil_message_p_v )
% 0.31/0.47 = ( Xs = nil_message_p_v ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq_simps(2)
% 0.31/0.47 thf(fact_187_ord_Olexordp__eq_OCons__eq,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ~ ( Less @ X3 @ Y )
% 0.31/0.47 => ( ~ ( Less @ Y @ X3 )
% 0.31/0.47 => ( ( lexord1758866263t_unit @ Less @ Xs @ Ys2 )
% 0.31/0.47 => ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Cons_eq
% 0.31/0.47 thf(fact_188_ord_Olexordp__eq_OCons__eq,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ~ ( Less @ X3 @ Y )
% 0.31/0.47 => ( ~ ( Less @ Y @ X3 )
% 0.31/0.47 => ( ( lexord2101627499ge_p_v @ Less @ Xs @ Ys2 )
% 0.31/0.47 => ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Cons_eq
% 0.31/0.47 thf(fact_189_ord_Olexordp__eq_OCons,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Less @ X3 @ Y )
% 0.31/0.47 => ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Cons
% 0.31/0.47 thf(fact_190_ord_Olexordp__eq_OCons,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( Less @ X3 @ Y )
% 0.31/0.47 => ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Cons
% 0.31/0.47 thf(fact_191_ord_Olexordp__eq_ONil,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,Ys2: list_c1059388851t_unit] : ( lexord1758866263t_unit @ Less @ nil_co1338500125t_unit @ Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Nil
% 0.31/0.47 thf(fact_192_ord_Olexordp__eq_ONil,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,Ys2: list_message_p_v] : ( lexord2101627499ge_p_v @ Less @ nil_message_p_v @ Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.Nil
% 0.31/0.47 thf(fact_193_listrelp_OCons,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( R @ X3 @ Y )
% 0.31/0.47 => ( ( listre990624391t_unit @ R @ Xs @ Ys2 )
% 0.31/0.47 => ( listre990624391t_unit @ R @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Cons
% 0.31/0.47 thf(fact_194_listrelp_OCons,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > message_p_v > $o,X3: config256849571t_unit,Y: message_p_v,Xs: list_c1059388851t_unit,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( R @ X3 @ Y )
% 0.31/0.47 => ( ( listre823101243ge_p_v @ R @ Xs @ Ys2 )
% 0.31/0.47 => ( listre823101243ge_p_v @ R @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Cons
% 0.31/0.47 thf(fact_195_listrelp_OCons,axiom,
% 0.31/0.47 ! [R: message_p_v > config256849571t_unit > $o,X3: message_p_v,Y: config256849571t_unit,Xs: list_message_p_v,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( R @ X3 @ Y )
% 0.31/0.47 => ( ( listre1171706563t_unit @ R @ Xs @ Ys2 )
% 0.31/0.47 => ( listre1171706563t_unit @ R @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Cons
% 0.31/0.47 thf(fact_196_listrelp_OCons,axiom,
% 0.31/0.47 ! [R: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( R @ X3 @ Y )
% 0.31/0.47 => ( ( listre1295695359ge_p_v @ R @ Xs @ Ys2 )
% 0.31/0.47 => ( listre1295695359ge_p_v @ R @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Cons
% 0.31/0.47 thf(fact_197_listrelp_ONil,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > config256849571t_unit > $o] : ( listre990624391t_unit @ R @ nil_co1338500125t_unit @ nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Nil
% 0.31/0.47 thf(fact_198_listrelp_ONil,axiom,
% 0.31/0.47 ! [R: config256849571t_unit > message_p_v > $o] : ( listre823101243ge_p_v @ R @ nil_co1338500125t_unit @ nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Nil
% 0.31/0.47 thf(fact_199_listrelp_ONil,axiom,
% 0.31/0.47 ! [R: message_p_v > config256849571t_unit > $o] : ( listre1171706563t_unit @ R @ nil_message_p_v @ nil_co1338500125t_unit ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Nil
% 0.31/0.47 thf(fact_200_listrelp_ONil,axiom,
% 0.31/0.47 ! [R: message_p_v > message_p_v > $o] : ( listre1295695359ge_p_v @ R @ nil_message_p_v @ nil_message_p_v ) ).
% 0.31/0.47
% 0.31/0.47 % listrelp.Nil
% 0.31/0.47 thf(fact_201_ord_Olexordp__eq_Oinducts,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,X12: list_c1059388851t_unit,X23: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.31/0.47 ( ( lexord1758866263t_unit @ Less @ X12 @ X23 )
% 0.31/0.47 => ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( Less @ X @ Y3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ~ ( Less @ X @ Y3 )
% 0.31/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.31/0.47 => ( ( lexord1758866263t_unit @ Less @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.inducts
% 0.31/0.47 thf(fact_202_ord_Olexordp__eq_Oinducts,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,X12: list_message_p_v,X23: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.31/0.47 ( ( lexord2101627499ge_p_v @ Less @ X12 @ X23 )
% 0.31/0.47 => ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ( Less @ X @ Y3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 0.31/0.47 ( ~ ( Less @ X @ Y3 )
% 0.31/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.31/0.47 => ( ( lexord2101627499ge_p_v @ Less @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.inducts
% 0.31/0.47 thf(fact_203_ord_Olexordp__eq_Osimps,axiom,
% 0.31/0.47 ( lexord1758866263t_unit
% 0.31/0.47 = ( ^ [Less2: config256849571t_unit > config256849571t_unit > $o,A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 0.31/0.47 ( ? [Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A12 = nil_co1338500125t_unit )
% 0.31/0.47 & ( A22 = Ys ) )
% 0.31/0.47 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.47 & ( Less2 @ X4 @ Y2 ) )
% 0.31/0.47 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.47 & ~ ( Less2 @ X4 @ Y2 )
% 0.31/0.47 & ~ ( Less2 @ Y2 @ X4 )
% 0.31/0.47 & ( lexord1758866263t_unit @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.simps
% 0.31/0.47 thf(fact_204_ord_Olexordp__eq_Osimps,axiom,
% 0.31/0.47 ( lexord2101627499ge_p_v
% 0.31/0.47 = ( ^ [Less2: message_p_v > message_p_v > $o,A12: list_message_p_v,A22: list_message_p_v] :
% 0.31/0.47 ( ? [Ys: list_message_p_v] :
% 0.31/0.47 ( ( A12 = nil_message_p_v )
% 0.31/0.47 & ( A22 = Ys ) )
% 0.31/0.47 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.47 & ( Less2 @ X4 @ Y2 ) )
% 0.31/0.47 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.47 & ~ ( Less2 @ X4 @ Y2 )
% 0.31/0.47 & ~ ( Less2 @ Y2 @ X4 )
% 0.31/0.47 & ( lexord2101627499ge_p_v @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.simps
% 0.31/0.47 thf(fact_205_ord_Olexordp__eq_Ocases,axiom,
% 0.31/0.47 ! [Less: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( lexord1758866263t_unit @ Less @ A1 @ A2 )
% 0.31/0.47 => ( ( A1 != nil_co1338500125t_unit )
% 0.31/0.47 => ( ! [X: config256849571t_unit] :
% 0.31/0.47 ( ? [Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( A1
% 0.31/0.47 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 0.31/0.47 => ! [Y3: config256849571t_unit] :
% 0.31/0.47 ( ? [Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( A2
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ~ ( Less @ X @ Y3 ) ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_c1059388851t_unit] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ~ ( Less @ X @ Y3 )
% 0.31/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.31/0.47 => ~ ( lexord1758866263t_unit @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.cases
% 0.31/0.47 thf(fact_206_ord_Olexordp__eq_Ocases,axiom,
% 0.31/0.47 ! [Less: message_p_v > message_p_v > $o,A1: list_message_p_v,A2: list_message_p_v] :
% 0.31/0.47 ( ( lexord2101627499ge_p_v @ Less @ A1 @ A2 )
% 0.31/0.47 => ( ( A1 != nil_message_p_v )
% 0.31/0.47 => ( ! [X: message_p_v] :
% 0.31/0.47 ( ? [Xs2: list_message_p_v] :
% 0.31/0.47 ( A1
% 0.31/0.47 = ( cons_message_p_v @ X @ Xs2 ) )
% 0.31/0.47 => ! [Y3: message_p_v] :
% 0.31/0.47 ( ? [Ys3: list_message_p_v] :
% 0.31/0.47 ( A2
% 0.31/0.47 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ~ ( Less @ X @ Y3 ) ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_message_p_v @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_message_p_v] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ~ ( Less @ X @ Y3 )
% 0.31/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.31/0.47 => ~ ( lexord2101627499ge_p_v @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord.lexordp_eq.cases
% 0.31/0.47 thf(fact_207_zero__natural_Orsp,axiom,
% 0.31/0.47 zero_zero_nat = zero_zero_nat ).
% 0.31/0.47
% 0.31/0.47 % zero_natural.rsp
% 0.31/0.47 thf(fact_208_member__rec_I2_J,axiom,
% 0.31/0.47 ! [Y: config256849571t_unit] :
% 0.31/0.47 ~ ( member1087090632t_unit @ nil_co1338500125t_unit @ Y ) ).
% 0.31/0.47
% 0.31/0.47 % member_rec(2)
% 0.31/0.47 thf(fact_209_member__rec_I2_J,axiom,
% 0.31/0.47 ! [Y: message_p_v] :
% 0.31/0.47 ~ ( member_message_p_v @ nil_message_p_v @ Y ) ).
% 0.31/0.47
% 0.31/0.47 % member_rec(2)
% 0.31/0.47 thf(fact_210_member__rec_I1_J,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit,Y: config256849571t_unit] :
% 0.31/0.47 ( ( member1087090632t_unit @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ Y )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 | ( member1087090632t_unit @ Xs @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % member_rec(1)
% 0.31/0.47 thf(fact_211_member__rec_I1_J,axiom,
% 0.31/0.47 ! [X3: message_p_v,Xs: list_message_p_v,Y: message_p_v] :
% 0.31/0.47 ( ( member_message_p_v @ ( cons_message_p_v @ X3 @ Xs ) @ Y )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 | ( member_message_p_v @ Xs @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % member_rec(1)
% 0.31/0.47 thf(fact_212_lexordp__eq_Ocases,axiom,
% 0.31/0.47 ! [A1: list_nat,A2: list_nat] :
% 0.31/0.47 ( ( ord_lexordp_eq_nat @ A1 @ A2 )
% 0.31/0.47 => ( ( A1 != nil_nat )
% 0.31/0.47 => ( ! [X: nat] :
% 0.31/0.47 ( ? [Xs2: list_nat] :
% 0.31/0.47 ( A1
% 0.31/0.47 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.47 => ! [Y3: nat] :
% 0.31/0.47 ( ? [Ys3: list_nat] :
% 0.31/0.47 ( A2
% 0.31/0.47 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.31/0.47 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_nat] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.31/0.47 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.31/0.47 => ~ ( ord_lexordp_eq_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq.cases
% 0.31/0.47 thf(fact_213_lexordp__eq_Osimps,axiom,
% 0.31/0.47 ( ord_lexordp_eq_nat
% 0.31/0.47 = ( ^ [A12: list_nat,A22: list_nat] :
% 0.31/0.47 ( ? [Ys: list_nat] :
% 0.31/0.47 ( ( A12 = nil_nat )
% 0.31/0.47 & ( A22 = Ys ) )
% 0.31/0.47 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_nat @ Y2 @ Ys ) )
% 0.31/0.47 & ( ord_less_nat @ X4 @ Y2 ) )
% 0.31/0.47 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.31/0.47 ( ( A12
% 0.31/0.47 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.47 & ( A22
% 0.31/0.47 = ( cons_nat @ Y2 @ Ys ) )
% 0.31/0.47 & ~ ( ord_less_nat @ X4 @ Y2 )
% 0.31/0.47 & ~ ( ord_less_nat @ Y2 @ X4 )
% 0.31/0.47 & ( ord_lexordp_eq_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq.simps
% 0.31/0.47 thf(fact_214_lexordp__eq_Oinducts,axiom,
% 0.31/0.47 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 0.31/0.47 ( ( ord_lexordp_eq_nat @ X12 @ X23 )
% 0.31/0.47 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.31/0.47 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.47 ( ( ord_less_nat @ X @ Y3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ X @ Y3 )
% 0.31/0.47 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.31/0.47 => ( ( ord_lexordp_eq_nat @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 0.31/0.47 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq.inducts
% 0.31/0.47 thf(fact_215_splice_Oelims,axiom,
% 0.31/0.47 ! [X3: list_c1059388851t_unit,Xa: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( splice888123018t_unit @ X3 @ Xa )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( X3 = nil_co1338500125t_unit )
% 0.31/0.47 => ( Y != Xa ) )
% 0.31/0.47 => ~ ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( X3
% 0.31/0.47 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_c1162654829t_unit @ X @ ( splice888123018t_unit @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.elims
% 0.31/0.47 thf(fact_216_splice_Oelims,axiom,
% 0.31/0.47 ! [X3: list_message_p_v,Xa: list_message_p_v,Y: list_message_p_v] :
% 0.31/0.47 ( ( ( splice_message_p_v @ X3 @ Xa )
% 0.31/0.47 = Y )
% 0.31/0.47 => ( ( ( X3 = nil_message_p_v )
% 0.31/0.47 => ( Y != Xa ) )
% 0.31/0.47 => ~ ! [X: message_p_v,Xs2: list_message_p_v] :
% 0.31/0.47 ( ( X3
% 0.31/0.47 = ( cons_message_p_v @ X @ Xs2 ) )
% 0.31/0.47 => ( Y
% 0.31/0.47 != ( cons_message_p_v @ X @ ( splice_message_p_v @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.elims
% 0.31/0.47 thf(fact_217_bot__nat__0_Onot__eq__extremum,axiom,
% 0.31/0.47 ! [A8: nat] :
% 0.31/0.47 ( ( A8 != zero_zero_nat )
% 0.31/0.47 = ( ord_less_nat @ zero_zero_nat @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_nat_0.not_eq_extremum
% 0.31/0.47 thf(fact_218_less__nat__zero__code,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % less_nat_zero_code
% 0.31/0.47 thf(fact_219_neq0__conv,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( N2 != zero_zero_nat )
% 0.31/0.47 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq0_conv
% 0.31/0.47 thf(fact_220_lessI,axiom,
% 0.31/0.47 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % lessI
% 0.31/0.47 thf(fact_221_Suc__mono,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_mono
% 0.31/0.47 thf(fact_222_Suc__less__eq,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 0.31/0.47 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_less_eq
% 0.31/0.47 thf(fact_223_not__gr__zero,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.31/0.47 = ( N2 = zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_gr_zero
% 0.31/0.47 thf(fact_224_zero__less__Suc,axiom,
% 0.31/0.47 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % zero_less_Suc
% 0.31/0.47 thf(fact_225_less__Suc0,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.31/0.47 = ( N2 = zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc0
% 0.31/0.47 thf(fact_226_split__Nil__iff,axiom,
% 0.31/0.47 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( ( splice888123018t_unit @ Xs @ Ys2 )
% 0.31/0.47 = nil_co1338500125t_unit )
% 0.31/0.47 = ( ( Xs = nil_co1338500125t_unit )
% 0.31/0.47 & ( Ys2 = nil_co1338500125t_unit ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_Nil_iff
% 0.31/0.47 thf(fact_227_split__Nil__iff,axiom,
% 0.31/0.47 ! [Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( ( splice_message_p_v @ Xs @ Ys2 )
% 0.31/0.47 = nil_message_p_v )
% 0.31/0.47 = ( ( Xs = nil_message_p_v )
% 0.31/0.47 & ( Ys2 = nil_message_p_v ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_Nil_iff
% 0.31/0.47 thf(fact_228_splice__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_c1059388851t_unit] :
% 0.31/0.47 ( ( splice888123018t_unit @ Xs @ nil_co1338500125t_unit )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % splice_Nil2
% 0.31/0.47 thf(fact_229_splice__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_message_p_v] :
% 0.31/0.47 ( ( splice_message_p_v @ Xs @ nil_message_p_v )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % splice_Nil2
% 0.31/0.47 thf(fact_230_lexordp__eq__simps_I4_J,axiom,
% 0.31/0.47 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 0.31/0.47 ( ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 0.31/0.47 = ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.47 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.47 & ( ord_lexordp_eq_nat @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq_simps(4)
% 0.31/0.47 thf(fact_231_gr__zeroI,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( N2 != zero_zero_nat )
% 0.31/0.47 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr_zeroI
% 0.31/0.47 thf(fact_232_not__less__zero,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_zero
% 0.31/0.47 thf(fact_233_gr__implies__not__zero,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( N2 != zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr_implies_not_zero
% 0.31/0.47 thf(fact_234_zero__less__iff__neq__zero,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.31/0.47 = ( N2 != zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % zero_less_iff_neq_zero
% 0.31/0.47 thf(fact_235_bot__nat__0_Oextremum__strict,axiom,
% 0.31/0.47 ! [A8: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ A8 @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % bot_nat_0.extremum_strict
% 0.31/0.47 thf(fact_236_infinite__descent0,axiom,
% 0.31/0.47 ! [P: nat > $o,N2: nat] :
% 0.31/0.47 ( ( P @ zero_zero_nat )
% 0.31/0.47 => ( ! [N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.31/0.47 => ( ~ ( P @ N )
% 0.31/0.47 => ? [M3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M3 @ N )
% 0.31/0.47 & ~ ( P @ M3 ) ) ) )
% 0.31/0.47 => ( P @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_descent0
% 0.31/0.47 thf(fact_237_gr__implies__not0,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( N2 != zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr_implies_not0
% 0.31/0.47 thf(fact_238_less__zeroE,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % less_zeroE
% 0.31/0.47 thf(fact_239_not__less0,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % not_less0
% 0.31/0.47 thf(fact_240_not__gr0,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.31/0.47 = ( N2 = zero_zero_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_gr0
% 0.31/0.47 thf(fact_241_gr0I,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( N2 != zero_zero_nat )
% 0.31/0.47 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr0I
% 0.31/0.47 thf(fact_242_Nat_OlessE,axiom,
% 0.31/0.47 ! [I: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I @ K )
% 0.31/0.47 => ( ( K
% 0.31/0.47 != ( suc @ I ) )
% 0.31/0.47 => ~ ! [J: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J )
% 0.31/0.47 => ( K
% 0.31/0.47 != ( suc @ J ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nat.lessE
% 0.31/0.47 thf(fact_243_Suc__lessD,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ N2 )
% 0.31/0.47 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_lessD
% 0.31/0.47 thf(fact_244_Suc__lessE,axiom,
% 0.31/0.47 ! [I: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.31/0.47 => ~ ! [J: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J )
% 0.31/0.47 => ( K
% 0.31/0.47 != ( suc @ J ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_lessE
% 0.31/0.47 thf(fact_245_Suc__lessI,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( ( ( suc @ M2 )
% 0.31/0.47 != N2 )
% 0.31/0.47 => ( ord_less_nat @ ( suc @ M2 ) @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_lessI
% 0.31/0.47 thf(fact_246_less__SucE,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 0.31/0.47 => ( ~ ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( M2 = N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_SucE
% 0.31/0.47 thf(fact_247_less__SucI,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 => ( ord_less_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_SucI
% 0.31/0.47 thf(fact_248_Ex__less__Suc,axiom,
% 0.31/0.47 ! [N2: nat,P: nat > $o] :
% 0.31/0.47 ( ( ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 0.31/0.47 & ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ N2 )
% 0.31/0.47 | ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N2 )
% 0.31/0.47 & ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ex_less_Suc
% 0.31/0.47 thf(fact_249_less__Suc__eq,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 0.31/0.47 = ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.47 | ( M2 = N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_eq
% 0.31/0.47 thf(fact_250_not__less__eq,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ~ ( ord_less_nat @ M2 @ N2 ) )
% 0.31/0.47 = ( ord_less_nat @ N2 @ ( suc @ M2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_eq
% 0.31/0.47 thf(fact_251_All__less__Suc,axiom,
% 0.31/0.47 ! [N2: nat,P: nat > $o] :
% 0.31/0.47 ( ( ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 0.31/0.47 => ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ N2 )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N2 )
% 0.31/0.47 => ( P @ I2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % All_less_Suc
% 0.31/0.47 thf(fact_252_Suc__less__eq2,axiom,
% 0.31/0.47 ! [N2: nat,M2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 0.31/0.47 = ( ? [M4: nat] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( suc @ M4 ) )
% 0.31/0.47 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_less_eq2
% 0.31/0.47 thf(fact_253_less__antisym,axiom,
% 0.31/0.47 ! [N2: nat,M2: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.31/0.47 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 0.31/0.47 => ( M2 = N2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_antisym
% 0.31/0.47 thf(fact_254_Suc__less__SucD,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 0.31/0.47 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Suc_less_SucD
% 0.31/0.47 thf(fact_255_less__trans__Suc,axiom,
% 0.31/0.47 ! [I: nat,J2: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.31/0.47 => ( ( ord_less_nat @ J2 @ K )
% 0.31/0.47 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_trans_Suc
% 0.31/0.47 thf(fact_256_less__Suc__induct,axiom,
% 0.31/0.47 ! [I: nat,J2: nat,P: nat > nat > $o] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.31/0.47 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.31/0.47 => ( ! [I3: nat,J: nat,K2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ J )
% 0.31/0.47 => ( ( ord_less_nat @ J @ K2 )
% 0.31/0.47 => ( ( P @ I3 @ J )
% 0.31/0.47 => ( ( P @ J @ K2 )
% 0.31/0.47 => ( P @ I3 @ K2 ) ) ) ) )
% 0.31/0.47 => ( P @ I @ J2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_induct
% 0.31/0.47 thf(fact_257_strict__inc__induct,axiom,
% 0.31/0.47 ! [I: nat,J2: nat,P: nat > $o] :
% 0.31/0.47 ( ( ord_less_nat @ I @ J2 )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( J2
% 0.31/0.47 = ( suc @ I3 ) )
% 0.31/0.47 => ( P @ I3 ) )
% 0.31/0.47 => ( ! [I3: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I3 @ J2 )
% 0.31/0.47 => ( ( P @ ( suc @ I3 ) )
% 0.31/0.47 => ( P @ I3 ) ) )
% 0.31/0.47 => ( P @ I ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % strict_inc_induct
% 0.31/0.47 thf(fact_258_not__less__less__Suc__eq,axiom,
% 0.31/0.47 ! [N2: nat,M2: nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ N2 @ M2 )
% 0.31/0.47 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 0.31/0.47 = ( N2 = M2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_less_Suc_eq
% 0.31/0.47 thf(fact_259_lift__Suc__mono__less,axiom,
% 0.31/0.47 ! [F2: nat > nat,N2: nat,N3: nat] :
% 0.31/0.47 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.31/0.47 => ( ( ord_less_nat @ N2 @ N3 )
% 0.31/0.47 => ( ord_less_nat @ ( F2 @ N2 ) @ ( F2 @ N3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_mono_less
% 0.31/0.47 thf(fact_260_lift__Suc__mono__less__iff,axiom,
% 0.31/0.47 ! [F2: nat > nat,N2: nat,M2: nat] :
% 0.31/0.47 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.31/0.47 => ( ( ord_less_nat @ ( F2 @ N2 ) @ ( F2 @ M2 ) )
% 0.31/0.47 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lift_Suc_mono_less_iff
% 0.31/0.47 thf(fact_261_splice_Osimps_I2_J,axiom,
% 0.31/0.47 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( splice888123018t_unit @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ Ys2 )
% 0.31/0.47 = ( cons_c1162654829t_unit @ X3 @ ( splice888123018t_unit @ Ys2 @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.simps(2)
% 0.31/0.47 thf(fact_262_splice_Osimps_I2_J,axiom,
% 0.31/0.47 ! [X3: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 0.31/0.47 ( ( splice_message_p_v @ ( cons_message_p_v @ X3 @ Xs ) @ Ys2 )
% 0.31/0.47 = ( cons_message_p_v @ X3 @ ( splice_message_p_v @ Ys2 @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.simps(2)
% 0.31/0.47 thf(fact_263_splice_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Ys2: list_c1059388851t_unit] :
% 0.31/0.47 ( ( splice888123018t_unit @ nil_co1338500125t_unit @ Ys2 )
% 0.31/0.47 = Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % splice.simps(1)
% 0.31/0.47 thf(fact_264_splice_Osimps_I1_J,axiom,
% 0.31/0.47 ! [Ys2: list_message_p_v] :
% 0.31/0.47 ( ( splice_message_p_v @ nil_message_p_v @ Ys2 )
% 0.31/0.47 = Ys2 ) ).
% 0.31/0.47
% 0.31/0.47 % splice.simps(1)
% 0.31/0.47 thf(fact_265_less__Suc__eq__0__disj,axiom,
% 0.31/0.47 ! [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 0.31/0.47 = ( ( M2 = zero_zero_nat )
% 0.31/0.47 | ? [J3: nat] :
% 0.31/0.47 ( ( M2
% 0.31/0.47 = ( suc @ J3 ) )
% 0.31/0.47 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_Suc_eq_0_disj
% 0.31/0.47 thf(fact_266_gr0__implies__Suc,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.31/0.47 => ? [M: nat] :
% 0.31/0.47 ( N2
% 0.31/0.47 = ( suc @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr0_implies_Suc
% 0.31/0.47 thf(fact_267_All__less__Suc2,axiom,
% 0.31/0.47 ! [N2: nat,P: nat > $o] :
% 0.31/0.47 ( ( ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 0.31/0.47 => ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ zero_zero_nat )
% 0.31/0.47 & ! [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N2 )
% 0.31/0.47 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % All_less_Suc2
% 0.31/0.47 thf(fact_268_gr0__conv__Suc,axiom,
% 0.31/0.47 ! [N2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.31/0.47 = ( ? [M5: nat] :
% 0.31/0.47 ( N2
% 0.31/0.47 = ( suc @ M5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr0_conv_Suc
% 0.31/0.47 thf(fact_269_Ex__less__Suc2,axiom,
% 0.31/0.47 ! [N2: nat,P: nat > $o] :
% 0.31/0.47 ( ( ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 0.31/0.47 & ( P @ I2 ) ) )
% 0.31/0.47 = ( ( P @ zero_zero_nat )
% 0.31/0.47 | ? [I2: nat] :
% 0.31/0.47 ( ( ord_less_nat @ I2 @ N2 )
% 0.31/0.47 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Ex_less_Suc2
% 0.31/0.47 thf(fact_270_lexordp__eq_OCons__eq,axiom,
% 0.31/0.47 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.31/0.47 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.47 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.47 => ( ( ord_lexordp_eq_nat @ Xs @ Ys2 )
% 0.31/0.47 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq.Cons_eq
% 0.31/0.47 thf(fact_271_lexordp__eq_OCons,axiom,
% 0.31/0.47 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.31/0.47 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.47 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % lexordp_eq.Cons
% 0.31/0.47 thf(fact_272_NatPredicateTippingPoint,axiom,
% 0.31/0.47 ! [N22: nat,Pr: nat > $o] :
% 0.31/0.47 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 0.31/0.47 => ( ( Pr @ zero_zero_nat )
% 0.31/0.47 => ( ~ ( Pr @ N22 )
% 0.31/0.47 => ? [N: nat] :
% 0.31/0.47 ( ( ord_less_nat @ N @ N22 )
% 0.31/0.47 & ( Pr @ N )
% 0.31/0.47 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % NatPredicateTippingPoint
% 0.31/0.47 thf(fact_273_less__numeral__extra_I3_J,axiom,
% 0.31/0.47 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.31/0.47
% 0.31/0.47 % less_numeral_extra(3)
% 0.31/0.47 thf(fact_274_lexordp_Ocases,axiom,
% 0.31/0.47 ! [A1: list_nat,A2: list_nat] :
% 0.31/0.47 ( ( ord_lexordp_nat @ A1 @ A2 )
% 0.31/0.47 => ( ( ( A1 = nil_nat )
% 0.31/0.47 => ! [Y3: nat,Ys3: list_nat] :
% 0.31/0.47 ( A2
% 0.31/0.47 != ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X: nat] :
% 0.31/0.47 ( ? [Xs2: list_nat] :
% 0.31/0.47 ( A1
% 0.31/0.47 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.47 => ! [Y3: nat] :
% 0.31/0.47 ( ? [Ys3: list_nat] :
% 0.31/0.47 ( A2
% 0.31/0.47 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.31/0.47 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 0.31/0.47 ( ( A1
% 0.31/0.47 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.47 => ! [Ys3: list_nat] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.47 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.31/0.47 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.31/0.48 => ~ ( ord_lexordp_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp.cases
% 0.31/0.48 thf(fact_275_lexordp_Osimps,axiom,
% 0.31/0.48 ( ord_lexordp_nat
% 0.31/0.48 = ( ^ [A12: list_nat,A22: list_nat] :
% 0.31/0.48 ( ? [Y2: nat,Ys: list_nat] :
% 0.31/0.48 ( ( A12 = nil_nat )
% 0.31/0.48 & ( A22
% 0.31/0.48 = ( cons_nat @ Y2 @ Ys ) ) )
% 0.31/0.48 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.31/0.48 ( ( A12
% 0.31/0.48 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.48 & ( A22
% 0.31/0.48 = ( cons_nat @ Y2 @ Ys ) )
% 0.31/0.48 & ( ord_less_nat @ X4 @ Y2 ) )
% 0.31/0.48 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 0.31/0.48 ( ( A12
% 0.31/0.48 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.48 & ( A22
% 0.31/0.48 = ( cons_nat @ Y2 @ Ys ) )
% 0.31/0.48 & ~ ( ord_less_nat @ X4 @ Y2 )
% 0.31/0.48 & ~ ( ord_less_nat @ Y2 @ X4 )
% 0.31/0.48 & ( ord_lexordp_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp.simps
% 0.31/0.48 thf(fact_276_lexordp__simps_I3_J,axiom,
% 0.31/0.48 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 0.31/0.48 ( ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 0.31/0.48 = ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.48 & ( ord_lexordp_nat @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp_simps(3)
% 0.31/0.48 thf(fact_277_lexordp__irreflexive,axiom,
% 0.31/0.48 ! [Xs: list_nat] :
% 0.31/0.48 ( ! [X: nat] :
% 0.31/0.48 ~ ( ord_less_nat @ X @ X )
% 0.31/0.48 => ~ ( ord_lexordp_nat @ Xs @ Xs ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp_irreflexive
% 0.31/0.48 thf(fact_278_linorder__neqE__nat,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat] :
% 0.31/0.48 ( ( X3 != Y )
% 0.31/0.48 => ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % linorder_neqE_nat
% 0.31/0.48 thf(fact_279_infinite__descent,axiom,
% 0.31/0.48 ! [P: nat > $o,N2: nat] :
% 0.31/0.48 ( ! [N: nat] :
% 0.31/0.48 ( ~ ( P @ N )
% 0.31/0.48 => ? [M3: nat] :
% 0.31/0.48 ( ( ord_less_nat @ M3 @ N )
% 0.31/0.48 & ~ ( P @ M3 ) ) )
% 0.31/0.48 => ( P @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % infinite_descent
% 0.31/0.48 thf(fact_280_nat__less__induct,axiom,
% 0.31/0.48 ! [P: nat > $o,N2: nat] :
% 0.31/0.48 ( ! [N: nat] :
% 0.31/0.48 ( ! [M3: nat] :
% 0.31/0.48 ( ( ord_less_nat @ M3 @ N )
% 0.31/0.48 => ( P @ M3 ) )
% 0.31/0.48 => ( P @ N ) )
% 0.31/0.48 => ( P @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_less_induct
% 0.31/0.48 thf(fact_281_less__irrefl__nat,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.31/0.48
% 0.31/0.48 % less_irrefl_nat
% 0.31/0.48 thf(fact_282_less__not__refl3,axiom,
% 0.31/0.48 ! [S: nat,T: nat] :
% 0.31/0.48 ( ( ord_less_nat @ S @ T )
% 0.31/0.48 => ( S != T ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_not_refl3
% 0.31/0.48 thf(fact_283_less__not__refl2,axiom,
% 0.31/0.48 ! [N2: nat,M2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ N2 @ M2 )
% 0.31/0.48 => ( M2 != N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_not_refl2
% 0.31/0.48 thf(fact_284_less__not__refl,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 0.31/0.48
% 0.31/0.48 % less_not_refl
% 0.31/0.48 thf(fact_285_nat__neq__iff,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( M2 != N2 )
% 0.31/0.48 = ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.48 | ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_neq_iff
% 0.31/0.48 thf(fact_286_lexordp_OCons,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.31/0.48 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp.Cons
% 0.31/0.48 thf(fact_287_lexordp_OCons__eq,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 0.31/0.48 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.48 => ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.31/0.48 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp.Cons_eq
% 0.31/0.48 thf(fact_288_lexordp__induct,axiom,
% 0.31/0.48 ! [Xs: list_nat,Ys2: list_nat,P: list_nat > list_nat > $o] :
% 0.31/0.48 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.31/0.48 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.48 => ( ! [X: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y3 )
% 0.31/0.48 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.48 => ( ! [X: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.48 ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ X @ Ys3 ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp_induct
% 0.31/0.48 thf(fact_289_lexordp__cases,axiom,
% 0.31/0.48 ! [Xs: list_nat,Ys2: list_nat] :
% 0.31/0.48 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 0.31/0.48 => ( ( ( Xs = nil_nat )
% 0.31/0.48 => ! [Y3: nat,Ys4: list_nat] :
% 0.31/0.48 ( Ys2
% 0.31/0.48 != ( cons_nat @ Y3 @ Ys4 ) ) )
% 0.31/0.48 => ( ! [X: nat] :
% 0.31/0.48 ( ? [Xs4: list_nat] :
% 0.31/0.48 ( Xs
% 0.31/0.48 = ( cons_nat @ X @ Xs4 ) )
% 0.31/0.48 => ! [Y3: nat] :
% 0.31/0.48 ( ? [Ys4: list_nat] :
% 0.31/0.48 ( Ys2
% 0.31/0.48 = ( cons_nat @ Y3 @ Ys4 ) )
% 0.31/0.48 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 0.31/0.48 => ~ ! [X: nat,Xs4: list_nat] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 = ( cons_nat @ X @ Xs4 ) )
% 0.31/0.48 => ! [Ys4: list_nat] :
% 0.31/0.48 ( ( Ys2
% 0.31/0.48 = ( cons_nat @ X @ Ys4 ) )
% 0.31/0.48 => ~ ( ord_lexordp_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp_cases
% 0.31/0.48 thf(fact_290_lexordp_Oinducts,axiom,
% 0.31/0.48 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 0.31/0.48 ( ( ord_lexordp_nat @ X12 @ X23 )
% 0.31/0.48 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 0.31/0.48 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y3 )
% 0.31/0.48 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 0.31/0.48 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 0.31/0.48 ( ~ ( ord_less_nat @ X @ Y3 )
% 0.31/0.48 => ( ~ ( ord_less_nat @ Y3 @ X )
% 0.31/0.48 => ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 0.31/0.48 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % lexordp.inducts
% 0.31/0.48 thf(fact_291_of__nat__0__less__iff,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N2 ) )
% 0.31/0.48 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_0_less_iff
% 0.31/0.48 thf(fact_292_Suc__pred,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.31/0.48 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 0.31/0.48 = N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % Suc_pred
% 0.31/0.48 thf(fact_293_length__greater__0__conv,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.31/0.48 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_greater_0_conv
% 0.31/0.48 thf(fact_294_length__greater__0__conv,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.31/0.48 = ( Xs != nil_message_p_v ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_greater_0_conv
% 0.31/0.48 thf(fact_295_zero__diff,axiom,
% 0.31/0.48 ! [A8: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ zero_zero_nat @ A8 )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % zero_diff
% 0.31/0.48 thf(fact_296_diff__zero,axiom,
% 0.31/0.48 ! [A8: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ A8 @ zero_zero_nat )
% 0.31/0.48 = A8 ) ).
% 0.31/0.48
% 0.31/0.48 % diff_zero
% 0.31/0.48 thf(fact_297_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.31/0.48 ! [A8: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ A8 @ A8 )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % cancel_comm_monoid_add_class.diff_cancel
% 0.31/0.48 thf(fact_298_diff__0__eq__0,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % diff_0_eq_0
% 0.31/0.48 thf(fact_299_diff__self__eq__0,axiom,
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ M2 @ M2 )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % diff_self_eq_0
% 0.31/0.48 thf(fact_300_Suc__diff__diff,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat,K: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N2 ) @ ( suc @ K ) )
% 0.31/0.48 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N2 ) @ K ) ) ).
% 0.31/0.48
% 0.31/0.48 % Suc_diff_diff
% 0.31/0.48 thf(fact_301_diff__Suc__Suc,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 0.31/0.48 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_Suc_Suc
% 0.31/0.48 thf(fact_302_of__nat__eq__0__iff,axiom,
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( ( semiri1382578993at_nat @ M2 )
% 0.31/0.48 = zero_zero_nat )
% 0.31/0.48 = ( M2 = zero_zero_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_eq_0_iff
% 0.31/0.48 thf(fact_303_of__nat__0__eq__iff,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ( ( zero_zero_nat
% 0.31/0.48 = ( semiri1382578993at_nat @ N2 ) )
% 0.31/0.48 = ( zero_zero_nat = N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_0_eq_iff
% 0.31/0.48 thf(fact_304_of__nat__0,axiom,
% 0.31/0.48 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_0
% 0.31/0.48 thf(fact_305_of__nat__less__iff,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) )
% 0.31/0.48 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_less_iff
% 0.31/0.48 thf(fact_306_length__0__conv,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = zero_zero_nat )
% 0.31/0.48 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_0_conv
% 0.31/0.48 thf(fact_307_length__0__conv,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = zero_zero_nat )
% 0.31/0.48 = ( Xs = nil_message_p_v ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_0_conv
% 0.31/0.48 thf(fact_308_zero__less__diff,axiom,
% 0.31/0.48 ! [N2: nat,M2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) )
% 0.31/0.48 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % zero_less_diff
% 0.31/0.48 thf(fact_309_diff__less,axiom,
% 0.31/0.48 ! [N2: nat,M2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.31/0.48 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.31/0.48 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_less
% 0.31/0.48 thf(fact_310_of__nat__less__imp__less,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_less_imp_less
% 0.31/0.48 thf(fact_311_less__imp__of__nat__less,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.48 => ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_imp_of_nat_less
% 0.31/0.48 thf(fact_312_less__imp__diff__less,axiom,
% 0.31/0.48 ! [J2: nat,K: nat,N2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ J2 @ K )
% 0.31/0.48 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N2 ) @ K ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_imp_diff_less
% 0.31/0.48 thf(fact_313_diff__less__mono2,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat,L: nat] :
% 0.31/0.48 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/0.48 => ( ( ord_less_nat @ M2 @ L )
% 0.31/0.48 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_less_mono2
% 0.31/0.48 thf(fact_314_Suc__diff__Suc,axiom,
% 0.31/0.48 ! [N2: nat,M2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ N2 @ M2 )
% 0.31/0.48 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N2 ) ) )
% 0.31/0.48 = ( minus_minus_nat @ M2 @ N2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Suc_diff_Suc
% 0.31/0.48 thf(fact_315_diff__less__Suc,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ ( suc @ M2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_less_Suc
% 0.31/0.48 thf(fact_316_of__nat__less__0__iff,axiom,
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_less_0_iff
% 0.31/0.48 thf(fact_317_of__nat__neq__0,axiom,
% 0.31/0.48 ! [N2: nat] :
% 0.31/0.48 ( ( semiri1382578993at_nat @ ( suc @ N2 ) )
% 0.31/0.48 != zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % of_nat_neq_0
% 0.31/0.48 thf(fact_318_length__Suc__conv,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,N2: nat] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( suc @ N2 ) )
% 0.31/0.48 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.48 & ( ( size_s1406904903t_unit @ Ys )
% 0.31/0.48 = N2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_Suc_conv
% 0.31/0.48 thf(fact_319_length__Suc__conv,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,N2: nat] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( suc @ N2 ) )
% 0.31/0.48 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.48 & ( ( size_s1168481041ge_p_v @ Ys )
% 0.31/0.48 = N2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % length_Suc_conv
% 0.31/0.48 thf(fact_320_Suc__length__conv,axiom,
% 0.31/0.48 ! [N2: nat,Xs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( suc @ N2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Xs ) )
% 0.31/0.48 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 0.31/0.48 & ( ( size_s1406904903t_unit @ Ys )
% 0.31/0.48 = N2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Suc_length_conv
% 0.31/0.48 thf(fact_321_Suc__length__conv,axiom,
% 0.31/0.48 ! [N2: nat,Xs: list_message_p_v] :
% 0.31/0.48 ( ( ( suc @ N2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Xs ) )
% 0.31/0.48 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 = ( cons_message_p_v @ Y2 @ Ys ) )
% 0.31/0.48 & ( ( size_s1168481041ge_p_v @ Ys )
% 0.31/0.48 = N2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Suc_length_conv
% 0.31/0.48 thf(fact_322_list_Osize_I3_J,axiom,
% 0.31/0.48 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % list.size(3)
% 0.31/0.48 thf(fact_323_list_Osize_I3_J,axiom,
% 0.31/0.48 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.31/0.48 = zero_zero_nat ) ).
% 0.31/0.48
% 0.31/0.48 % list.size(3)
% 0.31/0.48 thf(fact_324_list__induct2,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct2
% 0.31/0.48 thf(fact_325_list__induct2,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct2
% 0.31/0.48 thf(fact_326_list__induct2,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct2
% 0.31/0.48 thf(fact_327_list__induct2,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct2
% 0.31/0.48 thf(fact_328_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_329_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_330_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_331_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_332_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_333_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_334_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 0.31/0.48 = ( size_s1406904903t_unit @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_335_list__induct3,axiom,
% 0.31/0.48 ! [Xs: list_message_p_v,Ys2: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.31/0.48 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
% 0.31/0.48 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.31/0.48 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.31/0.48 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 0.31/0.48 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.31/0.48 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 0.31/0.48 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.31/0.48 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list_induct3
% 0.31/0.48 thf(fact_336_minus__nat_Odiff__0,axiom,
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 0.31/0.48 = M2 ) ).
% 0.31/0.48
% 0.31/0.48 % minus_nat.diff_0
% 0.31/0.48 thf(fact_337_diffs0__imp__equal,axiom,
% 0.31/0.48 ! [M2: nat,N2: nat] :
% 0.31/0.48 ( ( ( minus_minus_nat @ M2 @ N2 )
% 0.31/0.48 = zero_zero_nat )
% 0.31/0.48 => ( ( ( minus_minus_nat @ N2 @ M2 )
% 0.31/0.48 = zero_zero_nat )
% 0.31/0.48 => ( M2 = N2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diffs0_imp_equal
% 0.31/0.48 thf(fact_338_zero__induct__lemma,axiom,
% 0.31/0.48 ! [P: nat > $o,K: nat,I: nat] :
% 0.31/0.48 ( ( P @ K )
% 0.31/0.48 => ( ! [N: nat] :
% 0.31/0.48 ( ( P @ ( suc @ N ) )
% 0.31/0.48 => ( P @ N ) )
% 0.31/0.48 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % zero_induct_lemma
% 0.31/0.48 thf(fact_339_diff__right__commute,axiom,
% 0.31/0.48 ! [A8: nat,C: nat,B: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ ( minus_minus_nat @ A8 @ C ) @ B )
% 0.31/0.48 = ( minus_minus_nat @ ( minus_minus_nat @ A8 @ B ) @ C ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_right_commute
% 0.31/0.48 thf(fact_340_diff__commute,axiom,
% 0.31/0.48 ! [I: nat,J2: nat,K: nat] :
% 0.31/0.48 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J2 ) @ K )
% 0.31/0.48 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_commute
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 0.31/0.48 ( ( fe @ zero_zero_nat )
% 0.31/0.48 = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.94/1.57 ---- Embedded in THF ---
% 2.94/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.94/1.57 %%% Generated on Tue Feb 24 08:24:42 EST 2026
% 2.94/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.94/1.57 %%% Logic specification used:
% 2.94/1.57 %%% thf(spec, logic, $$dhol).
% 2.94/1.57
% 2.94/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2DTF14346.p
% See solution above
% 2.94/1.57 ------------------------
% 3.10/1.60 ---- Cleaned THF ---
% 3.10/1.60 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,
% 3.10/1.60 list_l611321411t_unit: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 3.10/1.60 list_c1059388851t_unit: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 config256849571t_unit: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 3.10/1.60 list_l1619404459ge_p_v: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 3.10/1.60 list_message_p_v: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 3.10/1.60 list_list_nat: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 message_p_v: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 3.10/1.60 messageValue_v: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 3.10/1.60 list_nat: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.10/1.60 set_nat: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_t__Nat__Onat,type,
% 3.10/1.60 nat: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_tf__s,type,
% 3.10/1.60 s: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(ty_n_tf__p,type,
% 3.10/1.60 p: $tType ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 3.10/1.60 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 3.10/1.60 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 ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 3.10/1.60 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 ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 3.10/1.60 minus_minus_nat: nat > nat > nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 3.10/1.60 zero_zero_nat: nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Obind_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 bind_c1439720399t_unit: list_c1059388851t_unit > ( config256849571t_unit > list_c1059388851t_unit ) > list_c1059388851t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Obind_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 bind_c246984691ge_p_v: list_c1059388851t_unit > ( config256849571t_unit > list_message_p_v ) > list_message_p_v ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Obind_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 bind_m595590011t_unit: list_message_p_v > ( message_p_v > list_c1059388851t_unit ) > list_c1059388851t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Obind_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 bind_m729301831ge_p_v: list_message_p_v > ( message_p_v > list_message_p_v ) > list_message_p_v ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Ocount__list_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 count_1396868135t_unit: list_c1059388851t_unit > config256849571t_unit > nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Ocount__list_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 count_1322329499ge_p_v: list_message_p_v > message_p_v > nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 3.10/1.60
% 3.10/1.60 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,
% 3.10/1.60 cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 3.10/1.60 cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 3.10/1.60 cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 3.10/1.60 cons_nat: nat > list_nat > list_nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 nil_message_p_v: list_message_p_v ).
% 3.10/1.60
% 3.10/1.60 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,
% 3.10/1.60 nil_li307996205t_unit: list_l611321411t_unit ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 3.10/1.60 nil_list_message_p_v: list_l1619404459ge_p_v ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 3.10/1.60 nil_list_nat: list_list_nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 3.10/1.60 nil_nat: list_nat ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 listre990624391t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.60 listre823101243ge_p_v: ( config256849571t_unit > message_p_v > $o ) > list_c1059388851t_unit > list_message_p_v > $o ).
% 3.10/1.60
% 3.10/1.60 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.60 listre1171706563t_unit: ( message_p_v > config256849571t_unit > $o ) > list_message_p_v > list_c1059388851t_unit > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Olistrelp_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 listre1295695359ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 map_ta91747645t_unit: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 map_ta782801413ge_p_v: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 map_ta1131406733t_unit: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omap__tailrec__rev_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 map_ta1016577461ge_p_v: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omember_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 member1087090632t_unit: list_c1059388851t_unit > config256849571t_unit > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Omember_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 member_message_p_v: list_message_p_v > message_p_v > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oord_Olexordp__eq_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 lexord1758866263t_unit: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oord_Olexordp__eq_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 lexord2101627499ge_p_v: ( message_p_v > message_p_v > $o ) > list_message_p_v > list_message_p_v > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oord__class_Olexordp_001t__Nat__Onat,type,
% 3.10/1.61 ord_lexordp_nat: list_nat > list_nat > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Nat__Onat,type,
% 3.10/1.61 ord_lexordp_eq_nat: list_nat > list_nat > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Osplice_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 splice888123018t_unit: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Osplice_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 splice_message_p_v: list_message_p_v > list_message_p_v > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 3.10/1.61 subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 3.10/1.61 subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_Nat_OSuc,type,
% 3.10/1.61 suc: nat > nat ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 3.10/1.61 semiri1382578993at_nat: nat > nat ).
% 3.10/1.61
% 3.10/1.61 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,
% 3.10/1.61 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 3.10/1.61 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.10/1.61 ord_less_nat: nat > nat > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_c_member_001t__Nat__Onat,type,
% 3.10/1.61 member_nat: nat > set_nat > $o ).
% 3.10/1.61
% 3.10/1.61 thf(sy_v_cfg,type,
% 3.10/1.61 cfg: config256849571t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_v_fStepCfg____,type,
% 3.10/1.61 fStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_v_fStepMsg____,type,
% 3.10/1.61 fStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(sy_v_fe____,type,
% 3.10/1.61 fe: nat > list_c1059388851t_unit ).
% 3.10/1.61
% 3.10/1.61 thf(sy_v_ft____,type,
% 3.10/1.61 ft: nat > list_message_p_v ).
% 3.10/1.61
% 3.10/1.61 thf(fact_0_ft__def,axiom,
% 3.10/1.61 ( ft
% 3.10/1.61 = ( fLPThe536531371_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_1_fe__def,axiom,
% 3.10/1.61 ( fe
% 3.10/1.61 = ( fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_2_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 3.10/1.61 = ( cons_c1162654829t_unit @ Cfg @ nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_3_list_Oinject,axiom,
% 3.10/1.61 ! [X21: list_message_p_v,X22: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( ( cons_l233104475ge_p_v @ X21 @ X22 )
% 3.10/1.61 = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
% 3.10/1.61 = ( ( X21 = Y21 )
% 3.10/1.61 & ( X22 = Y22 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_4_list_Oinject,axiom,
% 3.10/1.61 ! [X21: list_c1059388851t_unit,X22: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
% 3.10/1.61 ( ( ( cons_l1083444861t_unit @ X21 @ X22 )
% 3.10/1.61 = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
% 3.10/1.61 = ( ( X21 = Y21 )
% 3.10/1.61 & ( X22 = Y22 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_5_list_Oinject,axiom,
% 3.10/1.61 ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 3.10/1.61 ( ( ( cons_nat @ X21 @ X22 )
% 3.10/1.61 = ( cons_nat @ Y21 @ Y22 ) )
% 3.10/1.61 = ( ( X21 = Y21 )
% 3.10/1.61 & ( X22 = Y22 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_6_list_Oinject,axiom,
% 3.10/1.61 ! [X21: message_p_v,X22: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
% 3.10/1.61 ( ( ( cons_message_p_v @ X21 @ X22 )
% 3.10/1.61 = ( cons_message_p_v @ Y21 @ Y22 ) )
% 3.10/1.61 = ( ( X21 = Y21 )
% 3.10/1.61 & ( X22 = Y22 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_7_list_Oinject,axiom,
% 3.10/1.61 ! [X21: config256849571t_unit,X22: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( cons_c1162654829t_unit @ X21 @ X22 )
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
% 3.10/1.61 = ( ( X21 = Y21 )
% 3.10/1.61 & ( X22 = Y22 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_8_list_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X21: list_message_p_v,X22: list_l1619404459ge_p_v] :
% 3.10/1.61 ( nil_list_message_p_v
% 3.10/1.61 != ( cons_l233104475ge_p_v @ X21 @ X22 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_9_list_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X21: list_c1059388851t_unit,X22: list_l611321411t_unit] :
% 3.10/1.61 ( nil_li307996205t_unit
% 3.10/1.61 != ( cons_l1083444861t_unit @ X21 @ X22 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_10_list_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X21: nat,X22: list_nat] :
% 3.10/1.61 ( nil_nat
% 3.10/1.61 != ( cons_nat @ X21 @ X22 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_11_list_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X21: message_p_v,X22: list_message_p_v] :
% 3.10/1.61 ( nil_message_p_v
% 3.10/1.61 != ( cons_message_p_v @ X21 @ X22 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_12_list_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X21: config256849571t_unit,X22: list_c1059388851t_unit] :
% 3.10/1.61 ( nil_co1338500125t_unit
% 3.10/1.61 != ( cons_c1162654829t_unit @ X21 @ X22 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_13_list_OdiscI,axiom,
% 3.10/1.61 ! [List: list_l1619404459ge_p_v,X21: list_message_p_v,X22: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( List
% 3.10/1.61 = ( cons_l233104475ge_p_v @ X21 @ X22 ) )
% 3.10/1.61 => ( List != nil_list_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_14_list_OdiscI,axiom,
% 3.10/1.61 ! [List: list_l611321411t_unit,X21: list_c1059388851t_unit,X22: list_l611321411t_unit] :
% 3.10/1.61 ( ( List
% 3.10/1.61 = ( cons_l1083444861t_unit @ X21 @ X22 ) )
% 3.10/1.61 => ( List != nil_li307996205t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_15_list_OdiscI,axiom,
% 3.10/1.61 ! [List: list_nat,X21: nat,X22: list_nat] :
% 3.10/1.61 ( ( List
% 3.10/1.61 = ( cons_nat @ X21 @ X22 ) )
% 3.10/1.61 => ( List != nil_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_16_list_OdiscI,axiom,
% 3.10/1.61 ! [List: list_message_p_v,X21: message_p_v,X22: list_message_p_v] :
% 3.10/1.61 ( ( List
% 3.10/1.61 = ( cons_message_p_v @ X21 @ X22 ) )
% 3.10/1.61 => ( List != nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_17_list_OdiscI,axiom,
% 3.10/1.61 ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X22: list_c1059388851t_unit] :
% 3.10/1.61 ( ( List
% 3.10/1.61 = ( cons_c1162654829t_unit @ X21 @ X22 ) )
% 3.10/1.61 => ( List != nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_18_list_Oexhaust,axiom,
% 3.10/1.61 ! [Y: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( Y != nil_list_message_p_v )
% 3.10/1.61 => ~ ! [X212: list_message_p_v,X222: list_l1619404459ge_p_v] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( cons_l233104475ge_p_v @ X212 @ X222 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_19_list_Oexhaust,axiom,
% 3.10/1.61 ! [Y: list_l611321411t_unit] :
% 3.10/1.61 ( ( Y != nil_li307996205t_unit )
% 3.10/1.61 => ~ ! [X212: list_c1059388851t_unit,X222: list_l611321411t_unit] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( cons_l1083444861t_unit @ X212 @ X222 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_20_list_Oexhaust,axiom,
% 3.10/1.61 ! [Y: list_nat] :
% 3.10/1.61 ( ( Y != nil_nat )
% 3.10/1.61 => ~ ! [X212: nat,X222: list_nat] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( cons_nat @ X212 @ X222 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_21_list_Oexhaust,axiom,
% 3.10/1.61 ! [Y: list_message_p_v] :
% 3.10/1.61 ( ( Y != nil_message_p_v )
% 3.10/1.61 => ~ ! [X212: message_p_v,X222: list_message_p_v] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( cons_message_p_v @ X212 @ X222 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_22_list_Oexhaust,axiom,
% 3.10/1.61 ! [Y: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Y != nil_co1338500125t_unit )
% 3.10/1.61 => ~ ! [X212: config256849571t_unit,X222: list_c1059388851t_unit] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( cons_c1162654829t_unit @ X212 @ X222 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_23_list_Oinducts,axiom,
% 3.10/1.61 ! [P: list_l1619404459ge_p_v > $o,List: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [X1: list_message_p_v,X2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X1 @ X2 ) ) )
% 3.10/1.61 => ( P @ List ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_24_list_Oinducts,axiom,
% 3.10/1.61 ! [P: list_l611321411t_unit > $o,List: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ nil_li307996205t_unit )
% 3.10/1.61 => ( ! [X1: list_c1059388851t_unit,X2: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X1 @ X2 ) ) )
% 3.10/1.61 => ( P @ List ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_25_list_Oinducts,axiom,
% 3.10/1.61 ! [P: list_nat > $o,List: list_nat] :
% 3.10/1.61 ( ( P @ nil_nat )
% 3.10/1.61 => ( ! [X1: nat,X2: list_nat] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( P @ ( cons_nat @ X1 @ X2 ) ) )
% 3.10/1.61 => ( P @ List ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_26_list_Oinducts,axiom,
% 3.10/1.61 ! [P: list_message_p_v > $o,List: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_message_p_v )
% 3.10/1.61 => ( ! [X1: message_p_v,X2: list_message_p_v] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X1 @ X2 ) ) )
% 3.10/1.61 => ( P @ List ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_27_list_Oinducts,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X1: config256849571t_unit,X2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ X2 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X1 @ X2 ) ) )
% 3.10/1.61 => ( P @ List ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_28_neq__Nil__conv,axiom,
% 3.10/1.61 ! [Xs: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( Xs != nil_list_message_p_v )
% 3.10/1.61 = ( ? [Y2: list_message_p_v,Ys: list_l1619404459ge_p_v] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_l233104475ge_p_v @ Y2 @ Ys ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_29_neq__Nil__conv,axiom,
% 3.10/1.61 ! [Xs: list_l611321411t_unit] :
% 3.10/1.61 ( ( Xs != nil_li307996205t_unit )
% 3.10/1.61 = ( ? [Y2: list_c1059388851t_unit,Ys: list_l611321411t_unit] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_l1083444861t_unit @ Y2 @ Ys ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_30_neq__Nil__conv,axiom,
% 3.10/1.61 ! [Xs: list_nat] :
% 3.10/1.61 ( ( Xs != nil_nat )
% 3.10/1.61 = ( ? [Y2: nat,Ys: list_nat] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_31_neq__Nil__conv,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v] :
% 3.10/1.61 ( ( Xs != nil_message_p_v )
% 3.10/1.61 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_32_neq__Nil__conv,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xs != nil_co1338500125t_unit )
% 3.10/1.61 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_33_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_message_p_v @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_message_p_v )
% 3.10/1.61 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_34_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_message_p_v )
% 3.10/1.61 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_35_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_36_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_37_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ( P @ nil_nat @ nil_nat )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_nat )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_38_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_message_p_v > list_nat > $o,Xs: list_message_p_v,Ys2: list_nat] :
% 3.10/1.61 ( ( P @ nil_message_p_v @ nil_nat )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X @ Xs2 ) @ nil_nat )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_message_p_v @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_39_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_nat > list_message_p_v > $o,Xs: list_nat,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_nat @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_message_p_v )
% 3.10/1.61 => ( ! [Y3: message_p_v,Ys3: list_message_p_v] : ( P @ nil_nat @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_40_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_l1619404459ge_p_v > list_nat > $o,Xs: list_l1619404459ge_p_v,Ys2: list_nat] :
% 3.10/1.61 ( ( P @ nil_list_message_p_v @ nil_nat )
% 3.10/1.61 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ nil_nat )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_list_message_p_v @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_41_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_nat > list_l1619404459ge_p_v > $o,Xs: list_nat,Ys2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ nil_nat @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [Y3: list_message_p_v,Ys3: list_l1619404459ge_p_v] : ( P @ nil_nat @ ( cons_l233104475ge_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Y3: list_message_p_v,Ys3: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_42_list__induct2_H,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > list_nat > $o,Xs: list_c1059388851t_unit,Ys2: list_nat] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit @ nil_nat )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ nil_nat )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_co1338500125t_unit @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_43_splice_Oinduct,axiom,
% 3.10/1.61 ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v,Ys3: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ Ys3 @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) @ Ys3 ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_44_splice_Oinduct,axiom,
% 3.10/1.61 ! [P: list_l611321411t_unit > list_l611321411t_unit > $o,A0: list_l611321411t_unit,A1: list_l611321411t_unit] :
% 3.10/1.61 ( ! [X_1: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ X_1 )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Ys3: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ Ys3 @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) @ Ys3 ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_45_splice_Oinduct,axiom,
% 3.10/1.61 ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 3.10/1.61 ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Ys3 @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ Ys3 ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_46_splice_Oinduct,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 3.10/1.61 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ Ys3 @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Ys3 ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_47_splice_Oinduct,axiom,
% 3.10/1.61 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 3.10/1.61 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ Ys3 @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ Ys3 ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_48_induct__list012,axiom,
% 3.10/1.61 ! [P: list_l1619404459ge_p_v > $o,Xs: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 3.10/1.61 => ( ! [X: list_message_p_v,Y3: list_message_p_v,Zs: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ Zs )
% 3.10/1.61 => ( ( P @ ( cons_l233104475ge_p_v @ Y3 @ Zs ) )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_49_induct__list012,axiom,
% 3.10/1.61 ! [P: list_l611321411t_unit > $o,Xs: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ nil_li307996205t_unit )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Zs: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ Zs )
% 3.10/1.61 => ( ( P @ ( cons_l1083444861t_unit @ Y3 @ Zs ) )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_50_induct__list012,axiom,
% 3.10/1.61 ! [P: list_nat > $o,Xs: list_nat] :
% 3.10/1.61 ( ( P @ nil_nat )
% 3.10/1.61 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Zs: list_nat] :
% 3.10/1.61 ( ( P @ Zs )
% 3.10/1.61 => ( ( P @ ( cons_nat @ Y3 @ Zs ) )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_51_induct__list012,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ Zs )
% 3.10/1.61 => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_52_induct__list012,axiom,
% 3.10/1.61 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
% 3.10/1.61 ( ( P @ Zs )
% 3.10/1.61 => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_53_min__list_Ocases,axiom,
% 3.10/1.61 ! [X3: list_nat] :
% 3.10/1.61 ( ! [X: nat,Xs2: list_nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_nat @ X @ Xs2 ) )
% 3.10/1.61 => ( X3 = nil_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_54_min__list_Oinduct,axiom,
% 3.10/1.61 ! [P: list_nat > $o,A0: list_nat] :
% 3.10/1.61 ( ! [X: nat,Xs2: list_nat] :
% 3.10/1.61 ( ! [X213: nat,X223: list_nat] :
% 3.10/1.61 ( ( Xs2
% 3.10/1.61 = ( cons_nat @ X213 @ X223 ) )
% 3.10/1.61 => ( P @ Xs2 ) )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( P @ nil_nat )
% 3.10/1.61 => ( P @ A0 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_55_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 3.10/1.61 = nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_56_zero__reorient,axiom,
% 3.10/1.61 ! [X3: nat] :
% 3.10/1.61 ( ( zero_zero_nat = X3 )
% 3.10/1.61 = ( X3 = zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_57_not__Cons__self2,axiom,
% 3.10/1.61 ! [X3: list_message_p_v,Xs: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( cons_l233104475ge_p_v @ X3 @ Xs )
% 3.10/1.61 != Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_58_not__Cons__self2,axiom,
% 3.10/1.61 ! [X3: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
% 3.10/1.61 ( ( cons_l1083444861t_unit @ X3 @ Xs )
% 3.10/1.61 != Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_59_not__Cons__self2,axiom,
% 3.10/1.61 ! [X3: nat,Xs: list_nat] :
% 3.10/1.61 ( ( cons_nat @ X3 @ Xs )
% 3.10/1.61 != Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_60_not__Cons__self2,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( cons_c1162654829t_unit @ X3 @ Xs )
% 3.10/1.61 != Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_61_not__Cons__self2,axiom,
% 3.10/1.61 ! [X3: message_p_v,Xs: list_message_p_v] :
% 3.10/1.61 ( ( cons_message_p_v @ X3 @ Xs )
% 3.10/1.61 != Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_62_strict__sorted_Oinduct,axiom,
% 3.10/1.61 ! [P: list_nat > $o,A0: list_nat] :
% 3.10/1.61 ( ( P @ nil_nat )
% 3.10/1.61 => ( ! [X: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_63_strict__sorted_Ocases,axiom,
% 3.10/1.61 ! [X3: list_nat] :
% 3.10/1.61 ( ( X3 != nil_nat )
% 3.10/1.61 => ~ ! [X: nat,Ys3: list_nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_nat @ X @ Ys3 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_64_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [F: message_p_v > message_p_v,A: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_65_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [F: message_p_v > config256849571t_unit,A: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_66_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 3.10/1.61 => ( ! [F: config256849571t_unit > message_p_v,A: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_c1162654829t_unit @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_67_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 3.10/1.61 => ( ! [F: config256849571t_unit > config256849571t_unit,A: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_c1162654829t_unit @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_68_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > nat ) > list_nat > list_nat > $o,A0: nat > nat,A1: list_nat,A2: list_nat] :
% 3.10/1.61 ( ! [F: nat > nat,X_1: list_nat] : ( P @ F @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [F: nat > nat,A: nat,As: list_nat,Bs: list_nat] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_69_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > message_p_v ) > list_nat > list_message_p_v > $o,A0: nat > message_p_v,A1: list_nat,A2: list_message_p_v] :
% 3.10/1.61 ( ! [F: nat > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [F: nat > message_p_v,A: nat,As: list_nat,Bs: list_message_p_v] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_70_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( message_p_v > nat ) > list_message_p_v > list_nat > $o,A0: message_p_v > nat,A1: list_message_p_v,A2: list_nat] :
% 3.10/1.61 ( ! [F: message_p_v > nat,X_1: list_nat] : ( P @ F @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [F: message_p_v > nat,A: message_p_v,As: list_message_p_v,Bs: list_nat] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_message_p_v @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_71_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > list_message_p_v ) > list_nat > list_l1619404459ge_p_v > $o,A0: nat > list_message_p_v,A1: list_nat,A2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ! [F: nat > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [F: nat > list_message_p_v,A: nat,As: list_nat,Bs: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_72_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( list_message_p_v > nat ) > list_l1619404459ge_p_v > list_nat > $o,A0: list_message_p_v > nat,A1: list_l1619404459ge_p_v,A2: list_nat] :
% 3.10/1.61 ( ! [F: list_message_p_v > nat,X_1: list_nat] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [F: list_message_p_v > nat,A: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_nat] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_nat @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_l233104475ge_p_v @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_73_map__tailrec__rev_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > config256849571t_unit ) > list_nat > list_c1059388851t_unit > $o,A0: nat > config256849571t_unit,A1: list_nat,A2: list_c1059388851t_unit] :
% 3.10/1.61 ( ! [F: nat > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [F: nat > config256849571t_unit,A: nat,As: list_nat,Bs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A ) @ Bs ) )
% 3.10/1.61 => ( P @ F @ ( cons_nat @ A @ As ) @ Bs ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_74_list__nonempty__induct,axiom,
% 3.10/1.61 ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
% 3.10/1.61 ( ( Xs != nil_list_message_p_v )
% 3.10/1.61 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 3.10/1.61 => ( ! [X: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( Xs2 != nil_list_message_p_v )
% 3.10/1.61 => ( ( P @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_75_list__nonempty__induct,axiom,
% 3.10/1.61 ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
% 3.10/1.61 ( ( Xs != nil_li307996205t_unit )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 3.10/1.61 ( ( Xs2 != nil_li307996205t_unit )
% 3.10/1.61 => ( ( P @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_76_list__nonempty__induct,axiom,
% 3.10/1.61 ! [Xs: list_nat,P: list_nat > $o] :
% 3.10/1.61 ( ( Xs != nil_nat )
% 3.10/1.61 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat] :
% 3.10/1.61 ( ( Xs2 != nil_nat )
% 3.10/1.61 => ( ( P @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_77_list__nonempty__induct,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( Xs != nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xs2 != nil_co1338500125t_unit )
% 3.10/1.61 => ( ( P @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_78_list__nonempty__induct,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
% 3.10/1.61 ( ( Xs != nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( Xs2 != nil_message_p_v )
% 3.10/1.61 => ( ( P @ Xs2 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ Xs ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_79_successively_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 3.10/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
% 3.10/1.61 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_80_successively_Oinduct,axiom,
% 3.10/1.61 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 3.10/1.61 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 3.10/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 3.10/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
% 3.10/1.61 => ( P @ P2 @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_81_successively_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 3.10/1.61 ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 3.10/1.61 => ( ! [P2: nat > nat > $o,X: nat] : ( P @ P2 @ ( cons_nat @ X @ nil_nat ) )
% 3.10/1.61 => ( ! [P2: nat > nat > $o,X: nat,Y3: nat,Xs2: list_nat] :
% 3.10/1.61 ( ( P @ P2 @ ( cons_nat @ Y3 @ Xs2 ) )
% 3.10/1.61 => ( P @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_82_successively_Oinduct,axiom,
% 3.10/1.61 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 3.10/1.61 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 3.10/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
% 3.10/1.61 => ( P @ P2 @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_83_successively_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 3.10/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 3.10/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
% 3.10/1.61 => ( P @ P2 @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_84_remdups__adj_Oinduct,axiom,
% 3.10/1.61 ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [X: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 3.10/1.61 => ( ! [X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( ( X = Y3 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( ( X != Y3 )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
% 3.10/1.61 => ( P @ ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_85_remdups__adj_Oinduct,axiom,
% 3.10/1.61 ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ nil_li307996205t_unit )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 3.10/1.61 ( ( ( X = Y3 )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( ( X != Y3 )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
% 3.10/1.61 => ( P @ ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_86_remdups__adj_Oinduct,axiom,
% 3.10/1.61 ! [P: list_nat > $o,A0: list_nat] :
% 3.10/1.61 ( ( P @ nil_nat )
% 3.10/1.61 => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Xs2: list_nat] :
% 3.10/1.61 ( ( ( X = Y3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( ( X != Y3 )
% 3.10/1.61 => ( P @ ( cons_nat @ Y3 @ Xs2 ) ) )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_87_remdups__adj_Oinduct,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( X = Y3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( ( X != Y3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_88_remdups__adj_Oinduct,axiom,
% 3.10/1.61 ! [P: list_message_p_v > $o,A0: list_message_p_v] :
% 3.10/1.61 ( ( P @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v] : ( P @ ( cons_message_p_v @ X @ nil_message_p_v ) )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( ( X = Y3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) ) )
% 3.10/1.61 => ( ( ( X != Y3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
% 3.10/1.61 => ( P @ A0 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_89_sorted__wrt_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 3.10/1.61 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X: list_message_p_v,Ys3: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( P @ P2 @ Ys3 )
% 3.10/1.61 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_90_sorted__wrt_Oinduct,axiom,
% 3.10/1.61 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 3.10/1.61 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 3.10/1.61 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X: list_c1059388851t_unit,Ys3: list_l611321411t_unit] :
% 3.10/1.61 ( ( P @ P2 @ Ys3 )
% 3.10/1.61 => ( P @ P2 @ ( cons_l1083444861t_unit @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_91_sorted__wrt_Oinduct,axiom,
% 3.10/1.61 ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 3.10/1.61 ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 3.10/1.61 => ( ! [P2: nat > nat > $o,X: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( P @ P2 @ Ys3 )
% 3.10/1.61 => ( P @ P2 @ ( cons_nat @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_92_sorted__wrt_Oinduct,axiom,
% 3.10/1.61 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 3.10/1.61 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ P2 @ Ys3 )
% 3.10/1.61 => ( P @ P2 @ ( cons_c1162654829t_unit @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_93_sorted__wrt_Oinduct,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 3.10/1.61 => ( ! [P2: message_p_v > message_p_v > $o,X: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ P2 @ Ys3 )
% 3.10/1.61 => ( P @ P2 @ ( cons_message_p_v @ X @ Ys3 ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_94_remdups__adj_Ocases,axiom,
% 3.10/1.61 ! [X3: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( X3 != nil_list_message_p_v )
% 3.10/1.61 => ( ! [X: list_message_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l233104475ge_p_v @ X @ nil_list_message_p_v ) )
% 3.10/1.61 => ~ ! [X: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l233104475ge_p_v @ X @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_95_remdups__adj_Ocases,axiom,
% 3.10/1.61 ! [X3: list_l611321411t_unit] :
% 3.10/1.61 ( ( X3 != nil_li307996205t_unit )
% 3.10/1.61 => ( ! [X: list_c1059388851t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l1083444861t_unit @ X @ nil_li307996205t_unit ) )
% 3.10/1.61 => ~ ! [X: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l1083444861t_unit @ X @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_96_remdups__adj_Ocases,axiom,
% 3.10/1.61 ! [X3: list_nat] :
% 3.10/1.61 ( ( X3 != nil_nat )
% 3.10/1.61 => ( ! [X: nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_nat @ X @ nil_nat ) )
% 3.10/1.61 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_nat @ X @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_97_remdups__adj_Ocases,axiom,
% 3.10/1.61 ! [X3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( X3 != nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_c1162654829t_unit @ X @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_98_remdups__adj_Ocases,axiom,
% 3.10/1.61 ! [X3: list_message_p_v] :
% 3.10/1.61 ( ( X3 != nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_message_p_v @ X @ nil_message_p_v ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_message_p_v @ X @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_99_transpose_Ocases,axiom,
% 3.10/1.61 ! [X3: list_list_nat] :
% 3.10/1.61 ( ( X3 != nil_list_nat )
% 3.10/1.61 => ( ! [Xss: list_list_nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_list_nat @ nil_nat @ Xss ) )
% 3.10/1.61 => ~ ! [X: nat,Xs2: list_nat,Xss: list_list_nat] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_list_nat @ ( cons_nat @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_100_transpose_Ocases,axiom,
% 3.10/1.61 ! [X3: list_l611321411t_unit] :
% 3.10/1.61 ( ( X3 != nil_li307996205t_unit )
% 3.10/1.61 => ( ! [Xss: list_l611321411t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_101_transpose_Ocases,axiom,
% 3.10/1.61 ! [X3: list_l1619404459ge_p_v] :
% 3.10/1.61 ( ( X3 != nil_list_message_p_v )
% 3.10/1.61 => ( ! [Xss: list_l1619404459ge_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
% 3.10/1.61 ( X3
% 3.10/1.61 != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_102_shuffles_Oinduct,axiom,
% 3.10/1.61 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 3.10/1.61 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 3.10/1.61 => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_103_shuffles_Oinduct,axiom,
% 3.10/1.61 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 3.10/1.61 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( P @ ( cons_message_p_v @ X @ Xs2 ) @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_104_infiniteExecutionCfg_Oelims,axiom,
% 3.10/1.61 ! [X3: 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] :
% 3.10/1.61 ( ( ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xc = zero_zero_nat )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 3.10/1.61 => ~ ! [N: nat] :
% 3.10/1.61 ( ( Xc
% 3.10/1.61 = ( suc @ N ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( Xa @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_105_infiniteExecutionMsg_Oelims,axiom,
% 3.10/1.61 ! [X3: 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] :
% 3.10/1.61 ( ( ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xc = zero_zero_nat )
% 3.10/1.61 => ( Y != nil_message_p_v ) )
% 3.10/1.61 => ~ ! [N: nat] :
% 3.10/1.61 ( ( Xc
% 3.10/1.61 = ( suc @ N ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( Xb @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_106_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 3.10/1.61 ! [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,N2: nat] :
% 3.10/1.61 ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 3.10/1.61 = ( FStepCfg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_107_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 3.10/1.61 ! [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,N2: nat] :
% 3.10/1.61 ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 3.10/1.61 = ( FStepMsg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_108_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 3.10/1.61 = ( cons_c1162654829t_unit @ Cfg @ nil_co1338500125t_unit ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_109_n__lists__Nil,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ( N2 = zero_zero_nat )
% 3.10/1.61 => ( ( n_list1987762709t_unit @ N2 @ nil_co1338500125t_unit )
% 3.10/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
% 3.10/1.61 & ( ( N2 != zero_zero_nat )
% 3.10/1.61 => ( ( n_list1987762709t_unit @ N2 @ nil_co1338500125t_unit )
% 3.10/1.61 = nil_li307996205t_unit ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_110_n__lists__Nil,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ( N2 = zero_zero_nat )
% 3.10/1.61 => ( ( n_lists_message_p_v @ N2 @ nil_message_p_v )
% 3.10/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
% 3.10/1.61 & ( ( N2 != zero_zero_nat )
% 3.10/1.61 => ( ( n_lists_message_p_v @ N2 @ nil_message_p_v )
% 3.10/1.61 = nil_list_message_p_v ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_111_insert__Nil,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit] :
% 3.10/1.61 ( ( insert1308755079t_unit @ X3 @ nil_co1338500125t_unit )
% 3.10/1.61 = ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_112_insert__Nil,axiom,
% 3.10/1.61 ! [X3: message_p_v] :
% 3.10/1.61 ( ( insert_message_p_v @ X3 @ nil_message_p_v )
% 3.10/1.61 = ( cons_message_p_v @ X3 @ nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_113_nths__singleton,axiom,
% 3.10/1.61 ! [A3: set_nat,X3: config256849571t_unit] :
% 3.10/1.61 ( ( ( member_nat @ zero_zero_nat @ A3 )
% 3.10/1.61 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) @ A3 )
% 3.10/1.61 = ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 3.10/1.61 & ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 3.10/1.61 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) @ A3 )
% 3.10/1.61 = nil_co1338500125t_unit ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_114_nths__singleton,axiom,
% 3.10/1.61 ! [A3: set_nat,X3: message_p_v] :
% 3.10/1.61 ( ( ( member_nat @ zero_zero_nat @ A3 )
% 3.10/1.61 => ( ( nths_message_p_v @ ( cons_message_p_v @ X3 @ nil_message_p_v ) @ A3 )
% 3.10/1.61 = ( cons_message_p_v @ X3 @ nil_message_p_v ) ) )
% 3.10/1.61 & ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 3.10/1.61 => ( ( nths_message_p_v @ ( cons_message_p_v @ X3 @ nil_message_p_v ) @ A3 )
% 3.10/1.61 = nil_message_p_v ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_115_list__ex1__simps_I1_J,axiom,
% 3.10/1.61 ! [P: config256849571t_unit > $o] :
% 3.10/1.61 ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_116_list__ex1__simps_I1_J,axiom,
% 3.10/1.61 ! [P: message_p_v > $o] :
% 3.10/1.61 ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_117_n__lists_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
% 3.10/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_118_n__lists_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v] :
% 3.10/1.61 ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
% 3.10/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_119_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 3.10/1.61 ! [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] :
% 3.10/1.61 ( ! [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] : ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 3.10/1.61 => ( ! [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,N: nat] :
% 3.10/1.61 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 3.10/1.61 => ( ! [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] : ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 3.10/1.61 => ( ! [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,N: nat] :
% 3.10/1.61 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 3.10/1.61 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_120_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 3.10/1.61 ! [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,A32: nat] :
% 3.10/1.61 ( ! [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] : ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 3.10/1.61 => ( ! [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,N: nat] :
% 3.10/1.61 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 3.10/1.61 => ( ! [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] : ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 3.10/1.61 => ( ! [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,N: nat] :
% 3.10/1.61 ( ( P @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N )
% 3.10/1.61 => ( Q @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) ) ) )
% 3.10/1.61 => ( P @ A0 @ A1 @ A2 @ A32 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_121_nths__nil,axiom,
% 3.10/1.61 ! [A3: set_nat] :
% 3.10/1.61 ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A3 )
% 3.10/1.61 = nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_122_nths__nil,axiom,
% 3.10/1.61 ! [A3: set_nat] :
% 3.10/1.61 ( ( nths_message_p_v @ nil_message_p_v @ A3 )
% 3.10/1.61 = nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_123_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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,N2: nat] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 3.10/1.61 = ( FStepMsg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_124_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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,N2: nat] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) )
% 3.10/1.61 = ( FStepCfg @ ( fLPThe1519354920_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) @ ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_125_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X3: 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] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xc = zero_zero_nat )
% 3.10/1.61 => ( Y != nil_message_p_v ) )
% 3.10/1.61 => ~ ! [N: nat] :
% 3.10/1.61 ( ( Xc
% 3.10/1.61 = ( suc @ N ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( Xb @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_126_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,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] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( fLPThe536531371_p_v_s @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 3.10/1.61 = nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_127_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 3.10/1.61 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X3: 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] :
% 3.10/1.61 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 3.10/1.61 => ( ( ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ Xc )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xc = zero_zero_nat )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( cons_c1162654829t_unit @ X3 @ nil_co1338500125t_unit ) ) )
% 3.10/1.61 => ~ ! [N: nat] :
% 3.10/1.61 ( ( Xc
% 3.10/1.61 = ( suc @ N ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( Xa @ ( fLPThe1519354920_p_v_s @ X3 @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X3 @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_128_old_Onat_Oinject,axiom,
% 3.10/1.61 ! [Nat: nat,Nat2: nat] :
% 3.10/1.61 ( ( ( suc @ Nat )
% 3.10/1.61 = ( suc @ Nat2 ) )
% 3.10/1.61 = ( Nat = Nat2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_129_nat_Oinject,axiom,
% 3.10/1.61 ! [X23: nat,Y23: nat] :
% 3.10/1.61 ( ( ( suc @ X23 )
% 3.10/1.61 = ( suc @ Y23 ) )
% 3.10/1.61 = ( X23 = Y23 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_130_nat_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [X23: nat] :
% 3.10/1.61 ( zero_zero_nat
% 3.10/1.61 != ( suc @ X23 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_131_old_Onat_Odistinct_I2_J,axiom,
% 3.10/1.61 ! [Nat2: nat] :
% 3.10/1.61 ( ( suc @ Nat2 )
% 3.10/1.61 != zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_132_old_Onat_Odistinct_I1_J,axiom,
% 3.10/1.61 ! [Nat2: nat] :
% 3.10/1.61 ( zero_zero_nat
% 3.10/1.61 != ( suc @ Nat2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_133_nat_OdiscI,axiom,
% 3.10/1.61 ! [Nat: nat,X23: nat] :
% 3.10/1.61 ( ( Nat
% 3.10/1.61 = ( suc @ X23 ) )
% 3.10/1.61 => ( Nat != zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_134_nat__induct,axiom,
% 3.10/1.61 ! [P: nat > $o,N2: nat] :
% 3.10/1.61 ( ( P @ zero_zero_nat )
% 3.10/1.61 => ( ! [N: nat] :
% 3.10/1.61 ( ( P @ N )
% 3.10/1.61 => ( P @ ( suc @ N ) ) )
% 3.10/1.61 => ( P @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_135_Suc__inject,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat] :
% 3.10/1.61 ( ( ( suc @ X3 )
% 3.10/1.61 = ( suc @ Y ) )
% 3.10/1.61 => ( X3 = Y ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_136_n__not__Suc__n,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( N2
% 3.10/1.61 != ( suc @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_137_not0__implies__Suc,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( N2 != zero_zero_nat )
% 3.10/1.61 => ? [M: nat] :
% 3.10/1.61 ( N2
% 3.10/1.61 = ( suc @ M ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_138_old_Onat_Oinducts,axiom,
% 3.10/1.61 ! [P: nat > $o,Nat: nat] :
% 3.10/1.61 ( ( P @ zero_zero_nat )
% 3.10/1.61 => ( ! [Nat3: nat] :
% 3.10/1.61 ( ( P @ Nat3 )
% 3.10/1.61 => ( P @ ( suc @ Nat3 ) ) )
% 3.10/1.61 => ( P @ Nat ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_139_old_Onat_Oexhaust,axiom,
% 3.10/1.61 ! [Y: nat] :
% 3.10/1.61 ( ( Y != zero_zero_nat )
% 3.10/1.61 => ~ ! [Nat3: nat] :
% 3.10/1.61 ( Y
% 3.10/1.61 != ( suc @ Nat3 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_140_Zero__not__Suc,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( zero_zero_nat
% 3.10/1.61 != ( suc @ M2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_141_Zero__neq__Suc,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( zero_zero_nat
% 3.10/1.61 != ( suc @ M2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_142_Suc__neq__Zero,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( ( suc @ M2 )
% 3.10/1.61 != zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_143_zero__induct,axiom,
% 3.10/1.61 ! [P: nat > $o,K: nat] :
% 3.10/1.61 ( ( P @ K )
% 3.10/1.61 => ( ! [N: nat] :
% 3.10/1.61 ( ( P @ ( suc @ N ) )
% 3.10/1.61 => ( P @ N ) )
% 3.10/1.61 => ( P @ zero_zero_nat ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_144_diff__induct,axiom,
% 3.10/1.61 ! [P: nat > nat > $o,M2: nat,N2: nat] :
% 3.10/1.61 ( ! [X: nat] : ( P @ X @ zero_zero_nat )
% 3.10/1.61 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat] :
% 3.10/1.61 ( ( P @ X @ Y3 )
% 3.10/1.61 => ( P @ ( suc @ X ) @ ( suc @ Y3 ) ) )
% 3.10/1.61 => ( P @ M2 @ N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_145_product__lists_Osimps_I1_J,axiom,
% 3.10/1.61 ( ( produc663212148t_unit @ nil_li307996205t_unit )
% 3.10/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_146_product__lists_Osimps_I1_J,axiom,
% 3.10/1.61 ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
% 3.10/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_147_subseqs_Osimps_I1_J,axiom,
% 3.10/1.61 ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_148_subseqs_Osimps_I1_J,axiom,
% 3.10/1.61 ( ( subseqs_message_p_v @ nil_message_p_v )
% 3.10/1.61 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_149_gen__length__code_I2_J,axiom,
% 3.10/1.61 ! [N2: nat,X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( gen_le193291088t_unit @ N2 @ ( cons_c1162654829t_unit @ X3 @ Xs ) )
% 3.10/1.61 = ( gen_le193291088t_unit @ ( suc @ N2 ) @ Xs ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_150_gen__length__code_I2_J,axiom,
% 3.10/1.61 ! [N2: nat,X3: message_p_v,Xs: list_message_p_v] :
% 3.10/1.61 ( ( gen_le697204914ge_p_v @ N2 @ ( cons_message_p_v @ X3 @ Xs ) )
% 3.10/1.61 = ( gen_le697204914ge_p_v @ ( suc @ N2 ) @ Xs ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_151_count__list_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Y: config256849571t_unit] :
% 3.10/1.61 ( ( count_1396868135t_unit @ nil_co1338500125t_unit @ Y )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_152_count__list_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Y: message_p_v] :
% 3.10/1.61 ( ( count_1322329499ge_p_v @ nil_message_p_v @ Y )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_153_map__tailrec__rev_Oelims,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit > config256849571t_unit,Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( map_ta91747645t_unit @ X3 @ Xa @ Xb )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xa = nil_co1338500125t_unit )
% 3.10/1.61 => ( Y != Xb ) )
% 3.10/1.61 => ~ ! [A: config256849571t_unit,As: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xa
% 3.10/1.61 = ( cons_c1162654829t_unit @ A @ As ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( map_ta91747645t_unit @ X3 @ As @ ( cons_c1162654829t_unit @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_154_map__tailrec__rev_Oelims,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit > message_p_v,Xa: list_c1059388851t_unit,Xb: list_message_p_v,Y: list_message_p_v] :
% 3.10/1.61 ( ( ( map_ta782801413ge_p_v @ X3 @ Xa @ Xb )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xa = nil_co1338500125t_unit )
% 3.10/1.61 => ( Y != Xb ) )
% 3.10/1.61 => ~ ! [A: config256849571t_unit,As: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xa
% 3.10/1.61 = ( cons_c1162654829t_unit @ A @ As ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( map_ta782801413ge_p_v @ X3 @ As @ ( cons_message_p_v @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_155_map__tailrec__rev_Oelims,axiom,
% 3.10/1.61 ! [X3: message_p_v > config256849571t_unit,Xa: list_message_p_v,Xb: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( map_ta1131406733t_unit @ X3 @ Xa @ Xb )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xa = nil_message_p_v )
% 3.10/1.61 => ( Y != Xb ) )
% 3.10/1.61 => ~ ! [A: message_p_v,As: list_message_p_v] :
% 3.10/1.61 ( ( Xa
% 3.10/1.61 = ( cons_message_p_v @ A @ As ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( map_ta1131406733t_unit @ X3 @ As @ ( cons_c1162654829t_unit @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_156_map__tailrec__rev_Oelims,axiom,
% 3.10/1.61 ! [X3: message_p_v > message_p_v,Xa: list_message_p_v,Xb: list_message_p_v,Y: list_message_p_v] :
% 3.10/1.61 ( ( ( map_ta1016577461ge_p_v @ X3 @ Xa @ Xb )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( Xa = nil_message_p_v )
% 3.10/1.61 => ( Y != Xb ) )
% 3.10/1.61 => ~ ! [A: message_p_v,As: list_message_p_v] :
% 3.10/1.61 ( ( Xa
% 3.10/1.61 = ( cons_message_p_v @ A @ As ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( map_ta1016577461ge_p_v @ X3 @ As @ ( cons_message_p_v @ ( X3 @ A ) @ Xb ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_157_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.10/1.61 ! [F2: config256849571t_unit > config256849571t_unit,A8: config256849571t_unit,As2: list_c1059388851t_unit,Bs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( map_ta91747645t_unit @ F2 @ ( cons_c1162654829t_unit @ A8 @ As2 ) @ Bs2 )
% 3.10/1.61 = ( map_ta91747645t_unit @ F2 @ As2 @ ( cons_c1162654829t_unit @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_158_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.10/1.61 ! [F2: config256849571t_unit > message_p_v,A8: config256849571t_unit,As2: list_c1059388851t_unit,Bs2: list_message_p_v] :
% 3.10/1.61 ( ( map_ta782801413ge_p_v @ F2 @ ( cons_c1162654829t_unit @ A8 @ As2 ) @ Bs2 )
% 3.10/1.61 = ( map_ta782801413ge_p_v @ F2 @ As2 @ ( cons_message_p_v @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_159_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.10/1.61 ! [F2: message_p_v > config256849571t_unit,A8: message_p_v,As2: list_message_p_v,Bs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( map_ta1131406733t_unit @ F2 @ ( cons_message_p_v @ A8 @ As2 ) @ Bs2 )
% 3.10/1.61 = ( map_ta1131406733t_unit @ F2 @ As2 @ ( cons_c1162654829t_unit @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_160_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.10/1.61 ! [F2: message_p_v > message_p_v,A8: message_p_v,As2: list_message_p_v,Bs2: list_message_p_v] :
% 3.10/1.61 ( ( map_ta1016577461ge_p_v @ F2 @ ( cons_message_p_v @ A8 @ As2 ) @ Bs2 )
% 3.10/1.61 = ( map_ta1016577461ge_p_v @ F2 @ As2 @ ( cons_message_p_v @ ( F2 @ A8 ) @ Bs2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_161_gen__length__code_I1_J,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( gen_le193291088t_unit @ N2 @ nil_co1338500125t_unit )
% 3.10/1.61 = N2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_162_gen__length__code_I1_J,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( gen_le697204914ge_p_v @ N2 @ nil_message_p_v )
% 3.10/1.61 = N2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_163_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ~ ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_164_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Xs: list_message_p_v] :
% 3.10/1.61 ~ ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_165_bind__simps_I1_J,axiom,
% 3.10/1.61 ! [F2: config256849571t_unit > list_c1059388851t_unit] :
% 3.10/1.61 ( ( bind_c1439720399t_unit @ nil_co1338500125t_unit @ F2 )
% 3.10/1.61 = nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_166_bind__simps_I1_J,axiom,
% 3.10/1.61 ! [F2: config256849571t_unit > list_message_p_v] :
% 3.10/1.61 ( ( bind_c246984691ge_p_v @ nil_co1338500125t_unit @ F2 )
% 3.10/1.61 = nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_167_bind__simps_I1_J,axiom,
% 3.10/1.61 ! [F2: message_p_v > list_c1059388851t_unit] :
% 3.10/1.61 ( ( bind_m595590011t_unit @ nil_message_p_v @ F2 )
% 3.10/1.61 = nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_168_bind__simps_I1_J,axiom,
% 3.10/1.61 ! [F2: message_p_v > list_message_p_v] :
% 3.10/1.61 ( ( bind_m729301831ge_p_v @ nil_message_p_v @ F2 )
% 3.10/1.61 = nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_169_listrelp_Ocases,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( listre990624391t_unit @ R @ A1 @ A2 )
% 3.10/1.61 => ( ( ( A1 = nil_co1338500125t_unit )
% 3.10/1.61 => ( A2 != nil_co1338500125t_unit ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( R @ X @ Y3 )
% 3.10/1.61 => ~ ( listre990624391t_unit @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_170_listrelp_Ocases,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > message_p_v > $o,A1: list_c1059388851t_unit,A2: list_message_p_v] :
% 3.10/1.61 ( ( listre823101243ge_p_v @ R @ A1 @ A2 )
% 3.10/1.61 => ( ( ( A1 = nil_co1338500125t_unit )
% 3.10/1.61 => ( A2 != nil_message_p_v ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Y3: message_p_v,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_message_p_v] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( R @ X @ Y3 )
% 3.10/1.61 => ~ ( listre823101243ge_p_v @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_171_listrelp_Ocases,axiom,
% 3.10/1.61 ! [R: message_p_v > config256849571t_unit > $o,A1: list_message_p_v,A2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( listre1171706563t_unit @ R @ A1 @ A2 )
% 3.10/1.61 => ( ( ( A1 = nil_message_p_v )
% 3.10/1.61 => ( A2 != nil_co1338500125t_unit ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Y3: config256849571t_unit,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_message_p_v @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( R @ X @ Y3 )
% 3.10/1.61 => ~ ( listre1171706563t_unit @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_172_listrelp_Ocases,axiom,
% 3.10/1.61 ! [R: message_p_v > message_p_v > $o,A1: list_message_p_v,A2: list_message_p_v] :
% 3.10/1.61 ( ( listre1295695359ge_p_v @ R @ A1 @ A2 )
% 3.10/1.61 => ( ( ( A1 = nil_message_p_v )
% 3.10/1.61 => ( A2 != nil_message_p_v ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_message_p_v @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_message_p_v] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ( R @ X @ Y3 )
% 3.10/1.61 => ~ ( listre1295695359ge_p_v @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_173_listrelp_Osimps,axiom,
% 3.10/1.61 ( listre990624391t_unit
% 3.10/1.61 = ( ^ [R2: config256849571t_unit > config256849571t_unit > $o,A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( A12 = nil_co1338500125t_unit )
% 3.10/1.61 & ( A22 = nil_co1338500125t_unit ) )
% 3.10/1.61 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ( R2 @ X4 @ Y2 )
% 3.10/1.61 & ( listre990624391t_unit @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_174_listrelp_Osimps,axiom,
% 3.10/1.61 ( listre823101243ge_p_v
% 3.10/1.61 = ( ^ [R2: config256849571t_unit > message_p_v > $o,A12: list_c1059388851t_unit,A22: list_message_p_v] :
% 3.10/1.61 ( ( ( A12 = nil_co1338500125t_unit )
% 3.10/1.61 & ( A22 = nil_message_p_v ) )
% 3.10/1.61 | ? [X4: config256849571t_unit,Y2: message_p_v,Xs3: list_c1059388851t_unit,Ys: list_message_p_v] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ( R2 @ X4 @ Y2 )
% 3.10/1.61 & ( listre823101243ge_p_v @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_175_listrelp_Osimps,axiom,
% 3.10/1.61 ( listre1171706563t_unit
% 3.10/1.61 = ( ^ [R2: message_p_v > config256849571t_unit > $o,A12: list_message_p_v,A22: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( A12 = nil_message_p_v )
% 3.10/1.61 & ( A22 = nil_co1338500125t_unit ) )
% 3.10/1.61 | ? [X4: message_p_v,Y2: config256849571t_unit,Xs3: list_message_p_v,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ( R2 @ X4 @ Y2 )
% 3.10/1.61 & ( listre1171706563t_unit @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_176_listrelp_Osimps,axiom,
% 3.10/1.61 ( listre1295695359ge_p_v
% 3.10/1.61 = ( ^ [R2: message_p_v > message_p_v > $o,A12: list_message_p_v,A22: list_message_p_v] :
% 3.10/1.61 ( ( ( A12 = nil_message_p_v )
% 3.10/1.61 & ( A22 = nil_message_p_v ) )
% 3.10/1.61 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ( R2 @ X4 @ Y2 )
% 3.10/1.61 & ( listre1295695359ge_p_v @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_177_listrelp_Oinducts,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > config256849571t_unit > $o,X12: list_c1059388851t_unit,X23: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( listre990624391t_unit @ R @ X12 @ X23 )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( R @ X @ Y3 )
% 3.10/1.61 => ( ( listre990624391t_unit @ R @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_178_listrelp_Oinducts,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > message_p_v > $o,X12: list_c1059388851t_unit,X23: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 3.10/1.61 ( ( listre823101243ge_p_v @ R @ X12 @ X23 )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: message_p_v,Xs2: list_c1059388851t_unit,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( R @ X @ Y3 )
% 3.10/1.61 => ( ( listre823101243ge_p_v @ R @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_179_listrelp_Oinducts,axiom,
% 3.10/1.61 ! [R: message_p_v > config256849571t_unit > $o,X12: list_message_p_v,X23: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( listre1171706563t_unit @ R @ X12 @ X23 )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: config256849571t_unit,Xs2: list_message_p_v,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( R @ X @ Y3 )
% 3.10/1.61 => ( ( listre1171706563t_unit @ R @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_180_listrelp_Oinducts,axiom,
% 3.10/1.61 ! [R: message_p_v > message_p_v > $o,X12: list_message_p_v,X23: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 3.10/1.61 ( ( listre1295695359ge_p_v @ R @ X12 @ X23 )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( R @ X @ Y3 )
% 3.10/1.61 => ( ( listre1295695359ge_p_v @ R @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_181_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Xs: list_c1059388851t_unit,Y: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) )
% 3.10/1.61 = ( ( Less @ X3 @ Y )
% 3.10/1.61 | ( ~ ( Less @ Y @ X3 )
% 3.10/1.61 & ( lexord1758866263t_unit @ Less @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_182_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Xs: list_message_p_v,Y: message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) )
% 3.10/1.61 = ( ( Less @ X3 @ Y )
% 3.10/1.61 | ( ~ ( Less @ Y @ X3 )
% 3.10/1.61 & ( lexord2101627499ge_p_v @ Less @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_183_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,Ys2: list_c1059388851t_unit] : ( lexord1758866263t_unit @ Less @ nil_co1338500125t_unit @ Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_184_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,Ys2: list_message_p_v] : ( lexord2101627499ge_p_v @ Less @ nil_message_p_v @ Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_185_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( lexord1758866263t_unit @ Less @ Xs @ nil_co1338500125t_unit )
% 3.10/1.61 = ( Xs = nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_186_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,Xs: list_message_p_v] :
% 3.10/1.61 ( ( lexord2101627499ge_p_v @ Less @ Xs @ nil_message_p_v )
% 3.10/1.61 = ( Xs = nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_187_ord_Olexordp__eq_OCons__eq,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ~ ( Less @ X3 @ Y )
% 3.10/1.61 => ( ~ ( Less @ Y @ X3 )
% 3.10/1.61 => ( ( lexord1758866263t_unit @ Less @ Xs @ Ys2 )
% 3.10/1.61 => ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_188_ord_Olexordp__eq_OCons__eq,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ~ ( Less @ X3 @ Y )
% 3.10/1.61 => ( ~ ( Less @ Y @ X3 )
% 3.10/1.61 => ( ( lexord2101627499ge_p_v @ Less @ Xs @ Ys2 )
% 3.10/1.61 => ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_189_ord_Olexordp__eq_OCons,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Less @ X3 @ Y )
% 3.10/1.61 => ( lexord1758866263t_unit @ Less @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_190_ord_Olexordp__eq_OCons,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( Less @ X3 @ Y )
% 3.10/1.61 => ( lexord2101627499ge_p_v @ Less @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_191_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,Ys2: list_c1059388851t_unit] : ( lexord1758866263t_unit @ Less @ nil_co1338500125t_unit @ Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_192_ord_Olexordp__eq_ONil,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,Ys2: list_message_p_v] : ( lexord2101627499ge_p_v @ Less @ nil_message_p_v @ Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_193_listrelp_OCons,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > config256849571t_unit > $o,X3: config256849571t_unit,Y: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( R @ X3 @ Y )
% 3.10/1.61 => ( ( listre990624391t_unit @ R @ Xs @ Ys2 )
% 3.10/1.61 => ( listre990624391t_unit @ R @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_194_listrelp_OCons,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > message_p_v > $o,X3: config256849571t_unit,Y: message_p_v,Xs: list_c1059388851t_unit,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( R @ X3 @ Y )
% 3.10/1.61 => ( ( listre823101243ge_p_v @ R @ Xs @ Ys2 )
% 3.10/1.61 => ( listre823101243ge_p_v @ R @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_195_listrelp_OCons,axiom,
% 3.10/1.61 ! [R: message_p_v > config256849571t_unit > $o,X3: message_p_v,Y: config256849571t_unit,Xs: list_message_p_v,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( R @ X3 @ Y )
% 3.10/1.61 => ( ( listre1171706563t_unit @ R @ Xs @ Ys2 )
% 3.10/1.61 => ( listre1171706563t_unit @ R @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_c1162654829t_unit @ Y @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_196_listrelp_OCons,axiom,
% 3.10/1.61 ! [R: message_p_v > message_p_v > $o,X3: message_p_v,Y: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( R @ X3 @ Y )
% 3.10/1.61 => ( ( listre1295695359ge_p_v @ R @ Xs @ Ys2 )
% 3.10/1.61 => ( listre1295695359ge_p_v @ R @ ( cons_message_p_v @ X3 @ Xs ) @ ( cons_message_p_v @ Y @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_197_listrelp_ONil,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > config256849571t_unit > $o] : ( listre990624391t_unit @ R @ nil_co1338500125t_unit @ nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_198_listrelp_ONil,axiom,
% 3.10/1.61 ! [R: config256849571t_unit > message_p_v > $o] : ( listre823101243ge_p_v @ R @ nil_co1338500125t_unit @ nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_199_listrelp_ONil,axiom,
% 3.10/1.61 ! [R: message_p_v > config256849571t_unit > $o] : ( listre1171706563t_unit @ R @ nil_message_p_v @ nil_co1338500125t_unit ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_200_listrelp_ONil,axiom,
% 3.10/1.61 ! [R: message_p_v > message_p_v > $o] : ( listre1295695359ge_p_v @ R @ nil_message_p_v @ nil_message_p_v ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_201_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,X12: list_c1059388851t_unit,X23: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( lexord1758866263t_unit @ Less @ X12 @ X23 )
% 3.10/1.61 => ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Less @ X @ Y3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ~ ( Less @ X @ Y3 )
% 3.10/1.61 => ( ~ ( Less @ Y3 @ X )
% 3.10/1.61 => ( ( lexord1758866263t_unit @ Less @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_202_ord_Olexordp__eq_Oinducts,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,X12: list_message_p_v,X23: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 3.10/1.61 ( ( lexord2101627499ge_p_v @ Less @ X12 @ X23 )
% 3.10/1.61 => ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( Less @ X @ Y3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ~ ( Less @ X @ Y3 )
% 3.10/1.61 => ( ~ ( Less @ Y3 @ X )
% 3.10/1.61 => ( ( lexord2101627499ge_p_v @ Less @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_203_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.61 ( lexord1758866263t_unit
% 3.10/1.61 = ( ^ [Less2: config256849571t_unit > config256849571t_unit > $o,A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 3.10/1.61 ( ? [Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A12 = nil_co1338500125t_unit )
% 3.10/1.61 & ( A22 = Ys ) )
% 3.10/1.61 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ( Less2 @ X4 @ Y2 ) )
% 3.10/1.61 | ? [X4: config256849571t_unit,Y2: config256849571t_unit,Xs3: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_c1162654829t_unit @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ~ ( Less2 @ X4 @ Y2 )
% 3.10/1.61 & ~ ( Less2 @ Y2 @ X4 )
% 3.10/1.61 & ( lexord1758866263t_unit @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_204_ord_Olexordp__eq_Osimps,axiom,
% 3.10/1.61 ( lexord2101627499ge_p_v
% 3.10/1.61 = ( ^ [Less2: message_p_v > message_p_v > $o,A12: list_message_p_v,A22: list_message_p_v] :
% 3.10/1.61 ( ? [Ys: list_message_p_v] :
% 3.10/1.61 ( ( A12 = nil_message_p_v )
% 3.10/1.61 & ( A22 = Ys ) )
% 3.10/1.61 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ( Less2 @ X4 @ Y2 ) )
% 3.10/1.61 | ? [X4: message_p_v,Y2: message_p_v,Xs3: list_message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_message_p_v @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ~ ( Less2 @ X4 @ Y2 )
% 3.10/1.61 & ~ ( Less2 @ Y2 @ X4 )
% 3.10/1.61 & ( lexord2101627499ge_p_v @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_205_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.61 ! [Less: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( lexord1758866263t_unit @ Less @ A1 @ A2 )
% 3.10/1.61 => ( ( A1 != nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit] :
% 3.10/1.61 ( ? [Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( A1
% 3.10/1.61 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 3.10/1.61 => ! [Y3: config256849571t_unit] :
% 3.10/1.61 ( ? [Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( A2
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ~ ( Less @ X @ Y3 ) ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ~ ( Less @ X @ Y3 )
% 3.10/1.61 => ( ~ ( Less @ Y3 @ X )
% 3.10/1.61 => ~ ( lexord1758866263t_unit @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_206_ord_Olexordp__eq_Ocases,axiom,
% 3.10/1.61 ! [Less: message_p_v > message_p_v > $o,A1: list_message_p_v,A2: list_message_p_v] :
% 3.10/1.61 ( ( lexord2101627499ge_p_v @ Less @ A1 @ A2 )
% 3.10/1.61 => ( ( A1 != nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v] :
% 3.10/1.61 ( ? [Xs2: list_message_p_v] :
% 3.10/1.61 ( A1
% 3.10/1.61 = ( cons_message_p_v @ X @ Xs2 ) )
% 3.10/1.61 => ! [Y3: message_p_v] :
% 3.10/1.61 ( ? [Ys3: list_message_p_v] :
% 3.10/1.61 ( A2
% 3.10/1.61 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ~ ( Less @ X @ Y3 ) ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_message_p_v @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_message_p_v] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_message_p_v @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ~ ( Less @ X @ Y3 )
% 3.10/1.61 => ( ~ ( Less @ Y3 @ X )
% 3.10/1.61 => ~ ( lexord2101627499ge_p_v @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_207_zero__natural_Orsp,axiom,
% 3.10/1.61 zero_zero_nat = zero_zero_nat ).
% 3.10/1.61
% 3.10/1.61 thf(fact_208_member__rec_I2_J,axiom,
% 3.10/1.61 ! [Y: config256849571t_unit] :
% 3.10/1.61 ~ ( member1087090632t_unit @ nil_co1338500125t_unit @ Y ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_209_member__rec_I2_J,axiom,
% 3.10/1.61 ! [Y: message_p_v] :
% 3.10/1.61 ~ ( member_message_p_v @ nil_message_p_v @ Y ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_210_member__rec_I1_J,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit,Y: config256849571t_unit] :
% 3.10/1.61 ( ( member1087090632t_unit @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ Y )
% 3.10/1.61 = ( ( X3 = Y )
% 3.10/1.61 | ( member1087090632t_unit @ Xs @ Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_211_member__rec_I1_J,axiom,
% 3.10/1.61 ! [X3: message_p_v,Xs: list_message_p_v,Y: message_p_v] :
% 3.10/1.61 ( ( member_message_p_v @ ( cons_message_p_v @ X3 @ Xs ) @ Y )
% 3.10/1.61 = ( ( X3 = Y )
% 3.10/1.61 | ( member_message_p_v @ Xs @ Y ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_212_lexordp__eq_Ocases,axiom,
% 3.10/1.61 ! [A1: list_nat,A2: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_eq_nat @ A1 @ A2 )
% 3.10/1.61 => ( ( A1 != nil_nat )
% 3.10/1.61 => ( ! [X: nat] :
% 3.10/1.61 ( ? [Xs2: list_nat] :
% 3.10/1.61 ( A1
% 3.10/1.61 = ( cons_nat @ X @ Xs2 ) )
% 3.10/1.61 => ! [Y3: nat] :
% 3.10/1.61 ( ? [Ys3: list_nat] :
% 3.10/1.61 ( A2
% 3.10/1.61 = ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 3.10/1.61 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_nat @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_nat] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ~ ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y3 @ X )
% 3.10/1.61 => ~ ( ord_lexordp_eq_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_213_lexordp__eq_Osimps,axiom,
% 3.10/1.61 ( ord_lexordp_eq_nat
% 3.10/1.61 = ( ^ [A12: list_nat,A22: list_nat] :
% 3.10/1.61 ( ? [Ys: list_nat] :
% 3.10/1.61 ( ( A12 = nil_nat )
% 3.10/1.61 & ( A22 = Ys ) )
% 3.10/1.61 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_nat @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) )
% 3.10/1.61 & ( ord_less_nat @ X4 @ Y2 ) )
% 3.10/1.61 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_nat @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) )
% 3.10/1.61 & ~ ( ord_less_nat @ X4 @ Y2 )
% 3.10/1.61 & ~ ( ord_less_nat @ Y2 @ X4 )
% 3.10/1.61 & ( ord_lexordp_eq_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_214_lexordp__eq_Oinducts,axiom,
% 3.10/1.61 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 3.10/1.61 ( ( ord_lexordp_eq_nat @ X12 @ X23 )
% 3.10/1.61 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y3 @ X )
% 3.10/1.61 => ( ( ord_lexordp_eq_nat @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_215_splice_Oelims,axiom,
% 3.10/1.61 ! [X3: list_c1059388851t_unit,Xa: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( splice888123018t_unit @ X3 @ Xa )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( X3 = nil_co1338500125t_unit )
% 3.10/1.61 => ( Y != Xa ) )
% 3.10/1.61 => ~ ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( X3
% 3.10/1.61 = ( cons_c1162654829t_unit @ X @ Xs2 ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( cons_c1162654829t_unit @ X @ ( splice888123018t_unit @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_216_splice_Oelims,axiom,
% 3.10/1.61 ! [X3: list_message_p_v,Xa: list_message_p_v,Y: list_message_p_v] :
% 3.10/1.61 ( ( ( splice_message_p_v @ X3 @ Xa )
% 3.10/1.61 = Y )
% 3.10/1.61 => ( ( ( X3 = nil_message_p_v )
% 3.10/1.61 => ( Y != Xa ) )
% 3.10/1.61 => ~ ! [X: message_p_v,Xs2: list_message_p_v] :
% 3.10/1.61 ( ( X3
% 3.10/1.61 = ( cons_message_p_v @ X @ Xs2 ) )
% 3.10/1.61 => ( Y
% 3.10/1.61 != ( cons_message_p_v @ X @ ( splice_message_p_v @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_217_bot__nat__0_Onot__eq__extremum,axiom,
% 3.10/1.61 ! [A8: nat] :
% 3.10/1.61 ( ( A8 != zero_zero_nat )
% 3.10/1.61 = ( ord_less_nat @ zero_zero_nat @ A8 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_218_less__nat__zero__code,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_219_neq0__conv,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( N2 != zero_zero_nat )
% 3.10/1.61 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_220_lessI,axiom,
% 3.10/1.61 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_221_Suc__mono,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_222_Suc__less__eq,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.10/1.61 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_223_not__gr__zero,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 3.10/1.61 = ( N2 = zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_224_zero__less__Suc,axiom,
% 3.10/1.61 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_225_less__Suc0,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 3.10/1.61 = ( N2 = zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_226_split__Nil__iff,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( splice888123018t_unit @ Xs @ Ys2 )
% 3.10/1.61 = nil_co1338500125t_unit )
% 3.10/1.61 = ( ( Xs = nil_co1338500125t_unit )
% 3.10/1.61 & ( Ys2 = nil_co1338500125t_unit ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_227_split__Nil__iff,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( ( splice_message_p_v @ Xs @ Ys2 )
% 3.10/1.61 = nil_message_p_v )
% 3.10/1.61 = ( ( Xs = nil_message_p_v )
% 3.10/1.61 & ( Ys2 = nil_message_p_v ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_228_splice__Nil2,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( splice888123018t_unit @ Xs @ nil_co1338500125t_unit )
% 3.10/1.61 = Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_229_splice__Nil2,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v] :
% 3.10/1.61 ( ( splice_message_p_v @ Xs @ nil_message_p_v )
% 3.10/1.61 = Xs ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_230_lexordp__eq__simps_I4_J,axiom,
% 3.10/1.61 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 3.10/1.61 = ( ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 | ( ~ ( ord_less_nat @ Y @ X3 )
% 3.10/1.61 & ( ord_lexordp_eq_nat @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_231_gr__zeroI,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( N2 != zero_zero_nat )
% 3.10/1.61 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_232_not__less__zero,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_233_gr__implies__not__zero,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( N2 != zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_234_zero__less__iff__neq__zero,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 = ( N2 != zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_235_bot__nat__0_Oextremum__strict,axiom,
% 3.10/1.61 ! [A8: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ A8 @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_236_infinite__descent0,axiom,
% 3.10/1.61 ! [P: nat > $o,N2: nat] :
% 3.10/1.61 ( ( P @ zero_zero_nat )
% 3.10/1.61 => ( ! [N: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.10/1.61 => ( ~ ( P @ N )
% 3.10/1.61 => ? [M3: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M3 @ N )
% 3.10/1.61 & ~ ( P @ M3 ) ) ) )
% 3.10/1.61 => ( P @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_237_gr__implies__not0,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( N2 != zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_238_less__zeroE,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_239_not__less0,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_240_not__gr0,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 3.10/1.61 = ( N2 = zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_241_gr0I,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( N2 != zero_zero_nat )
% 3.10/1.61 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_242_Nat_OlessE,axiom,
% 3.10/1.61 ! [I: nat,K: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I @ K )
% 3.10/1.61 => ( ( K
% 3.10/1.61 != ( suc @ I ) )
% 3.10/1.61 => ~ ! [J: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I @ J )
% 3.10/1.61 => ( K
% 3.10/1.61 != ( suc @ J ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_243_Suc__lessD,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( suc @ M2 ) @ N2 )
% 3.10/1.61 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_244_Suc__lessE,axiom,
% 3.10/1.61 ! [I: nat,K: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 3.10/1.61 => ~ ! [J: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I @ J )
% 3.10/1.61 => ( K
% 3.10/1.61 != ( suc @ J ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_245_Suc__lessI,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( ( ( suc @ M2 )
% 3.10/1.61 != N2 )
% 3.10/1.61 => ( ord_less_nat @ ( suc @ M2 ) @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_246_less__SucE,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.10/1.61 => ( ~ ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( M2 = N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_247_less__SucI,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( ord_less_nat @ M2 @ ( suc @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_248_Ex__less__Suc,axiom,
% 3.10/1.61 ! [N2: nat,P: nat > $o] :
% 3.10/1.61 ( ( ? [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 3.10/1.61 & ( P @ I2 ) ) )
% 3.10/1.61 = ( ( P @ N2 )
% 3.10/1.61 | ? [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ N2 )
% 3.10/1.61 & ( P @ I2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_249_less__Suc__eq,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.10/1.61 = ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 | ( M2 = N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_250_not__less__eq,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ~ ( ord_less_nat @ M2 @ N2 ) )
% 3.10/1.61 = ( ord_less_nat @ N2 @ ( suc @ M2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_251_All__less__Suc,axiom,
% 3.10/1.61 ! [N2: nat,P: nat > $o] :
% 3.10/1.61 ( ( ! [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 3.10/1.61 => ( P @ I2 ) ) )
% 3.10/1.61 = ( ( P @ N2 )
% 3.10/1.61 & ! [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ N2 )
% 3.10/1.61 => ( P @ I2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_252_Suc__less__eq2,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( suc @ N2 ) @ M2 )
% 3.10/1.61 = ( ? [M4: nat] :
% 3.10/1.61 ( ( M2
% 3.10/1.61 = ( suc @ M4 ) )
% 3.10/1.61 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_253_less__antisym,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.10/1.61 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.10/1.61 => ( M2 = N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_254_Suc__less__SucD,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.10/1.61 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_255_less__trans__Suc,axiom,
% 3.10/1.61 ! [I: nat,J2: nat,K: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I @ J2 )
% 3.10/1.61 => ( ( ord_less_nat @ J2 @ K )
% 3.10/1.61 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_256_less__Suc__induct,axiom,
% 3.10/1.61 ! [I: nat,J2: nat,P: nat > nat > $o] :
% 3.10/1.61 ( ( ord_less_nat @ I @ J2 )
% 3.10/1.61 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 3.10/1.61 => ( ! [I3: nat,J: nat,K2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I3 @ J )
% 3.10/1.61 => ( ( ord_less_nat @ J @ K2 )
% 3.10/1.61 => ( ( P @ I3 @ J )
% 3.10/1.61 => ( ( P @ J @ K2 )
% 3.10/1.61 => ( P @ I3 @ K2 ) ) ) ) )
% 3.10/1.61 => ( P @ I @ J2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_257_strict__inc__induct,axiom,
% 3.10/1.61 ! [I: nat,J2: nat,P: nat > $o] :
% 3.10/1.61 ( ( ord_less_nat @ I @ J2 )
% 3.10/1.61 => ( ! [I3: nat] :
% 3.10/1.61 ( ( J2
% 3.10/1.61 = ( suc @ I3 ) )
% 3.10/1.61 => ( P @ I3 ) )
% 3.10/1.61 => ( ! [I3: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I3 @ J2 )
% 3.10/1.61 => ( ( P @ ( suc @ I3 ) )
% 3.10/1.61 => ( P @ I3 ) ) )
% 3.10/1.61 => ( P @ I ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_258_not__less__less__Suc__eq,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ N2 @ M2 )
% 3.10/1.61 => ( ( ord_less_nat @ N2 @ ( suc @ M2 ) )
% 3.10/1.61 = ( N2 = M2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_259_lift__Suc__mono__less,axiom,
% 3.10/1.61 ! [F2: nat > nat,N2: nat,N3: nat] :
% 3.10/1.61 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 3.10/1.61 => ( ( ord_less_nat @ N2 @ N3 )
% 3.10/1.61 => ( ord_less_nat @ ( F2 @ N2 ) @ ( F2 @ N3 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_260_lift__Suc__mono__less__iff,axiom,
% 3.10/1.61 ! [F2: nat > nat,N2: nat,M2: nat] :
% 3.10/1.61 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 3.10/1.61 => ( ( ord_less_nat @ ( F2 @ N2 ) @ ( F2 @ M2 ) )
% 3.10/1.61 = ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_261_splice_Osimps_I2_J,axiom,
% 3.10/1.61 ! [X3: config256849571t_unit,Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( splice888123018t_unit @ ( cons_c1162654829t_unit @ X3 @ Xs ) @ Ys2 )
% 3.10/1.61 = ( cons_c1162654829t_unit @ X3 @ ( splice888123018t_unit @ Ys2 @ Xs ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_262_splice_Osimps_I2_J,axiom,
% 3.10/1.61 ! [X3: message_p_v,Xs: list_message_p_v,Ys2: list_message_p_v] :
% 3.10/1.61 ( ( splice_message_p_v @ ( cons_message_p_v @ X3 @ Xs ) @ Ys2 )
% 3.10/1.61 = ( cons_message_p_v @ X3 @ ( splice_message_p_v @ Ys2 @ Xs ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_263_splice_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Ys2: list_c1059388851t_unit] :
% 3.10/1.61 ( ( splice888123018t_unit @ nil_co1338500125t_unit @ Ys2 )
% 3.10/1.61 = Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_264_splice_Osimps_I1_J,axiom,
% 3.10/1.61 ! [Ys2: list_message_p_v] :
% 3.10/1.61 ( ( splice_message_p_v @ nil_message_p_v @ Ys2 )
% 3.10/1.61 = Ys2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_265_less__Suc__eq__0__disj,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ ( suc @ N2 ) )
% 3.10/1.61 = ( ( M2 = zero_zero_nat )
% 3.10/1.61 | ? [J3: nat] :
% 3.10/1.61 ( ( M2
% 3.10/1.61 = ( suc @ J3 ) )
% 3.10/1.61 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_266_gr0__implies__Suc,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 => ? [M: nat] :
% 3.10/1.61 ( N2
% 3.10/1.61 = ( suc @ M ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_267_All__less__Suc2,axiom,
% 3.10/1.61 ! [N2: nat,P: nat > $o] :
% 3.10/1.61 ( ( ! [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 3.10/1.61 => ( P @ I2 ) ) )
% 3.10/1.61 = ( ( P @ zero_zero_nat )
% 3.10/1.61 & ! [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ N2 )
% 3.10/1.61 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_268_gr0__conv__Suc,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 = ( ? [M5: nat] :
% 3.10/1.61 ( N2
% 3.10/1.61 = ( suc @ M5 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_269_Ex__less__Suc2,axiom,
% 3.10/1.61 ! [N2: nat,P: nat > $o] :
% 3.10/1.61 ( ( ? [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ ( suc @ N2 ) )
% 3.10/1.61 & ( P @ I2 ) ) )
% 3.10/1.61 = ( ( P @ zero_zero_nat )
% 3.10/1.61 | ? [I2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ I2 @ N2 )
% 3.10/1.61 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_270_lexordp__eq_OCons__eq,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y @ X3 )
% 3.10/1.61 => ( ( ord_lexordp_eq_nat @ Xs @ Ys2 )
% 3.10/1.61 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_271_lexordp__eq_OCons,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_272_NatPredicateTippingPoint,axiom,
% 3.10/1.61 ! [N22: nat,Pr: nat > $o] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 3.10/1.61 => ( ( Pr @ zero_zero_nat )
% 3.10/1.61 => ( ~ ( Pr @ N22 )
% 3.10/1.61 => ? [N: nat] :
% 3.10/1.61 ( ( ord_less_nat @ N @ N22 )
% 3.10/1.61 & ( Pr @ N )
% 3.10/1.61 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_273_less__numeral__extra_I3_J,axiom,
% 3.10/1.61 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_274_lexordp_Ocases,axiom,
% 3.10/1.61 ! [A1: list_nat,A2: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_nat @ A1 @ A2 )
% 3.10/1.61 => ( ( ( A1 = nil_nat )
% 3.10/1.61 => ! [Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( A2
% 3.10/1.61 != ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: nat] :
% 3.10/1.61 ( ? [Xs2: list_nat] :
% 3.10/1.61 ( A1
% 3.10/1.61 = ( cons_nat @ X @ Xs2 ) )
% 3.10/1.61 => ! [Y3: nat] :
% 3.10/1.61 ( ? [Ys3: list_nat] :
% 3.10/1.61 ( A2
% 3.10/1.61 = ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 3.10/1.61 => ~ ! [X: nat,Y3: nat,Xs2: list_nat] :
% 3.10/1.61 ( ( A1
% 3.10/1.61 = ( cons_nat @ X @ Xs2 ) )
% 3.10/1.61 => ! [Ys3: list_nat] :
% 3.10/1.61 ( ( A2
% 3.10/1.61 = ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ~ ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y3 @ X )
% 3.10/1.61 => ~ ( ord_lexordp_nat @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_275_lexordp_Osimps,axiom,
% 3.10/1.61 ( ord_lexordp_nat
% 3.10/1.61 = ( ^ [A12: list_nat,A22: list_nat] :
% 3.10/1.61 ( ? [Y2: nat,Ys: list_nat] :
% 3.10/1.61 ( ( A12 = nil_nat )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) ) )
% 3.10/1.61 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_nat @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) )
% 3.10/1.61 & ( ord_less_nat @ X4 @ Y2 ) )
% 3.10/1.61 | ? [X4: nat,Y2: nat,Xs3: list_nat,Ys: list_nat] :
% 3.10/1.61 ( ( A12
% 3.10/1.61 = ( cons_nat @ X4 @ Xs3 ) )
% 3.10/1.61 & ( A22
% 3.10/1.61 = ( cons_nat @ Y2 @ Ys ) )
% 3.10/1.61 & ~ ( ord_less_nat @ X4 @ Y2 )
% 3.10/1.61 & ~ ( ord_less_nat @ Y2 @ X4 )
% 3.10/1.61 & ( ord_lexordp_nat @ Xs3 @ Ys ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_276_lexordp__simps_I3_J,axiom,
% 3.10/1.61 ! [X3: nat,Xs: list_nat,Y: nat,Ys2: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) )
% 3.10/1.61 = ( ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 | ( ~ ( ord_less_nat @ Y @ X3 )
% 3.10/1.61 & ( ord_lexordp_nat @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_277_lexordp__irreflexive,axiom,
% 3.10/1.61 ! [Xs: list_nat] :
% 3.10/1.61 ( ! [X: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ X @ X )
% 3.10/1.61 => ~ ( ord_lexordp_nat @ Xs @ Xs ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_278_linorder__neqE__nat,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat] :
% 3.10/1.61 ( ( X3 != Y )
% 3.10/1.61 => ( ~ ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_279_infinite__descent,axiom,
% 3.10/1.61 ! [P: nat > $o,N2: nat] :
% 3.10/1.61 ( ! [N: nat] :
% 3.10/1.61 ( ~ ( P @ N )
% 3.10/1.61 => ? [M3: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M3 @ N )
% 3.10/1.61 & ~ ( P @ M3 ) ) )
% 3.10/1.61 => ( P @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_280_nat__less__induct,axiom,
% 3.10/1.61 ! [P: nat > $o,N2: nat] :
% 3.10/1.61 ( ! [N: nat] :
% 3.10/1.61 ( ! [M3: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M3 @ N )
% 3.10/1.61 => ( P @ M3 ) )
% 3.10/1.61 => ( P @ N ) )
% 3.10/1.61 => ( P @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_281_less__irrefl__nat,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_282_less__not__refl3,axiom,
% 3.10/1.61 ! [S: nat,T: nat] :
% 3.10/1.61 ( ( ord_less_nat @ S @ T )
% 3.10/1.61 => ( S != T ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_283_less__not__refl2,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ N2 @ M2 )
% 3.10/1.61 => ( M2 != N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_284_less__not__refl,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_285_nat__neq__iff,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( M2 != N2 )
% 3.10/1.61 = ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 | ( ord_less_nat @ N2 @ M2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_286_lexordp_OCons,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_287_lexordp_OCons__eq,axiom,
% 3.10/1.61 ! [X3: nat,Y: nat,Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ X3 @ Y )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y @ X3 )
% 3.10/1.61 => ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 3.10/1.61 => ( ord_lexordp_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_288_lexordp__induct,axiom,
% 3.10/1.61 ! [Xs: list_nat,Ys2: list_nat,P: list_nat > list_nat > $o] :
% 3.10/1.61 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 3.10/1.61 ( ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ X @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_289_lexordp__cases,axiom,
% 3.10/1.61 ! [Xs: list_nat,Ys2: list_nat] :
% 3.10/1.61 ( ( ord_lexordp_nat @ Xs @ Ys2 )
% 3.10/1.61 => ( ( ( Xs = nil_nat )
% 3.10/1.61 => ! [Y3: nat,Ys4: list_nat] :
% 3.10/1.61 ( Ys2
% 3.10/1.61 != ( cons_nat @ Y3 @ Ys4 ) ) )
% 3.10/1.61 => ( ! [X: nat] :
% 3.10/1.61 ( ? [Xs4: list_nat] :
% 3.10/1.61 ( Xs
% 3.10/1.61 = ( cons_nat @ X @ Xs4 ) )
% 3.10/1.61 => ! [Y3: nat] :
% 3.10/1.61 ( ? [Ys4: list_nat] :
% 3.10/1.61 ( Ys2
% 3.10/1.61 = ( cons_nat @ Y3 @ Ys4 ) )
% 3.10/1.61 => ~ ( ord_less_nat @ X @ Y3 ) ) )
% 3.10/1.61 => ~ ! [X: nat,Xs4: list_nat] :
% 3.10/1.61 ( ( Xs
% 3.10/1.61 = ( cons_nat @ X @ Xs4 ) )
% 3.10/1.61 => ! [Ys4: list_nat] :
% 3.10/1.61 ( ( Ys2
% 3.10/1.61 = ( cons_nat @ X @ Ys4 ) )
% 3.10/1.61 => ~ ( ord_lexordp_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_290_lexordp_Oinducts,axiom,
% 3.10/1.61 ! [X12: list_nat,X23: list_nat,P: list_nat > list_nat > $o] :
% 3.10/1.61 ( ( ord_lexordp_nat @ X12 @ X23 )
% 3.10/1.61 => ( ! [Y3: nat,Ys3: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 3.10/1.61 => ( ! [X: nat,Y3: nat,Xs2: list_nat,Ys3: list_nat] :
% 3.10/1.61 ( ~ ( ord_less_nat @ X @ Y3 )
% 3.10/1.61 => ( ~ ( ord_less_nat @ Y3 @ X )
% 3.10/1.61 => ( ( ord_lexordp_nat @ Xs2 @ Ys3 )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) )
% 3.10/1.61 => ( P @ X12 @ X23 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_291_of__nat__0__less__iff,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N2 ) )
% 3.10/1.61 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_292_Suc__pred,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 3.10/1.61 = N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_293_length__greater__0__conv,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 3.10/1.61 = ( Xs != nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_294_length__greater__0__conv,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 3.10/1.61 = ( Xs != nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_295_zero__diff,axiom,
% 3.10/1.61 ! [A8: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ zero_zero_nat @ A8 )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_296_diff__zero,axiom,
% 3.10/1.61 ! [A8: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ A8 @ zero_zero_nat )
% 3.10/1.61 = A8 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_297_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.10/1.61 ! [A8: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ A8 @ A8 )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_298_diff__0__eq__0,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_299_diff__self__eq__0,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ M2 @ M2 )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_300_Suc__diff__diff,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat,K: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N2 ) @ ( suc @ K ) )
% 3.10/1.61 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N2 ) @ K ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_301_diff__Suc__Suc,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N2 ) )
% 3.10/1.61 = ( minus_minus_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_302_of__nat__eq__0__iff,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( ( ( semiri1382578993at_nat @ M2 )
% 3.10/1.61 = zero_zero_nat )
% 3.10/1.61 = ( M2 = zero_zero_nat ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_303_of__nat__0__eq__iff,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( zero_zero_nat
% 3.10/1.61 = ( semiri1382578993at_nat @ N2 ) )
% 3.10/1.61 = ( zero_zero_nat = N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_304_of__nat__0,axiom,
% 3.10/1.61 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_305_of__nat__less__iff,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) )
% 3.10/1.61 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_306_length__0__conv,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = zero_zero_nat )
% 3.10/1.61 = ( Xs = nil_co1338500125t_unit ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_307_length__0__conv,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = zero_zero_nat )
% 3.10/1.61 = ( Xs = nil_message_p_v ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_308_zero__less__diff,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M2 ) )
% 3.10/1.61 = ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_309_diff__less,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.10/1.61 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 3.10/1.61 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ M2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_310_of__nat__less__imp__less,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) )
% 3.10/1.61 => ( ord_less_nat @ M2 @ N2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_311_less__imp__of__nat__less,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ ( semiri1382578993at_nat @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_312_less__imp__diff__less,axiom,
% 3.10/1.61 ! [J2: nat,K: nat,N2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ J2 @ K )
% 3.10/1.61 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N2 ) @ K ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_313_diff__less__mono2,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat,L: nat] :
% 3.10/1.61 ( ( ord_less_nat @ M2 @ N2 )
% 3.10/1.61 => ( ( ord_less_nat @ M2 @ L )
% 3.10/1.61 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_314_Suc__diff__Suc,axiom,
% 3.10/1.61 ! [N2: nat,M2: nat] :
% 3.10/1.61 ( ( ord_less_nat @ N2 @ M2 )
% 3.10/1.61 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N2 ) ) )
% 3.10/1.61 = ( minus_minus_nat @ M2 @ N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_315_diff__less__Suc,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N2 ) @ ( suc @ M2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_316_of__nat__less__0__iff,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M2 ) @ zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_317_of__nat__neq__0,axiom,
% 3.10/1.61 ! [N2: nat] :
% 3.10/1.61 ( ( semiri1382578993at_nat @ ( suc @ N2 ) )
% 3.10/1.61 != zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_318_length__Suc__conv,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,N2: nat] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( suc @ N2 ) )
% 3.10/1.61 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xs
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ( ( size_s1406904903t_unit @ Ys )
% 3.10/1.61 = N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_319_length__Suc__conv,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,N2: nat] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( suc @ N2 ) )
% 3.10/1.61 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( ( Xs
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ( ( size_s1168481041ge_p_v @ Ys )
% 3.10/1.61 = N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_320_Suc__length__conv,axiom,
% 3.10/1.61 ! [N2: nat,Xs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( suc @ N2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Xs ) )
% 3.10/1.61 = ( ? [Y2: config256849571t_unit,Ys: list_c1059388851t_unit] :
% 3.10/1.61 ( ( Xs
% 3.10/1.61 = ( cons_c1162654829t_unit @ Y2 @ Ys ) )
% 3.10/1.61 & ( ( size_s1406904903t_unit @ Ys )
% 3.10/1.61 = N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_321_Suc__length__conv,axiom,
% 3.10/1.61 ! [N2: nat,Xs: list_message_p_v] :
% 3.10/1.61 ( ( ( suc @ N2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Xs ) )
% 3.10/1.61 = ( ? [Y2: message_p_v,Ys: list_message_p_v] :
% 3.10/1.61 ( ( Xs
% 3.10/1.61 = ( cons_message_p_v @ Y2 @ Ys ) )
% 3.10/1.61 & ( ( size_s1168481041ge_p_v @ Ys )
% 3.10/1.61 = N2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_322_list_Osize_I3_J,axiom,
% 3.10/1.61 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_323_list_Osize_I3_J,axiom,
% 3.10/1.61 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 3.10/1.61 = zero_zero_nat ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_324_list__induct2,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_325_list__induct2,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_326_list__induct2,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_327_list__induct2,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_328_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_329_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_330_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_331_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_c1059388851t_unit,Ys2: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys3: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1406904903t_unit @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_c1162654829t_unit @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_332_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_333_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys3: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1406904903t_unit @ Ys3 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_334_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 3.10/1.61 = ( size_s1406904903t_unit @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_335_list__induct3,axiom,
% 3.10/1.61 ! [Xs: list_message_p_v,Ys2: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 3.10/1.61 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
% 3.10/1.61 => ( ! [X: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys3: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 3.10/1.61 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 3.10/1.61 => ( ( ( size_s1168481041ge_p_v @ Ys3 )
% 3.10/1.61 = ( size_s1168481041ge_p_v @ Zs ) )
% 3.10/1.61 => ( ( P @ Xs2 @ Ys3 @ Zs )
% 3.10/1.61 => ( P @ ( cons_message_p_v @ X @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys3 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 3.10/1.61 => ( P @ Xs @ Ys2 @ Zs2 ) ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_336_minus__nat_Odiff__0,axiom,
% 3.10/1.61 ! [M2: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 3.10/1.61 = M2 ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_337_diffs0__imp__equal,axiom,
% 3.10/1.61 ! [M2: nat,N2: nat] :
% 3.10/1.61 ( ( ( minus_minus_nat @ M2 @ N2 )
% 3.10/1.61 = zero_zero_nat )
% 3.10/1.61 => ( ( ( minus_minus_nat @ N2 @ M2 )
% 3.10/1.61 = zero_zero_nat )
% 3.10/1.61 => ( M2 = N2 ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_338_zero__induct__lemma,axiom,
% 3.10/1.61 ! [P: nat > $o,K: nat,I: nat] :
% 3.10/1.61 ( ( P @ K )
% 3.10/1.61 => ( ! [N: nat] :
% 3.10/1.61 ( ( P @ ( suc @ N ) )
% 3.10/1.61 => ( P @ N ) )
% 3.10/1.61 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_339_diff__right__commute,axiom,
% 3.10/1.61 ! [A8: nat,C: nat,B: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ ( minus_minus_nat @ A8 @ C ) @ B )
% 3.10/1.61 = ( minus_minus_nat @ ( minus_minus_nat @ A8 @ B ) @ C ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(fact_340_diff__commute,axiom,
% 3.10/1.61 ! [I: nat,J2: nat,K: nat] :
% 3.10/1.61 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J2 ) @ K )
% 3.10/1.61 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J2 ) ) ).
% 3.10/1.61
% 3.10/1.61 thf(conj_0,conjecture,
% 3.10/1.61 ( ( fe @ zero_zero_nat )
% 3.10/1.61 = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% 3.10/1.61 ------------------------
% 3.10/1.65 % (14482)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_14346 for (2999ds/27Mi)
% 3.10/1.66 % (14485)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_14346 for (2999ds/275Mi)
% 3.10/1.66 % (14483)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14346 for (2999ds/2Mi)
% 3.10/1.66 % (14483)Instruction limit reached!
% 3.10/1.66 % (14483)------------------------------
% 3.10/1.66 % (14483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (14483)Termination reason: Unknown
% 3.10/1.66 % (14483)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (14483)Memory used [KB]: 1535
% 3.10/1.66 % (14483)Time elapsed: 0.004 s
% 3.10/1.66 % (14483)Instructions burned: 3 (million)
% 3.10/1.66 % (14483)------------------------------
% 3.10/1.66 % (14483)------------------------------
% 3.10/1.66 % (14486)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14346 for (2999ds/18Mi)
% 3.10/1.66 % (14481)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_14346 for (2999ds/4Mi)
% 3.10/1.66 % (14480)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14346 for (2999ds/183Mi)
% 3.10/1.66 % (14484)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_14346 for (2999ds/2Mi)
% 3.10/1.66 % (14482)Instruction limit reached!
% 3.10/1.66 % (14482)------------------------------
% 3.10/1.66 % (14482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (14482)Termination reason: Unknown
% 3.10/1.66 % (14482)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (14482)Memory used [KB]: 2046
% 3.10/1.66 % (14482)Time elapsed: 0.011 s
% 3.10/1.66 % (14482)Instructions burned: 28 (million)
% 3.10/1.66 % (14482)------------------------------
% 3.10/1.66 % (14482)------------------------------
% 3.10/1.66 % (14484)Instruction limit reached!
% 3.10/1.66 % (14484)------------------------------
% 3.10/1.66 % (14484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (14484)Termination reason: Unknown
% 3.10/1.66 % (14484)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (14484)Memory used [KB]: 1535
% 3.10/1.66 % (14484)Time elapsed: 0.004 s
% 3.10/1.66 % (14484)Instructions burned: 3 (million)
% 3.10/1.66 % (14484)------------------------------
% 3.10/1.66 % (14484)------------------------------
% 3.10/1.66 % (14481)Instruction limit reached!
% 3.10/1.66 % (14481)------------------------------
% 3.10/1.66 % (14481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.66 % (14481)Termination reason: Unknown
% 3.10/1.66 % (14481)Termination phase: shuffling
% 3.10/1.66
% 3.10/1.66 % (14481)Memory used [KB]: 1663
% 3.10/1.66 % (14481)Time elapsed: 0.005 s
% 3.10/1.66 % (14481)Instructions burned: 5 (million)
% 3.10/1.66 % (14481)------------------------------
% 3.10/1.66 % (14481)------------------------------
% 3.10/1.67 % (14486)Instruction limit reached!
% 3.10/1.67 % (14486)------------------------------
% 3.10/1.67 % (14486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.67 % (14486)Termination reason: Unknown
% 3.10/1.67 % (14486)Termination phase: shuffling
% 3.10/1.67
% 3.10/1.67 % (14486)Memory used [KB]: 1918
% 3.10/1.67 % (14486)Time elapsed: 0.008 s
% 3.10/1.67 % (14486)Instructions burned: 20 (million)
% 3.10/1.67 % (14486)------------------------------
% 3.10/1.67 % (14486)------------------------------
% 3.10/1.67 % (14488)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_14346 for (2999ds/37Mi)
% 3.10/1.68 % (14487)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14346 for (2999ds/3Mi)
% 3.10/1.68 % (14487)Instruction limit reached!
% 3.10/1.68 % (14487)------------------------------
% 3.10/1.68 % (14487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (14487)Termination reason: Unknown
% 3.10/1.68 % (14487)Termination phase: shuffling
% 3.10/1.68
% 3.10/1.68 % (14487)Memory used [KB]: 1535
% 3.10/1.68 % (14487)Time elapsed: 0.004 s
% 3.10/1.68 % (14487)Instructions burned: 5 (million)
% 3.10/1.68 % (14487)------------------------------
% 3.10/1.68 % (14487)------------------------------
% 3.10/1.68 % (14485)First to succeed.
% 3.10/1.68 % (14485)Refutation found. Thanks to Tanya!
% 3.10/1.68 % SZS status Theorem for DTF2THF_14346
% 3.10/1.68 % SZS output start Proof for DTF2THF_14346
% 3.10/1.68 thf(type_def_5, type, p: $tType).
% 3.10/1.68 thf(type_def_6, type, s: $tType).
% 3.10/1.68 thf(type_def_7, type, messageValue_v: $tType).
% 3.10/1.68 thf(type_def_9, type, message_p_v: $tType).
% 3.10/1.68 thf(type_def_10, type, nat: $tType).
% 3.10/1.68 thf(type_def_11, type, config256849571t_unit: $tType).
% 3.10/1.68 thf(type_def_12, type, list_c1059388851t_unit: $tType).
% 3.10/1.68 thf(type_def_13, type, list_message_p_v: $tType).
% 3.10/1.68 thf(type_def_14, type, list_l611321411t_unit: $tType).
% 3.10/1.68 thf(type_def_15, type, list_l1619404459ge_p_v: $tType).
% 3.10/1.68 thf(type_def_16, type, list_nat: $tType).
% 3.10/1.68 thf(type_def_17, type, list_list_nat: $tType).
% 3.10/1.68 thf(type_def_18, type, set_nat: $tType).
% 3.10/1.68 thf(func_def_0, type, list_l611321411t_unit: $tType).
% 3.10/1.68 thf(func_def_1, type, list_c1059388851t_unit: $tType).
% 3.10/1.68 thf(func_def_2, type, config256849571t_unit: $tType).
% 3.10/1.68 thf(func_def_3, type, list_l1619404459ge_p_v: $tType).
% 3.10/1.68 thf(func_def_4, type, list_message_p_v: $tType).
% 3.10/1.68 thf(func_def_5, type, list_list_nat: $tType).
% 3.10/1.68 thf(func_def_6, type, message_p_v: $tType).
% 3.10/1.68 thf(func_def_7, type, messageValue_v: $tType).
% 3.10/1.68 thf(func_def_8, type, list_nat: $tType).
% 3.10/1.68 thf(func_def_9, type, set_nat: $tType).
% 3.10/1.68 thf(func_def_10, type, nat: $tType).
% 3.10/1.68 thf(func_def_11, type, s: $tType).
% 3.10/1.68 thf(func_def_12, type, p: $tType).
% 3.10/1.68 thf(func_def_13, type, fLPThe9398366_p_s_v: (p > s > messageValue_v > s) > (p > s > messageValue_v > message_p_v > nat) > (p > s) > $o).
% 3.10/1.68 thf(func_def_14, 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).
% 3.10/1.68 thf(func_def_15, 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).
% 3.10/1.68 thf(func_def_16, type, minus_minus_nat: nat > nat > nat).
% 3.10/1.68 thf(func_def_17, type, zero_zero_nat: nat).
% 3.10/1.68 thf(func_def_18, type, bind_c1439720399t_unit: list_c1059388851t_unit > (config256849571t_unit > list_c1059388851t_unit) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_19, type, bind_c246984691ge_p_v: list_c1059388851t_unit > (config256849571t_unit > list_message_p_v) > list_message_p_v).
% 3.10/1.68 thf(func_def_20, type, bind_m595590011t_unit: list_message_p_v > (message_p_v > list_c1059388851t_unit) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_21, type, bind_m729301831ge_p_v: list_message_p_v > (message_p_v > list_message_p_v) > list_message_p_v).
% 3.10/1.68 thf(func_def_22, type, count_1396868135t_unit: list_c1059388851t_unit > config256849571t_unit > nat).
% 3.10/1.68 thf(func_def_23, type, count_1322329499ge_p_v: list_message_p_v > message_p_v > nat).
% 3.10/1.68 thf(func_def_24, type, gen_le193291088t_unit: nat > list_c1059388851t_unit > nat).
% 3.10/1.68 thf(func_def_25, type, gen_le697204914ge_p_v: nat > list_message_p_v > nat).
% 3.10/1.68 thf(func_def_26, type, insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_27, type, insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_28, type, cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_29, type, cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_30, type, cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit).
% 3.10/1.68 thf(func_def_31, type, cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v).
% 3.10/1.68 thf(func_def_32, type, cons_list_nat: list_nat > list_list_nat > list_list_nat).
% 3.10/1.68 thf(func_def_33, type, cons_nat: nat > list_nat > list_nat).
% 3.10/1.68 thf(func_def_34, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_35, type, nil_message_p_v: list_message_p_v).
% 3.10/1.68 thf(func_def_36, type, nil_li307996205t_unit: list_l611321411t_unit).
% 3.10/1.68 thf(func_def_37, type, nil_list_message_p_v: list_l1619404459ge_p_v).
% 3.10/1.68 thf(func_def_38, type, nil_list_nat: list_list_nat).
% 3.10/1.68 thf(func_def_39, type, nil_nat: list_nat).
% 3.10/1.68 thf(func_def_40, type, list_e1598815642t_unit: (config256849571t_unit > $o) > list_c1059388851t_unit > $o).
% 3.10/1.68 thf(func_def_41, type, list_ex1_message_p_v: (message_p_v > $o) > list_message_p_v > $o).
% 3.10/1.68 thf(func_def_42, type, listre990624391t_unit: (config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 3.10/1.68 thf(func_def_43, type, listre823101243ge_p_v: (config256849571t_unit > message_p_v > $o) > list_c1059388851t_unit > list_message_p_v > $o).
% 3.10/1.68 thf(func_def_44, type, listre1171706563t_unit: (message_p_v > config256849571t_unit > $o) > list_message_p_v > list_c1059388851t_unit > $o).
% 3.10/1.68 thf(func_def_45, type, listre1295695359ge_p_v: (message_p_v > message_p_v > $o) > list_message_p_v > list_message_p_v > $o).
% 3.10/1.68 thf(func_def_46, type, map_ta91747645t_unit: (config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_47, type, map_ta782801413ge_p_v: (config256849571t_unit > message_p_v) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_48, type, map_ta1131406733t_unit: (message_p_v > config256849571t_unit) > list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_49, type, map_ta1016577461ge_p_v: (message_p_v > message_p_v) > list_message_p_v > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_50, type, member1087090632t_unit: list_c1059388851t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_51, type, member_message_p_v: list_message_p_v > message_p_v > $o).
% 3.10/1.68 thf(func_def_52, type, n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit).
% 3.10/1.68 thf(func_def_53, type, n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v).
% 3.10/1.68 thf(func_def_54, type, nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_55, type, nths_message_p_v: list_message_p_v > set_nat > list_message_p_v).
% 3.10/1.68 thf(func_def_56, type, lexord1758866263t_unit: (config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 3.10/1.68 thf(func_def_57, type, lexord2101627499ge_p_v: (message_p_v > message_p_v > $o) > list_message_p_v > list_message_p_v > $o).
% 3.10/1.68 thf(func_def_58, type, ord_lexordp_nat: list_nat > list_nat > $o).
% 3.10/1.68 thf(func_def_59, type, ord_lexordp_eq_nat: list_nat > list_nat > $o).
% 3.10/1.68 thf(func_def_60, type, produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit).
% 3.10/1.68 thf(func_def_61, type, produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v).
% 3.10/1.68 thf(func_def_62, type, splice888123018t_unit: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_63, type, splice_message_p_v: list_message_p_v > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_64, type, subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit).
% 3.10/1.68 thf(func_def_65, type, subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v).
% 3.10/1.68 thf(func_def_66, type, suc: nat > nat).
% 3.10/1.68 thf(func_def_67, type, semiri1382578993at_nat: nat > nat).
% 3.10/1.68 thf(func_def_68, type, size_s1406904903t_unit: list_c1059388851t_unit > nat).
% 3.10/1.68 thf(func_def_69, type, size_s1168481041ge_p_v: list_message_p_v > nat).
% 3.10/1.68 thf(func_def_70, type, ord_less_nat: nat > nat > $o).
% 3.10/1.68 thf(func_def_71, type, member_nat: nat > set_nat > $o).
% 3.10/1.68 thf(func_def_72, type, cfg: config256849571t_unit).
% 3.10/1.68 thf(func_def_73, type, fStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_74, type, fStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 3.10/1.68 thf(func_def_75, type, fe: nat > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_76, type, ft: nat > list_message_p_v).
% 3.10/1.68 thf(func_def_93, type, sK0: list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_94, type, sK1: list_c1059388851t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_95, type, sK2: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_96, type, sK3: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_97, type, sK4: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_98, type, sK5: list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_99, type, sK6: list_c1059388851t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_100, type, sK7: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_101, type, sK8: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_102, type, sK9: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_103, type, sK10: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_104, type, sK11: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_105, type, sK12: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_106, type, sK13: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_107, type, sK14: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_108, type, sK15: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_109, type, sK16: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_110, type, sK17: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_111, type, sK18: ((config256849571t_unit > config256849571t_unit) > list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_112, type, sK19: list_c1059388851t_unit > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > nat > nat).
% 3.10/1.68 thf(func_def_113, type, sK20: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_114, type, sK21: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_115, type, sK22: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_116, type, sK23: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_117, type, sK24: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_118, type, sK25: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_119, type, sK26: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_120, type, sK27: (nat > $o) > nat).
% 3.10/1.68 thf(func_def_121, type, sK28: (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > list_message_p_v > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > config256849571t_unit > nat).
% 3.10/1.68 thf(func_def_122, type, sK29: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_123, type, sK30: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_124, type, sK31: (list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_125, type, sK32: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_126, type, sK33: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_127, type, sK34: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_128, type, sK35: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_129, type, sK36: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_130, type, sK37: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_131, type, sK38: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_132, type, sK39: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_133, type, sK40: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_134, type, sK41: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_135, type, sK42: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_136, type, sK43: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_137, type, sK44: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_138, type, sK45: (nat > $o) > nat).
% 3.10/1.68 thf(func_def_139, type, sK46: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_140, type, sK47: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit > config256849571t_unit > $o).
% 3.10/1.68 thf(func_def_141, type, sK48: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_142, type, sK49: ((config256849571t_unit > config256849571t_unit > $o) > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_143, type, sK50: list_c1059388851t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_144, type, sK51: list_c1059388851t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_145, type, sK52: list_c1059388851t_unit > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_146, type, sK53: list_c1059388851t_unit > config256849571t_unit).
% 3.10/1.68 thf(func_def_147, type, sK54: (nat > $o) > nat).
% 3.10/1.68 thf(func_def_148, type, sK55: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_149, type, sK56: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_150, type, sK57: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > config256849571t_unit).
% 3.10/1.68 thf(func_def_151, type, sK58: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_152, type, sK59: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_153, type, sK60: (list_c1059388851t_unit > list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 3.10/1.68 thf(func_def_155, type, ph62: !>[X0: $tType]:(X0)).
% 3.10/1.68 thf(f1053,plain,(
% 3.10/1.68 $false),
% 3.10/1.68 inference(subsumption_resolution,[status(thm)],[f1027,f1003])).
% 3.10/1.68 thf(f1003,plain,(
% 3.10/1.68 ( ! [X2 : list_c1059388851t_unit > list_message_p_v > list_message_p_v,X0 : config256849571t_unit,X1 : list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit] : (((fLPThe1519354920_p_v_s @ X0 @ X1 @ X2 @ zero_zero_nat) = (cons_c1162654829t_unit @ X0 @ nil_co1338500125t_unit))) )),
% 3.10/1.68 inference(cnf_transformation,[status(thm)],[f3])).
% 3.10/1.68 thf(f3,axiom,(
% 3.10/1.68 ! [X0 : config256849571t_unit,X1 : list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,X2 : list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ((fLPThe1519354920_p_v_s @ X0 @ X1 @ X2 @ zero_zero_nat) = (cons_c1162654829t_unit @ X0 @ nil_co1338500125t_unit))),
% 3.10/1.68 file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',fact_2_infiniteExecutionCfg_Osimps_I1_J)).
% 3.10/1.68 thf(f1027,plain,(
% 3.10/1.68 ((cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit) != (fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg @ zero_zero_nat))),
% 3.10/1.68 inference(definition_unfolding,[status(thm)],[f956,f946])).
% 3.10/1.68 thf(f946,plain,(
% 3.10/1.68 (fe = (fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg))),
% 3.10/1.68 inference(cnf_transformation,[status(thm)],[f2])).
% 3.10/1.68 thf(f2,axiom,(
% 3.10/1.68 (fe = (fLPThe1519354920_p_v_s @ cfg @ fStepCfg @ fStepMsg))),
% 3.10/1.68 file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',fact_1_fe__def)).
% 3.10/1.68 thf(f956,plain,(
% 3.10/1.68 ((fe @ zero_zero_nat) != (cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit))),
% 3.10/1.68 inference(cnf_transformation,[status(thm)],[f813])).
% 3.10/1.68 thf(f813,plain,(
% 3.10/1.68 ((fe @ zero_zero_nat) != (cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit))),
% 3.10/1.68 inference(flattening,[status(thm)],[f343])).
% 3.10/1.68 thf(f343,negated_conjecture,(
% 3.10/1.68 ~((fe @ zero_zero_nat) = (cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit))),
% 3.10/1.68 inference(negated_conjecture,[status(cth)],[f342])).
% 3.10/1.68 thf(f342,conjecture,(
% 3.10/1.68 ((fe @ zero_zero_nat) = (cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit))),
% 3.10/1.68 file('/export/starexec/sandbox/tmp/tmp.R6zWc8j3Xo/DTF2THF_14346.p',conj_0)).
% 3.10/1.68 % SZS output end Proof for DTF2THF_14346
% 3.10/1.68 % (14485)------------------------------
% 3.10/1.68 % (14485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.68 % (14485)Termination reason: Refutation
% 3.10/1.68
% 3.10/1.68 % (14485)Memory used [KB]: 7036
% 3.10/1.68 % (14485)Time elapsed: 0.027 s
% 3.10/1.68 % (14485)Instructions burned: 81 (million)
% 3.10/1.68 % (14485)------------------------------
% 3.10/1.68 % (14485)------------------------------
% 3.10/1.68 % (14479)Success in time 0.054 s
%------------------------------------------------------------------------------