%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP060^1 : 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 : n012.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 08:55:13 AM UTC 2026
% Result : Theorem 1.65s 1.10s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 220 ( 14 ~; 6 |; 0 &; 194 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 135 ( 132 usr; 13 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
config256849571t_unit: $tType ).
thf(type_def_6,type,
message_p_v: $tType ).
thf(type_def_8,type,
list_c1059388851t_unit: $tType ).
thf(type_def_9,type,
list_message_p_v: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(func_def_0,type,
list_c1059388851t_unit: $tType ).
thf(func_def_1,type,
config256849571t_unit: $tType ).
thf(func_def_2,type,
list_message_p_v: $tType ).
thf(func_def_3,type,
message_p_v: $tType ).
thf(func_def_4,type,
nat: $tType ).
thf(func_def_5,type,
enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
thf(func_def_6,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(func_def_7,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_8,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_9,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_10,type,
one_one_nat: nat ).
thf(func_def_11,type,
zero_zero_nat: nat ).
thf(func_def_12,type,
prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
thf(func_def_13,type,
prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
thf(func_def_14,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(func_def_15,type,
last_message_p_v: list_message_p_v > message_p_v ).
thf(func_def_16,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(func_def_17,type,
nil_message_p_v: list_message_p_v ).
thf(func_def_18,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(func_def_19,type,
nth_message_p_v: list_message_p_v > nat > message_p_v ).
thf(func_def_20,type,
suc: nat > nat ).
thf(func_def_21,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(func_def_22,type,
size_s1168481041ge_p_v: list_message_p_v > nat ).
thf(func_def_23,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_24,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_25,type,
fe: nat > list_c1059388851t_unit ).
thf(func_def_26,type,
ft: nat > list_message_p_v ).
thf(func_def_27,type,
index: nat ).
thf(func_def_28,type,
msgInSet: message_p_v ).
thf(func_def_29,type,
msg: message_p_v ).
thf(func_def_30,type,
n0: nat ).
thf(func_def_31,type,
n1: nat ).
thf(func_def_32,type,
nMsg: nat ).
thf(func_def_33,type,
n: nat ).
thf(func_def_47,type,
sP0: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_48,type,
sP1: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > $o ).
thf(func_def_49,type,
sK2: nat > nat > nat ).
thf(func_def_50,type,
sK3: ( nat > $o ) > nat > nat ).
thf(func_def_51,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_52,type,
sK5: ( nat > nat > $o ) > nat ).
thf(func_def_53,type,
sK6: ( nat > nat > $o ) > nat ).
thf(func_def_54,type,
sK7: ( nat > nat > $o ) > nat ).
thf(func_def_55,type,
sK8: ( nat > nat > $o ) > nat ).
thf(func_def_56,type,
sK9: ( nat > nat > $o ) > nat ).
thf(func_def_57,type,
sK10: nat > ( nat > $o ) > nat ).
thf(func_def_58,type,
sK11: nat > ( nat > $o ) > nat ).
thf(func_def_59,type,
sK12: nat > ( nat > $o ) > nat ).
thf(func_def_60,type,
sK13: ( nat > nat > $o ) > nat ).
thf(func_def_61,type,
sK14: ( nat > nat > $o ) > nat ).
thf(func_def_62,type,
sK15: ( nat > nat > $o ) > nat ).
thf(func_def_63,type,
sK16: ( nat > nat > $o ) > nat ).
thf(func_def_64,type,
sK17: ( nat > $o ) > ( nat > $o ) > nat > nat ).
thf(func_def_65,type,
sK18: nat > list_message_p_v ).
thf(func_def_66,type,
sK19: ( nat > $o ) > nat > nat > nat ).
thf(func_def_67,type,
sK20: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_68,type,
sK21: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_69,type,
sK22: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_70,type,
sK23: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_71,type,
sK24: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_72,type,
sK25: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_73,type,
sK26: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_74,type,
sK27: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_75,type,
sK28: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_76,type,
sK29: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_77,type,
sK30: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_78,type,
sK31: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_79,type,
sK32: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_80,type,
sK33: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_81,type,
sK34: ( nat > nat ) > nat ).
thf(func_def_82,type,
sK35: ( nat > nat ) > nat ).
thf(func_def_83,type,
sK36: ( nat > nat ) > nat ).
thf(func_def_84,type,
sK37: ( nat > nat ) > nat ).
thf(func_def_85,type,
sK38: ( nat > $o ) > nat ).
thf(func_def_86,type,
sK39: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_87,type,
sK40: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_88,type,
sK41: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_89,type,
sK42: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_90,type,
sK43: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_91,type,
sK44: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_92,type,
sK45: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_93,type,
sK46: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_94,type,
sK47: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_95,type,
sK48: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_96,type,
sK49: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > nat ).
thf(func_def_97,type,
sK50: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > config256849571t_unit ).
thf(func_def_98,type,
sK51: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_message_p_v ).
thf(func_def_99,type,
sK52: ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > ( config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o ) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ).
thf(func_def_100,type,
sK53: ( nat > nat ) > nat ).
thf(func_def_101,type,
sK54: ( nat > $o ) > nat > nat ).
thf(func_def_102,type,
sK55: ( nat > $o ) > nat ).
thf(func_def_103,type,
sK56: ( nat > $o ) > nat ).
thf(func_def_104,type,
sK57: nat > nat ).
thf(func_def_105,type,
sK58: ( nat > $o ) > nat ).
thf(func_def_106,type,
sK59: ( nat > nat ) > nat ).
thf(func_def_107,type,
sK60: nat > nat > nat ).
thf(func_def_108,type,
sK61: nat > ( nat > config256849571t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_109,type,
sK62: nat > ( nat > config256849571t_unit > $o ) > nat ).
thf(func_def_110,type,
sK63: nat > ( nat > config256849571t_unit > $o ) > config256849571t_unit ).
thf(func_def_111,type,
sK64: list_c1059388851t_unit > nat > ( nat > config256849571t_unit > $o ) > nat ).
thf(func_def_112,type,
sK65: ( nat > $o ) > nat > nat ).
thf(func_def_113,type,
sK66: ( nat > $o ) > nat > nat ).
thf(func_def_114,type,
sK67: nat > nat ).
thf(func_def_115,type,
sK68: nat > nat > nat ).
thf(func_def_116,type,
sK69: ( nat > $o ) > nat ).
thf(func_def_117,type,
sK70: ( nat > $o ) > nat > nat ).
thf(func_def_118,type,
sK71: nat > nat ).
thf(func_def_119,type,
sK72: nat > list_c1059388851t_unit ).
thf(func_def_120,type,
sK73: ( nat > $o ) > nat ).
thf(func_def_121,type,
sK74: ( nat > $o ) > nat ).
thf(func_def_122,type,
sK75: nat > nat ).
thf(func_def_123,type,
sK76: ( nat > $o ) > nat > nat ).
thf(func_def_124,type,
sK77: ( nat > $o ) > nat > nat ).
thf(func_def_125,type,
sK78: nat > ( nat > $o ) > nat ).
thf(func_def_126,type,
sK79: nat > ( nat > $o ) > nat ).
thf(func_def_127,type,
sK80: ( nat > $o ) > nat ).
thf(func_def_128,type,
sK81: nat > ( nat > $o ) > nat ).
thf(func_def_129,type,
sK82: list_message_p_v > list_message_p_v > nat ).
thf(func_def_130,type,
sK83: nat > nat > nat ).
thf(func_def_131,type,
sK84: nat > nat > ( nat > $o ) > nat ).
thf(func_def_132,type,
sK85: ( nat > $o ) > nat ).
thf(func_def_133,type,
sK86: ( list_message_p_v > $o ) > list_message_p_v ).
thf(func_def_134,type,
sK87: ( nat > message_p_v > $o ) > nat > list_message_p_v ).
thf(func_def_135,type,
sK88: ( nat > message_p_v > $o ) > nat > nat ).
thf(func_def_136,type,
sK89: nat > ( nat > message_p_v > $o ) > message_p_v ).
thf(func_def_137,type,
sK90: list_message_p_v > ( nat > message_p_v > $o ) > nat > nat ).
thf(func_def_138,type,
sK91: ( nat > $o ) > nat ).
thf(func_def_139,type,
sK92: nat > nat ).
thf(func_def_140,type,
sK93: nat > ( nat > $o ) > nat ).
thf(func_def_141,type,
sK94: nat > ( nat > $o ) > nat ).
thf(func_def_142,type,
sK95: ( list_c1059388851t_unit > $o ) > list_c1059388851t_unit ).
thf(func_def_143,type,
sK96: ( nat > $o ) > nat ).
thf(func_def_144,type,
sK97: ( nat > nat > $o ) > nat ).
thf(func_def_145,type,
sK98: ( nat > nat > $o ) > nat ).
thf(func_def_146,type,
sK99: ( nat > nat > $o ) > nat ).
thf(func_def_147,type,
sK100: ( nat > nat > $o ) > nat ).
thf(func_def_148,type,
sK101: list_c1059388851t_unit > list_c1059388851t_unit > nat ).
thf(func_def_150,type,
ph103:
!>[X0: $tType] : X0 ).
thf(f1460,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1439,f1273]) ).
thf(f1273,plain,
( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f422]) ).
thf(f422,plain,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_0_Occ3_H) ).
thf(f1439,plain,
( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1438]) ).
thf(f1438,plain,
( ( $true != $true )
| ( ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1422,f1082]) ).
thf(f1082,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ord_less_nat @ ( minus_minus_nat @ X1 @ X2 ) @ X0 )
= $true )
| ( ( ord_less_nat @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f815]) ).
thf(f815,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
!= $true )
| ( ( ord_less_nat @ ( minus_minus_nat @ X1 @ X2 ) @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f251]) ).
thf(f251,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
=> ( ( ord_less_nat @ ( minus_minus_nat @ X1 @ X2 ) @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f250]) ).
thf(f250,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less_nat @ X1 @ X0 )
=> ( ord_less_nat @ ( minus_minus_nat @ X1 @ X2 ) @ X0 ) ),
inference(rectify,[status(thm)],[f155]) ).
thf(f155,axiom,
! [X3: nat,X24: nat,X1: nat] :
( ( ord_less_nat @ X24 @ X3 )
=> ( ord_less_nat @ ( minus_minus_nat @ X24 @ X1 ) @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_154_less__imp__diff__less) ).
thf(f1422,plain,
( ( ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1421]) ).
thf(f1421,plain,
( ( ( ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true )
| ( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) )
!= ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) ) ) ),
inference(superposition,[status(thm)],[f1358,f1092]) ).
thf(f1092,plain,
! [X0: nat] :
( ( ( nth_co1649820636t_unit @ ( fe @ index ) @ X0 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
thf(f763,plain,
! [X0: nat] :
( ( ( nth_co1649820636t_unit @ ( fe @ index ) @ X0 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ X0 ) )
| ( ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f345]) ).
thf(f345,plain,
! [X0: nat] :
( ( ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
= $true )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ X0 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ X0 ) ) ),
inference(fool_elimination,[status(thm)],[f344]) ).
thf(f344,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ X0 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: nat] :
( ( ord_less_nat @ X0 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
=> ( ( nth_co1649820636t_unit @ ( fe @ index ) @ X0 )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_1_SameCfgOnLow) ).
thf(f1358,plain,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) )
!= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1154,f1153,f1153]) ).
thf(f1153,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
thf(f137,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_136_One__nat__def) ).
thf(f1154,plain,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
!= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(cnf_transformation,[status(thm)],[f638]) ).
thf(f638,plain,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
!= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(flattening,[status(thm)],[f246]) ).
thf(f246,negated_conjecture,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
!= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
inference(negated_conjecture,[status(cth)],[f245]) ).
thf(f245,conjecture,
( ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
= ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP060^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue Feb 24 08:24:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.31 thf(spec,logic,$$dhol).
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % File : ITP060^1 : TPTP v9.2.1. Released v7.5.0.
% 0.07/0.31 % Domain : Interactive Theorem Proving
% 0.07/0.31 % Problem : Sledgehammer FLPTheorem problem prob_828__3301664_1
% 0.07/0.31 % Version : Especial.
% 0.07/0.31 % English :
% 0.07/0.31
% 0.07/0.31 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.07/0.31 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.07/0.31 % Source : [Des21]
% 0.07/0.31 % Names : FLPTheorem/prob_828__3301664_1 [Des21]
% 0.07/0.31
% 0.07/0.31 % Status : Theorem
% 0.07/0.31 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.07/0.31 % Syntax : Number of formulae : 279 ( 134 unt; 34 typ; 0 def)
% 0.07/0.31 % Number of atoms : 517 ( 209 equ; 0 cnn)
% 0.07/0.31 % Maximal formula atoms : 7 ( 2 avg)
% 0.07/0.31 % Number of connectives : 1855 ( 85 ~; 11 |; 36 &;1466 @)
% 0.07/0.31 % ( 0 <=>; 257 =>; 0 <=; 0 <~>)
% 0.07/0.31 % Maximal formula depth : 21 ( 6 avg)
% 0.07/0.31 % Number of types : 6 ( 5 usr)
% 0.07/0.31 % Number of type conns : 173 ( 173 >; 0 *; 0 +; 0 <<)
% 0.07/0.31 % Number of symbols : 30 ( 29 usr; 11 con; 0-4 aty)
% 0.07/0.31 % Number of variables : 511 ( 13 ^; 467 !; 31 ?; 511 :)
% 0.07/0.31 % SPC : TH0_THM_EQU_NAR
% 0.07/0.31
% 0.07/0.31 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:36.188
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 % Could-be-implicit typings (5)
% 0.07/0.31 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.07/0.31 list_c1059388851t_unit: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.07/0.31 config256849571t_unit: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.07/0.31 list_message_p_v: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.07/0.31 message_p_v: $tType ).
% 0.07/0.31
% 0.07/0.31 thf(ty_n_t__Nat__Onat,type,
% 0.07/0.31 nat: $tType ).
% 0.07/0.31
% 0.07/0.31 % Explicit typings (29)
% 0.07/0.31 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.07/0.31 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.07/0.31 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 0.07/0.31 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 ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 0.07/0.31 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 ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.07/0.31 minus_minus_nat: nat > nat > nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.07/0.31 one_one_nat: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.07/0.31 zero_zero_nat: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.07/0.31 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.07/0.31 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.07/0.31 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.07/0.31 last_message_p_v: list_message_p_v > message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.07/0.31 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.07/0.31 nil_message_p_v: list_message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.07/0.31 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.07/0.31 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Nat_OSuc,type,
% 0.07/0.31 suc: nat > nat ).
% 0.07/0.31
% 0.07/0.31 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,
% 0.07/0.31 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.07/0.31 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.07/0.31 ord_less_nat: nat > nat > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.07/0.31 ord_less_eq_nat: nat > nat > $o ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_fe____,type,
% 0.07/0.31 fe: nat > list_c1059388851t_unit ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_ft____,type,
% 0.07/0.31 ft: nat > list_message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_index____,type,
% 0.07/0.31 index: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_msgInSet____,type,
% 0.07/0.31 msgInSet: message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_msg____,type,
% 0.07/0.31 msg: message_p_v ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_n0____,type,
% 0.07/0.31 n0: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_n1____,type,
% 0.07/0.31 n1: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_nMsg____,type,
% 0.07/0.31 nMsg: nat ).
% 0.07/0.31
% 0.07/0.31 thf(sy_v_n____,type,
% 0.07/0.31 n: nat ).
% 0.07/0.31
% 0.07/0.31 % Relevant facts (244)
% 0.07/0.31 thf(fact_0_Occ3_H,axiom,
% 0.07/0.31 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.07/0.31
% 0.07/0.31 % Occ3'
% 0.07/0.31 thf(fact_1_SameCfgOnLow,axiom,
% 0.07/0.31 ! [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 0.07/0.31 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I )
% 0.07/0.31 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % SameCfgOnLow
% 0.07/0.31 thf(fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062,axiom,
% 0.07/0.31 ( ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 )
% 0.07/0.31 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>fe index ! n1 = fe (Suc index) ! n1\<close>
% 0.07/0.31 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 0.07/0.31 ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>length (fe index) - 1 < length (fe index)\<close>
% 0.07/0.31 thf(fact_4_AssumptionSubset2_I3_J,axiom,
% 0.07/0.31 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset2(3)
% 0.07/0.31 thf(fact_5_AssumpOcc6_H_I1_J,axiom,
% 0.07/0.31 ord_less_nat @ zero_zero_nat @ n1 ).
% 0.07/0.31
% 0.07/0.31 % AssumpOcc6'(1)
% 0.07/0.31 thf(fact_6_diff__Suc__1,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.07/0.31 = N ) ).
% 0.07/0.31
% 0.07/0.31 % diff_Suc_1
% 0.07/0.31 thf(fact_7_diff__Suc__Suc,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.07/0.31 = ( minus_minus_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_Suc_Suc
% 0.07/0.31 thf(fact_8_Suc__diff__diff,axiom,
% 0.07/0.31 ! [M: nat,N: nat,K: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.07/0.31 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_diff_diff
% 0.07/0.31 thf(fact_9_NotEmpty_I1_J,axiom,
% 0.07/0.31 ( ( fe @ ( suc @ index ) )
% 0.07/0.31 != nil_co1338500125t_unit ) ).
% 0.07/0.31
% 0.07/0.31 % NotEmpty(1)
% 0.07/0.31 thf(fact_10_IPrefixListEx,axiom,
% 0.07/0.31 ! [I: nat] : ( prefix1615116500t_unit @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % IPrefixListEx
% 0.07/0.31 thf(fact_11_diff__Suc__eq__diff__pred,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.07/0.31 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_Suc_eq_diff_pred
% 0.07/0.31 thf(fact_12_AssumpOcc6_H_I3_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % AssumpOcc6'(3)
% 0.07/0.31 thf(fact_13__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.07/0.31 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.07/0.31 thf(fact_14_NotEmpty_I2_J,axiom,
% 0.07/0.31 ( ( fe @ index )
% 0.07/0.31 != nil_co1338500125t_unit ) ).
% 0.07/0.31
% 0.07/0.31 % NotEmpty(2)
% 0.07/0.31 thf(fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062,axiom,
% 0.07/0.31 ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>n1 - Suc 0 < length (fe index) - Suc 0\<close>
% 0.07/0.31 thf(fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.07/0.31 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 0.07/0.31 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.07/0.31 => ( ! [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] :
% 0.07/0.31 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.07/0.31 => ( ! [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] :
% 0.07/0.31 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.07/0.31 thf(fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.07/0.31 ! [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] :
% 0.07/0.31 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.07/0.31 => ( ! [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] :
% 0.07/0.31 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.07/0.31 => ( ! [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] :
% 0.07/0.31 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.07/0.31 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.07/0.31 thf(fact_18_old_Onat_Oinject,axiom,
% 0.07/0.31 ! [Nat: nat,Nat2: nat] :
% 0.07/0.31 ( ( ( suc @ Nat )
% 0.07/0.31 = ( suc @ Nat2 ) )
% 0.07/0.31 = ( Nat = Nat2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % old.nat.inject
% 0.07/0.31 thf(fact_19_nat_Oinject,axiom,
% 0.07/0.31 ! [X2: nat,Y2: nat] :
% 0.07/0.31 ( ( ( suc @ X2 )
% 0.07/0.31 = ( suc @ Y2 ) )
% 0.07/0.31 = ( X2 = Y2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat.inject
% 0.07/0.31 thf(fact_20_AssumptionSubset_I1_J,axiom,
% 0.07/0.31 ord_less_eq_nat @ n1 @ nMsg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset(1)
% 0.07/0.31 thf(fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062,axiom,
% 0.07/0.31 ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>fe index \<in># length\<close>
% 0.07/0.31 thf(fact_22_Suc__less__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.07/0.31 = ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_less_eq
% 0.07/0.31 thf(fact_23_Suc__mono,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_mono
% 0.07/0.31 thf(fact_24_lessI,axiom,
% 0.07/0.31 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % lessI
% 0.07/0.31 thf(fact_25_neq0__conv,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( N != zero_zero_nat )
% 0.07/0.31 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % neq0_conv
% 0.07/0.31 thf(fact_26_less__nat__zero__code,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % less_nat_zero_code
% 0.07/0.31 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( A != zero_zero_nat )
% 0.07/0.31 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.07/0.31
% 0.07/0.31 % bot_nat_0.not_eq_extremum
% 0.07/0.31 thf(fact_28_Suc__le__mono,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.07/0.31 = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_le_mono
% 0.07/0.31 thf(fact_29_le0,axiom,
% 0.07/0.31 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.07/0.31
% 0.07/0.31 % le0
% 0.07/0.31 thf(fact_30_bot__nat__0_Oextremum,axiom,
% 0.07/0.31 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.07/0.31
% 0.07/0.31 % bot_nat_0.extremum
% 0.07/0.31 thf(fact_31_diff__self__eq__0,axiom,
% 0.07/0.31 ! [M: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ M @ M )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % diff_self_eq_0
% 0.07/0.31 thf(fact_32_diff__0__eq__0,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % diff_0_eq_0
% 0.07/0.31 thf(fact_33_diff__diff__cancel,axiom,
% 0.07/0.31 ! [I2: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ N )
% 0.07/0.31 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 0.07/0.31 = I2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_diff_cancel
% 0.07/0.31 thf(fact_34_Occ4_H,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % Occ4'
% 0.07/0.31 thf(fact_35_AssumptionSubset2_I4_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset2(4)
% 0.07/0.31 thf(fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % \<open>enabled (fe index ! (length (fe index) - 1)) msgInSet\<close>
% 0.07/0.31 thf(fact_37_zero__less__Suc,axiom,
% 0.07/0.31 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_less_Suc
% 0.07/0.31 thf(fact_38_less__Suc0,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_Suc0
% 0.07/0.31 thf(fact_39_zero__less__diff,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.07/0.31 = ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_less_diff
% 0.07/0.31 thf(fact_40_diff__is__0__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ( minus_minus_nat @ M @ N )
% 0.07/0.31 = zero_zero_nat )
% 0.07/0.31 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_is_0_eq
% 0.07/0.31 thf(fact_41_diff__is__0__eq_H,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ( minus_minus_nat @ M @ N )
% 0.07/0.31 = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_is_0_eq'
% 0.07/0.31 thf(fact_42_less__one,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N @ one_one_nat )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_one
% 0.07/0.31 thf(fact_43_Suc__pred,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.07/0.31 = N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_pred
% 0.07/0.31 thf(fact_44_Suc__diff__1,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.07/0.31 = N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_diff_1
% 0.07/0.31 thf(fact_45_less__eq__nat_Osimps_I1_J,axiom,
% 0.07/0.31 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.07/0.31
% 0.07/0.31 % less_eq_nat.simps(1)
% 0.07/0.31 thf(fact_46_gr0I,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( N != zero_zero_nat )
% 0.07/0.31 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr0I
% 0.07/0.31 thf(fact_47_le__0__eq,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_0_eq
% 0.07/0.31 thf(fact_48_le__refl,axiom,
% 0.07/0.31 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.07/0.31
% 0.07/0.31 % le_refl
% 0.07/0.31 thf(fact_49_not__gr0,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % not_gr0
% 0.07/0.31 thf(fact_50_le__trans,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,K: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ J )
% 0.07/0.31 => ( ( ord_less_eq_nat @ J @ K )
% 0.07/0.31 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_trans
% 0.07/0.31 thf(fact_51_eq__imp__le,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( M = N )
% 0.07/0.31 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % eq_imp_le
% 0.07/0.31 thf(fact_52_not__less0,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % not_less0
% 0.07/0.31 thf(fact_53_le__antisym,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ( ord_less_eq_nat @ N @ M )
% 0.07/0.31 => ( M = N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_antisym
% 0.07/0.31 thf(fact_54_less__zeroE,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % less_zeroE
% 0.07/0.31 thf(fact_55_nat__less__le,axiom,
% 0.07/0.31 ( ord_less_nat
% 0.07/0.31 = ( ^ [M2: nat,N3: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M2 @ N3 )
% 0.07/0.31 & ( M2 != N3 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_less_le
% 0.07/0.31 thf(fact_56_nat__neq__iff,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( M != N )
% 0.07/0.31 = ( ( ord_less_nat @ M @ N )
% 0.07/0.31 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_neq_iff
% 0.07/0.31 thf(fact_57_less__not__refl,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ N ) ).
% 0.07/0.31
% 0.07/0.31 % less_not_refl
% 0.07/0.31 thf(fact_58_nat__le__linear,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_le_linear
% 0.07/0.31 thf(fact_59_less__not__refl2,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N @ M )
% 0.07/0.31 => ( M != N ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_not_refl2
% 0.07/0.31 thf(fact_60_less__not__refl3,axiom,
% 0.07/0.31 ! [S: nat,T: nat] :
% 0.07/0.31 ( ( ord_less_nat @ S @ T )
% 0.07/0.31 => ( S != T ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_not_refl3
% 0.07/0.31 thf(fact_61_ex__least__nat__le,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ( P @ N )
% 0.07/0.31 => ( ~ ( P @ zero_zero_nat )
% 0.07/0.31 => ? [K2: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ K2 @ N )
% 0.07/0.31 & ! [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ K2 )
% 0.07/0.31 => ~ ( P @ I ) )
% 0.07/0.31 & ( P @ K2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ex_least_nat_le
% 0.07/0.31 thf(fact_62_gr__implies__not0,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( N != zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr_implies_not0
% 0.07/0.31 thf(fact_63_less__imp__le__nat,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_imp_le_nat
% 0.07/0.31 thf(fact_64_less__irrefl__nat,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ N ) ).
% 0.07/0.31
% 0.07/0.31 % less_irrefl_nat
% 0.07/0.31 thf(fact_65_nat__less__induct,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ! [N2: nat] :
% 0.07/0.31 ( ! [M3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M3 @ N2 )
% 0.07/0.31 => ( P @ M3 ) )
% 0.07/0.31 => ( P @ N2 ) )
% 0.07/0.31 => ( P @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_less_induct
% 0.07/0.31 thf(fact_66_infinite__descent,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ! [N2: nat] :
% 0.07/0.31 ( ~ ( P @ N2 )
% 0.07/0.31 => ? [M3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M3 @ N2 )
% 0.07/0.31 & ~ ( P @ M3 ) ) )
% 0.07/0.31 => ( P @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % infinite_descent
% 0.07/0.31 thf(fact_67_le__eq__less__or__eq,axiom,
% 0.07/0.31 ( ord_less_eq_nat
% 0.07/0.31 = ( ^ [M2: nat,N3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M2 @ N3 )
% 0.07/0.31 | ( M2 = N3 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_eq_less_or_eq
% 0.07/0.31 thf(fact_68_ex__least__nat__less,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ( P @ N )
% 0.07/0.31 => ( ~ ( P @ zero_zero_nat )
% 0.07/0.31 => ? [K2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ K2 @ N )
% 0.07/0.31 & ! [I: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I @ K2 )
% 0.07/0.31 => ~ ( P @ I ) )
% 0.07/0.31 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ex_least_nat_less
% 0.07/0.31 thf(fact_69_infinite__descent0,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ( P @ zero_zero_nat )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.07/0.31 => ( ~ ( P @ N2 )
% 0.07/0.31 => ? [M3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M3 @ N2 )
% 0.07/0.31 & ~ ( P @ M3 ) ) ) )
% 0.07/0.31 => ( P @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infinite_descent0
% 0.07/0.31 thf(fact_70_less__or__eq__imp__le,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ( ord_less_nat @ M @ N )
% 0.07/0.31 | ( M = N ) )
% 0.07/0.31 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_or_eq_imp_le
% 0.07/0.31 thf(fact_71_linorder__neqE__nat,axiom,
% 0.07/0.31 ! [X: nat,Y: nat] :
% 0.07/0.31 ( ( X != Y )
% 0.07/0.31 => ( ~ ( ord_less_nat @ X @ Y )
% 0.07/0.31 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % linorder_neqE_nat
% 0.07/0.31 thf(fact_72_Nat_Oex__has__greatest__nat,axiom,
% 0.07/0.31 ! [P: nat > $o,K: nat,B: nat] :
% 0.07/0.31 ( ( P @ K )
% 0.07/0.31 => ( ! [Y3: nat] :
% 0.07/0.31 ( ( P @ Y3 )
% 0.07/0.31 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.07/0.31 => ? [X3: nat] :
% 0.07/0.31 ( ( P @ X3 )
% 0.07/0.31 & ! [Y4: nat] :
% 0.07/0.31 ( ( P @ Y4 )
% 0.07/0.31 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Nat.ex_has_greatest_nat
% 0.07/0.31 thf(fact_73_le__neq__implies__less,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ( M != N )
% 0.07/0.31 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_neq_implies_less
% 0.07/0.31 thf(fact_74_less__mono__imp__le__mono,axiom,
% 0.07/0.31 ! [F: nat > nat,I2: nat,J: nat] :
% 0.07/0.31 ( ! [I3: nat,J2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I3 @ J2 )
% 0.07/0.31 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ I2 @ J )
% 0.07/0.31 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_mono_imp_le_mono
% 0.07/0.31 thf(fact_75_size__neq__size__imp__neq,axiom,
% 0.07/0.31 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ X )
% 0.07/0.31 != ( size_s1406904903t_unit @ Y ) )
% 0.07/0.31 => ( X != Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % size_neq_size_imp_neq
% 0.07/0.31 thf(fact_76_size__neq__size__imp__neq,axiom,
% 0.07/0.31 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ X )
% 0.07/0.31 != ( size_s1168481041ge_p_v @ Y ) )
% 0.07/0.31 => ( X != Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % size_neq_size_imp_neq
% 0.07/0.31 thf(fact_77_bot__nat__0_Oextremum__strict,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % bot_nat_0.extremum_strict
% 0.07/0.31 thf(fact_78_bot__nat__0_Oextremum__unique,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.07/0.31 = ( A = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % bot_nat_0.extremum_unique
% 0.07/0.31 thf(fact_79_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.07/0.31 => ( A = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % bot_nat_0.extremum_uniqueI
% 0.07/0.31 thf(fact_80_lift__Suc__mono__le,axiom,
% 0.07/0.31 ! [F: nat > nat,N: nat,N4: nat] :
% 0.07/0.31 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.07/0.31 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % lift_Suc_mono_le
% 0.07/0.31 thf(fact_81_lift__Suc__antimono__le,axiom,
% 0.07/0.31 ! [F: nat > nat,N: nat,N4: nat] :
% 0.07/0.31 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.07/0.31 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % lift_Suc_antimono_le
% 0.07/0.31 thf(fact_82_le__imp__less__Suc,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_imp_less_Suc
% 0.07/0.31 thf(fact_83_less__eq__Suc__le,axiom,
% 0.07/0.31 ( ord_less_nat
% 0.07/0.31 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_eq_Suc_le
% 0.07/0.31 thf(fact_84_less__Suc__eq__le,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.07/0.31 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_Suc_eq_le
% 0.07/0.31 thf(fact_85_le__less__Suc__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.07/0.31 = ( N = M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_less_Suc_eq
% 0.07/0.31 thf(fact_86_Suc__le__lessD,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.07/0.31 => ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_le_lessD
% 0.07/0.31 thf(fact_87_inc__induct,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,P: nat > $o] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ J )
% 0.07/0.31 => ( ( P @ J )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ N2 )
% 0.07/0.31 => ( ( ord_less_nat @ N2 @ J )
% 0.07/0.31 => ( ( P @ ( suc @ N2 ) )
% 0.07/0.31 => ( P @ N2 ) ) ) )
% 0.07/0.31 => ( P @ I2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % inc_induct
% 0.07/0.31 thf(fact_88_dec__induct,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,P: nat > $o] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ J )
% 0.07/0.31 => ( ( P @ I2 )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ I2 @ N2 )
% 0.07/0.31 => ( ( ord_less_nat @ N2 @ J )
% 0.07/0.31 => ( ( P @ N2 )
% 0.07/0.31 => ( P @ ( suc @ N2 ) ) ) ) )
% 0.07/0.31 => ( P @ J ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % dec_induct
% 0.07/0.31 thf(fact_89_Suc__le__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.07/0.31 = ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_le_eq
% 0.07/0.31 thf(fact_90_Suc__leI,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_leI
% 0.07/0.31 thf(fact_91_diff__less__mono,axiom,
% 0.07/0.31 ! [A: nat,B: nat,C: nat] :
% 0.07/0.31 ( ( ord_less_nat @ A @ B )
% 0.07/0.31 => ( ( ord_less_eq_nat @ C @ A )
% 0.07/0.31 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_less_mono
% 0.07/0.31 thf(fact_92_less__diff__iff,axiom,
% 0.07/0.31 ! [K: nat,M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ K @ M )
% 0.07/0.31 => ( ( ord_less_eq_nat @ K @ N )
% 0.07/0.31 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.07/0.31 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_diff_iff
% 0.07/0.31 thf(fact_93_less__Suc__eq__0__disj,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.07/0.31 = ( ( M = zero_zero_nat )
% 0.07/0.31 | ? [J3: nat] :
% 0.07/0.31 ( ( M
% 0.07/0.31 = ( suc @ J3 ) )
% 0.07/0.31 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_Suc_eq_0_disj
% 0.07/0.31 thf(fact_94_gr0__implies__Suc,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ? [M4: nat] :
% 0.07/0.31 ( N
% 0.07/0.31 = ( suc @ M4 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr0_implies_Suc
% 0.07/0.31 thf(fact_95_All__less__Suc2,axiom,
% 0.07/0.31 ! [N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.07/0.31 => ( P @ I4 ) ) )
% 0.07/0.31 = ( ( P @ zero_zero_nat )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ N )
% 0.07/0.31 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % All_less_Suc2
% 0.07/0.31 thf(fact_96_gr0__conv__Suc,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 = ( ? [M2: nat] :
% 0.07/0.31 ( N
% 0.07/0.31 = ( suc @ M2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr0_conv_Suc
% 0.07/0.31 thf(fact_97_Ex__less__Suc2,axiom,
% 0.07/0.31 ! [N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ? [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.07/0.31 & ( P @ I4 ) ) )
% 0.07/0.31 = ( ( P @ zero_zero_nat )
% 0.07/0.31 | ? [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ N )
% 0.07/0.31 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Ex_less_Suc2
% 0.07/0.31 thf(fact_98_diff__less,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.07/0.31 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_less
% 0.07/0.31 thf(fact_99_transitive__stepwise__le,axiom,
% 0.07/0.31 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.07/0.31 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.07/0.31 ( ( R @ X3 @ Y3 )
% 0.07/0.31 => ( ( R @ Y3 @ Z )
% 0.07/0.31 => ( R @ X3 @ Z ) ) )
% 0.07/0.31 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.07/0.31 => ( R @ M @ N ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % transitive_stepwise_le
% 0.07/0.31 thf(fact_100_nat__induct__at__least,axiom,
% 0.07/0.31 ! [M: nat,N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ( P @ M )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N2 )
% 0.07/0.31 => ( ( P @ N2 )
% 0.07/0.31 => ( P @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( P @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_induct_at_least
% 0.07/0.31 thf(fact_101_full__nat__induct,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ! [N2: nat] :
% 0.07/0.31 ( ! [M3: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
% 0.07/0.31 => ( P @ M3 ) )
% 0.07/0.31 => ( P @ N2 ) )
% 0.07/0.31 => ( P @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % full_nat_induct
% 0.07/0.31 thf(fact_102_not__less__eq__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.07/0.31 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % not_less_eq_eq
% 0.07/0.31 thf(fact_103_Suc__n__not__le__n,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_n_not_le_n
% 0.07/0.31 thf(fact_104_le__Suc__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.07/0.31 = ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 | ( M
% 0.07/0.31 = ( suc @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_Suc_eq
% 0.07/0.31 thf(fact_105_Suc__le__D,axiom,
% 0.07/0.31 ! [N: nat,M5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ N ) @ M5 )
% 0.07/0.31 => ? [M4: nat] :
% 0.07/0.31 ( M5
% 0.07/0.31 = ( suc @ M4 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_le_D
% 0.07/0.31 thf(fact_106_le__SucI,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_SucI
% 0.07/0.31 thf(fact_107_le__SucE,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.07/0.31 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( M
% 0.07/0.31 = ( suc @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_SucE
% 0.07/0.31 thf(fact_108_Suc__leD,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_leD
% 0.07/0.31 thf(fact_109_diff__le__mono2,axiom,
% 0.07/0.31 ! [M: nat,N: nat,L: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_le_mono2
% 0.07/0.31 thf(fact_110_le__diff__iff_H,axiom,
% 0.07/0.31 ! [A: nat,C: nat,B: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ A @ C )
% 0.07/0.31 => ( ( ord_less_eq_nat @ B @ C )
% 0.07/0.31 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.07/0.31 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_diff_iff'
% 0.07/0.31 thf(fact_111_diff__le__self,axiom,
% 0.07/0.31 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.07/0.31
% 0.07/0.31 % diff_le_self
% 0.07/0.31 thf(fact_112_diff__le__mono,axiom,
% 0.07/0.31 ! [M: nat,N: nat,L: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ M @ N )
% 0.07/0.31 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_le_mono
% 0.07/0.31 thf(fact_113_Nat_Odiff__diff__eq,axiom,
% 0.07/0.31 ! [K: nat,M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ K @ M )
% 0.07/0.31 => ( ( ord_less_eq_nat @ K @ N )
% 0.07/0.31 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.07/0.31 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Nat.diff_diff_eq
% 0.07/0.31 thf(fact_114_le__diff__iff,axiom,
% 0.07/0.31 ! [K: nat,M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ K @ M )
% 0.07/0.31 => ( ( ord_less_eq_nat @ K @ N )
% 0.07/0.31 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.07/0.31 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_diff_iff
% 0.07/0.31 thf(fact_115_eq__diff__iff,axiom,
% 0.07/0.31 ! [K: nat,M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ K @ M )
% 0.07/0.31 => ( ( ord_less_eq_nat @ K @ N )
% 0.07/0.31 => ( ( ( minus_minus_nat @ M @ K )
% 0.07/0.31 = ( minus_minus_nat @ N @ K ) )
% 0.07/0.31 = ( M = N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % eq_diff_iff
% 0.07/0.31 thf(fact_116_not0__implies__Suc,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( N != zero_zero_nat )
% 0.07/0.31 => ? [M4: nat] :
% 0.07/0.31 ( N
% 0.07/0.31 = ( suc @ M4 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % not0_implies_Suc
% 0.07/0.31 thf(fact_117_old_Onat_Oinducts,axiom,
% 0.07/0.31 ! [P: nat > $o,Nat: nat] :
% 0.07/0.31 ( ( P @ zero_zero_nat )
% 0.07/0.31 => ( ! [Nat3: nat] :
% 0.07/0.31 ( ( P @ Nat3 )
% 0.07/0.31 => ( P @ ( suc @ Nat3 ) ) )
% 0.07/0.31 => ( P @ Nat ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % old.nat.inducts
% 0.07/0.31 thf(fact_118_old_Onat_Oexhaust,axiom,
% 0.07/0.31 ! [Y: nat] :
% 0.07/0.31 ( ( Y != zero_zero_nat )
% 0.07/0.31 => ~ ! [Nat3: nat] :
% 0.07/0.31 ( Y
% 0.07/0.31 != ( suc @ Nat3 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % old.nat.exhaust
% 0.07/0.31 thf(fact_119_Zero__not__Suc,axiom,
% 0.07/0.31 ! [M: nat] :
% 0.07/0.31 ( zero_zero_nat
% 0.07/0.31 != ( suc @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % Zero_not_Suc
% 0.07/0.31 thf(fact_120_Zero__neq__Suc,axiom,
% 0.07/0.31 ! [M: nat] :
% 0.07/0.31 ( zero_zero_nat
% 0.07/0.31 != ( suc @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % Zero_neq_Suc
% 0.07/0.31 thf(fact_121_Suc__neq__Zero,axiom,
% 0.07/0.31 ! [M: nat] :
% 0.07/0.31 ( ( suc @ M )
% 0.07/0.31 != zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_neq_Zero
% 0.07/0.31 thf(fact_122_zero__induct,axiom,
% 0.07/0.31 ! [P: nat > $o,K: nat] :
% 0.07/0.31 ( ( P @ K )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( P @ ( suc @ N2 ) )
% 0.07/0.31 => ( P @ N2 ) )
% 0.07/0.31 => ( P @ zero_zero_nat ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_induct
% 0.07/0.31 thf(fact_123_diff__induct,axiom,
% 0.07/0.31 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.07/0.31 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.07/0.31 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.07/0.31 => ( ! [X3: nat,Y3: nat] :
% 0.07/0.31 ( ( P @ X3 @ Y3 )
% 0.07/0.31 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.07/0.31 => ( P @ M @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_induct
% 0.07/0.31 thf(fact_124_nat__induct,axiom,
% 0.07/0.31 ! [P: nat > $o,N: nat] :
% 0.07/0.31 ( ( P @ zero_zero_nat )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( P @ N2 )
% 0.07/0.31 => ( P @ ( suc @ N2 ) ) )
% 0.07/0.31 => ( P @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_induct
% 0.07/0.31 thf(fact_125_nat_OdiscI,axiom,
% 0.07/0.31 ! [Nat: nat,X2: nat] :
% 0.07/0.31 ( ( Nat
% 0.07/0.31 = ( suc @ X2 ) )
% 0.07/0.31 => ( Nat != zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat.discI
% 0.07/0.31 thf(fact_126_old_Onat_Odistinct_I1_J,axiom,
% 0.07/0.31 ! [Nat2: nat] :
% 0.07/0.31 ( zero_zero_nat
% 0.07/0.31 != ( suc @ Nat2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % old.nat.distinct(1)
% 0.07/0.31 thf(fact_127_old_Onat_Odistinct_I2_J,axiom,
% 0.07/0.31 ! [Nat2: nat] :
% 0.07/0.31 ( ( suc @ Nat2 )
% 0.07/0.31 != zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % old.nat.distinct(2)
% 0.07/0.31 thf(fact_128_nat_Odistinct_I1_J,axiom,
% 0.07/0.31 ! [X2: nat] :
% 0.07/0.31 ( zero_zero_nat
% 0.07/0.31 != ( suc @ X2 ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat.distinct(1)
% 0.07/0.31 thf(fact_129_minus__nat_Odiff__0,axiom,
% 0.07/0.31 ! [M: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.07/0.31 = M ) ).
% 0.07/0.31
% 0.07/0.31 % minus_nat.diff_0
% 0.07/0.31 thf(fact_130_diffs0__imp__equal,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ( minus_minus_nat @ M @ N )
% 0.07/0.31 = zero_zero_nat )
% 0.07/0.31 => ( ( ( minus_minus_nat @ N @ M )
% 0.07/0.31 = zero_zero_nat )
% 0.07/0.31 => ( M = N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diffs0_imp_equal
% 0.07/0.31 thf(fact_131_lift__Suc__mono__less__iff,axiom,
% 0.07/0.31 ! [F: nat > nat,N: nat,M: nat] :
% 0.07/0.31 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.07/0.31 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.07/0.31 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % lift_Suc_mono_less_iff
% 0.07/0.31 thf(fact_132_lift__Suc__mono__less,axiom,
% 0.07/0.31 ! [F: nat > nat,N: nat,N4: nat] :
% 0.07/0.31 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.07/0.31 => ( ( ord_less_nat @ N @ N4 )
% 0.07/0.31 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % lift_Suc_mono_less
% 0.07/0.31 thf(fact_133_diff__Suc__less,axiom,
% 0.07/0.31 ! [N: nat,I2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_Suc_less
% 0.07/0.31 thf(fact_134_nat__induct__non__zero,axiom,
% 0.07/0.31 ! [N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ( P @ one_one_nat )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.07/0.31 => ( ( P @ N2 )
% 0.07/0.31 => ( P @ ( suc @ N2 ) ) ) )
% 0.07/0.31 => ( P @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nat_induct_non_zero
% 0.07/0.31 thf(fact_135_Suc__diff__le,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ N @ M )
% 0.07/0.31 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.07/0.31 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_diff_le
% 0.07/0.31 thf(fact_136_One__nat__def,axiom,
% 0.07/0.31 ( one_one_nat
% 0.07/0.31 = ( suc @ zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % One_nat_def
% 0.07/0.31 thf(fact_137_not__less__less__Suc__eq,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ~ ( ord_less_nat @ N @ M )
% 0.07/0.31 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.07/0.31 = ( N = M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % not_less_less_Suc_eq
% 0.07/0.31 thf(fact_138_strict__inc__induct,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,P: nat > $o] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ J )
% 0.07/0.31 => ( ! [I3: nat] :
% 0.07/0.31 ( ( J
% 0.07/0.31 = ( suc @ I3 ) )
% 0.07/0.31 => ( P @ I3 ) )
% 0.07/0.31 => ( ! [I3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I3 @ J )
% 0.07/0.31 => ( ( P @ ( suc @ I3 ) )
% 0.07/0.31 => ( P @ I3 ) ) )
% 0.07/0.31 => ( P @ I2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % strict_inc_induct
% 0.07/0.31 thf(fact_139_less__Suc__induct,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ J )
% 0.07/0.31 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.07/0.31 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I3 @ J2 )
% 0.07/0.31 => ( ( ord_less_nat @ J2 @ K2 )
% 0.07/0.31 => ( ( P @ I3 @ J2 )
% 0.07/0.31 => ( ( P @ J2 @ K2 )
% 0.07/0.31 => ( P @ I3 @ K2 ) ) ) ) )
% 0.07/0.31 => ( P @ I2 @ J ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_Suc_induct
% 0.07/0.31 thf(fact_140_less__trans__Suc,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,K: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ J )
% 0.07/0.31 => ( ( ord_less_nat @ J @ K )
% 0.07/0.31 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_trans_Suc
% 0.07/0.31 thf(fact_141_Suc__less__SucD,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.07/0.31 => ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_less_SucD
% 0.07/0.31 thf(fact_142_less__antisym,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ~ ( ord_less_nat @ N @ M )
% 0.07/0.31 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.07/0.31 => ( M = N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_antisym
% 0.07/0.31 thf(fact_143_Suc__less__eq2,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.07/0.31 = ( ? [M6: nat] :
% 0.07/0.31 ( ( M
% 0.07/0.31 = ( suc @ M6 ) )
% 0.07/0.31 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_less_eq2
% 0.07/0.31 thf(fact_144_All__less__Suc,axiom,
% 0.07/0.31 ! [N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.07/0.31 => ( P @ I4 ) ) )
% 0.07/0.31 = ( ( P @ N )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ N )
% 0.07/0.31 => ( P @ I4 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % All_less_Suc
% 0.07/0.31 thf(fact_145_not__less__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.07/0.31 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % not_less_eq
% 0.07/0.31 thf(fact_146_less__Suc__eq,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.07/0.31 = ( ( ord_less_nat @ M @ N )
% 0.07/0.31 | ( M = N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_Suc_eq
% 0.07/0.31 thf(fact_147_Ex__less__Suc,axiom,
% 0.07/0.31 ! [N: nat,P: nat > $o] :
% 0.07/0.31 ( ( ? [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 0.07/0.31 & ( P @ I4 ) ) )
% 0.07/0.31 = ( ( P @ N )
% 0.07/0.31 | ? [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ N )
% 0.07/0.31 & ( P @ I4 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Ex_less_Suc
% 0.07/0.31 thf(fact_148_less__SucI,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_SucI
% 0.07/0.31 thf(fact_149_less__SucE,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.07/0.31 => ( ~ ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( M = N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_SucE
% 0.07/0.31 thf(fact_150_Suc__lessI,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ( ( suc @ M )
% 0.07/0.31 != N )
% 0.07/0.31 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_lessI
% 0.07/0.31 thf(fact_151_Suc__lessE,axiom,
% 0.07/0.31 ! [I2: nat,K: nat] :
% 0.07/0.31 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 0.07/0.31 => ~ ! [J2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ J2 )
% 0.07/0.31 => ( K
% 0.07/0.31 != ( suc @ J2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_lessE
% 0.07/0.31 thf(fact_152_Suc__lessD,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.07/0.31 => ( ord_less_nat @ M @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_lessD
% 0.07/0.31 thf(fact_153_Nat_OlessE,axiom,
% 0.07/0.31 ! [I2: nat,K: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ K )
% 0.07/0.31 => ( ( K
% 0.07/0.31 != ( suc @ I2 ) )
% 0.07/0.31 => ~ ! [J2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I2 @ J2 )
% 0.07/0.31 => ( K
% 0.07/0.31 != ( suc @ J2 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Nat.lessE
% 0.07/0.31 thf(fact_154_less__imp__diff__less,axiom,
% 0.07/0.31 ! [J: nat,K: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ J @ K )
% 0.07/0.31 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.07/0.31
% 0.07/0.31 % less_imp_diff_less
% 0.07/0.31 thf(fact_155_diff__less__mono2,axiom,
% 0.07/0.31 ! [M: nat,N: nat,L: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( ( ord_less_nat @ M @ L )
% 0.07/0.31 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_less_mono2
% 0.07/0.31 thf(fact_156_Suc__diff__eq__diff__pred,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.07/0.31 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_diff_eq_diff_pred
% 0.07/0.31 thf(fact_157_Suc__pred_H,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 => ( N
% 0.07/0.31 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_pred'
% 0.07/0.31 thf(fact_158_n__not__Suc__n,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( N
% 0.07/0.31 != ( suc @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % n_not_Suc_n
% 0.07/0.31 thf(fact_159_Suc__inject,axiom,
% 0.07/0.31 ! [X: nat,Y: nat] :
% 0.07/0.31 ( ( ( suc @ X )
% 0.07/0.31 = ( suc @ Y ) )
% 0.07/0.31 => ( X = Y ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_inject
% 0.07/0.31 thf(fact_160_diff__commute,axiom,
% 0.07/0.31 ! [I2: nat,J: nat,K: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 0.07/0.31 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_commute
% 0.07/0.31 thf(fact_161_diff__less__Suc,axiom,
% 0.07/0.31 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_less_Suc
% 0.07/0.31 thf(fact_162_Suc__diff__Suc,axiom,
% 0.07/0.31 ! [N: nat,M: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N @ M )
% 0.07/0.31 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.07/0.31 = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Suc_diff_Suc
% 0.07/0.31 thf(fact_163_zero__induct__lemma,axiom,
% 0.07/0.31 ! [P: nat > $o,K: nat,I2: nat] :
% 0.07/0.31 ( ( P @ K )
% 0.07/0.31 => ( ! [N2: nat] :
% 0.07/0.31 ( ( P @ ( suc @ N2 ) )
% 0.07/0.31 => ( P @ N2 ) )
% 0.07/0.31 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_induct_lemma
% 0.07/0.31 thf(fact_164_AssumptionSubset3_I3_J,axiom,
% 0.07/0.31 ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset3(3)
% 0.07/0.31 thf(fact_165_length__greater__0__conv,axiom,
% 0.07/0.31 ! [Xs: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.07/0.31 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_greater_0_conv
% 0.07/0.31 thf(fact_166_length__greater__0__conv,axiom,
% 0.07/0.31 ! [Xs: list_message_p_v] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.07/0.31 = ( Xs != nil_message_p_v ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_greater_0_conv
% 0.07/0.31 thf(fact_167_length__0__conv,axiom,
% 0.07/0.31 ! [Xs: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ Xs )
% 0.07/0.31 = zero_zero_nat )
% 0.07/0.31 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_0_conv
% 0.07/0.31 thf(fact_168_length__0__conv,axiom,
% 0.07/0.31 ! [Xs: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.07/0.31 = zero_zero_nat )
% 0.07/0.31 = ( Xs = nil_message_p_v ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_0_conv
% 0.07/0.31 thf(fact_169_EnabledIntermediate,axiom,
% 0.07/0.31 ! [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I )
% 0.07/0.31 => ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % EnabledIntermediate
% 0.07/0.31 thf(fact_170__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
% 0.07/0.31 thf(fact_171_LastOfIndex,axiom,
% 0.07/0.31 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
% 0.07/0.31 = ( last_c571238084t_unit @ ( fe @ index ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % LastOfIndex
% 0.07/0.31 thf(fact_172_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ A @ A )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % cancel_comm_monoid_add_class.diff_cancel
% 0.07/0.31 thf(fact_173_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionFirstOccSetDecrOrConsumed(1)
% 0.07/0.31 thf(fact_174_Occ2_H,axiom,
% 0.07/0.31 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % Occ2'
% 0.07/0.31 thf(fact_175_le__zero__eq,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % le_zero_eq
% 0.07/0.31 thf(fact_176_not__gr__zero,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.07/0.31 = ( N = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % not_gr_zero
% 0.07/0.31 thf(fact_177_zero__diff,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % zero_diff
% 0.07/0.31 thf(fact_178_diff__zero,axiom,
% 0.07/0.31 ! [A: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.07/0.31 = A ) ).
% 0.07/0.31
% 0.07/0.31 % diff_zero
% 0.07/0.31 thf(fact_179_EnabledInSuc,axiom,
% 0.07/0.31 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % EnabledInSuc
% 0.07/0.31 thf(fact_180_AssumptionSubset2_I2_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset2(2)
% 0.07/0.31 thf(fact_181_AssumptionSubset3_I4_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset3(4)
% 0.07/0.31 thf(fact_182_AssumptionCase1ImplThesis_H,axiom,
% 0.07/0.31 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionCase1ImplThesis'
% 0.07/0.31 thf(fact_183_zero__reorient,axiom,
% 0.07/0.31 ! [X: nat] :
% 0.07/0.31 ( ( zero_zero_nat = X )
% 0.07/0.31 = ( X = zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_reorient
% 0.07/0.31 thf(fact_184_one__reorient,axiom,
% 0.07/0.31 ! [X: nat] :
% 0.07/0.31 ( ( one_one_nat = X )
% 0.07/0.31 = ( X = one_one_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % one_reorient
% 0.07/0.31 thf(fact_185_diff__right__commute,axiom,
% 0.07/0.31 ! [A: nat,C: nat,B: nat] :
% 0.07/0.31 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.07/0.31 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.07/0.31
% 0.07/0.31 % diff_right_commute
% 0.07/0.31 thf(fact_186_neq__if__length__neq,axiom,
% 0.07/0.31 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ Xs )
% 0.07/0.31 != ( size_s1406904903t_unit @ Ys ) )
% 0.07/0.31 => ( Xs != Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % neq_if_length_neq
% 0.07/0.31 thf(fact_187_neq__if__length__neq,axiom,
% 0.07/0.31 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.07/0.31 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.07/0.31 => ( Xs != Ys ) ) ).
% 0.07/0.31
% 0.07/0.31 % neq_if_length_neq
% 0.07/0.31 thf(fact_188_Ex__list__of__length,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ? [Xs2: list_c1059388851t_unit] :
% 0.07/0.31 ( ( size_s1406904903t_unit @ Xs2 )
% 0.07/0.31 = N ) ).
% 0.07/0.31
% 0.07/0.31 % Ex_list_of_length
% 0.07/0.31 thf(fact_189_Ex__list__of__length,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ? [Xs2: list_message_p_v] :
% 0.07/0.31 ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.07/0.31 = N ) ).
% 0.07/0.31
% 0.07/0.31 % Ex_list_of_length
% 0.07/0.31 thf(fact_190_last__conv__nth,axiom,
% 0.07/0.31 ! [Xs: list_c1059388851t_unit] :
% 0.07/0.31 ( ( Xs != nil_co1338500125t_unit )
% 0.07/0.31 => ( ( last_c571238084t_unit @ Xs )
% 0.07/0.31 = ( nth_co1649820636t_unit @ Xs @ ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % last_conv_nth
% 0.07/0.31 thf(fact_191_last__conv__nth,axiom,
% 0.07/0.31 ! [Xs: list_message_p_v] :
% 0.07/0.31 ( ( Xs != nil_message_p_v )
% 0.07/0.31 => ( ( last_message_p_v @ Xs )
% 0.07/0.31 = ( nth_message_p_v @ Xs @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % last_conv_nth
% 0.07/0.31 thf(fact_192_zero__le,axiom,
% 0.07/0.31 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.07/0.31
% 0.07/0.31 % zero_le
% 0.07/0.31 thf(fact_193_le__numeral__extra_I3_J,axiom,
% 0.07/0.31 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.07/0.31
% 0.07/0.31 % le_numeral_extra(3)
% 0.07/0.31 thf(fact_194_zero__less__iff__neq__zero,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.07/0.31 = ( N != zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % zero_less_iff_neq_zero
% 0.07/0.31 thf(fact_195_gr__implies__not__zero,axiom,
% 0.07/0.31 ! [M: nat,N: nat] :
% 0.07/0.31 ( ( ord_less_nat @ M @ N )
% 0.07/0.31 => ( N != zero_zero_nat ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr_implies_not_zero
% 0.07/0.31 thf(fact_196_not__less__zero,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % not_less_zero
% 0.07/0.31 thf(fact_197_gr__zeroI,axiom,
% 0.07/0.31 ! [N: nat] :
% 0.07/0.31 ( ( N != zero_zero_nat )
% 0.07/0.31 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.07/0.31
% 0.07/0.31 % gr_zeroI
% 0.07/0.31 thf(fact_198_less__numeral__extra_I3_J,axiom,
% 0.07/0.31 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % less_numeral_extra(3)
% 0.07/0.31 thf(fact_199_le__numeral__extra_I4_J,axiom,
% 0.07/0.31 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.07/0.31
% 0.07/0.31 % le_numeral_extra(4)
% 0.07/0.31 thf(fact_200_less__numeral__extra_I4_J,axiom,
% 0.07/0.31 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.07/0.31
% 0.07/0.31 % less_numeral_extra(4)
% 0.07/0.31 thf(fact_201_length__induct,axiom,
% 0.07/0.31 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.07/0.31 ( ! [Xs2: list_c1059388851t_unit] :
% 0.07/0.31 ( ! [Ys2: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.07/0.31 => ( P @ Ys2 ) )
% 0.07/0.31 => ( P @ Xs2 ) )
% 0.07/0.31 => ( P @ Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_induct
% 0.07/0.31 thf(fact_202_length__induct,axiom,
% 0.07/0.31 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.07/0.31 ( ! [Xs2: list_message_p_v] :
% 0.07/0.31 ( ! [Ys2: list_message_p_v] :
% 0.07/0.31 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 0.07/0.31 => ( P @ Ys2 ) )
% 0.07/0.31 => ( P @ Xs2 ) )
% 0.07/0.31 => ( P @ Xs ) ) ).
% 0.07/0.31
% 0.07/0.31 % length_induct
% 0.07/0.31 thf(fact_203_less__numeral__extra_I1_J,axiom,
% 0.07/0.31 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.07/0.31
% 0.07/0.31 % less_numeral_extra(1)
% 0.07/0.31 thf(fact_204_list_Osize_I3_J,axiom,
% 0.07/0.31 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % list.size(3)
% 0.07/0.31 thf(fact_205_list_Osize_I3_J,axiom,
% 0.07/0.31 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.07/0.31 = zero_zero_nat ) ).
% 0.07/0.31
% 0.07/0.31 % list.size(3)
% 0.07/0.31 thf(fact_206_nth__equalityI,axiom,
% 0.07/0.31 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ Xs )
% 0.07/0.31 = ( size_s1406904903t_unit @ Ys ) )
% 0.07/0.31 => ( ! [I3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs ) )
% 0.07/0.31 => ( ( nth_co1649820636t_unit @ Xs @ I3 )
% 0.07/0.31 = ( nth_co1649820636t_unit @ Ys @ I3 ) ) )
% 0.07/0.31 => ( Xs = Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nth_equalityI
% 0.07/0.31 thf(fact_207_nth__equalityI,axiom,
% 0.07/0.31 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.07/0.31 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.07/0.31 => ( ! [I3: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.07/0.31 => ( ( nth_message_p_v @ Xs @ I3 )
% 0.07/0.31 = ( nth_message_p_v @ Ys @ I3 ) ) )
% 0.07/0.31 => ( Xs = Ys ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % nth_equalityI
% 0.07/0.31 thf(fact_208_Skolem__list__nth,axiom,
% 0.07/0.31 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 0.07/0.31 ( ( ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ K )
% 0.07/0.31 => ? [X4: config256849571t_unit] : ( P @ I4 @ X4 ) ) )
% 0.07/0.31 = ( ? [Xs3: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.07/0.31 = K )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ K )
% 0.07/0.31 => ( P @ I4 @ ( nth_co1649820636t_unit @ Xs3 @ I4 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Skolem_list_nth
% 0.07/0.31 thf(fact_209_Skolem__list__nth,axiom,
% 0.07/0.31 ! [K: nat,P: nat > message_p_v > $o] :
% 0.07/0.31 ( ( ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ K )
% 0.07/0.31 => ? [X4: message_p_v] : ( P @ I4 @ X4 ) ) )
% 0.07/0.31 = ( ? [Xs3: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.07/0.31 = K )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ K )
% 0.07/0.31 => ( P @ I4 @ ( nth_message_p_v @ Xs3 @ I4 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Skolem_list_nth
% 0.07/0.31 thf(fact_210_list__eq__iff__nth__eq,axiom,
% 0.07/0.31 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 0.07/0.31 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.07/0.31 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.07/0.31 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ Xs3 ) )
% 0.07/0.31 => ( ( nth_co1649820636t_unit @ Xs3 @ I4 )
% 0.07/0.31 = ( nth_co1649820636t_unit @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_eq_iff_nth_eq
% 0.07/0.31 thf(fact_211_list__eq__iff__nth__eq,axiom,
% 0.07/0.31 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 0.07/0.31 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 0.07/0.31 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.07/0.31 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.07/0.31 & ! [I4: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 0.07/0.31 => ( ( nth_message_p_v @ Xs3 @ I4 )
% 0.07/0.31 = ( nth_message_p_v @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % list_eq_iff_nth_eq
% 0.07/0.31 thf(fact_212_PrefixSameOnLow,axiom,
% 0.07/0.31 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.07/0.31 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.07/0.31 => ! [Index: nat] :
% 0.07/0.31 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 0.07/0.31 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 0.07/0.31 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixSameOnLow
% 0.07/0.31 thf(fact_213_PrefixSameOnLow,axiom,
% 0.07/0.31 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.07/0.31 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.07/0.31 => ! [Index: nat] :
% 0.07/0.31 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 0.07/0.31 => ( ( nth_message_p_v @ L1 @ Index )
% 0.07/0.31 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixSameOnLow
% 0.07/0.31 thf(fact_214_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.07/0.31 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.07/0.31 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.07/0.31 = nil_message_p_v ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionMsg.simps(1)
% 0.07/0.31 thf(fact_215_AssumptionFair_I3_J,axiom,
% 0.07/0.31 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionFair(3)
% 0.07/0.31 thf(fact_216_AssumptionFair_I2_J,axiom,
% 0.07/0.31 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionFair(2)
% 0.07/0.31 thf(fact_217_MinPredicate,axiom,
% 0.07/0.31 ! [P: nat > $o] :
% 0.07/0.31 ( ? [X_1: nat] : ( P @ X_1 )
% 0.07/0.31 => ? [N0: nat] :
% 0.07/0.31 ( ( P @ N0 )
% 0.07/0.31 & ! [N5: nat] :
% 0.07/0.31 ( ( P @ N5 )
% 0.07/0.31 => ( ord_less_eq_nat @ N0 @ N5 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % MinPredicate
% 0.07/0.31 thf(fact_218_PrefixListTransitive,axiom,
% 0.07/0.31 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.07/0.31 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.07/0.31 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.07/0.31 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixListTransitive
% 0.07/0.31 thf(fact_219_PrefixListTransitive,axiom,
% 0.07/0.31 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.07/0.31 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.07/0.31 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.07/0.31 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixListTransitive
% 0.07/0.31 thf(fact_220_KeepProperty,axiom,
% 0.07/0.31 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 0.07/0.31 ( ! [I3: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ Low @ I3 )
% 0.07/0.31 => ( ( P @ I3 )
% 0.07/0.31 => ( ( P @ ( suc @ I3 ) )
% 0.07/0.31 & ( Q @ I3 ) ) ) )
% 0.07/0.31 => ( ( P @ Low )
% 0.07/0.31 => ! [I: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ Low @ I )
% 0.07/0.31 => ( Q @ I ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % KeepProperty
% 0.07/0.31 thf(fact_221_NatPredicateTippingPoint,axiom,
% 0.07/0.31 ! [N22: nat,Pr: nat > $o] :
% 0.07/0.31 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 0.07/0.31 => ( ( Pr @ zero_zero_nat )
% 0.07/0.31 => ( ~ ( Pr @ N22 )
% 0.07/0.31 => ? [N2: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N2 @ N22 )
% 0.07/0.31 & ( Pr @ N2 )
% 0.07/0.31 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % NatPredicateTippingPoint
% 0.07/0.31 thf(fact_222_MinPredicate2,axiom,
% 0.07/0.31 ! [P: nat > $o] :
% 0.07/0.31 ( ? [X_1: nat] : ( P @ X_1 )
% 0.07/0.31 => ? [N0: nat] :
% 0.07/0.31 ( ( P @ N0 )
% 0.07/0.31 & ( ( N0 = zero_zero_nat )
% 0.07/0.31 | ~ ( P @ ( minus_minus_nat @ N0 @ one_one_nat ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % MinPredicate2
% 0.07/0.31 thf(fact_223_PrefixListMonotonicity,axiom,
% 0.07/0.31 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.07/0.31 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.07/0.31 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixListMonotonicity
% 0.07/0.31 thf(fact_224_PrefixListMonotonicity,axiom,
% 0.07/0.31 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.07/0.31 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.07/0.31 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % PrefixListMonotonicity
% 0.07/0.31 thf(fact_225_infiniteExecutionMsg_Oelims,axiom,
% 0.07/0.31 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 0.07/0.31 ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.07/0.31 = Y )
% 0.07/0.31 => ( ( ( Xc = zero_zero_nat )
% 0.07/0.31 => ( Y != nil_message_p_v ) )
% 0.07/0.31 => ~ ! [N2: nat] :
% 0.07/0.31 ( ( Xc
% 0.07/0.31 = ( suc @ N2 ) )
% 0.07/0.31 => ( Y
% 0.07/0.31 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N2 ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N2 ) ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionMsg.elims
% 0.07/0.31 thf(fact_226_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.07/0.31 ! [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] :
% 0.07/0.31 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 0.07/0.31 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionCfg.simps(2)
% 0.07/0.31 thf(fact_227_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.07/0.31 ! [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] :
% 0.07/0.31 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 0.07/0.31 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % infiniteExecutionMsg.simps(2)
% 0.07/0.31 thf(fact_228_AssumpOcc6_H_I2_J,axiom,
% 0.07/0.31 ( msgInSet
% 0.07/0.31 != ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumpOcc6'(2)
% 0.07/0.31 thf(fact_229_AssumptionFairContr,axiom,
% 0.07/0.31 ! [N5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n @ N5 )
% 0.07/0.31 => ! [N02: nat] :
% 0.07/0.31 ( ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N02 )
% 0.07/0.31 => ( msg
% 0.07/0.31 != ( nth_message_p_v @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionFairContr
% 0.07/0.31 thf(fact_230_IPrefixList,axiom,
% 0.07/0.31 ! [I: nat] : ( prefix47729710ge_p_v @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % IPrefixList
% 0.07/0.31 thf(fact_231_ShorterTrace,axiom,
% 0.07/0.31 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % ShorterTrace
% 0.07/0.31 thf(fact_232_SameMsgOnLow,axiom,
% 0.07/0.31 ! [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.07/0.31 => ( ( nth_message_p_v @ ( ft @ index ) @ I )
% 0.07/0.31 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % SameMsgOnLow
% 0.07/0.31 thf(fact_233_SmallIndexTrace_H,axiom,
% 0.07/0.31 ord_less_nat @ ( minus_minus_nat @ n1 @ one_one_nat ) @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) ).
% 0.07/0.31
% 0.07/0.31 % SmallIndexTrace'
% 0.07/0.31 thf(fact_234_NotConsumedIntermediate,axiom,
% 0.07/0.31 ! [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.07/0.31 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
% 0.07/0.31 => ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I )
% 0.07/0.31 != msg ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % NotConsumedIntermediate
% 0.07/0.31 thf(fact_235__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.07/0.31 ~ ? [I: nat] :
% 0.07/0.31 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.07/0.31 & ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
% 0.07/0.31 & ( msg
% 0.07/0.31 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.07/0.31 thf(fact_236_OccSameMsg_H,axiom,
% 0.07/0.31 ! [N5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n1 @ N5 )
% 0.07/0.31 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.07/0.31 => ( ( nth_message_p_v @ ( ft @ index ) @ N5 )
% 0.07/0.31 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % OccSameMsg'
% 0.07/0.31 thf(fact_237_AssumptionSubset_I2_J,axiom,
% 0.07/0.31 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset(2)
% 0.07/0.31 thf(fact_238_MessageStaysOrConsumed,axiom,
% 0.07/0.31 ! [N1: nat,N22: nat,N: nat,Msg: message_p_v] :
% 0.07/0.31 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 0.07/0.31 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
% 0.07/0.31 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.07/0.31 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg )
% 0.07/0.31 | ? [N03: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ N1 @ N03 )
% 0.07/0.31 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
% 0.07/0.31 & ( ( nth_message_p_v @ ( ft @ N ) @ N03 )
% 0.07/0.31 = Msg ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % MessageStaysOrConsumed
% 0.07/0.31 thf(fact_239_AssumptionSubset_I3_J,axiom,
% 0.07/0.31 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset(3)
% 0.07/0.31 thf(fact_240_Occ5_H,axiom,
% 0.07/0.31 ! [N5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n1 @ N5 )
% 0.07/0.31 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.07/0.31 => ( msgInSet
% 0.07/0.31 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Occ5'
% 0.07/0.31 thf(fact_241_Case2ImplThesis,axiom,
% 0.07/0.31 ( ? [N02: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n0 @ N02 )
% 0.07/0.31 & ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 0.07/0.31 & ( ( nth_message_p_v @ ( ft @ n ) @ N02 )
% 0.07/0.31 = msg ) )
% 0.07/0.31 => ? [N6: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n @ N6 )
% 0.07/0.31 & ? [N03: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n0 @ N03 )
% 0.07/0.31 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N6 ) ) )
% 0.07/0.31 & ( msg
% 0.07/0.31 = ( nth_message_p_v @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % Case2ImplThesis
% 0.07/0.31 thf(fact_242_AssumptionSubset2_I5_J,axiom,
% 0.07/0.31 ! [N5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ n1 @ N5 )
% 0.07/0.31 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.07/0.31 => ( msgInSet
% 0.07/0.31 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset2(5)
% 0.07/0.31 thf(fact_243_AssumptionSubset3_I5_J,axiom,
% 0.07/0.31 ! [N5: nat] :
% 0.07/0.31 ( ( ord_less_eq_nat @ nMsg @ N5 )
% 0.07/0.31 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 0.07/0.31 => ( msg
% 0.07/0.31 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.07/0.31
% 0.07/0.31 % AssumptionSubset3(5)
% 0.07/0.31
% 0.07/0.31 % Conjectures (1)
% 0.07/0.31 thf(conj_0,conjecture,
% 0.07/0.31 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
% 0.07/0.31 = ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ).
% 0.07/0.31
% 0.07/0.31 %------------------------------------------------------------------------------
% 0.07/0.31 ------------------------
% 1.65/1.03 ---- Embedded in THF ---
% 1.65/1.03 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.03 %%% Generated on Tue Feb 24 08:24:46 EST 2026
% 1.65/1.03 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.03 %%% Logic specification used:
% 1.65/1.03 %%% thf(spec, logic, $$dhol).
% 1.65/1.03
% 1.65/1.03 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2DTF7568.p
% See solution above
% 1.65/1.03 ------------------------
% 1.65/1.05 ---- Cleaned THF ---
% 1.65/1.05 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 1.65/1.05 list_c1059388851t_unit: $tType ).
% 1.65/1.05
% 1.65/1.05 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 1.65/1.05 config256849571t_unit: $tType ).
% 1.65/1.05
% 1.65/1.05 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 1.65/1.05 list_message_p_v: $tType ).
% 1.65/1.05
% 1.65/1.05 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 1.65/1.05 message_p_v: $tType ).
% 1.65/1.05
% 1.65/1.05 thf(ty_n_t__Nat__Onat,type,
% 1.65/1.05 nat: $tType ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 1.65/1.05 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 1.65/1.05 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 1.65/1.05 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 ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 1.65/1.05 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 ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 1.65/1.05 minus_minus_nat: nat > nat > nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 1.65/1.05 one_one_nat: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 1.65/1.05 zero_zero_nat: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 1.65/1.05 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 1.65/1.05 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Olast_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 1.65/1.05 last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Olast_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 1.65/1.05 last_message_p_v: list_message_p_v > message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 1.65/1.05 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 1.65/1.05 nil_message_p_v: list_message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 1.65/1.05 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 1.65/1.05 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Nat_OSuc,type,
% 1.65/1.05 suc: nat > nat ).
% 1.65/1.05
% 1.65/1.05 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,
% 1.65/1.05 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 1.65/1.05 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 1.65/1.05 ord_less_nat: nat > nat > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 1.65/1.05 ord_less_eq_nat: nat > nat > $o ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_fe____,type,
% 1.65/1.05 fe: nat > list_c1059388851t_unit ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_ft____,type,
% 1.65/1.05 ft: nat > list_message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_index____,type,
% 1.65/1.05 index: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_msgInSet____,type,
% 1.65/1.05 msgInSet: message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_msg____,type,
% 1.65/1.05 msg: message_p_v ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_n0____,type,
% 1.65/1.05 n0: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_n1____,type,
% 1.65/1.05 n1: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_nMsg____,type,
% 1.65/1.05 nMsg: nat ).
% 1.65/1.05
% 1.65/1.05 thf(sy_v_n____,type,
% 1.65/1.05 n: nat ).
% 1.65/1.05
% 1.65/1.05 thf(fact_0_Occ3_H,axiom,
% 1.65/1.05 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_1_SameCfgOnLow,axiom,
% 1.65/1.05 ! [I: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 1.65/1.05 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I )
% 1.65/1.05 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062,axiom,
% 1.65/1.05 ( ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 )
% 1.65/1.05 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 1.65/1.05 ord_less_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_4_AssumptionSubset2_I3_J,axiom,
% 1.65/1.05 ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_5_AssumpOcc6_H_I1_J,axiom,
% 1.65/1.05 ord_less_nat @ zero_zero_nat @ n1 ).
% 1.65/1.05
% 1.65/1.05 thf(fact_6_diff__Suc__1,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 1.65/1.05 = N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_7_diff__Suc__Suc,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.65/1.05 = ( minus_minus_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_8_Suc__diff__diff,axiom,
% 1.65/1.05 ! [M: nat,N: nat,K: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 1.65/1.05 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_9_NotEmpty_I1_J,axiom,
% 1.65/1.05 ( ( fe @ ( suc @ index ) )
% 1.65/1.05 != nil_co1338500125t_unit ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_10_IPrefixListEx,axiom,
% 1.65/1.05 ! [I: nat] : ( prefix1615116500t_unit @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_11_diff__Suc__eq__diff__pred,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 1.65/1.05 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_12_AssumpOcc6_H_I3_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_13__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 1.65/1.05 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_14_NotEmpty_I2_J,axiom,
% 1.65/1.05 ( ( fe @ index )
% 1.65/1.05 != nil_co1338500125t_unit ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062,axiom,
% 1.65/1.05 ord_less_nat @ ( minus_minus_nat @ n1 @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 1.65/1.05 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 1.65/1.05 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 1.65/1.05 => ( ! [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] :
% 1.65/1.05 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 1.65/1.05 => ( ! [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] :
% 1.65/1.05 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 1.65/1.05 ! [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] :
% 1.65/1.05 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 1.65/1.05 => ( ! [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] :
% 1.65/1.05 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 1.65/1.05 => ( ! [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] :
% 1.65/1.05 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 1.65/1.05 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_18_old_Onat_Oinject,axiom,
% 1.65/1.05 ! [Nat: nat,Nat2: nat] :
% 1.65/1.05 ( ( ( suc @ Nat )
% 1.65/1.05 = ( suc @ Nat2 ) )
% 1.65/1.05 = ( Nat = Nat2 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_19_nat_Oinject,axiom,
% 1.65/1.05 ! [X2: nat,Y2: nat] :
% 1.65/1.05 ( ( ( suc @ X2 )
% 1.65/1.05 = ( suc @ Y2 ) )
% 1.65/1.05 = ( X2 = Y2 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_20_AssumptionSubset_I1_J,axiom,
% 1.65/1.05 ord_less_eq_nat @ n1 @ nMsg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062,axiom,
% 1.65/1.05 ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_22_Suc__less__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.65/1.05 = ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_23_Suc__mono,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_24_lessI,axiom,
% 1.65/1.05 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_25_neq0__conv,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( N != zero_zero_nat )
% 1.65/1.05 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_26_less__nat__zero__code,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( A != zero_zero_nat )
% 1.65/1.05 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_28_Suc__le__mono,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 1.65/1.05 = ( ord_less_eq_nat @ N @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_29_le0,axiom,
% 1.65/1.05 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_30_bot__nat__0_Oextremum,axiom,
% 1.65/1.05 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_31_diff__self__eq__0,axiom,
% 1.65/1.05 ! [M: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ M @ M )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_32_diff__0__eq__0,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_33_diff__diff__cancel,axiom,
% 1.65/1.05 ! [I2: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ N )
% 1.65/1.05 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 1.65/1.05 = I2 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_34_Occ4_H,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ n1 ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_35_AssumptionSubset2_I4_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_37_zero__less__Suc,axiom,
% 1.65/1.05 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_38_less__Suc0,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_39_zero__less__diff,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 1.65/1.05 = ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_40_diff__is__0__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ( minus_minus_nat @ M @ N )
% 1.65/1.05 = zero_zero_nat )
% 1.65/1.05 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_41_diff__is__0__eq_H,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ( minus_minus_nat @ M @ N )
% 1.65/1.05 = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_42_less__one,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N @ one_one_nat )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_43_Suc__pred,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 1.65/1.05 = N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_44_Suc__diff__1,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 1.65/1.05 = N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_45_less__eq__nat_Osimps_I1_J,axiom,
% 1.65/1.05 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_46_gr0I,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( N != zero_zero_nat )
% 1.65/1.05 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_47_le__0__eq,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_48_le__refl,axiom,
% 1.65/1.05 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_49_not__gr0,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_50_le__trans,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,K: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ J )
% 1.65/1.05 => ( ( ord_less_eq_nat @ J @ K )
% 1.65/1.05 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_51_eq__imp__le,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( M = N )
% 1.65/1.05 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_52_not__less0,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_53_le__antisym,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ( ord_less_eq_nat @ N @ M )
% 1.65/1.05 => ( M = N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_54_less__zeroE,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_55_nat__less__le,axiom,
% 1.65/1.05 ( ord_less_nat
% 1.65/1.05 = ( ^ [M2: nat,N3: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M2 @ N3 )
% 1.65/1.05 & ( M2 != N3 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_56_nat__neq__iff,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( M != N )
% 1.65/1.05 = ( ( ord_less_nat @ M @ N )
% 1.65/1.05 | ( ord_less_nat @ N @ M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_57_less__not__refl,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_58_nat__le__linear,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 | ( ord_less_eq_nat @ N @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_59_less__not__refl2,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N @ M )
% 1.65/1.05 => ( M != N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_60_less__not__refl3,axiom,
% 1.65/1.05 ! [S: nat,T: nat] :
% 1.65/1.05 ( ( ord_less_nat @ S @ T )
% 1.65/1.05 => ( S != T ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_61_ex__least__nat__le,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ( P @ N )
% 1.65/1.05 => ( ~ ( P @ zero_zero_nat )
% 1.65/1.05 => ? [K2: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ K2 @ N )
% 1.65/1.05 & ! [I: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I @ K2 )
% 1.65/1.05 => ~ ( P @ I ) )
% 1.65/1.05 & ( P @ K2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_62_gr__implies__not0,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( N != zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_63_less__imp__le__nat,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_64_less__irrefl__nat,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_65_nat__less__induct,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ! [N2: nat] :
% 1.65/1.05 ( ! [M3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M3 @ N2 )
% 1.65/1.05 => ( P @ M3 ) )
% 1.65/1.05 => ( P @ N2 ) )
% 1.65/1.05 => ( P @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_66_infinite__descent,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ! [N2: nat] :
% 1.65/1.05 ( ~ ( P @ N2 )
% 1.65/1.05 => ? [M3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M3 @ N2 )
% 1.65/1.05 & ~ ( P @ M3 ) ) )
% 1.65/1.05 => ( P @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_67_le__eq__less__or__eq,axiom,
% 1.65/1.05 ( ord_less_eq_nat
% 1.65/1.05 = ( ^ [M2: nat,N3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M2 @ N3 )
% 1.65/1.05 | ( M2 = N3 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_68_ex__least__nat__less,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ( P @ N )
% 1.65/1.05 => ( ~ ( P @ zero_zero_nat )
% 1.65/1.05 => ? [K2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ K2 @ N )
% 1.65/1.05 & ! [I: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I @ K2 )
% 1.65/1.05 => ~ ( P @ I ) )
% 1.65/1.05 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_69_infinite__descent0,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ( P @ zero_zero_nat )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 1.65/1.05 => ( ~ ( P @ N2 )
% 1.65/1.05 => ? [M3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M3 @ N2 )
% 1.65/1.05 & ~ ( P @ M3 ) ) ) )
% 1.65/1.05 => ( P @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_70_less__or__eq__imp__le,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ( ord_less_nat @ M @ N )
% 1.65/1.05 | ( M = N ) )
% 1.65/1.05 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_71_linorder__neqE__nat,axiom,
% 1.65/1.05 ! [X: nat,Y: nat] :
% 1.65/1.05 ( ( X != Y )
% 1.65/1.05 => ( ~ ( ord_less_nat @ X @ Y )
% 1.65/1.05 => ( ord_less_nat @ Y @ X ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_72_Nat_Oex__has__greatest__nat,axiom,
% 1.65/1.05 ! [P: nat > $o,K: nat,B: nat] :
% 1.65/1.05 ( ( P @ K )
% 1.65/1.05 => ( ! [Y3: nat] :
% 1.65/1.05 ( ( P @ Y3 )
% 1.65/1.05 => ( ord_less_eq_nat @ Y3 @ B ) )
% 1.65/1.05 => ? [X3: nat] :
% 1.65/1.05 ( ( P @ X3 )
% 1.65/1.05 & ! [Y4: nat] :
% 1.65/1.05 ( ( P @ Y4 )
% 1.65/1.05 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_73_le__neq__implies__less,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ( M != N )
% 1.65/1.05 => ( ord_less_nat @ M @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_74_less__mono__imp__le__mono,axiom,
% 1.65/1.05 ! [F: nat > nat,I2: nat,J: nat] :
% 1.65/1.05 ( ! [I3: nat,J2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I3 @ J2 )
% 1.65/1.05 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ I2 @ J )
% 1.65/1.05 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_75_size__neq__size__imp__neq,axiom,
% 1.65/1.05 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ X )
% 1.65/1.05 != ( size_s1406904903t_unit @ Y ) )
% 1.65/1.05 => ( X != Y ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_76_size__neq__size__imp__neq,axiom,
% 1.65/1.05 ! [X: list_message_p_v,Y: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ X )
% 1.65/1.05 != ( size_s1168481041ge_p_v @ Y ) )
% 1.65/1.05 => ( X != Y ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_77_bot__nat__0_Oextremum__strict,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_78_bot__nat__0_Oextremum__unique,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 1.65/1.05 = ( A = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_79_bot__nat__0_Oextremum__uniqueI,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 1.65/1.05 => ( A = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_80_lift__Suc__mono__le,axiom,
% 1.65/1.05 ! [F: nat > nat,N: nat,N4: nat] :
% 1.65/1.05 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ N @ N4 )
% 1.65/1.05 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_81_lift__Suc__antimono__le,axiom,
% 1.65/1.05 ! [F: nat > nat,N: nat,N4: nat] :
% 1.65/1.05 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ N @ N4 )
% 1.65/1.05 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_82_le__imp__less__Suc,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_83_less__eq__Suc__le,axiom,
% 1.65/1.05 ( ord_less_nat
% 1.65/1.05 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_84_less__Suc__eq__le,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.65/1.05 = ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_85_le__less__Suc__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.65/1.05 = ( N = M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_86_Suc__le__lessD,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.65/1.05 => ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_87_inc__induct,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,P: nat > $o] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ J )
% 1.65/1.05 => ( ( P @ J )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ N2 )
% 1.65/1.05 => ( ( ord_less_nat @ N2 @ J )
% 1.65/1.05 => ( ( P @ ( suc @ N2 ) )
% 1.65/1.05 => ( P @ N2 ) ) ) )
% 1.65/1.05 => ( P @ I2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_88_dec__induct,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,P: nat > $o] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ J )
% 1.65/1.05 => ( ( P @ I2 )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ I2 @ N2 )
% 1.65/1.05 => ( ( ord_less_nat @ N2 @ J )
% 1.65/1.05 => ( ( P @ N2 )
% 1.65/1.05 => ( P @ ( suc @ N2 ) ) ) ) )
% 1.65/1.05 => ( P @ J ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_89_Suc__le__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.65/1.05 = ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_90_Suc__leI,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_91_diff__less__mono,axiom,
% 1.65/1.05 ! [A: nat,B: nat,C: nat] :
% 1.65/1.05 ( ( ord_less_nat @ A @ B )
% 1.65/1.05 => ( ( ord_less_eq_nat @ C @ A )
% 1.65/1.05 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_92_less__diff__iff,axiom,
% 1.65/1.05 ! [K: nat,M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ K @ M )
% 1.65/1.05 => ( ( ord_less_eq_nat @ K @ N )
% 1.65/1.05 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.65/1.05 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_93_less__Suc__eq__0__disj,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.65/1.05 = ( ( M = zero_zero_nat )
% 1.65/1.05 | ? [J3: nat] :
% 1.65/1.05 ( ( M
% 1.65/1.05 = ( suc @ J3 ) )
% 1.65/1.05 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_94_gr0__implies__Suc,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ? [M4: nat] :
% 1.65/1.05 ( N
% 1.65/1.05 = ( suc @ M4 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_95_All__less__Suc2,axiom,
% 1.65/1.05 ! [N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.65/1.05 => ( P @ I4 ) ) )
% 1.65/1.05 = ( ( P @ zero_zero_nat )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ N )
% 1.65/1.05 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_96_gr0__conv__Suc,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 = ( ? [M2: nat] :
% 1.65/1.05 ( N
% 1.65/1.05 = ( suc @ M2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_97_Ex__less__Suc2,axiom,
% 1.65/1.05 ! [N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ? [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.65/1.05 & ( P @ I4 ) ) )
% 1.65/1.05 = ( ( P @ zero_zero_nat )
% 1.65/1.05 | ? [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ N )
% 1.65/1.05 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_98_diff__less,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 1.65/1.05 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_99_transitive__stepwise__le,axiom,
% 1.65/1.05 ! [M: nat,N: nat,R: nat > nat > $o] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 1.65/1.05 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 1.65/1.05 ( ( R @ X3 @ Y3 )
% 1.65/1.05 => ( ( R @ Y3 @ Z )
% 1.65/1.05 => ( R @ X3 @ Z ) ) )
% 1.65/1.05 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 1.65/1.05 => ( R @ M @ N ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_100_nat__induct__at__least,axiom,
% 1.65/1.05 ! [M: nat,N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ( P @ M )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N2 )
% 1.65/1.05 => ( ( P @ N2 )
% 1.65/1.05 => ( P @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( P @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_101_full__nat__induct,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ! [N2: nat] :
% 1.65/1.05 ( ! [M3: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
% 1.65/1.05 => ( P @ M3 ) )
% 1.65/1.05 => ( P @ N2 ) )
% 1.65/1.05 => ( P @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_102_not__less__eq__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 1.65/1.05 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_103_Suc__n__not__le__n,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_104_le__Suc__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 1.65/1.05 = ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 | ( M
% 1.65/1.05 = ( suc @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_105_Suc__le__D,axiom,
% 1.65/1.05 ! [N: nat,M5: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ N ) @ M5 )
% 1.65/1.05 => ? [M4: nat] :
% 1.65/1.05 ( M5
% 1.65/1.05 = ( suc @ M4 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_106_le__SucI,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_107_le__SucE,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 1.65/1.05 => ( ~ ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( M
% 1.65/1.05 = ( suc @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_108_Suc__leD,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_109_diff__le__mono2,axiom,
% 1.65/1.05 ! [M: nat,N: nat,L: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_110_le__diff__iff_H,axiom,
% 1.65/1.05 ! [A: nat,C: nat,B: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ A @ C )
% 1.65/1.05 => ( ( ord_less_eq_nat @ B @ C )
% 1.65/1.05 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 1.65/1.05 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_111_diff__le__self,axiom,
% 1.65/1.05 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_112_diff__le__mono,axiom,
% 1.65/1.05 ! [M: nat,N: nat,L: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ M @ N )
% 1.65/1.05 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_113_Nat_Odiff__diff__eq,axiom,
% 1.65/1.05 ! [K: nat,M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ K @ M )
% 1.65/1.05 => ( ( ord_less_eq_nat @ K @ N )
% 1.65/1.05 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.65/1.05 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_114_le__diff__iff,axiom,
% 1.65/1.05 ! [K: nat,M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ K @ M )
% 1.65/1.05 => ( ( ord_less_eq_nat @ K @ N )
% 1.65/1.05 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 1.65/1.05 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_115_eq__diff__iff,axiom,
% 1.65/1.05 ! [K: nat,M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ K @ M )
% 1.65/1.05 => ( ( ord_less_eq_nat @ K @ N )
% 1.65/1.05 => ( ( ( minus_minus_nat @ M @ K )
% 1.65/1.05 = ( minus_minus_nat @ N @ K ) )
% 1.65/1.05 = ( M = N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_116_not0__implies__Suc,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( N != zero_zero_nat )
% 1.65/1.05 => ? [M4: nat] :
% 1.65/1.05 ( N
% 1.65/1.05 = ( suc @ M4 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_117_old_Onat_Oinducts,axiom,
% 1.65/1.05 ! [P: nat > $o,Nat: nat] :
% 1.65/1.05 ( ( P @ zero_zero_nat )
% 1.65/1.05 => ( ! [Nat3: nat] :
% 1.65/1.05 ( ( P @ Nat3 )
% 1.65/1.05 => ( P @ ( suc @ Nat3 ) ) )
% 1.65/1.05 => ( P @ Nat ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_118_old_Onat_Oexhaust,axiom,
% 1.65/1.05 ! [Y: nat] :
% 1.65/1.05 ( ( Y != zero_zero_nat )
% 1.65/1.05 => ~ ! [Nat3: nat] :
% 1.65/1.05 ( Y
% 1.65/1.05 != ( suc @ Nat3 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_119_Zero__not__Suc,axiom,
% 1.65/1.05 ! [M: nat] :
% 1.65/1.05 ( zero_zero_nat
% 1.65/1.05 != ( suc @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_120_Zero__neq__Suc,axiom,
% 1.65/1.05 ! [M: nat] :
% 1.65/1.05 ( zero_zero_nat
% 1.65/1.05 != ( suc @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_121_Suc__neq__Zero,axiom,
% 1.65/1.05 ! [M: nat] :
% 1.65/1.05 ( ( suc @ M )
% 1.65/1.05 != zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_122_zero__induct,axiom,
% 1.65/1.05 ! [P: nat > $o,K: nat] :
% 1.65/1.05 ( ( P @ K )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( P @ ( suc @ N2 ) )
% 1.65/1.05 => ( P @ N2 ) )
% 1.65/1.05 => ( P @ zero_zero_nat ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_123_diff__induct,axiom,
% 1.65/1.05 ! [P: nat > nat > $o,M: nat,N: nat] :
% 1.65/1.05 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 1.65/1.05 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 1.65/1.05 => ( ! [X3: nat,Y3: nat] :
% 1.65/1.05 ( ( P @ X3 @ Y3 )
% 1.65/1.05 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 1.65/1.05 => ( P @ M @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_124_nat__induct,axiom,
% 1.65/1.05 ! [P: nat > $o,N: nat] :
% 1.65/1.05 ( ( P @ zero_zero_nat )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( P @ N2 )
% 1.65/1.05 => ( P @ ( suc @ N2 ) ) )
% 1.65/1.05 => ( P @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_125_nat_OdiscI,axiom,
% 1.65/1.05 ! [Nat: nat,X2: nat] :
% 1.65/1.05 ( ( Nat
% 1.65/1.05 = ( suc @ X2 ) )
% 1.65/1.05 => ( Nat != zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_126_old_Onat_Odistinct_I1_J,axiom,
% 1.65/1.05 ! [Nat2: nat] :
% 1.65/1.05 ( zero_zero_nat
% 1.65/1.05 != ( suc @ Nat2 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_127_old_Onat_Odistinct_I2_J,axiom,
% 1.65/1.05 ! [Nat2: nat] :
% 1.65/1.05 ( ( suc @ Nat2 )
% 1.65/1.05 != zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_128_nat_Odistinct_I1_J,axiom,
% 1.65/1.05 ! [X2: nat] :
% 1.65/1.05 ( zero_zero_nat
% 1.65/1.05 != ( suc @ X2 ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_129_minus__nat_Odiff__0,axiom,
% 1.65/1.05 ! [M: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 1.65/1.05 = M ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_130_diffs0__imp__equal,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ( minus_minus_nat @ M @ N )
% 1.65/1.05 = zero_zero_nat )
% 1.65/1.05 => ( ( ( minus_minus_nat @ N @ M )
% 1.65/1.05 = zero_zero_nat )
% 1.65/1.05 => ( M = N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_131_lift__Suc__mono__less__iff,axiom,
% 1.65/1.05 ! [F: nat > nat,N: nat,M: nat] :
% 1.65/1.05 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 1.65/1.05 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 1.65/1.05 = ( ord_less_nat @ N @ M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_132_lift__Suc__mono__less,axiom,
% 1.65/1.05 ! [F: nat > nat,N: nat,N4: nat] :
% 1.65/1.05 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 1.65/1.05 => ( ( ord_less_nat @ N @ N4 )
% 1.65/1.05 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_133_diff__Suc__less,axiom,
% 1.65/1.05 ! [N: nat,I2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_134_nat__induct__non__zero,axiom,
% 1.65/1.05 ! [N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ( P @ one_one_nat )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 1.65/1.05 => ( ( P @ N2 )
% 1.65/1.05 => ( P @ ( suc @ N2 ) ) ) )
% 1.65/1.05 => ( P @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_135_Suc__diff__le,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ N @ M )
% 1.65/1.05 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 1.65/1.05 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_136_One__nat__def,axiom,
% 1.65/1.05 ( one_one_nat
% 1.65/1.05 = ( suc @ zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_137_not__less__less__Suc__eq,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ~ ( ord_less_nat @ N @ M )
% 1.65/1.05 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.65/1.05 = ( N = M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_138_strict__inc__induct,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,P: nat > $o] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ J )
% 1.65/1.05 => ( ! [I3: nat] :
% 1.65/1.05 ( ( J
% 1.65/1.05 = ( suc @ I3 ) )
% 1.65/1.05 => ( P @ I3 ) )
% 1.65/1.05 => ( ! [I3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I3 @ J )
% 1.65/1.05 => ( ( P @ ( suc @ I3 ) )
% 1.65/1.05 => ( P @ I3 ) ) )
% 1.65/1.05 => ( P @ I2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_139_less__Suc__induct,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ J )
% 1.65/1.05 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 1.65/1.05 => ( ! [I3: nat,J2: nat,K2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I3 @ J2 )
% 1.65/1.05 => ( ( ord_less_nat @ J2 @ K2 )
% 1.65/1.05 => ( ( P @ I3 @ J2 )
% 1.65/1.05 => ( ( P @ J2 @ K2 )
% 1.65/1.05 => ( P @ I3 @ K2 ) ) ) ) )
% 1.65/1.05 => ( P @ I2 @ J ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_140_less__trans__Suc,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,K: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ J )
% 1.65/1.05 => ( ( ord_less_nat @ J @ K )
% 1.65/1.05 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_141_Suc__less__SucD,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 1.65/1.05 => ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_142_less__antisym,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ~ ( ord_less_nat @ N @ M )
% 1.65/1.05 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 1.65/1.05 => ( M = N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_143_Suc__less__eq2,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 1.65/1.05 = ( ? [M6: nat] :
% 1.65/1.05 ( ( M
% 1.65/1.05 = ( suc @ M6 ) )
% 1.65/1.05 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_144_All__less__Suc,axiom,
% 1.65/1.05 ! [N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.65/1.05 => ( P @ I4 ) ) )
% 1.65/1.05 = ( ( P @ N )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ N )
% 1.65/1.05 => ( P @ I4 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_145_not__less__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ~ ( ord_less_nat @ M @ N ) )
% 1.65/1.05 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_146_less__Suc__eq,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.65/1.05 = ( ( ord_less_nat @ M @ N )
% 1.65/1.05 | ( M = N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_147_Ex__less__Suc,axiom,
% 1.65/1.05 ! [N: nat,P: nat > $o] :
% 1.65/1.05 ( ( ? [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 1.65/1.05 & ( P @ I4 ) ) )
% 1.65/1.05 = ( ( P @ N )
% 1.65/1.05 | ? [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ N )
% 1.65/1.05 & ( P @ I4 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_148_less__SucI,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_149_less__SucE,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 1.65/1.05 => ( ~ ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( M = N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_150_Suc__lessI,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ( ( suc @ M )
% 1.65/1.05 != N )
% 1.65/1.05 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_151_Suc__lessE,axiom,
% 1.65/1.05 ! [I2: nat,K: nat] :
% 1.65/1.05 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 1.65/1.05 => ~ ! [J2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ J2 )
% 1.65/1.05 => ( K
% 1.65/1.05 != ( suc @ J2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_152_Suc__lessD,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 1.65/1.05 => ( ord_less_nat @ M @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_153_Nat_OlessE,axiom,
% 1.65/1.05 ! [I2: nat,K: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ K )
% 1.65/1.05 => ( ( K
% 1.65/1.05 != ( suc @ I2 ) )
% 1.65/1.05 => ~ ! [J2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I2 @ J2 )
% 1.65/1.05 => ( K
% 1.65/1.05 != ( suc @ J2 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_154_less__imp__diff__less,axiom,
% 1.65/1.05 ! [J: nat,K: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ J @ K )
% 1.65/1.05 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_155_diff__less__mono2,axiom,
% 1.65/1.05 ! [M: nat,N: nat,L: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( ( ord_less_nat @ M @ L )
% 1.65/1.05 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_156_Suc__diff__eq__diff__pred,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 1.65/1.05 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_157_Suc__pred_H,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 => ( N
% 1.65/1.05 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_158_n__not__Suc__n,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( N
% 1.65/1.05 != ( suc @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_159_Suc__inject,axiom,
% 1.65/1.05 ! [X: nat,Y: nat] :
% 1.65/1.05 ( ( ( suc @ X )
% 1.65/1.05 = ( suc @ Y ) )
% 1.65/1.05 => ( X = Y ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_160_diff__commute,axiom,
% 1.65/1.05 ! [I2: nat,J: nat,K: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 1.65/1.05 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_161_diff__less__Suc,axiom,
% 1.65/1.05 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_162_Suc__diff__Suc,axiom,
% 1.65/1.05 ! [N: nat,M: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N @ M )
% 1.65/1.05 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 1.65/1.05 = ( minus_minus_nat @ M @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_163_zero__induct__lemma,axiom,
% 1.65/1.05 ! [P: nat > $o,K: nat,I2: nat] :
% 1.65/1.05 ( ( P @ K )
% 1.65/1.05 => ( ! [N2: nat] :
% 1.65/1.05 ( ( P @ ( suc @ N2 ) )
% 1.65/1.05 => ( P @ N2 ) )
% 1.65/1.05 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_164_AssumptionSubset3_I3_J,axiom,
% 1.65/1.05 ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_165_length__greater__0__conv,axiom,
% 1.65/1.05 ! [Xs: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 1.65/1.05 = ( Xs != nil_co1338500125t_unit ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_166_length__greater__0__conv,axiom,
% 1.65/1.05 ! [Xs: list_message_p_v] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 1.65/1.05 = ( Xs != nil_message_p_v ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_167_length__0__conv,axiom,
% 1.65/1.05 ! [Xs: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ Xs )
% 1.65/1.05 = zero_zero_nat )
% 1.65/1.05 = ( Xs = nil_co1338500125t_unit ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_168_length__0__conv,axiom,
% 1.65/1.05 ! [Xs: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ Xs )
% 1.65/1.05 = zero_zero_nat )
% 1.65/1.05 = ( Xs = nil_message_p_v ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_169_EnabledIntermediate,axiom,
% 1.65/1.05 ! [I: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I )
% 1.65/1.05 => ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_170__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_171_LastOfIndex,axiom,
% 1.65/1.05 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) )
% 1.65/1.05 = ( last_c571238084t_unit @ ( fe @ index ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_172_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ A @ A )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_173_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_174_Occ2_H,axiom,
% 1.65/1.05 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ index ) ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_175_le__zero__eq,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_176_not__gr__zero,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 1.65/1.05 = ( N = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_177_zero__diff,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_178_diff__zero,axiom,
% 1.65/1.05 ! [A: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 1.65/1.05 = A ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_179_EnabledInSuc,axiom,
% 1.65/1.05 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_180_AssumptionSubset2_I2_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 1.65/1.05
% 1.65/1.05 thf(fact_181_AssumptionSubset3_I4_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_182_AssumptionCase1ImplThesis_H,axiom,
% 1.65/1.05 enabled_p_v_s @ ( last_c571238084t_unit @ ( fe @ n ) ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_183_zero__reorient,axiom,
% 1.65/1.05 ! [X: nat] :
% 1.65/1.05 ( ( zero_zero_nat = X )
% 1.65/1.05 = ( X = zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_184_one__reorient,axiom,
% 1.65/1.05 ! [X: nat] :
% 1.65/1.05 ( ( one_one_nat = X )
% 1.65/1.05 = ( X = one_one_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_185_diff__right__commute,axiom,
% 1.65/1.05 ! [A: nat,C: nat,B: nat] :
% 1.65/1.05 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 1.65/1.05 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_186_neq__if__length__neq,axiom,
% 1.65/1.05 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ Xs )
% 1.65/1.05 != ( size_s1406904903t_unit @ Ys ) )
% 1.65/1.05 => ( Xs != Ys ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_187_neq__if__length__neq,axiom,
% 1.65/1.05 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ Xs )
% 1.65/1.05 != ( size_s1168481041ge_p_v @ Ys ) )
% 1.65/1.05 => ( Xs != Ys ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_188_Ex__list__of__length,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ? [Xs2: list_c1059388851t_unit] :
% 1.65/1.05 ( ( size_s1406904903t_unit @ Xs2 )
% 1.65/1.05 = N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_189_Ex__list__of__length,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ? [Xs2: list_message_p_v] :
% 1.65/1.05 ( ( size_s1168481041ge_p_v @ Xs2 )
% 1.65/1.05 = N ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_190_last__conv__nth,axiom,
% 1.65/1.05 ! [Xs: list_c1059388851t_unit] :
% 1.65/1.05 ( ( Xs != nil_co1338500125t_unit )
% 1.65/1.05 => ( ( last_c571238084t_unit @ Xs )
% 1.65/1.05 = ( nth_co1649820636t_unit @ Xs @ ( minus_minus_nat @ ( size_s1406904903t_unit @ Xs ) @ one_one_nat ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_191_last__conv__nth,axiom,
% 1.65/1.05 ! [Xs: list_message_p_v] :
% 1.65/1.05 ( ( Xs != nil_message_p_v )
% 1.65/1.05 => ( ( last_message_p_v @ Xs )
% 1.65/1.05 = ( nth_message_p_v @ Xs @ ( minus_minus_nat @ ( size_s1168481041ge_p_v @ Xs ) @ one_one_nat ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_192_zero__le,axiom,
% 1.65/1.05 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_193_le__numeral__extra_I3_J,axiom,
% 1.65/1.05 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 1.65/1.05
% 1.65/1.05 thf(fact_194_zero__less__iff__neq__zero,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N )
% 1.65/1.05 = ( N != zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_195_gr__implies__not__zero,axiom,
% 1.65/1.05 ! [M: nat,N: nat] :
% 1.65/1.05 ( ( ord_less_nat @ M @ N )
% 1.65/1.05 => ( N != zero_zero_nat ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_196_not__less__zero,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_197_gr__zeroI,axiom,
% 1.65/1.05 ! [N: nat] :
% 1.65/1.05 ( ( N != zero_zero_nat )
% 1.65/1.05 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_198_less__numeral__extra_I3_J,axiom,
% 1.65/1.05 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_199_le__numeral__extra_I4_J,axiom,
% 1.65/1.05 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 1.65/1.05
% 1.65/1.05 thf(fact_200_less__numeral__extra_I4_J,axiom,
% 1.65/1.05 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_201_length__induct,axiom,
% 1.65/1.05 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 1.65/1.05 ( ! [Xs2: list_c1059388851t_unit] :
% 1.65/1.05 ( ! [Ys2: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 1.65/1.05 => ( P @ Ys2 ) )
% 1.65/1.05 => ( P @ Xs2 ) )
% 1.65/1.05 => ( P @ Xs ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_202_length__induct,axiom,
% 1.65/1.05 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 1.65/1.05 ( ! [Xs2: list_message_p_v] :
% 1.65/1.05 ( ! [Ys2: list_message_p_v] :
% 1.65/1.05 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 1.65/1.05 => ( P @ Ys2 ) )
% 1.65/1.05 => ( P @ Xs2 ) )
% 1.65/1.05 => ( P @ Xs ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_203_less__numeral__extra_I1_J,axiom,
% 1.65/1.05 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 1.65/1.05
% 1.65/1.05 thf(fact_204_list_Osize_I3_J,axiom,
% 1.65/1.05 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_205_list_Osize_I3_J,axiom,
% 1.65/1.05 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 1.65/1.05 = zero_zero_nat ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_206_nth__equalityI,axiom,
% 1.65/1.05 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ Xs )
% 1.65/1.05 = ( size_s1406904903t_unit @ Ys ) )
% 1.65/1.05 => ( ! [I3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs ) )
% 1.65/1.05 => ( ( nth_co1649820636t_unit @ Xs @ I3 )
% 1.65/1.05 = ( nth_co1649820636t_unit @ Ys @ I3 ) ) )
% 1.65/1.05 => ( Xs = Ys ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_207_nth__equalityI,axiom,
% 1.65/1.05 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ Xs )
% 1.65/1.05 = ( size_s1168481041ge_p_v @ Ys ) )
% 1.65/1.05 => ( ! [I3: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs ) )
% 1.65/1.05 => ( ( nth_message_p_v @ Xs @ I3 )
% 1.65/1.05 = ( nth_message_p_v @ Ys @ I3 ) ) )
% 1.65/1.05 => ( Xs = Ys ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_208_Skolem__list__nth,axiom,
% 1.65/1.05 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 1.65/1.05 ( ( ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ K )
% 1.65/1.05 => ? [X4: config256849571t_unit] : ( P @ I4 @ X4 ) ) )
% 1.65/1.05 = ( ? [Xs3: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ Xs3 )
% 1.65/1.05 = K )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ K )
% 1.65/1.05 => ( P @ I4 @ ( nth_co1649820636t_unit @ Xs3 @ I4 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_209_Skolem__list__nth,axiom,
% 1.65/1.05 ! [K: nat,P: nat > message_p_v > $o] :
% 1.65/1.05 ( ( ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ K )
% 1.65/1.05 => ? [X4: message_p_v] : ( P @ I4 @ X4 ) ) )
% 1.65/1.05 = ( ? [Xs3: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 1.65/1.05 = K )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ K )
% 1.65/1.05 => ( P @ I4 @ ( nth_message_p_v @ Xs3 @ I4 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_210_list__eq__iff__nth__eq,axiom,
% 1.65/1.05 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 1.65/1.05 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 1.65/1.05 ( ( ( size_s1406904903t_unit @ Xs3 )
% 1.65/1.05 = ( size_s1406904903t_unit @ Ys3 ) )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ Xs3 ) )
% 1.65/1.05 => ( ( nth_co1649820636t_unit @ Xs3 @ I4 )
% 1.65/1.05 = ( nth_co1649820636t_unit @ Ys3 @ I4 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_211_list__eq__iff__nth__eq,axiom,
% 1.65/1.05 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 1.65/1.05 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 1.65/1.05 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 1.65/1.05 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 1.65/1.05 & ! [I4: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 1.65/1.05 => ( ( nth_message_p_v @ Xs3 @ I4 )
% 1.65/1.05 = ( nth_message_p_v @ Ys3 @ I4 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_212_PrefixSameOnLow,axiom,
% 1.65/1.05 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 1.65/1.05 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 1.65/1.05 => ! [Index: nat] :
% 1.65/1.05 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 1.65/1.05 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 1.65/1.05 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_213_PrefixSameOnLow,axiom,
% 1.65/1.05 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 1.65/1.05 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 1.65/1.05 => ! [Index: nat] :
% 1.65/1.05 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 1.65/1.05 => ( ( nth_message_p_v @ L1 @ Index )
% 1.65/1.05 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_214_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 1.65/1.05 ! [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] :
% 1.65/1.05 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 1.65/1.05 = nil_message_p_v ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_215_AssumptionFair_I3_J,axiom,
% 1.65/1.05 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg ).
% 1.65/1.05
% 1.65/1.05 thf(fact_216_AssumptionFair_I2_J,axiom,
% 1.65/1.05 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_217_MinPredicate,axiom,
% 1.65/1.05 ! [P: nat > $o] :
% 1.65/1.05 ( ? [X_1: nat] : ( P @ X_1 )
% 1.65/1.05 => ? [N0: nat] :
% 1.65/1.05 ( ( P @ N0 )
% 1.65/1.05 & ! [N5: nat] :
% 1.65/1.05 ( ( P @ N5 )
% 1.65/1.05 => ( ord_less_eq_nat @ N0 @ N5 ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_218_PrefixListTransitive,axiom,
% 1.65/1.05 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 1.65/1.05 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 1.65/1.05 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 1.65/1.05 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_219_PrefixListTransitive,axiom,
% 1.65/1.05 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 1.65/1.05 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 1.65/1.05 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 1.65/1.05 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_220_KeepProperty,axiom,
% 1.65/1.05 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 1.65/1.05 ( ! [I3: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ Low @ I3 )
% 1.65/1.05 => ( ( P @ I3 )
% 1.65/1.05 => ( ( P @ ( suc @ I3 ) )
% 1.65/1.05 & ( Q @ I3 ) ) ) )
% 1.65/1.05 => ( ( P @ Low )
% 1.65/1.05 => ! [I: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ Low @ I )
% 1.65/1.05 => ( Q @ I ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_221_NatPredicateTippingPoint,axiom,
% 1.65/1.05 ! [N22: nat,Pr: nat > $o] :
% 1.65/1.05 ( ( ord_less_nat @ zero_zero_nat @ N22 )
% 1.65/1.05 => ( ( Pr @ zero_zero_nat )
% 1.65/1.05 => ( ~ ( Pr @ N22 )
% 1.65/1.05 => ? [N2: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N2 @ N22 )
% 1.65/1.05 & ( Pr @ N2 )
% 1.65/1.05 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_222_MinPredicate2,axiom,
% 1.65/1.05 ! [P: nat > $o] :
% 1.65/1.05 ( ? [X_1: nat] : ( P @ X_1 )
% 1.65/1.05 => ? [N0: nat] :
% 1.65/1.05 ( ( P @ N0 )
% 1.65/1.05 & ( ( N0 = zero_zero_nat )
% 1.65/1.05 | ~ ( P @ ( minus_minus_nat @ N0 @ one_one_nat ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_223_PrefixListMonotonicity,axiom,
% 1.65/1.05 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 1.65/1.05 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 1.65/1.05 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_224_PrefixListMonotonicity,axiom,
% 1.65/1.05 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 1.65/1.05 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 1.65/1.05 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_225_infiniteExecutionMsg_Oelims,axiom,
% 1.65/1.05 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 1.65/1.05 ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 1.65/1.05 = Y )
% 1.65/1.05 => ( ( ( Xc = zero_zero_nat )
% 1.65/1.05 => ( Y != nil_message_p_v ) )
% 1.65/1.05 => ~ ! [N2: nat] :
% 1.65/1.05 ( ( Xc
% 1.65/1.05 = ( suc @ N2 ) )
% 1.65/1.05 => ( Y
% 1.65/1.05 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N2 ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N2 ) ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_226_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 1.65/1.05 ! [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] :
% 1.65/1.05 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 1.65/1.05 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_227_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 1.65/1.05 ! [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] :
% 1.65/1.05 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 1.65/1.05 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_228_AssumpOcc6_H_I2_J,axiom,
% 1.65/1.05 ( msgInSet
% 1.65/1.05 != ( nth_message_p_v @ ( ft @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_229_AssumptionFairContr,axiom,
% 1.65/1.05 ! [N5: nat] :
% 1.65/1.05 ( ( ord_less_eq_nat @ n @ N5 )
% 1.65/1.05 => ! [N02: nat] :
% 1.65/1.05 ( ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N02 )
% 1.65/1.05 => ( msg
% 1.65/1.05 != ( nth_message_p_v @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_230_IPrefixList,axiom,
% 1.65/1.05 ! [I: nat] : ( prefix47729710ge_p_v @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_231_ShorterTrace,axiom,
% 1.65/1.05 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_232_SameMsgOnLow,axiom,
% 1.65/1.05 ! [I: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 1.65/1.05 => ( ( nth_message_p_v @ ( ft @ index ) @ I )
% 1.65/1.05 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_233_SmallIndexTrace_H,axiom,
% 1.65/1.05 ord_less_nat @ ( minus_minus_nat @ n1 @ one_one_nat ) @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_234_NotConsumedIntermediate,axiom,
% 1.65/1.05 ! [I: nat] :
% 1.65/1.05 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 1.65/1.05 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
% 1.65/1.05 => ( ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I )
% 1.65/1.05 != msg ) ) ) ).
% 1.65/1.05
% 1.65/1.05 thf(fact_235__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 1.65/1.06 ~ ? [I: nat] :
% 1.65/1.06 ( ( ord_less_nat @ I @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 1.65/1.06 & ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ I )
% 1.65/1.06 & ( msg
% 1.65/1.06 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_236_OccSameMsg_H,axiom,
% 1.65/1.06 ! [N5: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n1 @ N5 )
% 1.65/1.06 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 1.65/1.06 => ( ( nth_message_p_v @ ( ft @ index ) @ N5 )
% 1.65/1.06 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_237_AssumptionSubset_I2_J,axiom,
% 1.65/1.06 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 1.65/1.06
% 1.65/1.06 thf(fact_238_MessageStaysOrConsumed,axiom,
% 1.65/1.06 ! [N1: nat,N22: nat,N: nat,Msg: message_p_v] :
% 1.65/1.06 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 1.65/1.06 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
% 1.65/1.06 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg ) )
% 1.65/1.06 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg )
% 1.65/1.06 | ? [N03: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ N1 @ N03 )
% 1.65/1.06 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
% 1.65/1.06 & ( ( nth_message_p_v @ ( ft @ N ) @ N03 )
% 1.65/1.06 = Msg ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_239_AssumptionSubset_I3_J,axiom,
% 1.65/1.06 firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 1.65/1.06
% 1.65/1.06 thf(fact_240_Occ5_H,axiom,
% 1.65/1.06 ! [N5: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n1 @ N5 )
% 1.65/1.06 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 1.65/1.06 => ( msgInSet
% 1.65/1.06 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_241_Case2ImplThesis,axiom,
% 1.65/1.06 ( ? [N02: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n0 @ N02 )
% 1.65/1.06 & ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) )
% 1.65/1.06 & ( ( nth_message_p_v @ ( ft @ n ) @ N02 )
% 1.65/1.06 = msg ) )
% 1.65/1.06 => ? [N6: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n @ N6 )
% 1.65/1.06 & ? [N03: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n0 @ N03 )
% 1.65/1.06 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N6 ) ) )
% 1.65/1.06 & ( msg
% 1.65/1.06 = ( nth_message_p_v @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_242_AssumptionSubset2_I5_J,axiom,
% 1.65/1.06 ! [N5: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ n1 @ N5 )
% 1.65/1.06 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 1.65/1.06 => ( msgInSet
% 1.65/1.06 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(fact_243_AssumptionSubset3_I5_J,axiom,
% 1.65/1.06 ! [N5: nat] :
% 1.65/1.06 ( ( ord_less_eq_nat @ nMsg @ N5 )
% 1.65/1.06 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) )
% 1.65/1.06 => ( msg
% 1.65/1.06 != ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 1.65/1.06
% 1.65/1.06 thf(conj_0,conjecture,
% 1.65/1.06 ( ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ ( minus_minus_nat @ n1 @ one_one_nat ) )
% 1.65/1.06 = ( nth_co1649820636t_unit @ ( fe @ index ) @ ( minus_minus_nat @ n1 @ one_one_nat ) ) ) ).
% 1.65/1.06 ------------------------
% 1.65/1.07 % (7899)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_7568 for (2999ds/27Mi)
% 1.65/1.07 % (7897)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/183Mi)
% 1.65/1.07 % (7903)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/18Mi)
% 1.65/1.07 % (7901)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_7568 for (2999ds/2Mi)
% 1.65/1.07 % (7900)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/2Mi)
% 1.65/1.07 % (7898)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_7568 for (2999ds/4Mi)
% 1.65/1.07 % (7902)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_7568 for (2999ds/275Mi)
% 1.65/1.07 % (7900)Instruction limit reached!
% 1.65/1.07 % (7900)------------------------------
% 1.65/1.07 % (7900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.07 % (7900)Termination reason: Unknown
% 1.65/1.07 % (7900)Termination phase: shuffling
% 1.65/1.07
% 1.65/1.07 % (7900)Memory used [KB]: 1279
% 1.65/1.07 % (7900)Time elapsed: 0.002 s
% 1.65/1.07 % (7900)Instructions burned: 2 (million)
% 1.65/1.07 % (7900)------------------------------
% 1.65/1.07 % (7900)------------------------------
% 1.65/1.07 % (7901)Instruction limit reached!
% 1.65/1.07 % (7901)------------------------------
% 1.65/1.07 % (7901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.07 % (7901)Termination reason: Unknown
% 1.65/1.07 % (7901)Termination phase: shuffling
% 1.65/1.07
% 1.65/1.07 % (7901)Memory used [KB]: 1279
% 1.65/1.07 % (7901)Time elapsed: 0.002 s
% 1.65/1.07 % (7901)Instructions burned: 3 (million)
% 1.65/1.07 % (7901)------------------------------
% 1.65/1.07 % (7901)------------------------------
% 1.65/1.07 % (7898)Instruction limit reached!
% 1.65/1.07 % (7898)------------------------------
% 1.65/1.07 % (7898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.07 % (7898)Termination reason: Unknown
% 1.65/1.07 % (7898)Termination phase: shuffling
% 1.65/1.07
% 1.65/1.07 % (7898)Memory used [KB]: 1279
% 1.65/1.07 % (7898)Time elapsed: 0.003 s
% 1.65/1.07 % (7898)Instructions burned: 6 (million)
% 1.65/1.07 % (7898)------------------------------
% 1.65/1.07 % (7898)------------------------------
% 1.65/1.08 % (7903)Instruction limit reached!
% 1.65/1.08 % (7903)------------------------------
% 1.65/1.08 % (7903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.08 % (7903)Termination reason: Unknown
% 1.65/1.08 % (7903)Termination phase: Property scanning
% 1.65/1.08
% 1.65/1.08 % (7903)Memory used [KB]: 1535
% 1.65/1.08 % (7903)Time elapsed: 0.007 s
% 1.65/1.08 % (7903)Instructions burned: 19 (million)
% 1.65/1.08 % (7903)------------------------------
% 1.65/1.08 % (7903)------------------------------
% 1.65/1.08 % (7899)Instruction limit reached!
% 1.65/1.08 % (7899)------------------------------
% 1.65/1.08 % (7899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.08 % (7899)Termination reason: Unknown
% 1.65/1.08 % (7899)Termination phase: Preprocessing 3
% 1.65/1.08
% 1.65/1.08 % (7899)Memory used [KB]: 1663
% 1.65/1.08 % (7899)Time elapsed: 0.010 s
% 1.65/1.08 % (7899)Instructions burned: 29 (million)
% 1.65/1.08 % (7899)------------------------------
% 1.65/1.08 % (7899)------------------------------
% 1.65/1.08 % (7904)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/3Mi)
% 1.65/1.08 % (7905)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_7568 for (2999ds/37Mi)
% 1.65/1.08 % (7906)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/15Mi)
% 1.65/1.08 % (7904)Instruction limit reached!
% 1.65/1.08 % (7904)------------------------------
% 1.65/1.08 % (7904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.08 % (7904)Termination reason: Unknown
% 1.65/1.08 % (7904)Termination phase: shuffling
% 1.65/1.08
% 1.65/1.08 % (7904)Memory used [KB]: 1279
% 1.65/1.08 % (7904)Time elapsed: 0.002 s
% 1.65/1.08 % (7904)Instructions burned: 3 (million)
% 1.65/1.08 % (7904)------------------------------
% 1.65/1.08 % (7904)------------------------------
% 1.65/1.09 % (7907)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/3Mi)
% 1.65/1.09 % (7906)Instruction limit reached!
% 1.65/1.09 % (7906)------------------------------
% 1.65/1.09 % (7906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.09 % (7906)Termination reason: Unknown
% 1.65/1.09 % (7906)Termination phase: shuffling
% 1.65/1.09
% 1.65/1.09 % (7906)Memory used [KB]: 1535
% 1.65/1.09 % (7906)Time elapsed: 0.006 s
% 1.65/1.09 % (7906)Instructions burned: 15 (million)
% 1.65/1.09 % (7906)------------------------------
% 1.65/1.09 % (7906)------------------------------
% 1.65/1.09 % (7907)Instruction limit reached!
% 1.65/1.09 % (7907)------------------------------
% 1.65/1.09 % (7907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.09 % (7907)Termination reason: Unknown
% 1.65/1.09 % (7907)Termination phase: shuffling
% 1.65/1.09
% 1.65/1.09 % (7907)Memory used [KB]: 1279
% 1.65/1.09 % (7907)Time elapsed: 0.002 s
% 1.65/1.09 % (7907)Instructions burned: 3 (million)
% 1.65/1.09 % (7907)------------------------------
% 1.65/1.09 % (7907)------------------------------
% 1.65/1.09 % (7908)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/1041Mi)
% 1.65/1.09 % (7905)Instruction limit reached!
% 1.65/1.09 % (7905)------------------------------
% 1.65/1.09 % (7905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.09 % (7905)Termination reason: Unknown
% 1.65/1.09 % (7905)Termination phase: Property scanning
% 1.65/1.09
% 1.65/1.09 % (7905)Memory used [KB]: 1791
% 1.65/1.09 % (7905)Time elapsed: 0.011 s
% 1.65/1.09 % (7905)Instructions burned: 37 (million)
% 1.65/1.09 % (7905)------------------------------
% 1.65/1.09 % (7905)------------------------------
% 1.65/1.09 % (7909)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/7Mi)
% 1.65/1.09 % (7909)Instruction limit reached!
% 1.65/1.09 % (7909)------------------------------
% 1.65/1.09 % (7909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.09 % (7909)Termination reason: Unknown
% 1.65/1.09 % (7909)Termination phase: shuffling
% 1.65/1.09
% 1.65/1.09 % (7909)Memory used [KB]: 1407
% 1.65/1.09 % (7909)Time elapsed: 0.004 s
% 1.65/1.09 % (7909)Instructions burned: 9 (million)
% 1.65/1.09 % (7909)------------------------------
% 1.65/1.09 % (7909)------------------------------
% 1.65/1.10 % (7910)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/16Mi)
% 1.65/1.10 % (7911)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7568 for (2999ds/3Mi)
% 1.65/1.10 % (7911)Instruction limit reached!
% 1.65/1.10 % (7911)------------------------------
% 1.65/1.10 % (7911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.10 % (7911)Termination reason: Unknown
% 1.65/1.10 % (7911)Termination phase: shuffling
% 1.65/1.10
% 1.65/1.10 % (7911)Memory used [KB]: 1279
% 1.65/1.10 % (7911)Time elapsed: 0.003 s
% 1.65/1.10 % (7911)Instructions burned: 5 (million)
% 1.65/1.10 % (7911)------------------------------
% 1.65/1.10 % (7911)------------------------------
% 1.65/1.10 % (7902)First to succeed.
% 1.65/1.10 % (7902)Refutation found. Thanks to Tanya!
% 1.65/1.10 % SZS status Theorem for DTF2THF_7568
% 1.65/1.10 % SZS output start Proof for DTF2THF_7568
% 1.65/1.10 thf(type_def_5, type, config256849571t_unit: $tType).
% 1.65/1.10 thf(type_def_6, type, message_p_v: $tType).
% 1.65/1.10 thf(type_def_8, type, list_c1059388851t_unit: $tType).
% 1.65/1.10 thf(type_def_9, type, list_message_p_v: $tType).
% 1.65/1.10 thf(type_def_10, type, nat: $tType).
% 1.65/1.10 thf(func_def_0, type, list_c1059388851t_unit: $tType).
% 1.65/1.10 thf(func_def_1, type, config256849571t_unit: $tType).
% 1.65/1.10 thf(func_def_2, type, list_message_p_v: $tType).
% 1.65/1.10 thf(func_def_3, type, message_p_v: $tType).
% 1.65/1.10 thf(func_def_4, type, nat: $tType).
% 1.65/1.10 thf(func_def_5, type, enabled_p_v_s: config256849571t_unit > message_p_v > $o).
% 1.65/1.10 thf(func_def_6, type, firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o).
% 1.65/1.10 thf(func_def_7, 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).
% 1.65/1.10 thf(func_def_8, 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).
% 1.65/1.10 thf(func_def_9, type, minus_minus_nat: nat > nat > nat).
% 1.65/1.10 thf(func_def_10, type, one_one_nat: nat).
% 1.65/1.10 thf(func_def_11, type, zero_zero_nat: nat).
% 1.65/1.10 thf(func_def_12, type, prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o).
% 1.65/1.10 thf(func_def_13, type, prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o).
% 1.65/1.10 thf(func_def_14, type, last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit).
% 1.65/1.10 thf(func_def_15, type, last_message_p_v: list_message_p_v > message_p_v).
% 1.65/1.10 thf(func_def_16, type, nil_co1338500125t_unit: list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_17, type, nil_message_p_v: list_message_p_v).
% 1.65/1.10 thf(func_def_18, type, nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit).
% 1.65/1.10 thf(func_def_19, type, nth_message_p_v: list_message_p_v > nat > message_p_v).
% 1.65/1.10 thf(func_def_20, type, suc: nat > nat).
% 1.65/1.10 thf(func_def_21, type, size_s1406904903t_unit: list_c1059388851t_unit > nat).
% 1.65/1.10 thf(func_def_22, type, size_s1168481041ge_p_v: list_message_p_v > nat).
% 1.65/1.10 thf(func_def_23, type, ord_less_nat: nat > nat > $o).
% 1.65/1.10 thf(func_def_24, type, ord_less_eq_nat: nat > nat > $o).
% 1.65/1.10 thf(func_def_25, type, fe: nat > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_26, type, ft: nat > list_message_p_v).
% 1.65/1.10 thf(func_def_27, type, index: nat).
% 1.65/1.10 thf(func_def_28, type, msgInSet: message_p_v).
% 1.65/1.10 thf(func_def_29, type, msg: message_p_v).
% 1.65/1.10 thf(func_def_30, type, n0: nat).
% 1.65/1.10 thf(func_def_31, type, n1: nat).
% 1.65/1.10 thf(func_def_32, type, nMsg: nat).
% 1.65/1.10 thf(func_def_33, type, n: nat).
% 1.65/1.10 thf(func_def_47, type, sP0: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o).
% 1.65/1.10 thf(func_def_48, type, sP1: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > $o).
% 1.65/1.10 thf(func_def_49, type, sK2: nat > nat > nat).
% 1.65/1.10 thf(func_def_50, type, sK3: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_51, type, sK4: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_52, type, sK5: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_53, type, sK6: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_54, type, sK7: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_55, type, sK8: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_56, type, sK9: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_57, type, sK10: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_58, type, sK11: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_59, type, sK12: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_60, type, sK13: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_61, type, sK14: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_62, type, sK15: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_63, type, sK16: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_64, type, sK17: (nat > $o) > (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_65, type, sK18: nat > list_message_p_v).
% 1.65/1.10 thf(func_def_66, type, sK19: (nat > $o) > nat > nat > nat).
% 1.65/1.10 thf(func_def_67, type, sK20: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 1.65/1.10 thf(func_def_68, type, sK21: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_69, type, sK22: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_70, type, sK23: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_71, type, sK24: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_72, type, sK25: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_73, type, sK26: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_74, type, sK27: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_75, type, sK28: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_76, type, sK29: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_77, type, sK30: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 1.65/1.10 thf(func_def_78, type, sK31: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_79, type, sK32: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_80, type, sK33: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_81, type, sK34: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_82, type, sK35: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_83, type, sK36: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_84, type, sK37: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_85, type, sK38: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_86, type, sK39: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_87, type, sK40: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_88, type, sK41: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 1.65/1.10 thf(func_def_89, type, sK42: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_90, type, sK43: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_91, type, sK44: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_92, type, sK45: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_93, type, sK46: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_94, type, sK47: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_95, type, sK48: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_96, type, sK49: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > nat).
% 1.65/1.10 thf(func_def_97, type, sK50: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_98, type, sK51: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_message_p_v).
% 1.65/1.10 thf(func_def_99, type, sK52: (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > (config256849571t_unit > (list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit) > (list_c1059388851t_unit > list_message_p_v > list_message_p_v) > nat > $o) > list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_100, type, sK53: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_101, type, sK54: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_102, type, sK55: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_103, type, sK56: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_104, type, sK57: nat > nat).
% 1.65/1.10 thf(func_def_105, type, sK58: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_106, type, sK59: (nat > nat) > nat).
% 1.65/1.10 thf(func_def_107, type, sK60: nat > nat > nat).
% 1.65/1.10 thf(func_def_108, type, sK61: nat > (nat > config256849571t_unit > $o) > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_109, type, sK62: nat > (nat > config256849571t_unit > $o) > nat).
% 1.65/1.10 thf(func_def_110, type, sK63: nat > (nat > config256849571t_unit > $o) > config256849571t_unit).
% 1.65/1.10 thf(func_def_111, type, sK64: list_c1059388851t_unit > nat > (nat > config256849571t_unit > $o) > nat).
% 1.65/1.10 thf(func_def_112, type, sK65: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_113, type, sK66: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_114, type, sK67: nat > nat).
% 1.65/1.10 thf(func_def_115, type, sK68: nat > nat > nat).
% 1.65/1.10 thf(func_def_116, type, sK69: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_117, type, sK70: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_118, type, sK71: nat > nat).
% 1.65/1.10 thf(func_def_119, type, sK72: nat > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_120, type, sK73: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_121, type, sK74: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_122, type, sK75: nat > nat).
% 1.65/1.10 thf(func_def_123, type, sK76: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_124, type, sK77: (nat > $o) > nat > nat).
% 1.65/1.10 thf(func_def_125, type, sK78: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_126, type, sK79: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_127, type, sK80: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_128, type, sK81: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_129, type, sK82: list_message_p_v > list_message_p_v > nat).
% 1.65/1.10 thf(func_def_130, type, sK83: nat > nat > nat).
% 1.65/1.10 thf(func_def_131, type, sK84: nat > nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_132, type, sK85: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_133, type, sK86: (list_message_p_v > $o) > list_message_p_v).
% 1.65/1.10 thf(func_def_134, type, sK87: (nat > message_p_v > $o) > nat > list_message_p_v).
% 1.65/1.10 thf(func_def_135, type, sK88: (nat > message_p_v > $o) > nat > nat).
% 1.65/1.10 thf(func_def_136, type, sK89: nat > (nat > message_p_v > $o) > message_p_v).
% 1.65/1.10 thf(func_def_137, type, sK90: list_message_p_v > (nat > message_p_v > $o) > nat > nat).
% 1.65/1.10 thf(func_def_138, type, sK91: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_139, type, sK92: nat > nat).
% 1.65/1.10 thf(func_def_140, type, sK93: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_141, type, sK94: nat > (nat > $o) > nat).
% 1.65/1.10 thf(func_def_142, type, sK95: (list_c1059388851t_unit > $o) > list_c1059388851t_unit).
% 1.65/1.10 thf(func_def_143, type, sK96: (nat > $o) > nat).
% 1.65/1.10 thf(func_def_144, type, sK97: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_145, type, sK98: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_146, type, sK99: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_147, type, sK100: (nat > nat > $o) > nat).
% 1.65/1.10 thf(func_def_148, type, sK101: list_c1059388851t_unit > list_c1059388851t_unit > nat).
% 1.65/1.10 thf(func_def_150, type, ph103: !>[X0: $tType]:(X0)).
% 1.65/1.10 thf(f1460,plain,(
% 1.65/1.10 $false),
% 1.65/1.10 inference(subsumption_resolution,[status(thm)],[f1439,f1273])).
% 1.65/1.10 thf(f1273,plain,(
% 1.65/1.10 ((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))) = $true)),
% 1.65/1.10 inference(cnf_transformation,[status(thm)],[f423])).
% 1.65/1.10 thf(f423,plain,(
% 1.65/1.10 ((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))) = $true)),
% 1.65/1.10 inference(fool_elimination,[status(thm)],[f422])).
% 1.65/1.10 thf(f422,plain,(
% 1.65/1.10 (ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))),
% 1.65/1.10 inference(rectify,[status(thm)],[f1])).
% 1.65/1.10 thf(f1,axiom,(
% 1.65/1.10 (ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index)))),
% 1.65/1.10 file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_0_Occ3_H)).
% 1.65/1.10 thf(f1439,plain,(
% 1.65/1.10 ((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))) != $true)),
% 1.65/1.10 inference(trivial_inequality_removal,[status(thm)],[f1438])).
% 1.65/1.10 thf(f1438,plain,(
% 1.65/1.10 ($true != $true) | ((ord_less_nat @ n1 @ (size_s1406904903t_unit @ (fe @ index))) != $true)),
% 1.65/1.10 inference(superposition,[status(thm)],[f1422,f1082])).
% 1.65/1.10 thf(f1082,plain,(
% 1.65/1.10 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less_nat @ (minus_minus_nat @ X1 @ X2) @ X0) = $true) | ((ord_less_nat @ X1 @ X0) != $true)) )),
% 1.65/1.10 inference(cnf_transformation,[status(thm)],[f815])).
% 1.65/1.10 thf(f815,plain,(
% 1.65/1.10 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X1 @ X0) != $true) | ((ord_less_nat @ (minus_minus_nat @ X1 @ X2) @ X0) = $true))),
% 1.65/1.10 inference(ennf_transformation,[status(thm)],[f251])).
% 1.65/1.10 thf(f251,plain,(
% 1.65/1.10 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X1 @ X0) = $true) => ((ord_less_nat @ (minus_minus_nat @ X1 @ X2) @ X0) = $true))),
% 1.65/1.10 inference(fool_elimination,[status(thm)],[f250])).
% 1.65/1.10 thf(f250,plain,(
% 1.65/1.10 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_nat @ X1 @ X0) => (ord_less_nat @ (minus_minus_nat @ X1 @ X2) @ X0))),
% 1.65/1.10 inference(rectify,[status(thm)],[f155])).
% 1.65/1.10 thf(f155,axiom,(
% 1.65/1.10 ! [X3 : nat,X24 : nat,X1 : nat] : ((ord_less_nat @ X24 @ X3) => (ord_less_nat @ (minus_minus_nat @ X24 @ X1) @ X3))),
% 1.65/1.10 file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_154_less__imp__diff__less)).
% 1.65/1.10 thf(f1422,plain,(
% 1.65/1.10 ((ord_less_nat @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat)) @ (size_s1406904903t_unit @ (fe @ index))) != $true)),
% 1.65/1.10 inference(trivial_inequality_removal,[status(thm)],[f1421])).
% 1.65/1.10 thf(f1421,plain,(
% 1.65/1.10 ((ord_less_nat @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat)) @ (size_s1406904903t_unit @ (fe @ index))) != $true) | ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat))) != (nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat))))),
% 1.65/1.10 inference(superposition,[status(thm)],[f1358,f1092])).
% 1.65/1.10 thf(f1092,plain,(
% 1.65/1.10 ( ! [X0 : nat] : (((nth_co1649820636t_unit @ (fe @ index) @ X0) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0)) | ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) != $true)) )),
% 1.65/1.10 inference(cnf_transformation,[status(thm)],[f763])).
% 1.65/1.10 thf(f763,plain,(
% 1.65/1.10 ! [X0 : nat] : (((nth_co1649820636t_unit @ (fe @ index) @ X0) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0)) | ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) != $true))),
% 1.65/1.10 inference(ennf_transformation,[status(thm)],[f345])).
% 1.65/1.10 thf(f345,plain,(
% 1.65/1.10 ! [X0 : nat] : (((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) = $true) => ((nth_co1649820636t_unit @ (fe @ index) @ X0) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0)))),
% 1.65/1.10 inference(fool_elimination,[status(thm)],[f344])).
% 1.65/1.10 thf(f344,plain,(
% 1.65/1.10 ! [X0 : nat] : ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) => ((nth_co1649820636t_unit @ (fe @ index) @ X0) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0)))),
% 1.65/1.10 inference(rectify,[status(thm)],[f2])).
% 1.65/1.10 thf(f2,axiom,(
% 1.65/1.10 ! [X0 : nat] : ((ord_less_nat @ X0 @ (size_s1406904903t_unit @ (fe @ index))) => ((nth_co1649820636t_unit @ (fe @ index) @ X0) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ X0)))),
% 1.65/1.10 file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_1_SameCfgOnLow)).
% 1.65/1.10 thf(f1358,plain,(
% 1.65/1.10 ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat))) != (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ (suc @ zero_zero_nat))))),
% 1.65/1.10 inference(definition_unfolding,[status(thm)],[f1154,f1153,f1153])).
% 1.65/1.10 thf(f1153,plain,(
% 1.65/1.10 (one_one_nat = (suc @ zero_zero_nat))),
% 1.65/1.10 inference(cnf_transformation,[status(thm)],[f137])).
% 1.65/1.10 thf(f137,axiom,(
% 1.65/1.10 (one_one_nat = (suc @ zero_zero_nat))),
% 1.65/1.10 file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',fact_136_One__nat__def)).
% 1.65/1.10 thf(f1154,plain,(
% 1.65/1.10 ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat)) != (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))),
% 1.65/1.10 inference(cnf_transformation,[status(thm)],[f638])).
% 1.65/1.10 thf(f638,plain,(
% 1.65/1.10 ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat)) != (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))),
% 1.65/1.10 inference(flattening,[status(thm)],[f246])).
% 1.65/1.10 thf(f246,negated_conjecture,(
% 1.65/1.10 ~((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat)) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))),
% 1.65/1.10 inference(negated_conjecture,[status(cth)],[f245])).
% 1.65/1.10 thf(f245,conjecture,(
% 1.65/1.10 ((nth_co1649820636t_unit @ (fe @ index) @ (minus_minus_nat @ n1 @ one_one_nat)) = (nth_co1649820636t_unit @ (fe @ (suc @ index)) @ (minus_minus_nat @ n1 @ one_one_nat)))),
% 1.65/1.10 file('/export/starexec/sandbox/tmp/tmp.e2IvO4B5av/DTF2THF_7568.p',conj_0)).
% 1.65/1.10 % SZS output end Proof for DTF2THF_7568
% 1.65/1.10 % (7902)------------------------------
% 1.65/1.10 % (7902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.10 % (7902)Termination reason: Refutation
% 1.65/1.10
% 1.65/1.10 % (7902)Memory used [KB]: 6780
% 1.65/1.10 % (7902)Time elapsed: 0.030 s
% 1.65/1.10 % (7902)Instructions burned: 90 (million)
% 1.65/1.10 % (7902)------------------------------
% 1.65/1.10 % (7902)------------------------------
% 1.65/1.10 % (7896)Success in time 0.041 s
%------------------------------------------------------------------------------