%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP125^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n021.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 08:55:45 AM UTC 2026
% Result : Theorem 2.76s 1.81s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 156 ( 20 ~; 10 |; 0 &; 120 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 154 ( 151 usr; 18 con; 0-4 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
formula_a: $tType ).
thf(type_def_8,type,
i: $tType ).
thf(type_def_9,type,
trace_1367752404list_a: $tType ).
thf(type_def_10,type,
list_a: $tType ).
thf(type_def_11,type,
prefix1027212443list_a: $tType ).
thf(func_def_0,type,
prefix1027212443list_a: $tType ).
thf(func_def_1,type,
trace_1367752404list_a: $tType ).
thf(func_def_2,type,
i: $tType ).
thf(func_def_3,type,
formula_a: $tType ).
thf(func_def_4,type,
list_a: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
one_one_nat: nat ).
thf(func_def_7,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_8,type,
until_a: formula_a > i > formula_a > formula_a ).
thf(func_def_9,type,
sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).
thf(func_def_10,type,
monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).
thf(func_def_11,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_12,type,
ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
thf(func_def_13,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_14,type,
ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
thf(func_def_15,type,
tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).
thf(func_def_16,type,
plen_P694648887list_a: prefix1027212443list_a > nat ).
thf(func_def_17,type,
prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).
thf(func_def_18,type,
i2: i ).
thf(func_def_19,type,
phi: formula_a ).
thf(func_def_20,type,
phi_1: formula_a ).
thf(func_def_21,type,
phi_2: formula_a ).
thf(func_def_22,type,
pi: prefix1027212443list_a ).
thf(func_def_23,type,
sigma: trace_1367752404list_a ).
thf(func_def_24,type,
sigma2: trace_1367752404list_a ).
thf(func_def_25,type,
b: nat ).
thf(func_def_26,type,
i3: nat ).
thf(func_def_27,type,
ia: nat ).
thf(func_def_28,type,
j: nat ).
thf(func_def_29,type,
ja: nat ).
thf(func_def_30,type,
k: nat ).
thf(func_def_45,type,
sP0: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_46,type,
sP1: nat > nat > nat > $o ).
thf(func_def_47,type,
sP2: nat > nat > nat > $o ).
thf(func_def_48,type,
sP3: nat > nat > nat > $o ).
thf(func_def_49,type,
sP4: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_50,type,
sP5: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_51,type,
sP6: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_52,type,
sK7: nat > nat ).
thf(func_def_53,type,
sK8: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_54,type,
sK9: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_55,type,
sK10: ( nat > nat ) > nat ).
thf(func_def_56,type,
sK11: ( nat > nat ) > nat ).
thf(func_def_57,type,
sK12: nat ).
thf(func_def_58,type,
sK13: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_59,type,
sK14: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_60,type,
sK15: ( nat > nat ) > nat ).
thf(func_def_61,type,
sK16: ( nat > nat ) > nat ).
thf(func_def_62,type,
sK17: ( nat > nat ) > nat ).
thf(func_def_63,type,
sK18: ( nat > nat ) > nat ).
thf(func_def_64,type,
sK19: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_65,type,
sK20: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_66,type,
sK21: ( nat > nat ) > nat ).
thf(func_def_67,type,
sK22: ( nat > nat ) > nat ).
thf(func_def_68,type,
sK23: nat > nat > nat ).
thf(func_def_69,type,
sK24: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_70,type,
sK25: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_71,type,
sK26: nat > nat ).
thf(func_def_72,type,
sK27: ( nat > $o ) > nat ).
thf(func_def_73,type,
sK28: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_74,type,
sK29: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_75,type,
sK30: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_76,type,
sK31: ( nat > nat ) > nat ).
thf(func_def_77,type,
sK32: ( nat > nat ) > nat ).
thf(func_def_78,type,
sK33: ( nat > $o ) > nat ).
thf(func_def_79,type,
sK34: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_80,type,
sK35: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_81,type,
sK36: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_82,type,
sK37: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_83,type,
sK38: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_84,type,
sK39: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_85,type,
sK40: trace_1367752404list_a > nat > trace_1367752404list_a > nat ).
thf(func_def_86,type,
sK41: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_87,type,
sK42: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_88,type,
sK43: ( nat > nat > $o ) > nat ).
thf(func_def_89,type,
sK44: ( nat > nat > $o ) > nat ).
thf(func_def_90,type,
sK45: ( nat > nat > $o ) > nat ).
thf(func_def_91,type,
sK46: ( nat > nat > $o ) > nat ).
thf(func_def_92,type,
sK47: ( nat > nat > $o ) > nat ).
thf(func_def_93,type,
sK48: ( nat > nat > $o ) > nat ).
thf(func_def_94,type,
sK49: ( nat > nat > $o ) > nat ).
thf(func_def_95,type,
sK50: ( nat > nat > $o ) > nat ).
thf(func_def_96,type,
sK51: ( nat > nat > $o ) > nat ).
thf(func_def_97,type,
sK52: nat > trace_1367752404list_a > nat > nat ).
thf(func_def_98,type,
sK53: ( nat > nat ) > nat ).
thf(func_def_99,type,
sK54: ( nat > nat ) > nat ).
thf(func_def_100,type,
sK55: ( nat > nat ) > nat ).
thf(func_def_101,type,
sK56: ( nat > nat ) > nat ).
thf(func_def_102,type,
sK57: ( nat > nat ) > nat ).
thf(func_def_103,type,
sK58: ( nat > nat ) > nat ).
thf(func_def_104,type,
sK59: nat > nat ).
thf(func_def_105,type,
sK60: ( nat > nat ) > nat ).
thf(func_def_106,type,
sK61: ( nat > nat ) > nat ).
thf(func_def_107,type,
sK62: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_108,type,
sK63: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_109,type,
sK64: ( nat > $o ) > nat > nat ).
thf(func_def_110,type,
sK65: ( nat > $o ) > nat > nat ).
thf(func_def_111,type,
sK66: nat > nat ).
thf(func_def_112,type,
sK67: nat > nat ).
thf(func_def_113,type,
sK68: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_114,type,
sK69: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_115,type,
sK70: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_116,type,
sK71: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_117,type,
sK72: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_118,type,
sK73: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_119,type,
sK74: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_120,type,
sK75: ( nat > nat ) > nat ).
thf(func_def_121,type,
sK76: ( nat > nat ) > nat ).
thf(func_def_122,type,
sK77: nat > nat ).
thf(func_def_123,type,
sK78: nat > nat ).
thf(func_def_124,type,
sK79: nat ).
thf(func_def_125,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_126,type,
sK81: ( nat > nat ) > nat ).
thf(func_def_127,type,
sK82: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_128,type,
sK83: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_129,type,
sK84: nat > nat ).
thf(func_def_130,type,
sK85: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_131,type,
sK86: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_132,type,
sK87: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_133,type,
sK88: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_134,type,
sK89: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_135,type,
sK90: ( nat > nat ) > nat ).
thf(func_def_136,type,
sK91: ( nat > nat ) > nat ).
thf(func_def_137,type,
sK92: prefix1027212443list_a > trace_1367752404list_a ).
thf(func_def_138,type,
sK93: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_139,type,
sK94: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_140,type,
sK95: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_141,type,
sK96: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_142,type,
sK97: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_143,type,
sK98: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_144,type,
sK99: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_145,type,
sK100: nat > nat ).
thf(func_def_146,type,
sK101: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_147,type,
sK102: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_148,type,
sK103: ( nat > nat ) > nat ).
thf(func_def_149,type,
sK104: ( nat > nat ) > nat ).
thf(func_def_150,type,
sK105: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_151,type,
sK106: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).
thf(func_def_152,type,
sK107: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_153,type,
sK108: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).
thf(func_def_154,type,
sK109: ( nat > nat ) > nat ).
thf(func_def_155,type,
sK110: ( nat > nat ) > nat ).
thf(func_def_156,type,
sK111: nat > nat ).
thf(func_def_157,type,
sK112: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_158,type,
sK113: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_159,type,
sK114: nat > nat ).
thf(func_def_160,type,
sK115: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_161,type,
sK116: ( nat > prefix1027212443list_a ) > nat ).
thf(func_def_162,type,
sK117: nat > nat ).
thf(func_def_163,type,
sK118: nat > ( nat > $o ) > nat > nat ).
thf(func_def_164,type,
sK119: nat > nat > ( nat > $o ) > nat ).
thf(func_def_165,type,
sK120: ( nat > $o ) > nat > nat ).
thf(func_def_166,type,
sK121: ( nat > $o ) > nat ).
thf(func_def_167,type,
sK122: nat > nat ).
thf(func_def_168,type,
sK123: ( nat > $o ) > nat ).
thf(func_def_169,type,
sK124: nat > nat > nat ).
thf(func_def_171,type,
ph126:
!>[X0: $tType] : X0 ).
thf(f6951,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f6924]) ).
thf(f6924,plain,
$true != $true,
inference(superposition,[status(thm)],[f2110,f1604]) ).
thf(f1604,plain,
( ( ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f680]) ).
thf(f680,plain,
( ( ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f679]) ).
thf(f679,plain,
ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).
thf(f2110,plain,
! [X0: trace_1367752404list_a,X1: formula_a] :
( ( ord_less_nat @ k @ ( monito1457594016ress_a @ X0 @ X1 @ ( plen_P694648887list_a @ pi ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2104]) ).
thf(f2104,plain,
! [X0: trace_1367752404list_a,X1: formula_a] :
( ( ( ord_less_nat @ k @ ( monito1457594016ress_a @ X0 @ X1 @ ( plen_P694648887list_a @ pi ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1913,f1462]) ).
thf(f1462,plain,
! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] :
( ( ord_less_eq_nat @ ( monito1457594016ress_a @ X0 @ X1 @ X2 ) @ X2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f686]) ).
thf(f686,plain,
! [X0: trace_1367752404list_a,X1: formula_a,X2: nat] :
( ( ord_less_eq_nat @ ( monito1457594016ress_a @ X0 @ X1 @ X2 ) @ X2 )
= $true ),
inference(fool_elimination,[status(thm)],[f685]) ).
thf(f685,plain,
! [X0: trace_1367752404list_a,X1: formula_a,X2: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X0 @ X1 @ X2 ) @ X2 ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
! [X16: trace_1367752404list_a,X17: formula_a,X10: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X16 @ X17 @ X10 ) @ X10 ),
file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_20_progress__le) ).
thf(f1913,plain,
! [X0: nat] :
( ( ( ord_less_eq_nat @ X0 @ ( plen_P694648887list_a @ pi ) )
!= $true )
| ( ( ord_less_nat @ k @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1910]) ).
thf(f1910,plain,
! [X0: nat] :
( ( ( ord_less_eq_nat @ X0 @ ( plen_P694648887list_a @ pi ) )
!= $true )
| ( ( ord_less_nat @ k @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1739,f1807]) ).
thf(f1807,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X2 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X2 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f973]) ).
thf(f973,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X0 @ X2 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X2 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f972]) ).
thf(f972,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X0 @ X2 )
= $true )
| ( ( ord_less_eq_nat @ X1 @ X2 )
!= $true )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f782]) ).
thf(f782,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
=> ( ( ( ord_less_eq_nat @ X1 @ X2 )
= $true )
=> ( ( ord_less_nat @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f781]) ).
thf(f781,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( ( ord_less_eq_nat @ X1 @ X2 )
=> ( ord_less_nat @ X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
! [X35: nat,X12: nat,X42: nat] :
( ( ord_less_nat @ X35 @ X12 )
=> ( ( ord_less_eq_nat @ X12 @ X42 )
=> ( ord_less_nat @ X35 @ X42 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_186_order_Ostrict__trans2) ).
thf(f1739,plain,
( ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f879]) ).
thf(f879,plain,
( ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) )
!= $true ),
inference(flattening,[status(thm)],[f772]) ).
thf(f772,plain,
( ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f771]) ).
thf(f771,plain,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(rectify,[status(thm)],[f285]) ).
thf(f285,negated_conjecture,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(negated_conjecture,[status(cth)],[f284]) ).
thf(f284,conjecture,
ord_less_nat @ k @ ( plen_P694648887list_a @ pi ),
file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP125^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:27:08 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : ITP125^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.47 % Domain : Interactive Theorem Proving
% 0.29/0.47 % Problem : Sledgehammer Monitor problem prob_453__6453916_1
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Des21]
% 0.29/0.47 % Names : Monitor/prob_453__6453916_1 [Des21]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.29/0.47 % Syntax : Number of formulae : 315 ( 83 unt; 31 typ; 0 def)
% 0.29/0.47 % Number of atoms : 823 ( 183 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 12 ( 2 avg)
% 0.29/0.47 % Number of connectives : 2451 ( 87 ~; 25 |; 40 &;1887 @)
% 0.29/0.47 % ( 0 <=>; 412 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 18 ( 8 avg)
% 0.29/0.47 % Number of types : 7 ( 6 usr)
% 0.29/0.47 % Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 26 ( 25 usr; 14 con; 0-4 aty)
% 0.29/0.47 % Number of variables : 866 ( 67 ^; 764 !; 35 ?; 866 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:11.449
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % Could-be-implicit typings (6)
% 0.29/0.47 thf(ty_n_t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.29/0.47 prefix1027212443list_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Trace__Otrace_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.29/0.47 trace_1367752404list_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Interval__O__092__060I__062,type,
% 0.29/0.47 i: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 0.29/0.47 formula_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.29/0.47 list_a: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(ty_n_t__Nat__Onat,type,
% 0.29/0.47 nat: $tType ).
% 0.29/0.47
% 0.29/0.47 % Explicit typings (25)
% 0.29/0.47 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.29/0.47 one_one_nat: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.29/0.47 plus_plus_nat: nat > nat > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_MFOTL_Oformula_OUntil_001tf__a,type,
% 0.29/0.47 until_a: formula_a > i > formula_a > formula_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_MFOTL_Osat_001tf__a,type,
% 0.29/0.47 sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Monitor__Mirabelle__prbptmgypa_Oprogress_001tf__a,type,
% 0.29/0.47 monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.29/0.47 ord_less_nat: nat > nat > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.29/0.47 ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.29/0.47 ord_less_eq_nat: nat > nat > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.29/0.47 ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Trace_O_092_060tau_062_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.29/0.47 tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Trace_Oplen_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.29/0.47 plen_P694648887list_a: prefix1027212443list_a > nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_c_Trace_Oprefix__of_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.29/0.47 prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_I____,type,
% 0.29/0.47 i2: i ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060phi_062,type,
% 0.29/0.47 phi: formula_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060phi_0621____,type,
% 0.29/0.47 phi_1: formula_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060phi_0622____,type,
% 0.29/0.47 phi_2: formula_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060pi_062,type,
% 0.29/0.47 pi: prefix1027212443list_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060sigma_062,type,
% 0.29/0.47 sigma: trace_1367752404list_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v__092_060sigma_062_H,type,
% 0.29/0.47 sigma2: trace_1367752404list_a ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_b____,type,
% 0.29/0.47 b: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_i,type,
% 0.29/0.47 i3: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_ia____,type,
% 0.29/0.47 ia: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_j____,type,
% 0.29/0.47 j: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_ja____,type,
% 0.29/0.47 ja: nat ).
% 0.29/0.47
% 0.29/0.47 thf(sy_v_k____,type,
% 0.29/0.47 k: nat ).
% 0.29/0.47
% 0.29/0.47 % Relevant facts (283)
% 0.29/0.47 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>k < Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_1_assms_I3_J,axiom,
% 0.29/0.47 ord_less_nat @ i3 @ ( monito1457594016ress_a @ sigma @ phi @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % assms(3)
% 0.29/0.47 thf(fact_2_assms_I1_J,axiom,
% 0.29/0.47 prefix1041802747list_a @ pi @ sigma ).
% 0.29/0.47
% 0.29/0.47 % assms(1)
% 0.29/0.47 thf(fact_3_nat__neq__iff,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( M != N )
% 0.29/0.47 = ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_neq_iff
% 0.29/0.47 thf(fact_4_less__not__refl,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 % less_not_refl
% 0.29/0.47 thf(fact_5_less__not__refl2,axiom,
% 0.29/0.47 ! [N: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_nat @ N @ M )
% 0.29/0.47 => ( M != N ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_not_refl2
% 0.29/0.47 thf(fact_6_less__not__refl3,axiom,
% 0.29/0.47 ! [S: nat,T: nat] :
% 0.29/0.47 ( ( ord_less_nat @ S @ T )
% 0.29/0.47 => ( S != T ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_not_refl3
% 0.29/0.47 thf(fact_7_less__irrefl__nat,axiom,
% 0.29/0.47 ! [N: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 % less_irrefl_nat
% 0.29/0.47 thf(fact_8_nat__less__induct,axiom,
% 0.29/0.47 ! [P: nat > $o,N: nat] :
% 0.29/0.47 ( ! [N2: nat] :
% 0.29/0.47 ( ! [M2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.47 => ( P @ M2 ) )
% 0.29/0.47 => ( P @ N2 ) )
% 0.29/0.47 => ( P @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_less_induct
% 0.29/0.47 thf(fact_9_infinite__descent,axiom,
% 0.29/0.47 ! [P: nat > $o,N: nat] :
% 0.29/0.47 ( ! [N2: nat] :
% 0.29/0.47 ( ~ ( P @ N2 )
% 0.29/0.47 => ? [M2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.47 & ~ ( P @ M2 ) ) )
% 0.29/0.47 => ( P @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % infinite_descent
% 0.29/0.47 thf(fact_10_linorder__neqE__nat,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_neqE_nat
% 0.29/0.47 thf(fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>j__ \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_12_assms_I2_J,axiom,
% 0.29/0.47 prefix1041802747list_a @ pi @ sigma2 ).
% 0.29/0.47
% 0.29/0.47 % assms(2)
% 0.29/0.47 thf(fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>j__ \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>2 (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_14_le__refl,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 % le_refl
% 0.29/0.47 thf(fact_15_le__trans,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_trans
% 0.29/0.47 thf(fact_16_eq__imp__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( M = N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_imp_le
% 0.29/0.47 thf(fact_17_le__antisym,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.47 => ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_antisym
% 0.29/0.47 thf(fact_18_nat__le__linear,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_linear
% 0.29/0.47 thf(fact_19_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.47 ! [P: nat > $o,K: nat,B: nat] :
% 0.29/0.47 ( ( P @ K )
% 0.29/0.47 => ( ! [Y2: nat] :
% 0.29/0.47 ( ( P @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.29/0.47 => ? [X2: nat] :
% 0.29/0.47 ( ( P @ X2 )
% 0.29/0.47 & ! [Y3: nat] :
% 0.29/0.47 ( ( P @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.ex_has_greatest_nat
% 0.29/0.47 thf(fact_20_progress__le,axiom,
% 0.29/0.47 ! [Sigma: trace_1367752404list_a,Phi: formula_a,J: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ J ) ).
% 0.29/0.47
% 0.29/0.47 % progress_le
% 0.29/0.47 thf(fact_21_progress__mono,axiom,
% 0.29/0.47 ! [J: nat,J2: nat,Sigma: trace_1367752404list_a,Phi: formula_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ J @ J2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ ( monito1457594016ress_a @ Sigma @ Phi @ J2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % progress_mono
% 0.29/0.47 thf(fact_22_pinf_I6_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(6)
% 0.29/0.47 thf(fact_23_pinf_I8_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(8)
% 0.29/0.47 thf(fact_24_minf_I6_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(6)
% 0.29/0.47 thf(fact_25_minf_I8_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(8)
% 0.29/0.47 thf(fact_26_less__mono__imp__le__mono,axiom,
% 0.29/0.47 ! [F: nat > nat,I: nat,J: nat] :
% 0.29/0.47 ( ! [I2: nat,J3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I2 @ J3 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J3 ) ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_mono_imp_le_mono
% 0.29/0.47 thf(fact_27_le__neq__implies__less,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( M != N )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_neq_implies_less
% 0.29/0.47 thf(fact_28_less__or__eq__imp__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( ord_less_nat @ M @ N )
% 0.29/0.47 | ( M = N ) )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_or_eq_imp_le
% 0.29/0.47 thf(fact_29_le__eq__less__or__eq,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.29/0.47 | ( M3 = N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_eq_less_or_eq
% 0.29/0.47 thf(fact_30_less__imp__le__nat,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_le_nat
% 0.29/0.47 thf(fact_31_nat__less__le,axiom,
% 0.29/0.47 ( ord_less_nat
% 0.29/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.29/0.47 & ( M3 != N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_less_le
% 0.29/0.47 thf(fact_32_progress__prefix__conv,axiom,
% 0.29/0.47 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.29/0.47 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.29/0.47 => ( ( prefix1041802747list_a @ Pi @ Sigma2 )
% 0.29/0.47 => ( ( monito1457594016ress_a @ Sigma @ Phi @ ( plen_P694648887list_a @ Pi ) )
% 0.29/0.47 = ( monito1457594016ress_a @ Sigma2 @ Phi @ ( plen_P694648887list_a @ Pi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % progress_prefix_conv
% 0.29/0.47 thf(fact_33_pinf_I1_J,axiom,
% 0.29/0.47 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.29/0.47 ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.47 => ( ( P @ X2 )
% 0.29/0.47 = ( P2 @ X2 ) ) )
% 0.29/0.47 => ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.47 => ( ( Q @ X2 )
% 0.29/0.47 = ( Q2 @ X2 ) ) )
% 0.29/0.47 => ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( ( ( P @ X3 )
% 0.29/0.47 & ( Q @ X3 ) )
% 0.29/0.47 = ( ( P2 @ X3 )
% 0.29/0.47 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(1)
% 0.29/0.47 thf(fact_34_pinf_I2_J,axiom,
% 0.29/0.47 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.29/0.47 ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.47 => ( ( P @ X2 )
% 0.29/0.47 = ( P2 @ X2 ) ) )
% 0.29/0.47 => ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z2 @ X2 )
% 0.29/0.47 => ( ( Q @ X2 )
% 0.29/0.47 = ( Q2 @ X2 ) ) )
% 0.29/0.47 => ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( ( ( P @ X3 )
% 0.29/0.47 | ( Q @ X3 ) )
% 0.29/0.47 = ( ( P2 @ X3 )
% 0.29/0.47 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(2)
% 0.29/0.47 thf(fact_35_pinf_I3_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( X3 != T ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(3)
% 0.29/0.47 thf(fact_36_pinf_I4_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( X3 != T ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(4)
% 0.29/0.47 thf(fact_37_pinf_I5_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ~ ( ord_less_nat @ X3 @ T ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(5)
% 0.29/0.47 thf(fact_38_pinf_I7_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Z @ X3 )
% 0.29/0.47 => ( ord_less_nat @ T @ X3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % pinf(7)
% 0.29/0.47 thf(fact_39_minf_I1_J,axiom,
% 0.29/0.47 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.29/0.47 ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.47 => ( ( P @ X2 )
% 0.29/0.47 = ( P2 @ X2 ) ) )
% 0.29/0.47 => ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.47 => ( ( Q @ X2 )
% 0.29/0.47 = ( Q2 @ X2 ) ) )
% 0.29/0.47 => ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( ( ( P @ X3 )
% 0.29/0.47 & ( Q @ X3 ) )
% 0.29/0.47 = ( ( P2 @ X3 )
% 0.29/0.47 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(1)
% 0.29/0.47 thf(fact_40_minf_I2_J,axiom,
% 0.29/0.47 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.29/0.47 ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.47 => ( ( P @ X2 )
% 0.29/0.47 = ( P2 @ X2 ) ) )
% 0.29/0.47 => ( ? [Z2: nat] :
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Z2 )
% 0.29/0.47 => ( ( Q @ X2 )
% 0.29/0.47 = ( Q2 @ X2 ) ) )
% 0.29/0.47 => ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( ( ( P @ X3 )
% 0.29/0.47 | ( Q @ X3 ) )
% 0.29/0.47 = ( ( P2 @ X3 )
% 0.29/0.47 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(2)
% 0.29/0.47 thf(fact_41_minf_I3_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( X3 != T ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(3)
% 0.29/0.47 thf(fact_42_minf_I4_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( X3 != T ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(4)
% 0.29/0.47 thf(fact_43_minf_I5_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ( ord_less_nat @ X3 @ T ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(5)
% 0.29/0.47 thf(fact_44_minf_I7_J,axiom,
% 0.29/0.47 ! [T: nat] :
% 0.29/0.47 ? [Z: nat] :
% 0.29/0.47 ! [X3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X3 @ Z )
% 0.29/0.47 => ~ ( ord_less_nat @ T @ X3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % minf(7)
% 0.29/0.47 thf(fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>1 (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_46_order__refl,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a] : ( ord_le699472955list_a @ X @ X ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_47_order__refl,axiom,
% 0.29/0.47 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_48_Until_OIH_I1_J,axiom,
% 0.29/0.47 ! [I: nat,V: list_a] :
% 0.29/0.47 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.29/0.47 => ( ( sat_a @ sigma @ V @ I @ phi_1 )
% 0.29/0.47 = ( sat_a @ sigma2 @ V @ I @ phi_1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Until.IH(1)
% 0.29/0.47 thf(fact_49_nat__descend__induct,axiom,
% 0.29/0.47 ! [N: nat,P: nat > $o,M: nat] :
% 0.29/0.47 ( ! [K2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ N @ K2 )
% 0.29/0.47 => ( P @ K2 ) )
% 0.29/0.47 => ( ! [K2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K2 @ N )
% 0.29/0.47 => ( ! [I3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ K2 @ I3 )
% 0.29/0.47 => ( P @ I3 ) )
% 0.29/0.47 => ( P @ K2 ) ) )
% 0.29/0.47 => ( P @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_descend_induct
% 0.29/0.47 thf(fact_50_complete__interval,axiom,
% 0.29/0.47 ! [A: nat,B: nat,P: nat > $o] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( P @ A )
% 0.29/0.47 => ( ~ ( P @ B )
% 0.29/0.47 => ? [C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.47 & ( ord_less_eq_nat @ C @ B )
% 0.29/0.47 & ! [X3: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.29/0.47 & ( ord_less_nat @ X3 @ C ) )
% 0.29/0.47 => ( P @ X3 ) )
% 0.29/0.47 & ! [D: nat] :
% 0.29/0.47 ( ! [X2: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ A @ X2 )
% 0.29/0.47 & ( ord_less_nat @ X2 @ D ) )
% 0.29/0.47 => ( P @ X2 ) )
% 0.29/0.47 => ( ord_less_eq_nat @ D @ C ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % complete_interval
% 0.29/0.47 thf(fact_51_order_Onot__eq__order__implies__strict,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.29/0.47 ( ( A != B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.not_eq_order_implies_strict
% 0.29/0.47 thf(fact_52_order_Onot__eq__order__implies__strict,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( A != B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.not_eq_order_implies_strict
% 0.29/0.47 thf(fact_53_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.47 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ B @ A )
% 0.29/0.47 => ( ord_le699472955list_a @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_order
% 0.29/0.47 thf(fact_54_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.47 ! [B: nat,A: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B @ A )
% 0.29/0.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_order
% 0.29/0.47 thf(fact_55_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.47 ( ord_le887097159list_a
% 0.29/0.47 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.29/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_iff_order
% 0.29/0.47 thf(fact_56_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.47 ( ord_less_nat
% 0.29/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.29/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_iff_order
% 0.29/0.47 thf(fact_57_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.47 ( ord_le699472955list_a
% 0.29/0.47 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ B2 @ A2 )
% 0.29/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.order_iff_strict
% 0.29/0.47 thf(fact_58_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [B2: nat,A2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B2 @ A2 )
% 0.29/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.order_iff_strict
% 0.29/0.47 thf(fact_59_order_Ostrict__implies__order,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ A @ B )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_order
% 0.29/0.47 thf(fact_60_order_Ostrict__implies__order,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_order
% 0.29/0.47 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>2 (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_62_Until_OIH_I2_J,axiom,
% 0.29/0.47 ! [I: nat,V: list_a] :
% 0.29/0.47 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) )
% 0.29/0.47 => ( ( sat_a @ sigma @ V @ I @ phi_2 )
% 0.29/0.47 = ( sat_a @ sigma2 @ V @ I @ phi_2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Until.IH(2)
% 0.29/0.47 thf(fact_63_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ B @ A )
% 0.29/0.47 => ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_64_dual__order_Oantisym,axiom,
% 0.29/0.47 ! [B: nat,A: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.antisym
% 0.29/0.47 thf(fact_65_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.29/0.47 & ( ord_le699472955list_a @ A2 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_66_dual__order_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.29/0.47 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.eq_iff
% 0.29/0.47 thf(fact_67_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ B @ A )
% 0.29/0.47 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.29/0.47 => ( ord_le699472955list_a @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_68_dual__order_Otrans,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.29/0.47 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.trans
% 0.29/0.47 thf(fact_69_linorder__wlog,axiom,
% 0.29/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.47 ( ! [A3: nat,B3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.29/0.47 => ( P @ A3 @ B3 ) )
% 0.29/0.47 => ( ! [A3: nat,B3: nat] :
% 0.29/0.47 ( ( P @ B3 @ A3 )
% 0.29/0.47 => ( P @ A3 @ B3 ) )
% 0.29/0.47 => ( P @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_wlog
% 0.29/0.47 thf(fact_70_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_71_dual__order_Orefl,axiom,
% 0.29/0.47 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.refl
% 0.29/0.47 thf(fact_72_order__trans,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.29/0.47 => ( ord_le699472955list_a @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_73_order__trans,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_trans
% 0.29/0.47 thf(fact_74_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_75_order__class_Oorder_Oantisym,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.antisym
% 0.29/0.47 thf(fact_76_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( B = C2 )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_77_ord__le__eq__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( B = C2 )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_trans
% 0.29/0.47 thf(fact_78_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_79_ord__eq__le__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_trans
% 0.29/0.47 thf(fact_80_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.29/0.47 & ( ord_le699472955list_a @ B2 @ A2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_81_order__class_Oorder_Oeq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.29/0.47 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_class.order.eq_iff
% 0.29/0.47 thf(fact_82_antisym__conv,axiom,
% 0.29/0.47 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ Y @ X )
% 0.29/0.47 => ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_83_antisym__conv,axiom,
% 0.29/0.47 ! [Y: nat,X: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_84_le__cases3,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z4: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y @ Z4 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X @ Z4 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ X @ Z4 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z4 @ Y ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Z4 @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z4 @ X ) )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat @ Z4 @ X )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases3
% 0.29/0.47 thf(fact_85_order_Otrans,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_86_order_Otrans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_87_le__cases,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases
% 0.29/0.47 thf(fact_88_eq__refl,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ( X = Y )
% 0.29/0.47 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_89_eq__refl,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X = Y )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_90_linear,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % linear
% 0.29/0.47 thf(fact_91_antisym,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le699472955list_a @ Y @ X )
% 0.29/0.47 => ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_92_antisym,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.47 => ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_93_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.29/0.47 & ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_94_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.29/0.47 = ( ^ [X4: nat,Y5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.29/0.47 & ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_95_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( F @ B )
% 0.29/0.47 = C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_96_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ( F @ B )
% 0.29/0.47 = C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_97_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ( F @ B )
% 0.29/0.47 = C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_98_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( F @ B )
% 0.29/0.47 = C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_99_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_100_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_101_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_102_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_103_order__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_104_order__subst2,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_105_order__subst2,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_106_order__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_107_order__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_108_order__subst1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_109_order__subst1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_110_order__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_111_ord__eq__less__subst,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_subst
% 0.29/0.47 thf(fact_112_ord__less__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ( F @ B )
% 0.29/0.47 = C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_less_eq_subst
% 0.29/0.47 thf(fact_113_order__less__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_subst1
% 0.29/0.47 thf(fact_114_order__less__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_subst2
% 0.29/0.47 thf(fact_115_gt__ex,axiom,
% 0.29/0.47 ! [X: nat] :
% 0.29/0.47 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 % gt_ex
% 0.29/0.47 thf(fact_116_neqE,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neqE
% 0.29/0.47 thf(fact_117_neq__iff,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( X != Y )
% 0.29/0.47 = ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neq_iff
% 0.29/0.47 thf(fact_118_order_Oasym,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.asym
% 0.29/0.47 thf(fact_119_less__imp__neq,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( X != Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_neq
% 0.29/0.47 thf(fact_120_less__asym,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_asym
% 0.29/0.47 thf(fact_121_less__asym_H,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_asym'
% 0.29/0.47 thf(fact_122_less__trans,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z4: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_nat @ Y @ Z4 )
% 0.29/0.47 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_trans
% 0.29/0.47 thf(fact_123_less__linear,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 | ( X = Y )
% 0.29/0.47 | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_linear
% 0.29/0.47 thf(fact_124_less__irrefl,axiom,
% 0.29/0.47 ! [X: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ X @ X ) ).
% 0.29/0.47
% 0.29/0.47 % less_irrefl
% 0.29/0.47 thf(fact_125_ord__eq__less__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_less_trans
% 0.29/0.47 thf(fact_126_ord__less__eq__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( B = C2 )
% 0.29/0.47 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_less_eq_trans
% 0.29/0.47 thf(fact_127_dual__order_Oasym,axiom,
% 0.29/0.47 ! [B: nat,A: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B @ A )
% 0.29/0.47 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.asym
% 0.29/0.47 thf(fact_128_less__imp__not__eq,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( X != Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_not_eq
% 0.29/0.47 thf(fact_129_less__not__sym,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_not_sym
% 0.29/0.47 thf(fact_130_less__induct,axiom,
% 0.29/0.47 ! [P: nat > $o,A: nat] :
% 0.29/0.47 ( ! [X2: nat] :
% 0.29/0.47 ( ! [Y3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ Y3 @ X2 )
% 0.29/0.47 => ( P @ Y3 ) )
% 0.29/0.47 => ( P @ X2 ) )
% 0.29/0.47 => ( P @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_induct
% 0.29/0.47 thf(fact_131_antisym__conv3,axiom,
% 0.29/0.47 ! [Y: nat,X: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ Y @ X )
% 0.29/0.47 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv3
% 0.29/0.47 thf(fact_132_less__imp__not__eq2,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( Y != X ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_not_eq2
% 0.29/0.47 thf(fact_133_less__imp__triv,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,P: $o] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_nat @ Y @ X )
% 0.29/0.47 => P ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_triv
% 0.29/0.47 thf(fact_134_linorder__cases,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ( X != Y )
% 0.29/0.47 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_cases
% 0.29/0.47 thf(fact_135_dual__order_Oirrefl,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.irrefl
% 0.29/0.47 thf(fact_136_order_Ostrict__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_trans
% 0.29/0.47 thf(fact_137_less__imp__not__less,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_not_less
% 0.29/0.47 thf(fact_138_exists__least__iff,axiom,
% 0.29/0.47 ( ( ^ [P3: nat > $o] :
% 0.29/0.47 ? [X5: nat] : ( P3 @ X5 ) )
% 0.29/0.47 = ( ^ [P4: nat > $o] :
% 0.29/0.47 ? [N3: nat] :
% 0.29/0.47 ( ( P4 @ N3 )
% 0.29/0.47 & ! [M3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M3 @ N3 )
% 0.29/0.47 => ~ ( P4 @ M3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % exists_least_iff
% 0.29/0.47 thf(fact_139_linorder__less__wlog,axiom,
% 0.29/0.47 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.47 ( ! [A3: nat,B3: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A3 @ B3 )
% 0.29/0.47 => ( P @ A3 @ B3 ) )
% 0.29/0.47 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.29/0.47 => ( ! [A3: nat,B3: nat] :
% 0.29/0.47 ( ( P @ B3 @ A3 )
% 0.29/0.47 => ( P @ A3 @ B3 ) )
% 0.29/0.47 => ( P @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % linorder_less_wlog
% 0.29/0.47 thf(fact_140_dual__order_Ostrict__trans,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B @ A )
% 0.29/0.47 => ( ( ord_less_nat @ C2 @ B )
% 0.29/0.47 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans
% 0.29/0.47 thf(fact_141_not__less__iff__gr__or__eq,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.47 = ( ( ord_less_nat @ Y @ X )
% 0.29/0.47 | ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_less_iff_gr_or_eq
% 0.29/0.47 thf(fact_142_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( A != B ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_implies_not_eq
% 0.29/0.47 thf(fact_143_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.47 ! [B: nat,A: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B @ A )
% 0.29/0.47 => ( A != B ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_implies_not_eq
% 0.29/0.47 thf(fact_144_leD,axiom,
% 0.29/0.47 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ Y @ X )
% 0.29/0.47 => ~ ( ord_le887097159list_a @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % leD
% 0.29/0.47 thf(fact_145_leD,axiom,
% 0.29/0.47 ! [Y: nat,X: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.47 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % leD
% 0.29/0.47 thf(fact_146_leI,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % leI
% 0.29/0.47 thf(fact_147_le__less,axiom,
% 0.29/0.47 ( ord_le699472955list_a
% 0.29/0.47 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ X4 @ Y5 )
% 0.29/0.47 | ( X4 = Y5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_less
% 0.29/0.47 thf(fact_148_le__less,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [X4: nat,Y5: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X4 @ Y5 )
% 0.29/0.47 | ( X4 = Y5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_less
% 0.29/0.47 thf(fact_149_less__le,axiom,
% 0.29/0.47 ( ord_le887097159list_a
% 0.29/0.47 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.29/0.47 & ( X4 != Y5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le
% 0.29/0.47 thf(fact_150_less__le,axiom,
% 0.29/0.47 ( ord_less_nat
% 0.29/0.47 = ( ^ [X4: nat,Y5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.29/0.47 & ( X4 != Y5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le
% 0.29/0.47 thf(fact_151_order__le__less__subst1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst1
% 0.29/0.47 thf(fact_152_order__le__less__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst1
% 0.29/0.47 thf(fact_153_order__le__less__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst2
% 0.29/0.47 thf(fact_154_order__le__less__subst2,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst2
% 0.29/0.47 thf(fact_155_order__le__less__subst2,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst2
% 0.29/0.47 thf(fact_156_order__le__less__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_le_less_subst2
% 0.29/0.47 thf(fact_157_order__less__le__subst1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst1
% 0.29/0.47 thf(fact_158_order__less__le__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst1
% 0.29/0.47 thf(fact_159_order__less__le__subst1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst1
% 0.29/0.47 thf(fact_160_order__less__le__subst1,axiom,
% 0.29/0.47 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst1
% 0.29/0.47 thf(fact_161_order__less__le__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst2
% 0.29/0.47 thf(fact_162_order__less__le__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.29/0.47 => ( ! [X2: nat,Y2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.29/0.47 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_less_le_subst2
% 0.29/0.47 thf(fact_163_not__le,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.29/0.47 = ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_le
% 0.29/0.47 thf(fact_164_not__less,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.47 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_less
% 0.29/0.47 thf(fact_165_le__neq__trans,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( A != B )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_neq_trans
% 0.29/0.47 thf(fact_166_le__neq__trans,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( A != B )
% 0.29/0.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_neq_trans
% 0.29/0.47 thf(fact_167_antisym__conv1,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ~ ( ord_le887097159list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv1
% 0.29/0.47 thf(fact_168_antisym__conv1,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv1
% 0.29/0.47 thf(fact_169_antisym__conv2,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 => ( ( ~ ( ord_le887097159list_a @ X @ Y ) )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv2
% 0.29/0.47 thf(fact_170_antisym__conv2,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.47 = ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv2
% 0.29/0.47 thf(fact_171_less__imp__le,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ X @ Y )
% 0.29/0.47 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_le
% 0.29/0.47 thf(fact_172_less__imp__le,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_le
% 0.29/0.47 thf(fact_173_le__less__trans,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le887097159list_a @ Y @ Z4 )
% 0.29/0.47 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_less_trans
% 0.29/0.47 thf(fact_174_le__less__trans,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z4: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_nat @ Y @ Z4 )
% 0.29/0.47 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_less_trans
% 0.29/0.47 thf(fact_175_less__le__trans,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.29/0.47 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le_trans
% 0.29/0.47 thf(fact_176_less__le__trans,axiom,
% 0.29/0.47 ! [X: nat,Y: nat,Z4: nat] :
% 0.29/0.47 ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.29/0.47 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le_trans
% 0.29/0.47 thf(fact_177_le__less__linear,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_less_linear
% 0.29/0.47 thf(fact_178_le__imp__less__or__eq,axiom,
% 0.29/0.47 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X @ Y )
% 0.29/0.47 => ( ( ord_le887097159list_a @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_imp_less_or_eq
% 0.29/0.47 thf(fact_179_le__imp__less__or__eq,axiom,
% 0.29/0.47 ! [X: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.47 => ( ( ord_less_nat @ X @ Y )
% 0.29/0.47 | ( X = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_imp_less_or_eq
% 0.29/0.47 thf(fact_180_less__le__not__le,axiom,
% 0.29/0.47 ( ord_le887097159list_a
% 0.29/0.47 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.29/0.47 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le_not_le
% 0.29/0.47 thf(fact_181_less__le__not__le,axiom,
% 0.29/0.47 ( ord_less_nat
% 0.29/0.47 = ( ^ [X4: nat,Y5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.29/0.47 & ~ ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_le_not_le
% 0.29/0.47 thf(fact_182_not__le__imp__less,axiom,
% 0.29/0.47 ! [Y: nat,X: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.29/0.47 => ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_le_imp_less
% 0.29/0.47 thf(fact_183_order_Ostrict__trans1,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le887097159list_a @ B @ C2 )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_trans1
% 0.29/0.47 thf(fact_184_order_Ostrict__trans1,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_trans1
% 0.29/0.47 thf(fact_185_order_Ostrict__trans2,axiom,
% 0.29/0.47 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ A @ B )
% 0.29/0.47 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.29/0.47 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_trans2
% 0.29/0.47 thf(fact_186_order_Ostrict__trans2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.47 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_trans2
% 0.29/0.47 thf(fact_187_order_Oorder__iff__strict,axiom,
% 0.29/0.47 ( ord_le699472955list_a
% 0.29/0.47 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ A2 @ B2 )
% 0.29/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.order_iff_strict
% 0.29/0.47 thf(fact_188_order_Oorder__iff__strict,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ A2 @ B2 )
% 0.29/0.47 | ( A2 = B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.order_iff_strict
% 0.29/0.47 thf(fact_189_order_Ostrict__iff__order,axiom,
% 0.29/0.47 ( ord_le887097159list_a
% 0.29/0.47 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.29/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_iff_order
% 0.29/0.47 thf(fact_190_order_Ostrict__iff__order,axiom,
% 0.29/0.47 ( ord_less_nat
% 0.29/0.47 = ( ^ [A2: nat,B2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.29/0.47 & ( A2 != B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.strict_iff_order
% 0.29/0.47 thf(fact_191_dual__order_Ostrict__trans1,axiom,
% 0.29/0.47 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ B @ A )
% 0.29/0.47 => ( ( ord_le887097159list_a @ C2 @ B )
% 0.29/0.47 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans1
% 0.29/0.47 thf(fact_192_dual__order_Ostrict__trans1,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.47 => ( ( ord_less_nat @ C2 @ B )
% 0.29/0.47 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans1
% 0.29/0.47 thf(fact_193_dual__order_Ostrict__trans2,axiom,
% 0.29/0.47 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le887097159list_a @ B @ A )
% 0.29/0.47 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.29/0.47 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans2
% 0.29/0.47 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ B @ A )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.29/0.47 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dual_order.strict_trans2
% 0.29/0.47 thf(fact_195_Until_Oprems,axiom,
% 0.29/0.47 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % Until.prems
% 0.29/0.47 thf(fact_196_plen__mono,axiom,
% 0.29/0.47 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plen_P694648887list_a @ Pi ) @ ( plen_P694648887list_a @ Pi2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % plen_mono
% 0.29/0.47 thf(fact_197_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.47 ! [B4: nat,A4: nat] :
% 0.29/0.47 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.29/0.47 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_comp_simplify1(3)
% 0.29/0.47 thf(fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.29/0.47 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma2 @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>i < Monitor_Mirabelle_prbptmgypa.progress \<sigma>' (formula.Until \<phi>1 I \<phi>2) (plen \<pi>)\<close>
% 0.29/0.47 thf(fact_199_less__prefix__def,axiom,
% 0.29/0.47 ( ord_le887097159list_a
% 0.29/0.47 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.29/0.47 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_prefix_def
% 0.29/0.47 thf(fact_200_verit__la__disequality,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 | ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_la_disequality
% 0.29/0.47 thf(fact_201_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.47
% 0.29/0.47 % verit_comp_simplify1(1)
% 0.29/0.47 thf(fact_202_ex__prefix__of,axiom,
% 0.29/0.47 ! [P5: prefix1027212443list_a] :
% 0.29/0.47 ? [X_1: trace_1367752404list_a] : ( prefix1041802747list_a @ P5 @ X_1 ) ).
% 0.29/0.47
% 0.29/0.47 % ex_prefix_of
% 0.29/0.47 thf(fact_203_prefix__of__antimono,axiom,
% 0.29/0.47 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a,S: trace_1367752404list_a] :
% 0.29/0.47 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.29/0.47 => ( ( prefix1041802747list_a @ Pi2 @ S )
% 0.29/0.47 => ( prefix1041802747list_a @ Pi @ S ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prefix_of_antimono
% 0.29/0.47 thf(fact_204_prefix__of__imp__linear,axiom,
% 0.29/0.47 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Pi2: prefix1027212443list_a] :
% 0.29/0.47 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.29/0.47 => ( ( prefix1041802747list_a @ Pi2 @ Sigma )
% 0.29/0.47 => ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.29/0.47 | ( ord_le699472955list_a @ Pi2 @ Pi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prefix_of_imp_linear
% 0.29/0.47 thf(fact_205_formula_Oinject_I9_J,axiom,
% 0.29/0.47 ! [X91: formula_a,X92: i,X93: formula_a,Y91: formula_a,Y92: i,Y93: formula_a] :
% 0.29/0.47 ( ( ( until_a @ X91 @ X92 @ X93 )
% 0.29/0.47 = ( until_a @ Y91 @ Y92 @ Y93 ) )
% 0.29/0.47 = ( ( X91 = Y91 )
% 0.29/0.47 & ( X92 = Y92 )
% 0.29/0.47 & ( X93 = Y93 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % formula.inject(9)
% 0.29/0.47 thf(fact_206__C21_C,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.29/0.47 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % "21"
% 0.29/0.47 thf(fact_207__C11_C,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.29/0.47 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % "11"
% 0.29/0.47 thf(fact_208_that,axiom,
% 0.29/0.47 ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ k ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) ).
% 0.29/0.47
% 0.29/0.47 % that
% 0.29/0.47 thf(fact_209_nat__add__left__cancel__less,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_add_left_cancel_less
% 0.29/0.47 thf(fact_210_nat__add__left__cancel__le,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_add_left_cancel_le
% 0.29/0.47 thf(fact_211__C3_C,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.29/0.47 => ( ord_less_nat @ K @ ( plen_P694648887list_a @ pi ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % "3"
% 0.29/0.47 thf(fact_212__C1_C,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.29/0.47 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % "1"
% 0.29/0.47 thf(fact_213__C2_C,axiom,
% 0.29/0.47 ! [K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.29/0.47 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % "2"
% 0.29/0.47 thf(fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ j ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j__\<close>
% 0.29/0.47 thf(fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062,axiom,
% 0.29/0.47 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ ja ) ).
% 0.29/0.47
% 0.29/0.47 % \<open>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j\<close>
% 0.29/0.47 thf(fact_216_less___092_060tau_062D,axiom,
% 0.29/0.47 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.29/0.47 => ( ord_less_nat @ I @ J ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_\<tau>D
% 0.29/0.47 thf(fact_217_ex__le___092_060tau_062,axiom,
% 0.29/0.47 ! [I: nat,X: nat,S: trace_1367752404list_a] :
% 0.29/0.47 ? [J3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J3 )
% 0.29/0.47 & ( ord_less_eq_nat @ X @ ( tau_Pr257024512list_a @ S @ J3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ex_le_\<tau>
% 0.29/0.47 thf(fact_218__092_060tau_062__mono,axiom,
% 0.29/0.47 ! [I: nat,J: nat,S: trace_1367752404list_a] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ S @ I ) @ ( tau_Pr257024512list_a @ S @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<tau>_mono
% 0.29/0.47 thf(fact_219_less__add__eq__less,axiom,
% 0.29/0.47 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_nat @ K @ L )
% 0.29/0.47 => ( ( ( plus_plus_nat @ M @ L )
% 0.29/0.47 = ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_add_eq_less
% 0.29/0.47 thf(fact_220_trans__less__add2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % trans_less_add2
% 0.29/0.47 thf(fact_221_trans__less__add1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % trans_less_add1
% 0.29/0.47 thf(fact_222_add__less__mono1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_less_mono1
% 0.29/0.47 thf(fact_223_not__add__less2,axiom,
% 0.29/0.47 ! [J: nat,I: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.29/0.47
% 0.29/0.47 % not_add_less2
% 0.29/0.47 thf(fact_224_not__add__less1,axiom,
% 0.29/0.47 ! [I: nat,J: nat] :
% 0.29/0.47 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.29/0.47
% 0.29/0.47 % not_add_less1
% 0.29/0.47 thf(fact_225_add__less__mono,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_nat @ K @ L )
% 0.29/0.47 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_less_mono
% 0.29/0.47 thf(fact_226_add__lessD1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.29/0.47 => ( ord_less_nat @ I @ K ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_lessD1
% 0.29/0.47 thf(fact_227_add__leE,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_leE
% 0.29/0.47 thf(fact_228_le__add1,axiom,
% 0.29/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_add1
% 0.29/0.47 thf(fact_229_le__add2,axiom,
% 0.29/0.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_add2
% 0.29/0.47 thf(fact_230_add__leD1,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_leD1
% 0.29/0.47 thf(fact_231_add__leD2,axiom,
% 0.29/0.47 ! [M: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_leD2
% 0.29/0.47 thf(fact_232_le__Suc__ex,axiom,
% 0.29/0.47 ! [K: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.47 => ? [N2: nat] :
% 0.29/0.47 ( L
% 0.29/0.47 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_Suc_ex
% 0.29/0.47 thf(fact_233_add__le__mono,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_mono
% 0.29/0.47 thf(fact_234_add__le__mono1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_mono1
% 0.29/0.47 thf(fact_235_trans__le__add1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % trans_le_add1
% 0.29/0.47 thf(fact_236_trans__le__add2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,M: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % trans_le_add2
% 0.29/0.47 thf(fact_237_nat__le__iff__add,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [M3: nat,N3: nat] :
% 0.29/0.47 ? [K3: nat] :
% 0.29/0.47 ( N3
% 0.29/0.47 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_iff_add
% 0.29/0.47 thf(fact_238_mono__nat__linear__lb,axiom,
% 0.29/0.47 ! [F: nat > nat,M: nat,K: nat] :
% 0.29/0.47 ( ! [M4: nat,N2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ M4 @ N2 )
% 0.29/0.47 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mono_nat_linear_lb
% 0.29/0.47 thf(fact_239_progress__time__conv,axiom,
% 0.29/0.47 ! [J: nat,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.29/0.47 ( ! [I2: nat] :
% 0.29/0.47 ( ( ord_less_nat @ I2 @ J )
% 0.29/0.47 => ( ( tau_Pr257024512list_a @ Sigma @ I2 )
% 0.29/0.47 = ( tau_Pr257024512list_a @ Sigma2 @ I2 ) ) )
% 0.29/0.47 => ( ( monito1457594016ress_a @ Sigma @ Phi @ J )
% 0.29/0.47 = ( monito1457594016ress_a @ Sigma2 @ Phi @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % progress_time_conv
% 0.29/0.47 thf(fact_240_le___092_060tau_062__less,axiom,
% 0.29/0.47 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.29/0.47 => ( ( ord_less_nat @ J @ I )
% 0.29/0.47 => ( ( tau_Pr257024512list_a @ Sigma @ I )
% 0.29/0.47 = ( tau_Pr257024512list_a @ Sigma @ J ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_\<tau>_less
% 0.29/0.47 thf(fact_241__092_060tau_062__prefix__conv,axiom,
% 0.29/0.47 ! [P5: prefix1027212443list_a,S: trace_1367752404list_a,S2: trace_1367752404list_a,I: nat] :
% 0.29/0.47 ( ( prefix1041802747list_a @ P5 @ S )
% 0.29/0.47 => ( ( prefix1041802747list_a @ P5 @ S2 )
% 0.29/0.47 => ( ( ord_less_nat @ I @ ( plen_P694648887list_a @ P5 ) )
% 0.29/0.47 => ( ( tau_Pr257024512list_a @ S @ I )
% 0.29/0.47 = ( tau_Pr257024512list_a @ S2 @ I ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % \<tau>_prefix_conv
% 0.29/0.47 thf(fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.48 ~ ! [J3: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ J3 ) )
% 0.29/0.48 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.29/0.48 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j; j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.48 thf(fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.48 ~ ! [J3: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ J3 ) )
% 0.29/0.48 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.29/0.48 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j; j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.48 thf(fact_244_add__less__cancel__right,axiom,
% 0.29/0.48 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.29/0.48 = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_less_cancel_right
% 0.29/0.48 thf(fact_245_add__left__cancel,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.48 = ( plus_plus_nat @ A @ C2 ) )
% 0.29/0.48 = ( B = C2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_left_cancel
% 0.29/0.48 thf(fact_246_add__right__cancel,axiom,
% 0.29/0.48 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.48 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.48 = ( plus_plus_nat @ C2 @ A ) )
% 0.29/0.48 = ( B = C2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_right_cancel
% 0.29/0.48 thf(fact_247_add__le__cancel__left,axiom,
% 0.29/0.48 ! [C2: nat,A: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.29/0.48 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_le_cancel_left
% 0.29/0.48 thf(fact_248_add__le__cancel__right,axiom,
% 0.29/0.48 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.29/0.48 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_le_cancel_right
% 0.29/0.48 thf(fact_249_add__less__cancel__left,axiom,
% 0.29/0.48 ! [C2: nat,A: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.29/0.48 = ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_less_cancel_left
% 0.29/0.48 thf(fact_250_one__reorient,axiom,
% 0.29/0.48 ! [X: nat] :
% 0.29/0.48 ( ( one_one_nat = X )
% 0.29/0.48 = ( X = one_one_nat ) ) ).
% 0.29/0.48
% 0.29/0.48 % one_reorient
% 0.29/0.48 thf(fact_251_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.29/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.48 thf(fact_252_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( I = J )
% 0.29/0.48 & ( K = L ) )
% 0.29/0.48 => ( ( plus_plus_nat @ I @ K )
% 0.29/0.48 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_semiring(4)
% 0.29/0.48 thf(fact_253_group__cancel_Oadd1,axiom,
% 0.29/0.48 ! [A5: nat,K: nat,A: nat,B: nat] :
% 0.29/0.48 ( ( A5
% 0.29/0.48 = ( plus_plus_nat @ K @ A ) )
% 0.29/0.48 => ( ( plus_plus_nat @ A5 @ B )
% 0.29/0.48 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % group_cancel.add1
% 0.29/0.48 thf(fact_254_group__cancel_Oadd2,axiom,
% 0.29/0.48 ! [B5: nat,K: nat,B: nat,A: nat] :
% 0.29/0.48 ( ( B5
% 0.29/0.48 = ( plus_plus_nat @ K @ B ) )
% 0.29/0.48 => ( ( plus_plus_nat @ A @ B5 )
% 0.29/0.48 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % group_cancel.add2
% 0.29/0.48 thf(fact_255_add_Oassoc,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.29/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add.assoc
% 0.29/0.48 thf(fact_256_add_Ocommute,axiom,
% 0.29/0.48 ( plus_plus_nat
% 0.29/0.48 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add.commute
% 0.29/0.48 thf(fact_257_add_Oleft__commute,axiom,
% 0.29/0.48 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.48 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 0.29/0.48 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add.left_commute
% 0.29/0.48 thf(fact_258_add__left__imp__eq,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.48 = ( plus_plus_nat @ A @ C2 ) )
% 0.29/0.48 => ( B = C2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_left_imp_eq
% 0.29/0.48 thf(fact_259_add__right__imp__eq,axiom,
% 0.29/0.48 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.48 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.48 = ( plus_plus_nat @ C2 @ A ) )
% 0.29/0.48 => ( B = C2 ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_right_imp_eq
% 0.29/0.48 thf(fact_260_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.48 & ( K = L ) )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_semiring(3)
% 0.29/0.48 thf(fact_261_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( I = J )
% 0.29/0.48 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_semiring(2)
% 0.29/0.48 thf(fact_262_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.48 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_semiring(1)
% 0.29/0.48 thf(fact_263_add__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.48 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono
% 0.29/0.48 thf(fact_264_add__left__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_left_mono
% 0.29/0.48 thf(fact_265_less__eqE,axiom,
% 0.29/0.48 ! [A: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.48 => ~ ! [C: nat] :
% 0.29/0.48 ( B
% 0.29/0.48 != ( plus_plus_nat @ A @ C ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % less_eqE
% 0.29/0.48 thf(fact_266_add__right__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.48 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_right_mono
% 0.29/0.48 thf(fact_267_le__iff__add,axiom,
% 0.29/0.48 ( ord_less_eq_nat
% 0.29/0.48 = ( ^ [A2: nat,B2: nat] :
% 0.29/0.48 ? [C3: nat] :
% 0.29/0.48 ( B2
% 0.29/0.48 = ( plus_plus_nat @ A2 @ C3 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % le_iff_add
% 0.29/0.48 thf(fact_268_add__le__imp__le__left,axiom,
% 0.29/0.48 ! [C2: nat,A: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.29/0.48 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_le_imp_le_left
% 0.29/0.48 thf(fact_269_add__le__imp__le__right,axiom,
% 0.29/0.48 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.29/0.48 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_le_imp_le_right
% 0.29/0.48 thf(fact_270_add__mono__thms__linordered__field_I5_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.48 & ( ord_less_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_field(5)
% 0.29/0.48 thf(fact_271_add__mono__thms__linordered__field_I2_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( I = J )
% 0.29/0.48 & ( ord_less_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_field(2)
% 0.29/0.48 thf(fact_272_add__mono__thms__linordered__field_I1_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.48 & ( K = L ) )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_field(1)
% 0.29/0.48 thf(fact_273_add__strict__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A @ B )
% 0.29/0.48 => ( ( ord_less_nat @ C2 @ D2 )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_strict_mono
% 0.29/0.48 thf(fact_274_add__strict__left__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A @ B )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_strict_left_mono
% 0.29/0.48 thf(fact_275_add__strict__right__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A @ B )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_strict_right_mono
% 0.29/0.48 thf(fact_276_add__less__imp__less__left,axiom,
% 0.29/0.48 ! [C2: nat,A: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.29/0.48 => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_less_imp_less_left
% 0.29/0.48 thf(fact_277_add__less__imp__less__right,axiom,
% 0.29/0.48 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.48 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.29/0.48 => ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_less_imp_less_right
% 0.29/0.48 thf(fact_278_add__less__le__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.29/0.48 ( ( ord_less_nat @ A @ B )
% 0.29/0.48 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_less_le_mono
% 0.29/0.48 thf(fact_279_add__le__less__mono,axiom,
% 0.29/0.48 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.29/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.48 => ( ( ord_less_nat @ C2 @ D2 )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_le_less_mono
% 0.29/0.48 thf(fact_280_add__mono__thms__linordered__field_I3_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_nat @ I @ J )
% 0.29/0.48 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_field(3)
% 0.29/0.48 thf(fact_281_add__mono__thms__linordered__field_I4_J,axiom,
% 0.29/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.48 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.48 & ( ord_less_nat @ K @ L ) )
% 0.29/0.48 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % add_mono_thms_linordered_field(4)
% 0.29/0.48 thf(fact_282_discrete,axiom,
% 0.29/0.48 ( ord_less_nat
% 0.29/0.48 = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 0.29/0.48
% 0.29/0.48 % discrete
% 0.29/0.48
% 0.29/0.48 % Conjectures (1)
% 0.29/0.48 thf(conj_0,conjecture,
% 0.29/0.48 ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ).
% 0.29/0.48
% 0.29/0.48 %------------------------------------------------------------------------------
% 0.29/0.48 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:27:09 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2DTF22906.p
% See solution above
% 0.31/1.50 ------------------------
% 0.31/1.54 ---- Cleaned THF ---
% 0.31/1.54 thf(ty_n_t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.31/1.54 prefix1027212443list_a: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_n_t__Trace__Otrace_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.31/1.54 trace_1367752404list_a: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_n_t__Interval__O__092__060I__062,type,
% 0.31/1.54 i: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 0.31/1.54 formula_a: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.31/1.54 list_a: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_n_t__Nat__Onat,type,
% 0.31/1.54 nat: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.31/1.54 one_one_nat: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.31/1.54 plus_plus_nat: nat > nat > nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_MFOTL_Oformula_OUntil_001tf__a,type,
% 0.31/1.54 until_a: formula_a > i > formula_a > formula_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_MFOTL_Osat_001tf__a,type,
% 0.31/1.54 sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Monitor__Mirabelle__prbptmgypa_Oprogress_001tf__a,type,
% 0.31/1.54 monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.31/1.54 ord_less_nat: nat > nat > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.31/1.54 ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.31/1.54 ord_less_eq_nat: nat > nat > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.31/1.54 ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Trace_O_092_060tau_062_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.31/1.54 tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Trace_Oplen_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.31/1.54 plen_P694648887list_a: prefix1027212443list_a > nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Trace_Oprefix__of_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.31/1.54 prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_I____,type,
% 0.31/1.54 i2: i ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060phi_062,type,
% 0.31/1.54 phi: formula_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060phi_0621____,type,
% 0.31/1.54 phi_1: formula_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060phi_0622____,type,
% 0.31/1.54 phi_2: formula_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060pi_062,type,
% 0.31/1.54 pi: prefix1027212443list_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060sigma_062,type,
% 0.31/1.54 sigma: trace_1367752404list_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v__092_060sigma_062_H,type,
% 0.31/1.54 sigma2: trace_1367752404list_a ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_b____,type,
% 0.31/1.54 b: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_i,type,
% 0.31/1.54 i3: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_ia____,type,
% 0.31/1.54 ia: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_j____,type,
% 0.31/1.54 j: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_ja____,type,
% 0.31/1.54 ja: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_k____,type,
% 0.31/1.54 k: nat ).
% 0.31/1.54
% 0.31/1.54 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.54 ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_1_assms_I3_J,axiom,
% 0.31/1.54 ord_less_nat @ i3 @ ( monito1457594016ress_a @ sigma @ phi @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_2_assms_I1_J,axiom,
% 0.31/1.54 prefix1041802747list_a @ pi @ sigma ).
% 0.31/1.54
% 0.31/1.54 thf(fact_3_nat__neq__iff,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( M != N )
% 0.31/1.54 = ( ( ord_less_nat @ M @ N )
% 0.31/1.54 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_4_less__not__refl,axiom,
% 0.31/1.54 ! [N: nat] :
% 0.31/1.54 ~ ( ord_less_nat @ N @ N ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_5_less__not__refl2,axiom,
% 0.31/1.54 ! [N: nat,M: nat] :
% 0.31/1.54 ( ( ord_less_nat @ N @ M )
% 0.31/1.54 => ( M != N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_6_less__not__refl3,axiom,
% 0.31/1.54 ! [S: nat,T: nat] :
% 0.31/1.54 ( ( ord_less_nat @ S @ T )
% 0.31/1.54 => ( S != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_7_less__irrefl__nat,axiom,
% 0.31/1.54 ! [N: nat] :
% 0.31/1.54 ~ ( ord_less_nat @ N @ N ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_8_nat__less__induct,axiom,
% 0.31/1.54 ! [P: nat > $o,N: nat] :
% 0.31/1.54 ( ! [N2: nat] :
% 0.31/1.54 ( ! [M2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/1.54 => ( P @ M2 ) )
% 0.31/1.54 => ( P @ N2 ) )
% 0.31/1.54 => ( P @ N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_9_infinite__descent,axiom,
% 0.31/1.54 ! [P: nat > $o,N: nat] :
% 0.31/1.54 ( ! [N2: nat] :
% 0.31/1.54 ( ~ ( P @ N2 )
% 0.31/1.54 => ? [M2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ M2 @ N2 )
% 0.31/1.54 & ~ ( P @ M2 ) ) )
% 0.31/1.54 => ( P @ N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_10_linorder__neqE__nat,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( X != Y )
% 0.31/1.54 => ( ~ ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.54 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_12_assms_I2_J,axiom,
% 0.31/1.54 prefix1041802747list_a @ pi @ sigma2 ).
% 0.31/1.54
% 0.31/1.54 thf(fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.54 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_14_le__refl,axiom,
% 0.31/1.54 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_15_le__trans,axiom,
% 0.31/1.54 ! [I: nat,J: nat,K: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.54 => ( ( ord_less_eq_nat @ J @ K )
% 0.31/1.54 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_16_eq__imp__le,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( M = N )
% 0.31/1.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_17_le__antisym,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ M @ N )
% 0.31/1.54 => ( ( ord_less_eq_nat @ N @ M )
% 0.31/1.54 => ( M = N ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_18_nat__le__linear,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ M @ N )
% 0.31/1.54 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_19_Nat_Oex__has__greatest__nat,axiom,
% 0.31/1.54 ! [P: nat > $o,K: nat,B: nat] :
% 0.31/1.54 ( ( P @ K )
% 0.31/1.54 => ( ! [Y2: nat] :
% 0.31/1.54 ( ( P @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.31/1.54 => ? [X2: nat] :
% 0.31/1.54 ( ( P @ X2 )
% 0.31/1.54 & ! [Y3: nat] :
% 0.31/1.54 ( ( P @ Y3 )
% 0.31/1.54 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_20_progress__le,axiom,
% 0.31/1.54 ! [Sigma: trace_1367752404list_a,Phi: formula_a,J: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ J ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_21_progress__mono,axiom,
% 0.31/1.54 ! [J: nat,J2: nat,Sigma: trace_1367752404list_a,Phi: formula_a] :
% 0.31/1.54 ( ( ord_less_eq_nat @ J @ J2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ ( monito1457594016ress_a @ Sigma @ Phi @ J2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_22_pinf_I6_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_23_pinf_I8_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_24_minf_I6_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_25_minf_I8_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_26_less__mono__imp__le__mono,axiom,
% 0.31/1.54 ! [F: nat > nat,I: nat,J: nat] :
% 0.31/1.54 ( ! [I2: nat,J3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ I2 @ J3 )
% 0.31/1.54 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J3 ) ) )
% 0.31/1.54 => ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_27_le__neq__implies__less,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ M @ N )
% 0.31/1.54 => ( ( M != N )
% 0.31/1.54 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_28_less__or__eq__imp__le,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( ( ord_less_nat @ M @ N )
% 0.31/1.54 | ( M = N ) )
% 0.31/1.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_29_le__eq__less__or__eq,axiom,
% 0.31/1.54 ( ord_less_eq_nat
% 0.31/1.54 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ M3 @ N3 )
% 0.31/1.54 | ( M3 = N3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_30_less__imp__le__nat,axiom,
% 0.31/1.54 ! [M: nat,N: nat] :
% 0.31/1.54 ( ( ord_less_nat @ M @ N )
% 0.31/1.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_31_nat__less__le,axiom,
% 0.31/1.54 ( ord_less_nat
% 0.31/1.54 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.31/1.54 & ( M3 != N3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_32_progress__prefix__conv,axiom,
% 0.31/1.54 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.31/1.54 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.31/1.54 => ( ( prefix1041802747list_a @ Pi @ Sigma2 )
% 0.31/1.54 => ( ( monito1457594016ress_a @ Sigma @ Phi @ ( plen_P694648887list_a @ Pi ) )
% 0.31/1.54 = ( monito1457594016ress_a @ Sigma2 @ Phi @ ( plen_P694648887list_a @ Pi ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_33_pinf_I1_J,axiom,
% 0.31/1.54 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.31/1.54 ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z2 @ X2 )
% 0.31/1.54 => ( ( P @ X2 )
% 0.31/1.54 = ( P2 @ X2 ) ) )
% 0.31/1.54 => ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z2 @ X2 )
% 0.31/1.54 => ( ( Q @ X2 )
% 0.31/1.54 = ( Q2 @ X2 ) ) )
% 0.31/1.54 => ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( ( ( P @ X3 )
% 0.31/1.54 & ( Q @ X3 ) )
% 0.31/1.54 = ( ( P2 @ X3 )
% 0.31/1.54 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_34_pinf_I2_J,axiom,
% 0.31/1.54 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.31/1.54 ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z2 @ X2 )
% 0.31/1.54 => ( ( P @ X2 )
% 0.31/1.54 = ( P2 @ X2 ) ) )
% 0.31/1.54 => ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z2 @ X2 )
% 0.31/1.54 => ( ( Q @ X2 )
% 0.31/1.54 = ( Q2 @ X2 ) ) )
% 0.31/1.54 => ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( ( ( P @ X3 )
% 0.31/1.54 | ( Q @ X3 ) )
% 0.31/1.54 = ( ( P2 @ X3 )
% 0.31/1.54 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_35_pinf_I3_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( X3 != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_36_pinf_I4_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( X3 != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_37_pinf_I5_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ~ ( ord_less_nat @ X3 @ T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_38_pinf_I7_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Z @ X3 )
% 0.31/1.54 => ( ord_less_nat @ T @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_39_minf_I1_J,axiom,
% 0.31/1.54 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.31/1.54 ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Z2 )
% 0.31/1.54 => ( ( P @ X2 )
% 0.31/1.54 = ( P2 @ X2 ) ) )
% 0.31/1.54 => ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Z2 )
% 0.31/1.54 => ( ( Q @ X2 )
% 0.31/1.54 = ( Q2 @ X2 ) ) )
% 0.31/1.54 => ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( ( ( P @ X3 )
% 0.31/1.54 & ( Q @ X3 ) )
% 0.31/1.54 = ( ( P2 @ X3 )
% 0.31/1.54 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_40_minf_I2_J,axiom,
% 0.31/1.54 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.31/1.54 ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Z2 )
% 0.31/1.54 => ( ( P @ X2 )
% 0.31/1.54 = ( P2 @ X2 ) ) )
% 0.31/1.54 => ( ? [Z2: nat] :
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Z2 )
% 0.31/1.54 => ( ( Q @ X2 )
% 0.31/1.54 = ( Q2 @ X2 ) ) )
% 0.31/1.54 => ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( ( ( P @ X3 )
% 0.31/1.54 | ( Q @ X3 ) )
% 0.31/1.54 = ( ( P2 @ X3 )
% 0.31/1.54 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_41_minf_I3_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( X3 != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_42_minf_I4_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( X3 != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_43_minf_I5_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ( ord_less_nat @ X3 @ T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_44_minf_I7_J,axiom,
% 0.31/1.54 ! [T: nat] :
% 0.31/1.54 ? [Z: nat] :
% 0.31/1.54 ! [X3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X3 @ Z )
% 0.31/1.54 => ~ ( ord_less_nat @ T @ X3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.54 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_46_order__refl,axiom,
% 0.31/1.54 ! [X: prefix1027212443list_a] : ( ord_le699472955list_a @ X @ X ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_47_order__refl,axiom,
% 0.31/1.54 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_48_Until_OIH_I1_J,axiom,
% 0.31/1.54 ! [I: nat,V: list_a] :
% 0.31/1.54 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.31/1.54 => ( ( sat_a @ sigma @ V @ I @ phi_1 )
% 0.31/1.54 = ( sat_a @ sigma2 @ V @ I @ phi_1 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_49_nat__descend__induct,axiom,
% 0.31/1.54 ! [N: nat,P: nat > $o,M: nat] :
% 0.31/1.54 ( ! [K2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ N @ K2 )
% 0.31/1.54 => ( P @ K2 ) )
% 0.31/1.54 => ( ! [K2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ K2 @ N )
% 0.31/1.54 => ( ! [I3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ K2 @ I3 )
% 0.31/1.54 => ( P @ I3 ) )
% 0.31/1.54 => ( P @ K2 ) ) )
% 0.31/1.54 => ( P @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_50_complete__interval,axiom,
% 0.31/1.54 ! [A: nat,B: nat,P: nat > $o] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ( P @ A )
% 0.31/1.54 => ( ~ ( P @ B )
% 0.31/1.54 => ? [C: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ C )
% 0.31/1.54 & ( ord_less_eq_nat @ C @ B )
% 0.31/1.54 & ! [X3: nat] :
% 0.31/1.54 ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.31/1.54 & ( ord_less_nat @ X3 @ C ) )
% 0.31/1.54 => ( P @ X3 ) )
% 0.31/1.54 & ! [D: nat] :
% 0.31/1.54 ( ! [X2: nat] :
% 0.31/1.54 ( ( ( ord_less_eq_nat @ A @ X2 )
% 0.31/1.54 & ( ord_less_nat @ X2 @ D ) )
% 0.31/1.54 => ( P @ X2 ) )
% 0.31/1.54 => ( ord_less_eq_nat @ D @ C ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_51_order_Onot__eq__order__implies__strict,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.31/1.54 ( ( A != B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_52_order_Onot__eq__order__implies__strict,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( A != B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_53_dual__order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le887097159list_a @ B @ A )
% 0.31/1.54 => ( ord_le699472955list_a @ B @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_54_dual__order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [B: nat,A: nat] :
% 0.31/1.54 ( ( ord_less_nat @ B @ A )
% 0.31/1.54 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_55_dual__order_Ostrict__iff__order,axiom,
% 0.31/1.54 ( ord_le887097159list_a
% 0.31/1.54 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.31/1.54 & ( A2 != B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_56_dual__order_Ostrict__iff__order,axiom,
% 0.31/1.54 ( ord_less_nat
% 0.31/1.54 = ( ^ [B2: nat,A2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.31/1.54 & ( A2 != B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_57_dual__order_Oorder__iff__strict,axiom,
% 0.31/1.54 ( ord_le699472955list_a
% 0.31/1.54 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le887097159list_a @ B2 @ A2 )
% 0.31/1.54 | ( A2 = B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_58_dual__order_Oorder__iff__strict,axiom,
% 0.31/1.54 ( ord_less_eq_nat
% 0.31/1.54 = ( ^ [B2: nat,A2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ B2 @ A2 )
% 0.31/1.54 | ( A2 = B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_59_order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le887097159list_a @ A @ B )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ B ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_60_order_Ostrict__implies__order,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.54 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_62_Until_OIH_I2_J,axiom,
% 0.31/1.54 ! [I: nat,V: list_a] :
% 0.31/1.54 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) )
% 0.31/1.54 => ( ( sat_a @ sigma @ V @ I @ phi_2 )
% 0.31/1.54 = ( sat_a @ sigma2 @ V @ I @ phi_2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_63_dual__order_Oantisym,axiom,
% 0.31/1.54 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ B @ A )
% 0.31/1.54 => ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( A = B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_64_dual__order_Oantisym,axiom,
% 0.31/1.54 ! [B: nat,A: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ B @ A )
% 0.31/1.54 => ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( A = B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_65_dual__order_Oeq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.31/1.54 & ( ord_le699472955list_a @ A2 @ B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_66_dual__order_Oeq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [A2: nat,B2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.31/1.54 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_67_dual__order_Otrans,axiom,
% 0.31/1.54 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ B @ A )
% 0.31/1.54 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.31/1.54 => ( ord_le699472955list_a @ C2 @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_68_dual__order_Otrans,axiom,
% 0.31/1.54 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ B @ A )
% 0.31/1.54 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.31/1.54 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_69_linorder__wlog,axiom,
% 0.31/1.54 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.31/1.54 ( ! [A3: nat,B3: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.31/1.54 => ( P @ A3 @ B3 ) )
% 0.31/1.54 => ( ! [A3: nat,B3: nat] :
% 0.31/1.54 ( ( P @ B3 @ A3 )
% 0.31/1.54 => ( P @ A3 @ B3 ) )
% 0.31/1.54 => ( P @ A @ B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_70_dual__order_Orefl,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_71_dual__order_Orefl,axiom,
% 0.31/1.54 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_72_order__trans,axiom,
% 0.31/1.54 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.54 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.31/1.54 => ( ord_le699472955list_a @ X @ Z4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_73_order__trans,axiom,
% 0.31/1.54 ! [X: nat,Y: nat,Z4: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.31/1.54 => ( ord_less_eq_nat @ X @ Z4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_74_order__class_Oorder_Oantisym,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ A )
% 0.31/1.54 => ( A = B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_75_order__class_Oorder_Oantisym,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ A )
% 0.31/1.54 => ( A = B ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_76_ord__le__eq__trans,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( B = C2 )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_77_ord__le__eq__trans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( B = C2 )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_78_ord__eq__le__trans,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( A = B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_79_ord__eq__le__trans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( A = B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_80_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.31/1.54 & ( ord_le699472955list_a @ B2 @ A2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_81_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [A2: nat,B2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.31/1.54 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_82_antisym__conv,axiom,
% 0.31/1.54 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ Y @ X )
% 0.31/1.54 => ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.54 = ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_83_antisym__conv,axiom,
% 0.31/1.54 ! [Y: nat,X: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ Y @ X )
% 0.31/1.54 => ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 = ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_84_le__cases3,axiom,
% 0.31/1.54 ! [X: nat,Y: nat,Z4: nat] :
% 0.31/1.54 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ Y @ Z4 ) )
% 0.31/1.54 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ X @ Z4 ) )
% 0.31/1.54 => ( ( ( ord_less_eq_nat @ X @ Z4 )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ Z4 @ Y ) )
% 0.31/1.54 => ( ( ( ord_less_eq_nat @ Z4 @ Y )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.31/1.54 => ( ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ Z4 @ X ) )
% 0.31/1.54 => ~ ( ( ord_less_eq_nat @ Z4 @ X )
% 0.31/1.54 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_85_order_Otrans,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_86_order_Otrans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_87_le__cases,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_88_eq__refl,axiom,
% 0.31/1.54 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.54 ( ( X = Y )
% 0.31/1.54 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_89_eq__refl,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( X = Y )
% 0.31/1.54 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_90_linear,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_91_antisym,axiom,
% 0.31/1.54 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.54 => ( ( ord_le699472955list_a @ Y @ X )
% 0.31/1.54 => ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_92_antisym,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.54 => ( ( ord_less_eq_nat @ Y @ X )
% 0.31/1.54 => ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_93_eq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.31/1.54 & ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_94_eq__iff,axiom,
% 0.31/1.54 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.31/1.54 = ( ^ [X4: nat,Y5: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.31/1.54 & ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_95_ord__le__eq__subst,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ( F @ B )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_96_ord__le__eq__subst,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ( F @ B )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_97_ord__le__eq__subst,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ( F @ B )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_98_ord__le__eq__subst,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ( F @ B )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_99_ord__eq__le__subst,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.31/1.54 ( ( A
% 0.31/1.54 = ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_100_ord__eq__le__subst,axiom,
% 0.31/1.54 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( A
% 0.31/1.54 = ( F @ B ) )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_101_ord__eq__le__subst,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( A
% 0.31/1.54 = ( F @ B ) )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_102_ord__eq__le__subst,axiom,
% 0.31/1.54 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( A
% 0.31/1.54 = ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_103_order__subst2,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_104_order__subst2,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_105_order__subst2,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.54 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_106_order__subst2,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.54 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_107_order__subst1,axiom,
% 0.31/1.54 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_108_order__subst1,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_109_order__subst1,axiom,
% 0.31/1.54 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.31/1.54 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.54 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.54 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_110_order__subst1,axiom,
% 0.31/1.54 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_111_ord__eq__less__subst,axiom,
% 0.31/1.54 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( A
% 0.31/1.54 = ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_112_ord__less__eq__subst,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ( ( F @ B )
% 0.31/1.54 = C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_113_order__less__subst1,axiom,
% 0.31/1.54 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.31/1.54 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_114_order__less__subst2,axiom,
% 0.31/1.54 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.31/1.54 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.54 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_115_gt__ex,axiom,
% 0.31/1.54 ! [X: nat] :
% 0.31/1.54 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_116_neqE,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( X != Y )
% 0.31/1.54 => ( ~ ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_117_neq__iff,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( X != Y )
% 0.31/1.54 = ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_118_order_Oasym,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_119_less__imp__neq,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( X != Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_120_less__asym,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_121_less__asym_H,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_122_less__trans,axiom,
% 0.31/1.54 ! [X: nat,Y: nat,Z4: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ( ord_less_nat @ Y @ Z4 )
% 0.31/1.54 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_123_less__linear,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 | ( X = Y )
% 0.31/1.54 | ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_124_less__irrefl,axiom,
% 0.31/1.54 ! [X: nat] :
% 0.31/1.54 ~ ( ord_less_nat @ X @ X ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_125_ord__eq__less__trans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( A = B )
% 0.31/1.54 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_126_ord__less__eq__trans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ( B = C2 )
% 0.31/1.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_127_dual__order_Oasym,axiom,
% 0.31/1.54 ! [B: nat,A: nat] :
% 0.31/1.54 ( ( ord_less_nat @ B @ A )
% 0.31/1.54 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_128_less__imp__not__eq,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( X != Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_129_less__not__sym,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_130_less__induct,axiom,
% 0.31/1.54 ! [P: nat > $o,A: nat] :
% 0.31/1.54 ( ! [X2: nat] :
% 0.31/1.54 ( ! [Y3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ Y3 @ X2 )
% 0.31/1.54 => ( P @ Y3 ) )
% 0.31/1.54 => ( P @ X2 ) )
% 0.31/1.54 => ( P @ A ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_131_antisym__conv3,axiom,
% 0.31/1.54 ! [Y: nat,X: nat] :
% 0.31/1.54 ( ~ ( ord_less_nat @ Y @ X )
% 0.31/1.54 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/1.54 = ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_132_less__imp__not__eq2,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( Y != X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_133_less__imp__triv,axiom,
% 0.31/1.54 ! [X: nat,Y: nat,P: $o] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ( ord_less_nat @ Y @ X )
% 0.31/1.54 => P ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_134_linorder__cases,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ( X != Y )
% 0.31/1.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_135_dual__order_Oirrefl,axiom,
% 0.31/1.54 ! [A: nat] :
% 0.31/1.54 ~ ( ord_less_nat @ A @ A ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_136_order_Ostrict__trans,axiom,
% 0.31/1.54 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_137_less__imp__not__less,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_138_exists__least__iff,axiom,
% 0.31/1.54 ( ( ^ [P3: nat > $o] :
% 0.31/1.54 ? [X5: nat] : ( P3 @ X5 ) )
% 0.31/1.54 = ( ^ [P4: nat > $o] :
% 0.31/1.54 ? [N3: nat] :
% 0.31/1.54 ( ( P4 @ N3 )
% 0.31/1.54 & ! [M3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ M3 @ N3 )
% 0.31/1.54 => ~ ( P4 @ M3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_139_linorder__less__wlog,axiom,
% 0.31/1.54 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.31/1.54 ( ! [A3: nat,B3: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A3 @ B3 )
% 0.31/1.54 => ( P @ A3 @ B3 ) )
% 0.31/1.54 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.31/1.54 => ( ! [A3: nat,B3: nat] :
% 0.31/1.54 ( ( P @ B3 @ A3 )
% 0.31/1.54 => ( P @ A3 @ B3 ) )
% 0.31/1.54 => ( P @ A @ B ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_140_dual__order_Ostrict__trans,axiom,
% 0.31/1.54 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.54 ( ( ord_less_nat @ B @ A )
% 0.31/1.54 => ( ( ord_less_nat @ C2 @ B )
% 0.31/1.54 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_141_not__less__iff__gr__or__eq,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/1.54 = ( ( ord_less_nat @ Y @ X )
% 0.31/1.54 | ( X = Y ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_142_order_Ostrict__implies__not__eq,axiom,
% 0.31/1.54 ! [A: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_nat @ A @ B )
% 0.31/1.54 => ( A != B ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_143_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/1.54 ! [B: nat,A: nat] :
% 0.31/1.54 ( ( ord_less_nat @ B @ A )
% 0.31/1.54 => ( A != B ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_144_leD,axiom,
% 0.31/1.54 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ Y @ X )
% 0.31/1.54 => ~ ( ord_le887097159list_a @ X @ Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_145_leD,axiom,
% 0.31/1.54 ! [Y: nat,X: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ Y @ X )
% 0.31/1.54 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_146_leI,axiom,
% 0.31/1.54 ! [X: nat,Y: nat] :
% 0.31/1.54 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/1.54 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_147_le__less,axiom,
% 0.31/1.54 ( ord_le699472955list_a
% 0.31/1.54 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le887097159list_a @ X4 @ Y5 )
% 0.31/1.54 | ( X4 = Y5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_148_le__less,axiom,
% 0.31/1.54 ( ord_less_eq_nat
% 0.31/1.54 = ( ^ [X4: nat,Y5: nat] :
% 0.31/1.54 ( ( ord_less_nat @ X4 @ Y5 )
% 0.31/1.54 | ( X4 = Y5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_149_less__le,axiom,
% 0.31/1.54 ( ord_le887097159list_a
% 0.31/1.54 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.31/1.54 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.31/1.54 & ( X4 != Y5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_150_less__le,axiom,
% 0.31/1.54 ( ord_less_nat
% 0.31/1.54 = ( ^ [X4: nat,Y5: nat] :
% 0.31/1.54 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.31/1.54 & ( X4 != Y5 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_151_order__le__less__subst1,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_152_order__le__less__subst1,axiom,
% 0.31/1.55 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_153_order__le__less__subst2,axiom,
% 0.31/1.55 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_154_order__le__less__subst2,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.55 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_155_order__le__less__subst2,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.55 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_156_order__le__less__subst2,axiom,
% 0.31/1.55 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_157_order__less__le__subst1,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_158_order__less__le__subst1,axiom,
% 0.31/1.55 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_159_order__less__le__subst1,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_160_order__less__le__subst1,axiom,
% 0.31/1.55 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.31/1.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_161_order__less__le__subst2,axiom,
% 0.31/1.55 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_162_order__less__le__subst2,axiom,
% 0.31/1.55 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.31/1.55 => ( ! [X2: nat,Y2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X2 @ Y2 )
% 0.31/1.55 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.31/1.55 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_163_not__le,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.31/1.55 = ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_164_not__less,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/1.55 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_165_le__neq__trans,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.55 => ( ( A != B )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_166_le__neq__trans,axiom,
% 0.31/1.55 ! [A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( A != B )
% 0.31/1.55 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_167_antisym__conv1,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.55 ( ~ ( ord_le887097159list_a @ X @ Y )
% 0.31/1.55 => ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.55 = ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_168_antisym__conv1,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.55 = ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_169_antisym__conv2,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.55 => ( ( ~ ( ord_le887097159list_a @ X @ Y ) )
% 0.31/1.55 = ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_170_antisym__conv2,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.55 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.31/1.55 = ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_171_less__imp__le,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ X @ Y )
% 0.31/1.55 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_172_less__imp__le,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X @ Y )
% 0.31/1.55 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_173_le__less__trans,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.55 => ( ( ord_le887097159list_a @ Y @ Z4 )
% 0.31/1.55 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_174_le__less__trans,axiom,
% 0.31/1.55 ! [X: nat,Y: nat,Z4: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.55 => ( ( ord_less_nat @ Y @ Z4 )
% 0.31/1.55 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_175_less__le__trans,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ X @ Y )
% 0.31/1.55 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.31/1.55 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_176_less__le__trans,axiom,
% 0.31/1.55 ! [X: nat,Y: nat,Z4: nat] :
% 0.31/1.55 ( ( ord_less_nat @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.31/1.55 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_177_le__less__linear,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.55 | ( ord_less_nat @ Y @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_178_le__imp__less__or__eq,axiom,
% 0.31/1.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X @ Y )
% 0.31/1.55 => ( ( ord_le887097159list_a @ X @ Y )
% 0.31/1.55 | ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_179_le__imp__less__or__eq,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.31/1.55 => ( ( ord_less_nat @ X @ Y )
% 0.31/1.55 | ( X = Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_180_less__le__not__le,axiom,
% 0.31/1.55 ( ord_le887097159list_a
% 0.31/1.55 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.31/1.55 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_181_less__le__not__le,axiom,
% 0.31/1.55 ( ord_less_nat
% 0.31/1.55 = ( ^ [X4: nat,Y5: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.31/1.55 & ~ ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_182_not__le__imp__less,axiom,
% 0.31/1.55 ! [Y: nat,X: nat] :
% 0.31/1.55 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.31/1.55 => ( ord_less_nat @ X @ Y ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_183_order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A @ B )
% 0.31/1.55 => ( ( ord_le887097159list_a @ B @ C2 )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_184_order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_nat @ B @ C2 )
% 0.31/1.55 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_185_order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ A @ B )
% 0.31/1.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.31/1.55 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_186_order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.31/1.55 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_187_order_Oorder__iff__strict,axiom,
% 0.31/1.55 ( ord_le699472955list_a
% 0.31/1.55 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ A2 @ B2 )
% 0.31/1.55 | ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_188_order_Oorder__iff__strict,axiom,
% 0.31/1.55 ( ord_less_eq_nat
% 0.31/1.55 = ( ^ [A2: nat,B2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A2 @ B2 )
% 0.31/1.55 | ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_189_order_Ostrict__iff__order,axiom,
% 0.31/1.55 ( ord_le887097159list_a
% 0.31/1.55 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.31/1.55 & ( A2 != B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_190_order_Ostrict__iff__order,axiom,
% 0.31/1.55 ( ord_less_nat
% 0.31/1.55 = ( ^ [A2: nat,B2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.31/1.55 & ( A2 != B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_191_dual__order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ B @ A )
% 0.31/1.55 => ( ( ord_le887097159list_a @ C2 @ B )
% 0.31/1.55 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_192_dual__order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ B @ A )
% 0.31/1.55 => ( ( ord_less_nat @ C2 @ B )
% 0.31/1.55 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_193_dual__order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le887097159list_a @ B @ A )
% 0.31/1.55 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.31/1.55 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ B @ A )
% 0.31/1.55 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.31/1.55 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_195_Until_Oprems,axiom,
% 0.31/1.55 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_196_plen__mono,axiom,
% 0.31/1.55 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plen_P694648887list_a @ Pi ) @ ( plen_P694648887list_a @ Pi2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_197_verit__comp__simplify1_I3_J,axiom,
% 0.31/1.55 ! [B4: nat,A4: nat] :
% 0.31/1.55 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.31/1.55 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma2 @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_199_less__prefix__def,axiom,
% 0.31/1.55 ( ord_le887097159list_a
% 0.31/1.55 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.31/1.55 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_200_verit__la__disequality,axiom,
% 0.31/1.55 ! [A: nat,B: nat] :
% 0.31/1.55 ( ( A = B )
% 0.31/1.55 | ~ ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_201_verit__comp__simplify1_I1_J,axiom,
% 0.31/1.55 ! [A: nat] :
% 0.31/1.55 ~ ( ord_less_nat @ A @ A ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_202_ex__prefix__of,axiom,
% 0.31/1.55 ! [P5: prefix1027212443list_a] :
% 0.31/1.55 ? [X_1: trace_1367752404list_a] : ( prefix1041802747list_a @ P5 @ X_1 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_203_prefix__of__antimono,axiom,
% 0.31/1.55 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a,S: trace_1367752404list_a] :
% 0.31/1.55 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.31/1.55 => ( ( prefix1041802747list_a @ Pi2 @ S )
% 0.31/1.55 => ( prefix1041802747list_a @ Pi @ S ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_204_prefix__of__imp__linear,axiom,
% 0.31/1.55 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Pi2: prefix1027212443list_a] :
% 0.31/1.55 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.31/1.55 => ( ( prefix1041802747list_a @ Pi2 @ Sigma )
% 0.31/1.55 => ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.31/1.55 | ( ord_le699472955list_a @ Pi2 @ Pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_205_formula_Oinject_I9_J,axiom,
% 0.31/1.55 ! [X91: formula_a,X92: i,X93: formula_a,Y91: formula_a,Y92: i,Y93: formula_a] :
% 0.31/1.55 ( ( ( until_a @ X91 @ X92 @ X93 )
% 0.31/1.55 = ( until_a @ Y91 @ Y92 @ Y93 ) )
% 0.31/1.55 = ( ( X91 = Y91 )
% 0.31/1.55 & ( X92 = Y92 )
% 0.31/1.55 & ( X93 = Y93 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_206__C21_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_207__C11_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_208_that,axiom,
% 0.31/1.55 ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ k ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_209_nat__add__left__cancel__less,axiom,
% 0.31/1.55 ! [K: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.31/1.55 = ( ord_less_nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_210_nat__add__left__cancel__le,axiom,
% 0.31/1.55 ! [K: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.31/1.55 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_211__C3_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less_nat @ K @ ( plen_P694648887list_a @ pi ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_212__C1_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_213__C2_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062,axiom,
% 0.31/1.55 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ j ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ ja ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_216_less___092_060tau_062D,axiom,
% 0.31/1.55 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.31/1.55 => ( ord_less_nat @ I @ J ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_217_ex__le___092_060tau_062,axiom,
% 0.31/1.55 ! [I: nat,X: nat,S: trace_1367752404list_a] :
% 0.31/1.55 ? [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J3 )
% 0.31/1.55 & ( ord_less_eq_nat @ X @ ( tau_Pr257024512list_a @ S @ J3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_218__092_060tau_062__mono,axiom,
% 0.31/1.55 ! [I: nat,J: nat,S: trace_1367752404list_a] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ S @ I ) @ ( tau_Pr257024512list_a @ S @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_219_less__add__eq__less,axiom,
% 0.31/1.55 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_nat @ K @ L )
% 0.31/1.55 => ( ( ( plus_plus_nat @ M @ L )
% 0.31/1.55 = ( plus_plus_nat @ K @ N ) )
% 0.31/1.55 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_220_trans__less__add2,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_nat @ I @ J )
% 0.31/1.55 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_221_trans__less__add1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_nat @ I @ J )
% 0.31/1.55 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_222_add__less__mono1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less_nat @ I @ J )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_223_not__add__less2,axiom,
% 0.31/1.55 ! [J: nat,I: nat] :
% 0.31/1.55 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_224_not__add__less1,axiom,
% 0.31/1.55 ! [I: nat,J: nat] :
% 0.31/1.55 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_225_add__less__mono,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less_nat @ I @ J )
% 0.31/1.55 => ( ( ord_less_nat @ K @ L )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_226_add__lessD1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.31/1.55 => ( ord_less_nat @ I @ K ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_227_add__leE,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.31/1.55 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.31/1.55 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_228_le__add1,axiom,
% 0.31/1.55 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_229_le__add2,axiom,
% 0.31/1.55 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_230_add__leD1,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.31/1.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_231_add__leD2,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.31/1.55 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_232_le__Suc__ex,axiom,
% 0.31/1.55 ! [K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ K @ L )
% 0.31/1.55 => ? [N2: nat] :
% 0.31/1.55 ( L
% 0.31/1.55 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_233_add__le__mono,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 => ( ( ord_less_eq_nat @ K @ L )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_234_add__le__mono1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_235_trans__le__add1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_236_trans__le__add2,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_237_nat__le__iff__add,axiom,
% 0.31/1.55 ( ord_less_eq_nat
% 0.31/1.55 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.55 ? [K3: nat] :
% 0.31/1.55 ( N3
% 0.31/1.55 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_238_mono__nat__linear__lb,axiom,
% 0.31/1.55 ! [F: nat > nat,M: nat,K: nat] :
% 0.31/1.55 ( ! [M4: nat,N2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ M4 @ N2 )
% 0.31/1.55 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_239_progress__time__conv,axiom,
% 0.31/1.55 ! [J: nat,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.31/1.55 ( ! [I2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ I2 @ J )
% 0.31/1.55 => ( ( tau_Pr257024512list_a @ Sigma @ I2 )
% 0.31/1.55 = ( tau_Pr257024512list_a @ Sigma2 @ I2 ) ) )
% 0.31/1.55 => ( ( monito1457594016ress_a @ Sigma @ Phi @ J )
% 0.31/1.55 = ( monito1457594016ress_a @ Sigma2 @ Phi @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_240_le___092_060tau_062__less,axiom,
% 0.31/1.55 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.31/1.55 => ( ( ord_less_nat @ J @ I )
% 0.31/1.55 => ( ( tau_Pr257024512list_a @ Sigma @ I )
% 0.31/1.55 = ( tau_Pr257024512list_a @ Sigma @ J ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_241__092_060tau_062__prefix__conv,axiom,
% 0.31/1.55 ! [P5: prefix1027212443list_a,S: trace_1367752404list_a,S2: trace_1367752404list_a,I: nat] :
% 0.31/1.55 ( ( prefix1041802747list_a @ P5 @ S )
% 0.31/1.55 => ( ( prefix1041802747list_a @ P5 @ S2 )
% 0.31/1.55 => ( ( ord_less_nat @ I @ ( plen_P694648887list_a @ P5 ) )
% 0.31/1.55 => ( ( tau_Pr257024512list_a @ S @ I )
% 0.31/1.55 = ( tau_Pr257024512list_a @ S2 @ I ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.31/1.55 ~ ! [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ J3 ) )
% 0.31/1.55 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.31/1.55 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.31/1.55 ~ ! [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ J3 ) )
% 0.31/1.55 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.31/1.55 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_244_add__less__cancel__right,axiom,
% 0.31/1.55 ! [A: nat,C2: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.31/1.55 = ( ord_less_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_245_add__left__cancel,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ( plus_plus_nat @ A @ B )
% 0.31/1.55 = ( plus_plus_nat @ A @ C2 ) )
% 0.31/1.55 = ( B = C2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_246_add__right__cancel,axiom,
% 0.31/1.55 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.55 ( ( ( plus_plus_nat @ B @ A )
% 0.31/1.55 = ( plus_plus_nat @ C2 @ A ) )
% 0.31/1.55 = ( B = C2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_247_add__le__cancel__left,axiom,
% 0.31/1.55 ! [C2: nat,A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.31/1.55 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_248_add__le__cancel__right,axiom,
% 0.31/1.55 ! [A: nat,C2: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.31/1.55 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_249_add__less__cancel__left,axiom,
% 0.31/1.55 ! [C2: nat,A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.31/1.55 = ( ord_less_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_250_one__reorient,axiom,
% 0.31/1.55 ! [X: nat] :
% 0.31/1.55 ( ( one_one_nat = X )
% 0.31/1.55 = ( X = one_one_nat ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_251_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.31/1.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_252_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ( plus_plus_nat @ I @ K )
% 0.31/1.55 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_253_group__cancel_Oadd1,axiom,
% 0.31/1.55 ! [A5: nat,K: nat,A: nat,B: nat] :
% 0.31/1.55 ( ( A5
% 0.31/1.55 = ( plus_plus_nat @ K @ A ) )
% 0.31/1.55 => ( ( plus_plus_nat @ A5 @ B )
% 0.31/1.55 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_254_group__cancel_Oadd2,axiom,
% 0.31/1.55 ! [B5: nat,K: nat,B: nat,A: nat] :
% 0.31/1.55 ( ( B5
% 0.31/1.55 = ( plus_plus_nat @ K @ B ) )
% 0.31/1.55 => ( ( plus_plus_nat @ A @ B5 )
% 0.31/1.55 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_255_add_Oassoc,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.31/1.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_256_add_Ocommute,axiom,
% 0.31/1.55 ( plus_plus_nat
% 0.31/1.55 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_257_add_Oleft__commute,axiom,
% 0.31/1.55 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.55 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 0.31/1.55 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_258_add__left__imp__eq,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ( plus_plus_nat @ A @ B )
% 0.31/1.55 = ( plus_plus_nat @ A @ C2 ) )
% 0.31/1.55 => ( B = C2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_259_add__right__imp__eq,axiom,
% 0.31/1.55 ! [B: nat,A: nat,C2: nat] :
% 0.31/1.55 ( ( ( plus_plus_nat @ B @ A )
% 0.31/1.55 = ( plus_plus_nat @ C2 @ A ) )
% 0.31/1.55 => ( B = C2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_260_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_261_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( ord_less_eq_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_262_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 & ( ord_less_eq_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_263_add__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_264_add__left__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_265_less__eqE,axiom,
% 0.31/1.55 ! [A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ~ ! [C: nat] :
% 0.31/1.55 ( B
% 0.31/1.55 != ( plus_plus_nat @ A @ C ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_266_add__right__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_267_le__iff__add,axiom,
% 0.31/1.55 ( ord_less_eq_nat
% 0.31/1.55 = ( ^ [A2: nat,B2: nat] :
% 0.31/1.55 ? [C3: nat] :
% 0.31/1.55 ( B2
% 0.31/1.55 = ( plus_plus_nat @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_268_add__le__imp__le__left,axiom,
% 0.31/1.55 ! [C2: nat,A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.31/1.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_269_add__le__imp__le__right,axiom,
% 0.31/1.55 ! [A: nat,C2: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.31/1.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_270_add__mono__thms__linordered__field_I5_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_nat @ I @ J )
% 0.31/1.55 & ( ord_less_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_271_add__mono__thms__linordered__field_I2_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( ord_less_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_272_add__mono__thms__linordered__field_I1_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_nat @ I @ J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_273_add__strict__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_nat @ C2 @ D2 )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_274_add__strict__left__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_275_add__strict__right__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_276_add__less__imp__less__left,axiom,
% 0.31/1.55 ! [C2: nat,A: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.31/1.55 => ( ord_less_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_277_add__less__imp__less__right,axiom,
% 0.31/1.55 ! [A: nat,C2: nat,B: nat] :
% 0.31/1.55 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.31/1.55 => ( ord_less_nat @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_278_add__less__le__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.31/1.55 ( ( ord_less_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_279_add__le__less__mono,axiom,
% 0.31/1.55 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.31/1.55 ( ( ord_less_eq_nat @ A @ B )
% 0.31/1.55 => ( ( ord_less_nat @ C2 @ D2 )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_280_add__mono__thms__linordered__field_I3_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_nat @ I @ J )
% 0.31/1.55 & ( ord_less_eq_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_281_add__mono__thms__linordered__field_I4_J,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ( ord_less_eq_nat @ I @ J )
% 0.31/1.55 & ( ord_less_nat @ K @ L ) )
% 0.31/1.55 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_282_discrete,axiom,
% 0.31/1.55 ( ord_less_nat
% 0.31/1.55 = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(conj_0,conjecture,
% 0.31/1.55 ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ).
% 0.31/1.55 ------------------------
% 0.31/1.57 % (23009)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/2Mi)
% 0.31/1.57 % (23008)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_22906 for (2999ds/27Mi)
% 0.31/1.57 % (23011)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_22906 for (2999ds/275Mi)
% 0.31/1.57 % (23007)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_22906 for (2999ds/4Mi)
% 0.31/1.57 % (23009)Instruction limit reached!
% 0.31/1.57 % (23009)------------------------------
% 0.31/1.57 % (23009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (23009)Termination reason: Unknown
% 0.31/1.57 % (23009)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (23009)Memory used [KB]: 1279
% 0.31/1.57 % (23009)Time elapsed: 0.003 s
% 0.31/1.57 % (23009)Instructions burned: 4 (million)
% 0.31/1.57 % (23009)------------------------------
% 0.31/1.57 % (23009)------------------------------
% 0.31/1.58 % (23007)Instruction limit reached!
% 0.31/1.58 % (23007)------------------------------
% 0.31/1.58 % (23007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (23007)Termination reason: Unknown
% 0.31/1.58 % (23007)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (23007)Memory used [KB]: 1407
% 0.31/1.58 % (23007)Time elapsed: 0.003 s
% 0.31/1.58 % (23007)Instructions burned: 5 (million)
% 0.31/1.58 % (23007)------------------------------
% 0.31/1.58 % (23007)------------------------------
% 0.31/1.58 % (23006)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/183Mi)
% 0.31/1.58 % (23010)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_22906 for (2999ds/2Mi)
% 0.31/1.58 % (23012)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/18Mi)
% 0.31/1.58 % (23008)Instruction limit reached!
% 0.31/1.58 % (23008)------------------------------
% 0.31/1.58 % (23008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (23008)Termination reason: Unknown
% 0.31/1.58 % (23008)Termination phase: Property scanning
% 0.31/1.58
% 0.31/1.58 % (23008)Memory used [KB]: 1663
% 0.31/1.58 % (23008)Time elapsed: 0.010 s
% 0.31/1.58 % (23008)Instructions burned: 28 (million)
% 0.31/1.58 % (23008)------------------------------
% 0.31/1.58 % (23008)------------------------------
% 0.31/1.58 % (23010)Instruction limit reached!
% 0.31/1.58 % (23010)------------------------------
% 0.31/1.58 % (23010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (23010)Termination reason: Unknown
% 0.31/1.58 % (23010)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (23010)Memory used [KB]: 1279
% 0.31/1.58 % (23010)Time elapsed: 0.004 s
% 0.31/1.58 % (23010)Instructions burned: 3 (million)
% 0.31/1.58 % (23010)------------------------------
% 0.31/1.58 % (23010)------------------------------
% 0.31/1.58 % (23013)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/3Mi)
% 0.31/1.58 % (23013)Instruction limit reached!
% 0.31/1.58 % (23013)------------------------------
% 0.31/1.58 % (23013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (23013)Termination reason: Unknown
% 0.31/1.58 % (23013)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (23013)Memory used [KB]: 1279
% 0.31/1.58 % (23013)Time elapsed: 0.002 s
% 0.31/1.58 % (23013)Instructions burned: 3 (million)
% 0.31/1.59 % (23013)------------------------------
% 0.31/1.59 % (23013)------------------------------
% 0.31/1.59 % (23014)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_22906 for (2999ds/37Mi)
% 0.31/1.59 % (23015)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_22906 for (2999ds/15Mi)
% 0.31/1.59 % (23012)Instruction limit reached!
% 0.31/1.59 % (23012)------------------------------
% 0.31/1.59 % (23012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (23012)Termination reason: Unknown
% 0.31/1.59 % (23012)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (23012)Memory used [KB]: 1663
% 0.31/1.59 % (23012)Time elapsed: 0.014 s
% 0.31/1.59 % (23012)Instructions burned: 19 (million)
% 0.31/1.59 % (23012)------------------------------
% 0.31/1.59 % (23012)------------------------------
% 0.31/1.60 % (23015)Instruction limit reached!
% 0.31/1.60 % (23015)------------------------------
% 0.31/1.60 % (23015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.60 % (23015)Termination reason: Unknown
% 0.31/1.60 % (23015)Termination phase: shuffling
% 0.31/1.60
% 0.31/1.60 % (23015)Memory used [KB]: 1535
% 0.31/1.60 % (23015)Time elapsed: 0.006 s
% 0.31/1.60 % (23015)Instructions burned: 16 (million)
% 0.31/1.60 % (23015)------------------------------
% 0.31/1.60 % (23015)------------------------------
% 2.76/1.60 % (23014)Instruction limit reached!
% 2.76/1.60 % (23014)------------------------------
% 2.76/1.60 % (23014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.60 % (23014)Termination reason: Unknown
% 2.76/1.60 % (23014)Termination phase: shuffling
% 2.76/1.60
% 2.76/1.60 % (23014)Memory used [KB]: 2046
% 2.76/1.60 % (23014)Time elapsed: 0.013 s
% 2.76/1.60 % (23014)Instructions burned: 39 (million)
% 2.76/1.60 % (23014)------------------------------
% 2.76/1.60 % (23014)------------------------------
% 2.76/1.60 % (23017)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_22906 for (2999ds/1041Mi)
% 2.76/1.60 % (23016)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_22906 for (2999ds/3Mi)
% 2.76/1.60 % (23016)Instruction limit reached!
% 2.76/1.60 % (23016)------------------------------
% 2.76/1.60 % (23016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.60 % (23016)Termination reason: Unknown
% 2.76/1.60 % (23016)Termination phase: shuffling
% 2.76/1.60
% 2.76/1.60 % (23016)Memory used [KB]: 1279
% 2.76/1.60 % (23016)Time elapsed: 0.004 s
% 2.76/1.60 % (23016)Instructions burned: 4 (million)
% 2.76/1.60 % (23016)------------------------------
% 2.76/1.60 % (23016)------------------------------
% 2.76/1.61 % (23019)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/16Mi)
% 2.76/1.61 % (23020)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_22906 for (2999ds/3Mi)
% 2.76/1.61 % (23020)Instruction limit reached!
% 2.76/1.61 % (23020)------------------------------
% 2.76/1.61 % (23020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (23020)Termination reason: Unknown
% 2.76/1.61 % (23020)Termination phase: shuffling
% 2.76/1.61
% 2.76/1.61 % (23020)Memory used [KB]: 1279
% 2.76/1.61 % (23020)Time elapsed: 0.003 s
% 2.76/1.61 % (23020)Instructions burned: 3 (million)
% 2.76/1.61 % (23020)------------------------------
% 2.76/1.61 % (23020)------------------------------
% 2.76/1.61 % (23019)Instruction limit reached!
% 2.76/1.61 % (23019)------------------------------
% 2.76/1.61 % (23019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.61 % (23019)Termination reason: Unknown
% 2.76/1.61 % (23019)Termination phase: shuffling
% 2.76/1.61
% 2.76/1.61 % (23019)Memory used [KB]: 1535
% 2.76/1.61 % (23019)Time elapsed: 0.006 s
% 2.76/1.61 % (23019)Instructions burned: 16 (million)
% 2.76/1.61 % (23019)------------------------------
% 2.76/1.61 % (23019)------------------------------
% 2.76/1.61 % (23018)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/7Mi)
% 2.76/1.62 % (23018)Instruction limit reached!
% 2.76/1.62 % (23018)------------------------------
% 2.76/1.62 % (23018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.62 % (23018)Termination reason: Unknown
% 2.76/1.62 % (23018)Termination phase: shuffling
% 2.76/1.62
% 2.76/1.62 % (23018)Memory used [KB]: 1407
% 2.76/1.62 % (23018)Time elapsed: 0.007 s
% 2.76/1.62 % (23018)Instructions burned: 8 (million)
% 2.76/1.62 % (23018)------------------------------
% 2.76/1.62 % (23018)------------------------------
% 2.76/1.62 % (23021)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/3Mi)
% 2.76/1.62 % (23021)Instruction limit reached!
% 2.76/1.62 % (23021)------------------------------
% 2.76/1.62 % (23021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.62 % (23021)Termination reason: Unknown
% 2.76/1.62 % (23021)Termination phase: shuffling
% 2.76/1.62
% 2.76/1.62 % (23021)Memory used [KB]: 1279
% 2.76/1.62 % (23021)Time elapsed: 0.003 s
% 2.76/1.62 % (23021)Instructions burned: 4 (million)
% 2.76/1.62 % (23021)------------------------------
% 2.76/1.62 % (23021)------------------------------
% 2.76/1.62 % (23022)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/7Mi)
% 2.76/1.62 % (23023)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/3Mi)
% 2.76/1.62 % (23022)Instruction limit reached!
% 2.76/1.62 % (23022)------------------------------
% 2.76/1.62 % (23022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.62 % (23022)Termination reason: Unknown
% 2.76/1.62 % (23023)Instruction limit reached!
% 2.76/1.62 % (23023)------------------------------
% 2.76/1.62 % (23023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.62 % (23022)Termination phase: shuffling
% 2.76/1.62
% 2.76/1.62 % (23022)Memory used [KB]: 1407
% 2.76/1.62 % (23022)Time elapsed: 0.004 s
% 2.76/1.62 % (23022)Instructions burned: 7 (million)
% 2.76/1.62 % (23022)------------------------------
% 2.76/1.62 % (23022)------------------------------
% 2.76/1.62 % (23023)Termination reason: Unknown
% 2.76/1.62 % (23023)Termination phase: shuffling
% 2.76/1.62
% 2.76/1.62 % (23023)Memory used [KB]: 1279
% 2.76/1.62 % (23023)Time elapsed: 0.002 s
% 2.76/1.62 % (23023)Instructions burned: 4 (million)
% 2.76/1.62 % (23023)------------------------------
% 2.76/1.62 % (23023)------------------------------
% 2.76/1.63 % (23025)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/18Mi)
% 2.76/1.63 % (23026)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/710Mi)
% 2.76/1.63 % (23027)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/6Mi)
% 2.76/1.63 % (23027)Instruction limit reached!
% 2.76/1.63 % (23027)------------------------------
% 2.76/1.63 % (23027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.63 % (23027)Termination reason: Unknown
% 2.76/1.63 % (23027)Termination phase: shuffling
% 2.76/1.63
% 2.76/1.63 % (23027)Memory used [KB]: 1407
% 2.76/1.63 % (23027)Time elapsed: 0.003 s
% 2.76/1.63 % (23027)Instructions burned: 6 (million)
% 2.76/1.63 % (23027)------------------------------
% 2.76/1.63 % (23027)------------------------------
% 2.76/1.63 % (23024)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/4Mi)
% 2.76/1.63 % (23025)Instruction limit reached!
% 2.76/1.63 % (23025)------------------------------
% 2.76/1.63 % (23025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.63 % (23025)Termination reason: Unknown
% 2.76/1.63 % (23025)Termination phase: shuffling
% 2.76/1.63
% 2.76/1.63 % (23025)Memory used [KB]: 1535
% 2.76/1.63 % (23025)Time elapsed: 0.008 s
% 2.76/1.63 % (23025)Instructions burned: 18 (million)
% 2.76/1.63 % (23025)------------------------------
% 2.76/1.63 % (23025)------------------------------
% 2.76/1.64 % (23024)Instruction limit reached!
% 2.76/1.64 % (23024)------------------------------
% 2.76/1.64 % (23024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.64 % (23024)Termination reason: Unknown
% 2.76/1.64 % (23024)Termination phase: shuffling
% 2.76/1.64
% 2.76/1.64 % (23024)Memory used [KB]: 1279
% 2.76/1.64 % (23024)Time elapsed: 0.005 s
% 2.76/1.64 % (23024)Instructions burned: 5 (million)
% 2.76/1.64 % (23024)------------------------------
% 2.76/1.64 % (23024)------------------------------
% 2.76/1.64 % (23028)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/902Mi)
% 2.76/1.64 % (23029)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/21Mi)
% 2.76/1.65 % (23029)Instruction limit reached!
% 2.76/1.65 % (23029)------------------------------
% 2.76/1.65 % (23029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (23029)Termination reason: Unknown
% 2.76/1.65 % (23029)Termination phase: shuffling
% 2.76/1.65
% 2.76/1.65 % (23029)Memory used [KB]: 1663
% 2.76/1.65 % (23029)Time elapsed: 0.009 s
% 2.76/1.65 % (23029)Instructions burned: 21 (million)
% 2.76/1.65 % (23029)------------------------------
% 2.76/1.65 % (23029)------------------------------
% 2.76/1.65 % (23030)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/5Mi)
% 2.76/1.65 % (23011)Instruction limit reached!
% 2.76/1.65 % (23011)------------------------------
% 2.76/1.65 % (23011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (23011)Termination reason: Unknown
% 2.76/1.65 % (23011)Termination phase: Saturation
% 2.76/1.65
% 2.76/1.65 % (23011)Memory used [KB]: 7036
% 2.76/1.65 % (23011)Time elapsed: 0.082 s
% 2.76/1.65 % (23011)Instructions burned: 277 (million)
% 2.76/1.65 % (23011)------------------------------
% 2.76/1.65 % (23011)------------------------------
% 2.76/1.65 % (23006)Instruction limit reached!
% 2.76/1.65 % (23006)------------------------------
% 2.76/1.65 % (23006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.65 % (23006)Termination reason: Unknown
% 2.76/1.65 % (23006)Termination phase: Saturation
% 2.76/1.65
% 2.76/1.65 % (23006)Memory used [KB]: 7164
% 2.76/1.65 % (23006)Time elapsed: 0.076 s
% 2.76/1.65 % (23006)Instructions burned: 184 (million)
% 2.76/1.65 % (23006)------------------------------
% 2.76/1.65 % (23006)------------------------------
% 2.76/1.66 % (23030)Instruction limit reached!
% 2.76/1.66 % (23030)------------------------------
% 2.76/1.66 % (23030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.66 % (23030)Termination reason: Unknown
% 2.76/1.66 % (23030)Termination phase: shuffling
% 2.76/1.66
% 2.76/1.66 % (23030)Memory used [KB]: 1407
% 2.76/1.66 % (23030)Time elapsed: 0.005 s
% 2.76/1.66 % (23030)Instructions burned: 6 (million)
% 2.76/1.66 % (23030)------------------------------
% 2.76/1.66 % (23030)------------------------------
% 2.76/1.66 % (23031)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/6Mi)
% 2.76/1.66 % (23032)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/377Mi)
% 2.76/1.66 % (23031)Instruction limit reached!
% 2.76/1.66 % (23031)------------------------------
% 2.76/1.66 % (23031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.66 % (23031)Termination reason: Unknown
% 2.76/1.66 % (23031)Termination phase: shuffling
% 2.76/1.66
% 2.76/1.66 % (23031)Memory used [KB]: 1407
% 2.76/1.66 % (23031)Time elapsed: 0.004 s
% 2.76/1.66 % (23031)Instructions burned: 8 (million)
% 2.76/1.66 % (23031)------------------------------
% 2.76/1.66 % (23031)------------------------------
% 2.76/1.66 % (23033)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/779Mi)
% 2.76/1.67 % (23034)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_22906 for (2999ds/19Mi)
% 2.76/1.67 % (23034)Instruction limit reached!
% 2.76/1.67 % (23034)------------------------------
% 2.76/1.67 % (23034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.67 % (23034)Termination reason: Unknown
% 2.76/1.67 % (23034)Termination phase: shuffling
% 2.76/1.67
% 2.76/1.67 % (23034)Memory used [KB]: 1663
% 2.76/1.67 % (23034)Time elapsed: 0.007 s
% 2.76/1.67 % (23034)Instructions burned: 20 (million)
% 2.76/1.67 % (23034)------------------------------
% 2.76/1.67 % (23034)------------------------------
% 2.76/1.67 % (23035)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22906 for (2998ds/879Mi)
% 2.76/1.68 % (23036)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22906 for (2998ds/17Mi)
% 2.76/1.69 % (23036)Instruction limit reached!
% 2.76/1.69 % (23036)------------------------------
% 2.76/1.69 % (23036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.69 % (23036)Termination reason: Unknown
% 2.76/1.69 % (23036)Termination phase: shuffling
% 2.76/1.69
% 2.76/1.69 % (23036)Memory used [KB]: 1535
% 2.76/1.69 % (23036)Time elapsed: 0.008 s
% 2.76/1.69 % (23036)Instructions burned: 17 (million)
% 2.76/1.69 % (23036)------------------------------
% 2.76/1.69 % (23036)------------------------------
% 2.76/1.70 % (23037)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22906 for (2998ds/3Mi)
% 2.76/1.70 % (23037)Instruction limit reached!
% 2.76/1.70 % (23037)------------------------------
% 2.76/1.70 % (23037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.70 % (23037)Termination reason: Unknown
% 2.76/1.70 % (23037)Termination phase: shuffling
% 2.76/1.70
% 2.76/1.70 % (23037)Memory used [KB]: 1279
% 2.76/1.70 % (23037)Time elapsed: 0.003 s
% 2.76/1.70 % (23037)Instructions burned: 3 (million)
% 2.76/1.70 % (23037)------------------------------
% 2.76/1.70 % (23037)------------------------------
% 2.76/1.71 % (23038)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22906 for (2998ds/30Mi)
% 2.76/1.72 % (23038)Instruction limit reached!
% 2.76/1.72 % (23038)------------------------------
% 2.76/1.72 % (23038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.72 % (23038)Termination reason: Unknown
% 2.76/1.72 % (23038)Termination phase: Property scanning
% 2.76/1.72
% 2.76/1.72 % (23038)Memory used [KB]: 1663
% 2.76/1.72 % (23038)Time elapsed: 0.012 s
% 2.76/1.72 % (23038)Instructions burned: 31 (million)
% 2.76/1.72 % (23038)------------------------------
% 2.76/1.72 % (23038)------------------------------
% 2.76/1.73 % (23039)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22906 for (2998ds/127Mi)
% 2.76/1.77 % (23039)Instruction limit reached!
% 2.76/1.77 % (23039)------------------------------
% 2.76/1.77 % (23039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.77 % (23039)Termination reason: Unknown
% 2.76/1.77 % (23039)Termination phase: Property scanning
% 2.76/1.77
% 2.76/1.77 % (23039)Memory used [KB]: 2174
% 2.76/1.77 % (23039)Time elapsed: 0.039 s
% 2.76/1.77 % (23039)Instructions burned: 128 (million)
% 2.76/1.77 % (23039)------------------------------
% 2.76/1.77 % (23039)------------------------------
% 2.76/1.77 % (23032)Instruction limit reached!
% 2.76/1.77 % (23032)------------------------------
% 2.76/1.77 % (23032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.77 % (23032)Termination reason: Unknown
% 2.76/1.77 % (23032)Termination phase: Saturation
% 2.76/1.77
% 2.76/1.77 % (23032)Memory used [KB]: 7803
% 2.76/1.77 % (23032)Time elapsed: 0.109 s
% 2.76/1.77 % (23032)Instructions burned: 378 (million)
% 2.76/1.77 % (23032)------------------------------
% 2.76/1.77 % (23032)------------------------------
% 2.76/1.78 % (23040)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22906 for (2997ds/100Mi)
% 2.76/1.78 % (23041)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_22906 for (2997ds/3Mi)
% 2.76/1.78 % (23041)Instruction limit reached!
% 2.76/1.78 % (23041)------------------------------
% 2.76/1.78 % (23041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.78 % (23041)Termination reason: Unknown
% 2.76/1.78 % (23041)Termination phase: shuffling
% 2.76/1.78
% 2.76/1.78 % (23041)Memory used [KB]: 1279
% 2.76/1.78 % (23041)Time elapsed: 0.002 s
% 2.76/1.78 % (23041)Instructions burned: 3 (million)
% 2.76/1.78 % (23041)------------------------------
% 2.76/1.78 % (23041)------------------------------
% 2.76/1.79 % (23042)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_22906 for (2997ds/20Mi)
% 2.76/1.80 % (23042)Instruction limit reached!
% 2.76/1.80 % (23042)------------------------------
% 2.76/1.80 % (23042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.80 % (23042)Termination reason: Unknown
% 2.76/1.80 % (23042)Termination phase: Property scanning
% 2.76/1.80
% 2.76/1.80 % (23042)Memory used [KB]: 1663
% 2.76/1.80 % (23042)Time elapsed: 0.008 s
% 2.76/1.80 % (23042)Instructions burned: 21 (million)
% 2.76/1.80 % (23042)------------------------------
% 2.76/1.80 % (23042)------------------------------
% 2.76/1.81 % (23043)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_22906 for (2997ds/86Mi)
% 2.76/1.81 % (23040)Instruction limit reached!
% 2.76/1.81 % (23040)------------------------------
% 2.76/1.81 % (23040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.81 % (23040)Termination reason: Unknown
% 2.76/1.81 % (23040)Termination phase: Function definition elimination
% 2.76/1.81
% 2.76/1.81 % (23040)Memory used [KB]: 2302
% 2.76/1.81 % (23040)Time elapsed: 0.029 s
% 2.76/1.81 % (23040)Instructions burned: 102 (million)
% 2.76/1.81 % (23040)------------------------------
% 2.76/1.81 % (23040)------------------------------
% 2.76/1.81 % (23028)First to succeed.
% 2.76/1.81 % (23028)Refutation found. Thanks to Tanya!
% 2.76/1.81 % SZS status Theorem for DTF2THF_22906
% 2.76/1.81 % SZS output start Proof for DTF2THF_22906
% 2.76/1.81 thf(type_def_5, type, nat: $tType).
% 2.76/1.81 thf(type_def_7, type, formula_a: $tType).
% 2.76/1.81 thf(type_def_8, type, i: $tType).
% 2.76/1.81 thf(type_def_9, type, trace_1367752404list_a: $tType).
% 2.76/1.81 thf(type_def_10, type, list_a: $tType).
% 2.76/1.81 thf(type_def_11, type, prefix1027212443list_a: $tType).
% 2.76/1.81 thf(func_def_0, type, prefix1027212443list_a: $tType).
% 2.76/1.81 thf(func_def_1, type, trace_1367752404list_a: $tType).
% 2.76/1.81 thf(func_def_2, type, i: $tType).
% 2.76/1.81 thf(func_def_3, type, formula_a: $tType).
% 2.76/1.81 thf(func_def_4, type, list_a: $tType).
% 2.76/1.81 thf(func_def_5, type, nat: $tType).
% 2.76/1.81 thf(func_def_6, type, one_one_nat: nat).
% 2.76/1.81 thf(func_def_7, type, plus_plus_nat: nat > nat > nat).
% 2.76/1.81 thf(func_def_8, type, until_a: formula_a > i > formula_a > formula_a).
% 2.76/1.81 thf(func_def_9, type, sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o).
% 2.76/1.81 thf(func_def_10, type, monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat).
% 2.76/1.81 thf(func_def_11, type, ord_less_nat: nat > nat > $o).
% 2.76/1.81 thf(func_def_12, type, ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o).
% 2.76/1.81 thf(func_def_13, type, ord_less_eq_nat: nat > nat > $o).
% 2.76/1.81 thf(func_def_14, type, ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o).
% 2.76/1.81 thf(func_def_15, type, tau_Pr257024512list_a: trace_1367752404list_a > nat > nat).
% 2.76/1.81 thf(func_def_16, type, plen_P694648887list_a: prefix1027212443list_a > nat).
% 2.76/1.81 thf(func_def_17, type, prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o).
% 2.76/1.81 thf(func_def_18, type, i2: i).
% 2.76/1.81 thf(func_def_19, type, phi: formula_a).
% 2.76/1.81 thf(func_def_20, type, phi_1: formula_a).
% 2.76/1.81 thf(func_def_21, type, phi_2: formula_a).
% 2.76/1.81 thf(func_def_22, type, pi: prefix1027212443list_a).
% 2.76/1.81 thf(func_def_23, type, sigma: trace_1367752404list_a).
% 2.76/1.81 thf(func_def_24, type, sigma2: trace_1367752404list_a).
% 2.76/1.81 thf(func_def_25, type, b: nat).
% 2.76/1.81 thf(func_def_26, type, i3: nat).
% 2.76/1.81 thf(func_def_27, type, ia: nat).
% 2.76/1.81 thf(func_def_28, type, j: nat).
% 2.76/1.81 thf(func_def_29, type, ja: nat).
% 2.76/1.81 thf(func_def_30, type, k: nat).
% 2.76/1.81 thf(func_def_45, type, sP0: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 2.76/1.81 thf(func_def_46, type, sP1: nat > nat > nat > $o).
% 2.76/1.81 thf(func_def_47, type, sP2: nat > nat > nat > $o).
% 2.76/1.81 thf(func_def_48, type, sP3: nat > nat > nat > $o).
% 2.76/1.81 thf(func_def_49, type, sP4: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 2.76/1.81 thf(func_def_50, type, sP5: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 2.76/1.81 thf(func_def_51, type, sP6: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 2.76/1.81 thf(func_def_52, type, sK7: nat > nat).
% 2.76/1.81 thf(func_def_53, type, sK8: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_54, type, sK9: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_55, type, sK10: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_56, type, sK11: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_57, type, sK12: nat).
% 2.76/1.81 thf(func_def_58, type, sK13: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_59, type, sK14: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_60, type, sK15: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_61, type, sK16: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_62, type, sK17: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_63, type, sK18: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_64, type, sK19: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_65, type, sK20: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_66, type, sK21: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_67, type, sK22: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_68, type, sK23: nat > nat > nat).
% 2.76/1.81 thf(func_def_69, type, sK24: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_70, type, sK25: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_71, type, sK26: nat > nat).
% 2.76/1.81 thf(func_def_72, type, sK27: (nat > $o) > nat).
% 2.76/1.81 thf(func_def_73, type, sK28: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_74, type, sK29: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_75, type, sK30: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_76, type, sK31: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_77, type, sK32: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_78, type, sK33: (nat > $o) > nat).
% 2.76/1.81 thf(func_def_79, type, sK34: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_80, type, sK35: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_81, type, sK36: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_82, type, sK37: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_83, type, sK38: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_84, type, sK39: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_85, type, sK40: trace_1367752404list_a > nat > trace_1367752404list_a > nat).
% 2.76/1.81 thf(func_def_86, type, sK41: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_87, type, sK42: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_88, type, sK43: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_89, type, sK44: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_90, type, sK45: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_91, type, sK46: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_92, type, sK47: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_93, type, sK48: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_94, type, sK49: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_95, type, sK50: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_96, type, sK51: (nat > nat > $o) > nat).
% 2.76/1.81 thf(func_def_97, type, sK52: nat > trace_1367752404list_a > nat > nat).
% 2.76/1.81 thf(func_def_98, type, sK53: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_99, type, sK54: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_100, type, sK55: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_101, type, sK56: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_102, type, sK57: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_103, type, sK58: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_104, type, sK59: nat > nat).
% 2.76/1.81 thf(func_def_105, type, sK60: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_106, type, sK61: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_107, type, sK62: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_108, type, sK63: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_109, type, sK64: (nat > $o) > nat > nat).
% 2.76/1.81 thf(func_def_110, type, sK65: (nat > $o) > nat > nat).
% 2.76/1.81 thf(func_def_111, type, sK66: nat > nat).
% 2.76/1.81 thf(func_def_112, type, sK67: nat > nat).
% 2.76/1.81 thf(func_def_113, type, sK68: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_114, type, sK69: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_115, type, sK70: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_116, type, sK71: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_117, type, sK72: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_118, type, sK73: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_119, type, sK74: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_120, type, sK75: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_121, type, sK76: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_122, type, sK77: nat > nat).
% 2.76/1.81 thf(func_def_123, type, sK78: nat > nat).
% 2.76/1.81 thf(func_def_124, type, sK79: nat).
% 2.76/1.81 thf(func_def_125, type, sK80: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_126, type, sK81: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_127, type, sK82: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_128, type, sK83: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_129, type, sK84: nat > nat).
% 2.76/1.81 thf(func_def_130, type, sK85: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_131, type, sK86: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_132, type, sK87: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_133, type, sK88: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_134, type, sK89: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_135, type, sK90: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_136, type, sK91: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_137, type, sK92: prefix1027212443list_a > trace_1367752404list_a).
% 2.76/1.81 thf(func_def_138, type, sK93: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_139, type, sK94: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_140, type, sK95: nat > (nat > $o) > (nat > $o) > nat).
% 2.76/1.81 thf(func_def_141, type, sK96: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_142, type, sK97: (nat > prefix1027212443list_a) > nat).
% 2.76/1.81 thf(func_def_143, type, sK98: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_144, type, sK99: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_145, type, sK100: nat > nat).
% 2.76/1.81 thf(func_def_146, type, sK101: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_147, type, sK102: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_148, type, sK103: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_149, type, sK104: (nat > nat) > nat).
% 2.76/1.81 thf(func_def_150, type, sK105: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_151, type, sK106: (prefix1027212443list_a > prefix1027212443list_a) > prefix1027212443list_a).
% 2.76/1.81 thf(func_def_152, type, sK107: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.82 thf(func_def_153, type, sK108: (prefix1027212443list_a > nat) > prefix1027212443list_a).
% 2.76/1.82 thf(func_def_154, type, sK109: (nat > nat) > nat).
% 2.76/1.82 thf(func_def_155, type, sK110: (nat > nat) > nat).
% 2.76/1.82 thf(func_def_156, type, sK111: nat > nat).
% 2.76/1.82 thf(func_def_157, type, sK112: (nat > prefix1027212443list_a) > nat).
% 2.76/1.82 thf(func_def_158, type, sK113: (nat > prefix1027212443list_a) > nat).
% 2.76/1.82 thf(func_def_159, type, sK114: nat > nat).
% 2.76/1.82 thf(func_def_160, type, sK115: (nat > prefix1027212443list_a) > nat).
% 2.76/1.82 thf(func_def_161, type, sK116: (nat > prefix1027212443list_a) > nat).
% 2.76/1.82 thf(func_def_162, type, sK117: nat > nat).
% 2.76/1.82 thf(func_def_163, type, sK118: nat > (nat > $o) > nat > nat).
% 2.76/1.82 thf(func_def_164, type, sK119: nat > nat > (nat > $o) > nat).
% 2.76/1.82 thf(func_def_165, type, sK120: (nat > $o) > nat > nat).
% 2.76/1.82 thf(func_def_166, type, sK121: (nat > $o) > nat).
% 2.76/1.82 thf(func_def_167, type, sK122: nat > nat).
% 2.76/1.82 thf(func_def_168, type, sK123: (nat > $o) > nat).
% 2.76/1.82 thf(func_def_169, type, sK124: nat > nat > nat).
% 2.76/1.82 thf(func_def_171, type, ph126: !>[X0: $tType]:(X0)).
% 2.76/1.82 thf(f6951,plain,(
% 2.76/1.82 $false),
% 2.76/1.82 inference(trivial_inequality_removal,[status(thm)],[f6924])).
% 2.76/1.82 thf(f6924,plain,(
% 2.76/1.82 ($true != $true)),
% 2.76/1.82 inference(superposition,[status(thm)],[f2110,f1604])).
% 2.76/1.82 thf(f1604,plain,(
% 2.76/1.82 ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) = $true)),
% 2.76/1.82 inference(cnf_transformation,[status(thm)],[f680])).
% 2.76/1.82 thf(f680,plain,(
% 2.76/1.82 ((ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi))) = $true)),
% 2.76/1.82 inference(fool_elimination,[status(thm)],[f679])).
% 2.76/1.82 thf(f679,plain,(
% 2.76/1.82 (ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),
% 2.76/1.82 inference(rectify,[status(thm)],[f1])).
% 2.76/1.82 thf(f1,axiom,(
% 2.76/1.82 (ord_less_nat @ k @ (monito1457594016ress_a @ sigma @ phi_1 @ (plen_P694648887list_a @ pi)))),
% 2.76/1.82 file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)).
% 2.76/1.82 thf(f2110,plain,(
% 2.76/1.82 ( ! [X0 : trace_1367752404list_a,X1 : formula_a] : (((ord_less_nat @ k @ (monito1457594016ress_a @ X0 @ X1 @ (plen_P694648887list_a @ pi))) != $true)) )),
% 2.76/1.82 inference(trivial_inequality_removal,[status(thm)],[f2104])).
% 2.76/1.82 thf(f2104,plain,(
% 2.76/1.82 ( ! [X0 : trace_1367752404list_a,X1 : formula_a] : (((ord_less_nat @ k @ (monito1457594016ress_a @ X0 @ X1 @ (plen_P694648887list_a @ pi))) != $true) | ($true != $true)) )),
% 2.76/1.82 inference(superposition,[status(thm)],[f1913,f1462])).
% 2.76/1.82 thf(f1462,plain,(
% 2.76/1.82 ( ! [X2 : nat,X0 : trace_1367752404list_a,X1 : formula_a] : (((ord_less_eq_nat @ (monito1457594016ress_a @ X0 @ X1 @ X2) @ X2) = $true)) )),
% 2.76/1.82 inference(cnf_transformation,[status(thm)],[f686])).
% 2.76/1.82 thf(f686,plain,(
% 2.76/1.82 ! [X0 : trace_1367752404list_a,X1 : formula_a,X2 : nat] : ((ord_less_eq_nat @ (monito1457594016ress_a @ X0 @ X1 @ X2) @ X2) = $true)),
% 2.76/1.82 inference(fool_elimination,[status(thm)],[f685])).
% 2.76/1.82 thf(f685,plain,(
% 2.76/1.82 ! [X0 : trace_1367752404list_a,X1 : formula_a,X2 : nat] : (ord_less_eq_nat @ (monito1457594016ress_a @ X0 @ X1 @ X2) @ X2)),
% 2.76/1.82 inference(rectify,[status(thm)],[f21])).
% 2.76/1.82 thf(f21,axiom,(
% 2.76/1.82 ! [X16 : trace_1367752404list_a,X17 : formula_a,X10 : nat] : (ord_less_eq_nat @ (monito1457594016ress_a @ X16 @ X17 @ X10) @ X10)),
% 2.76/1.82 file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_20_progress__le)).
% 2.76/1.82 thf(f1913,plain,(
% 2.76/1.82 ( ! [X0 : nat] : (((ord_less_eq_nat @ X0 @ (plen_P694648887list_a @ pi)) != $true) | ((ord_less_nat @ k @ X0) != $true)) )),
% 2.76/1.82 inference(trivial_inequality_removal,[status(thm)],[f1910])).
% 2.76/1.82 thf(f1910,plain,(
% 2.76/1.82 ( ! [X0 : nat] : (((ord_less_eq_nat @ X0 @ (plen_P694648887list_a @ pi)) != $true) | ((ord_less_nat @ k @ X0) != $true) | ($true != $true)) )),
% 2.76/1.82 inference(superposition,[status(thm)],[f1739,f1807])).
% 2.76/1.82 thf(f1807,plain,(
% 2.76/1.82 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X2) = $true) | ((ord_less_eq_nat @ X1 @ X2) != $true) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 2.76/1.82 inference(cnf_transformation,[status(thm)],[f973])).
% 2.76/1.82 thf(f973,plain,(
% 2.76/1.82 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X0 @ X2) = $true) | ((ord_less_eq_nat @ X1 @ X2) != $true) | ((ord_less_nat @ X0 @ X1) != $true))),
% 2.76/1.82 inference(flattening,[status(thm)],[f972])).
% 2.76/1.82 thf(f972,plain,(
% 2.76/1.82 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less_nat @ X0 @ X2) = $true) | ((ord_less_eq_nat @ X1 @ X2) != $true)) | ((ord_less_nat @ X0 @ X1) != $true))),
% 2.76/1.82 inference(ennf_transformation,[status(thm)],[f782])).
% 2.76/1.82 thf(f782,plain,(
% 2.76/1.82 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less_nat @ X0 @ X1) = $true) => (((ord_less_eq_nat @ X1 @ X2) = $true) => ((ord_less_nat @ X0 @ X2) = $true)))),
% 2.76/1.82 inference(fool_elimination,[status(thm)],[f781])).
% 2.76/1.82 thf(f781,plain,(
% 2.76/1.82 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_nat @ X0 @ X1) => ((ord_less_eq_nat @ X1 @ X2) => (ord_less_nat @ X0 @ X2)))),
% 2.76/1.82 inference(rectify,[status(thm)],[f187])).
% 2.76/1.82 thf(f187,axiom,(
% 2.76/1.82 ! [X35 : nat,X12 : nat,X42 : nat] : ((ord_less_nat @ X35 @ X12) => ((ord_less_eq_nat @ X12 @ X42) => (ord_less_nat @ X35 @ X42)))),
% 2.76/1.82 file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',fact_186_order_Ostrict__trans2)).
% 2.76/1.82 thf(f1739,plain,(
% 2.76/1.82 ((ord_less_nat @ k @ (plen_P694648887list_a @ pi)) != $true)),
% 2.76/1.82 inference(cnf_transformation,[status(thm)],[f879])).
% 2.76/1.82 thf(f879,plain,(
% 2.76/1.82 ((ord_less_nat @ k @ (plen_P694648887list_a @ pi)) != $true)),
% 2.76/1.82 inference(flattening,[status(thm)],[f772])).
% 2.76/1.82 thf(f772,plain,(
% 2.76/1.82 ~((ord_less_nat @ k @ (plen_P694648887list_a @ pi)) = $true)),
% 2.76/1.82 inference(fool_elimination,[status(thm)],[f771])).
% 2.76/1.82 thf(f771,plain,(
% 2.76/1.82 ~(ord_less_nat @ k @ (plen_P694648887list_a @ pi))),
% 2.76/1.82 inference(rectify,[status(thm)],[f285])).
% 2.76/1.82 thf(f285,negated_conjecture,(
% 2.76/1.82 ~(ord_less_nat @ k @ (plen_P694648887list_a @ pi))),
% 2.76/1.82 inference(negated_conjecture,[status(cth)],[f284])).
% 2.76/1.82 thf(f284,conjecture,(
% 2.76/1.82 (ord_less_nat @ k @ (plen_P694648887list_a @ pi))),
% 2.76/1.82 file('/export/starexec/sandbox2/tmp/tmp.ijjgF3LqV1/DTF2THF_22906.p',conj_0)).
% 2.76/1.82 % SZS output end Proof for DTF2THF_22906
% 2.76/1.82 % (23028)------------------------------
% 2.76/1.82 % (23028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.76/1.82 % (23028)Termination reason: Refutation
% 2.76/1.82
% 2.76/1.82 % (23028)Memory used [KB]: 8059
% 2.76/1.82 % (23028)Time elapsed: 0.173 s
% 2.76/1.82 % (23028)Instructions burned: 615 (million)
% 2.76/1.82 % (23028)------------------------------
% 2.76/1.82 % (23028)------------------------------
% 2.76/1.82 % (23005)Success in time 0.253 s
%------------------------------------------------------------------------------