%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP199^1 : 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 : n025.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 08:56:21 AM UTC 2026
% Result : Theorem 9.31s 2.67s
% Output : Refutation 9.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 56 unt; 0 typ; 3 def)
% Number of atoms : 196 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 673 ( 41 ~; 26 |; 0 &; 585 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 19 ( 18 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 219 ( 215 usr; 27 con; 0-7 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 79 ( 26 ^; 53 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
variable: $tType ).
thf(type_def_6,type,
real: $tType ).
thf(type_def_8,type,
set_variable: $tType ).
thf(type_def_9,type,
denotational_interp: $tType ).
thf(type_def_10,type,
char: $tType ).
thf(type_def_11,type,
trm: $tType ).
thf(type_def_12,type,
set_variable_real: $tType ).
thf(type_def_13,type,
nat: $tType ).
thf(type_def_14,type,
set_nat: $tType ).
thf(type_def_15,type,
set_real: $tType ).
thf(type_def_16,type,
option_variable_real: $tType ).
thf(type_def_17,type,
option_trm: $tType ).
thf(type_def_18,type,
option_variable: $tType ).
thf(type_def_19,type,
set_trm: $tType ).
thf(type_def_20,type,
set_op12188086e_real: $tType ).
thf(type_def_21,type,
set_option_trm: $tType ).
thf(type_def_22,type,
set_option_variable: $tType ).
thf(type_def_23,type,
produc1418842292n_game: $tType ).
thf(func_def_0,type,
produc1418842292n_game: $tType ).
thf(func_def_1,type,
set_op12188086e_real: $tType ).
thf(func_def_2,type,
option_variable_real: $tType ).
thf(func_def_3,type,
set_variable_real: $tType ).
thf(func_def_4,type,
set_option_variable: $tType ).
thf(func_def_5,type,
set_option_trm: $tType ).
thf(func_def_6,type,
option_variable: $tType ).
thf(func_def_7,type,
option_trm: $tType ).
thf(func_def_8,type,
denotational_interp: $tType ).
thf(func_def_9,type,
set_variable: $tType ).
thf(func_def_10,type,
set_trm: $tType ).
thf(func_def_11,type,
set_real: $tType ).
thf(func_def_12,type,
set_nat: $tType ).
thf(func_def_13,type,
variable: $tType ).
thf(func_def_14,type,
char: $tType ).
thf(func_def_15,type,
trm: $tType ).
thf(func_def_16,type,
real: $tType ).
thf(func_def_17,type,
nat: $tType ).
thf(func_def_18,type,
statediff: ( variable > real ) > ( variable > real ) > set_variable ).
thf(func_def_19,type,
stateinterpol: ( variable > real ) > ( variable > real ) > set_variable > variable > real ).
thf(func_def_20,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_21,type,
denotational_Vagree: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_22,type,
denotational_repv: ( variable > real ) > variable > real > variable > real ).
thf(func_def_23,type,
denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
thf(func_def_24,type,
denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
thf(func_def_25,type,
uminus_uminus_real: real > real ).
thf(func_def_26,type,
uminus430703407e_real: set_variable_real > set_variable_real ).
thf(func_def_27,type,
uminus1851247844riable: set_variable > set_variable ).
thf(func_def_28,type,
zero_zero_nat: nat ).
thf(func_def_29,type,
zero_zero_real: real ).
thf(func_def_30,type,
zero_zero_set_nat: set_nat ).
thf(func_def_31,type,
zero_zero_set_real: set_real ).
thf(func_def_32,type,
if_real: $o > real > real > real ).
thf(func_def_33,type,
inf_in1556002680e_real: set_variable_real > set_variable_real > set_variable_real ).
thf(func_def_34,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_35,type,
sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
thf(func_def_36,type,
sup_sup_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_37,type,
size_size_variable: variable > nat ).
thf(func_def_38,type,
none_variable_real: option_variable_real ).
thf(func_def_39,type,
none_trm: option_trm ).
thf(func_def_40,type,
none_variable: option_variable ).
thf(func_def_41,type,
some_variable_real: ( variable > real ) > option_variable_real ).
thf(func_def_42,type,
some_trm: trm > option_trm ).
thf(func_def_43,type,
some_variable: variable > option_variable ).
thf(func_def_44,type,
set_op697949218e_real: option_variable_real > set_variable_real ).
thf(func_def_45,type,
set_option_trm2: option_trm > set_trm ).
thf(func_def_46,type,
set_option_variable2: option_variable > set_variable ).
thf(func_def_47,type,
the_variable_real: option_variable_real > variable > real ).
thf(func_def_48,type,
the_trm: option_trm > trm ).
thf(func_def_49,type,
the_variable: option_variable > variable ).
thf(func_def_50,type,
these_variable_real: set_op12188086e_real > set_variable_real ).
thf(func_def_51,type,
these_trm: set_option_trm > set_trm ).
thf(func_def_52,type,
these_variable: set_option_variable > set_variable ).
thf(func_def_53,type,
bot_bo1661475211real_o: ( variable > real ) > $o ).
thf(func_def_54,type,
bot_bot_variable_o: variable > $o ).
thf(func_def_55,type,
bot_bo721182586e_real: set_variable_real ).
thf(func_def_56,type,
bot_bot_set_nat: set_nat ).
thf(func_def_57,type,
bot_bo1411475018e_real: set_op12188086e_real ).
thf(func_def_58,type,
bot_bo946428664on_trm: set_option_trm ).
thf(func_def_59,type,
bot_bo266290559riable: set_option_variable ).
thf(func_def_60,type,
bot_bot_set_real: set_real ).
thf(func_def_61,type,
bot_bot_set_trm: set_trm ).
thf(func_def_62,type,
bot_bot_set_variable: set_variable ).
thf(func_def_63,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_64,type,
ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
thf(func_def_65,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_66,type,
collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
thf(func_def_67,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_68,type,
insert_variable_real: ( variable > real ) > set_variable_real > set_variable_real ).
thf(func_def_69,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_70,type,
insert526581936e_real: option_variable_real > set_op12188086e_real > set_op12188086e_real ).
thf(func_def_71,type,
insert_option_trm: option_trm > set_option_trm > set_option_trm ).
thf(func_def_72,type,
insert1340772453riable: option_variable > set_option_variable > set_option_variable ).
thf(func_def_73,type,
insert_real: real > set_real > set_real ).
thf(func_def_74,type,
insert_trm: trm > set_trm > set_trm ).
thf(func_def_75,type,
insert_variable: variable > set_variable > set_variable ).
thf(func_def_76,type,
is_emp227886046e_real: set_variable_real > $o ).
thf(func_def_77,type,
is_empty_variable: set_variable > $o ).
thf(func_def_78,type,
is_sin524757308e_real: set_variable_real > $o ).
thf(func_def_79,type,
is_sin155454833riable: set_variable > $o ).
thf(func_def_80,type,
the_el1059226619e_real: set_variable_real > variable > real ).
thf(func_def_81,type,
the_elem_variable: set_variable > variable ).
thf(func_def_82,type,
static_FVT: trm > set_variable ).
thf(func_def_83,type,
static_selectlike: set_variable_real > ( variable > real ) > set_variable > set_variable_real ).
thf(func_def_84,type,
times: trm > trm > trm ).
thf(func_def_85,type,
dVar: char > variable ).
thf(func_def_86,type,
rVar: char > variable ).
thf(func_def_87,type,
size_variable: variable > nat ).
thf(func_def_88,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_89,type,
uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
thf(func_def_90,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_91,type,
member_variable_real: ( variable > real ) > set_variable_real > $o ).
thf(func_def_92,type,
member523846807e_real: option_variable_real > set_op12188086e_real > $o ).
thf(func_def_93,type,
member_option_trm: option_trm > set_option_trm > $o ).
thf(func_def_94,type,
member814448204riable: option_variable > set_option_variable > $o ).
thf(func_def_95,type,
member_trm: trm > set_trm > $o ).
thf(func_def_96,type,
member_variable: variable > set_variable > $o ).
thf(func_def_97,type,
f: real > variable > real ).
thf(func_def_98,type,
i: denotational_interp ).
thf(func_def_99,type,
u: set_variable ).
thf(func_def_100,type,
omega: variable > real ).
thf(func_def_101,type,
sigma: produc1418842292n_game ).
thf(func_def_102,type,
theta: trm ).
thf(func_def_103,type,
rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
thf(func_def_104,type,
x: char ).
thf(func_def_120,type,
sP0: ( option_trm > option_trm > $o ) > option_trm > option_trm > $o ).
thf(func_def_121,type,
sP1: option_trm > option_trm > option_trm > $o ).
thf(func_def_122,type,
sK2: char > ( real > variable > real ) > trm > trm > denotational_interp > denotational_interp > variable > real ).
thf(func_def_123,type,
sK3: set_variable > variable ).
thf(func_def_124,type,
sK4: set_variable_real > variable > real ).
thf(func_def_125,type,
sK5: set_variable > variable > set_variable ).
thf(func_def_126,type,
sK6: set_variable_real > set_variable_real > variable > real ).
thf(func_def_127,type,
sK7: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_128,type,
sK8: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_129,type,
sK9: set_variable_real > ( variable > real ) > set_variable_real ).
thf(func_def_130,type,
sK10: set_variable > variable ).
thf(func_def_131,type,
sK11: set_variable > variable ).
thf(func_def_132,type,
sK12: option_trm > trm ).
thf(func_def_133,type,
sK13: set_variable > variable > set_variable ).
thf(func_def_134,type,
sK14: set_variable_real > ( variable > real ) > set_variable_real > set_variable > variable > real ).
thf(func_def_135,type,
sK15: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
thf(func_def_136,type,
sK16: ( variable > $o ) > char ).
thf(func_def_137,type,
sK17: ( variable > $o ) > char ).
thf(func_def_138,type,
sK18: ( trm > $o ) > option_trm > trm ).
thf(func_def_139,type,
sK19: ( option_trm > $o ) > trm ).
thf(func_def_140,type,
sK20: set_variable_real > ( variable > real ) > set_variable > set_variable_real > variable > real ).
thf(func_def_141,type,
sK21: option_trm > option_trm > option_trm > trm ).
thf(func_def_142,type,
sK22: option_trm > option_trm > option_trm > trm ).
thf(func_def_143,type,
sK23: option_trm > trm ).
thf(func_def_144,type,
sK24: ( variable > option_trm > $o ) > variable ).
thf(func_def_145,type,
sK25: ( variable > option_trm > $o ) > trm ).
thf(func_def_146,type,
sK26: ( variable > option_trm > $o ) > variable ).
thf(func_def_147,type,
sK27: variable > char ).
thf(func_def_148,type,
sK28: variable > char ).
thf(func_def_149,type,
sK29: option_trm > trm ).
thf(func_def_150,type,
sK30: set_variable_real > variable > real ).
thf(func_def_151,type,
sK31: set_variable_real > variable > real ).
thf(func_def_152,type,
sK32: set_variable > variable ).
thf(func_def_153,type,
sK33: ( option_trm > $o ) > trm ).
thf(func_def_154,type,
sK34: set_variable_real > ( variable > real ) > set_variable_real ).
thf(func_def_155,type,
sK35: set_variable > set_variable > variable ).
thf(func_def_156,type,
sK36: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_157,type,
sK37: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_158,type,
sK38: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_159,type,
sK39: ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_160,type,
sK40: set_variable_real > variable > real ).
thf(func_def_161,type,
sK41: ( char > option_trm > $o ) > char ).
thf(func_def_162,type,
sK42: ( char > option_trm > $o ) > trm ).
thf(func_def_163,type,
sK43: ( char > option_trm > $o ) > char ).
thf(func_def_165,type,
sK45: set_variable > variable ).
thf(func_def_166,type,
sK46: ( variable > real ) > ( variable > real ) > set_variable > variable ).
thf(func_def_167,type,
sK47: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_168,type,
sK48: set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_169,type,
sK49: set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_170,type,
sK50: set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_171,type,
sK51: set_variable_real > set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_172,type,
sK52: set_variable_real > set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_173,type,
sK53: set_variable > set_variable_real > set_variable_real > ( variable > real ) > variable > real ).
thf(func_def_174,type,
sK54: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_175,type,
sK55: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_176,type,
sK56: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_177,type,
sK57: ( variable > real ) > set_variable > ( variable > real ) > variable ).
thf(func_def_178,type,
sK58: ( variable > real ) > real > variable > variable ).
thf(func_def_179,type,
sK59: variable > variable ).
thf(func_def_180,type,
sK60: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_181,type,
sK61: set_variable_real > variable > real ).
thf(func_def_182,type,
sK62: ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_183,type,
sK63: option_trm > trm ).
thf(func_def_184,type,
sK64: ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_185,type,
sK65: set_variable > variable ).
thf(func_def_186,type,
sK66: ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_187,type,
sK67: set_variable_real > variable > real ).
thf(func_def_188,type,
sK68: ( variable > real ) > set_variable > ( variable > real ) > variable ).
thf(func_def_189,type,
sK69: ( variable > real ) > set_variable > ( variable > real ) > variable ).
thf(func_def_190,type,
sK70: ( variable > $o ) > variable ).
thf(func_def_191,type,
sK71: set_variable_real > variable > real ).
thf(func_def_192,type,
sK72: ( variable > real ) > ( variable > real ) > set_variable > variable ).
thf(func_def_193,type,
sK73: ( variable > real ) > trm > ( variable > real ) > variable ).
thf(func_def_194,type,
sK74: ( variable > real ) > variable > real ).
thf(func_def_195,type,
sK75: ( variable > real ) > variable ).
thf(func_def_196,type,
sK76: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_197,type,
sK77: option_trm > trm ).
thf(func_def_198,type,
sK78: trm > char > denotational_interp > trm > denotational_interp > ( real > variable > real ) > variable ).
thf(func_def_199,type,
sK79: trm > denotational_interp > denotational_interp > ( real > variable > real ) > trm > char > variable > real ).
thf(func_def_200,type,
sK80: char > ( real > variable > real ) > ( variable > real ) > variable ).
thf(func_def_201,type,
sK81: char > ( real > variable > real ) > ( variable > real ) > variable ).
thf(func_def_202,type,
sK82: ( variable > $o ) > variable ).
thf(func_def_203,type,
sK83: set_variable > ( variable > real ) > ( real > variable > real ) > variable ).
thf(func_def_204,type,
sK84: set_variable_real > set_variable_real > ( variable > real ) > ( variable > real ) > set_variable_real ).
thf(func_def_205,type,
sK85: option_trm > trm ).
thf(func_def_206,type,
sK86: ( variable > real ) > set_variable > ( variable > real ) > set_variable > variable ).
thf(func_def_207,type,
sK87: ( variable > real ) > set_variable > ( variable > real ) > set_variable > variable ).
thf(func_def_208,type,
sK88: ( variable > real ) > set_variable > ( variable > real ) > variable ).
thf(func_def_209,type,
sK89: ( variable > real ) > ( variable > real ) > set_variable > variable ).
thf(func_def_210,type,
sK90: ( variable > real ) > ( variable > real ) > set_variable > variable ).
thf(func_def_211,type,
sK91: variable ).
thf(func_def_212,type,
sK92: set_variable > variable ).
thf(func_def_213,type,
sK93: set_variable_real > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_214,type,
sK94: set_variable_real > ( variable > real ) > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_215,type,
sK95: set_variable_real > ( variable > real ) > ( ( variable > real ) > $o ) > variable > real ).
thf(func_def_216,type,
sK96: set_variable_real > variable > real ).
thf(func_def_217,type,
sK97: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_218,type,
sK98: char > ( variable > real ) > ( real > variable > real ) > variable ).
thf(func_def_219,type,
sK99: char > ( variable > real ) > ( real > variable > real ) > variable ).
thf(func_def_220,type,
sK100: char > trm > denotational_interp > ( real > variable > real ) > denotational_interp > trm > variable > real ).
thf(func_def_221,type,
sK101: char > trm > ( real > variable > real ) > denotational_interp > denotational_interp > trm > variable ).
thf(func_def_222,type,
sK102: char > trm > ( real > variable > real ) > denotational_interp > denotational_interp > trm > variable ).
thf(func_def_223,type,
sK103: set_variable > ( variable > $o ) > set_variable > variable ).
thf(func_def_224,type,
sK104: set_variable > ( variable > $o ) > variable ).
thf(func_def_225,type,
sK105: set_variable > ( variable > $o ) > variable ).
thf(func_def_226,type,
sK106: set_variable > ( variable > $o ) > variable ).
thf(func_def_227,type,
sK107: ( ( variable > real ) > $o ) > set_variable_real > variable > real ).
thf(func_def_228,type,
sK108: ( ( variable > real ) > $o ) > set_variable_real > variable > real ).
thf(func_def_229,type,
sK109: ( ( variable > real ) > $o ) > set_variable_real > set_variable_real > variable > real ).
thf(func_def_230,type,
sK110: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_231,type,
sK111: ( variable > real ) > set_variable > ( variable > real ) > variable ).
thf(func_def_232,type,
sK112: set_variable_real > variable > real ).
thf(func_def_233,type,
sK113: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_234,type,
sK114: variable > variable > set_variable > set_variable > set_variable ).
thf(func_def_235,type,
sK115: set_variable > ( variable > real ) > ( variable > real ) > variable ).
thf(func_def_236,type,
sK116: set_variable_real > set_variable > set_variable_real > ( variable > real ) > variable > real ).
thf(func_def_237,type,
sK117: set_variable > variable ).
thf(func_def_238,type,
sK118: variable > set_variable > ( variable > $o ) > variable ).
thf(func_def_239,type,
sK119: variable > set_variable > ( variable > $o ) > variable ).
thf(func_def_240,type,
sK120: ( variable > $o ) > set_variable > variable ).
thf(func_def_241,type,
sK121: ( variable > $o ) > set_variable > set_variable > variable ).
thf(func_def_242,type,
sK122: ( variable > $o ) > set_variable > variable ).
thf(func_def_243,type,
sK123: ( variable > $o ) > set_variable > variable ).
thf(func_def_244,type,
sK124: set_variable > variable ).
thf(func_def_245,type,
ph125:
!>[X0: $tType] : X0 ).
thf(f5025,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3552,f3706,f3821,f5024]) ).
thf(f5024,plain,
( spl44_3
| ~ spl44_4
| ~ spl44_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f5023]) ).
thf(f5023,plain,
( $false
| spl44_3
| ~ spl44_4
| ~ spl44_6 ),
inference(subsumption_resolution,[status(thm)],[f5019,f3551]) ).
thf(f3551,plain,
( ( ( omega @ sK91 )
!= ( f @ zero_zero_real @ sK91 ) )
| spl44_3 ),
inference(avatar_component_clause,[status(thm)],[f3549]) ).
thf(f3549,definition,
( spl44_3
<=> ( ( omega @ sK91 )
= ( f @ zero_zero_real @ sK91 ) ) ),
introduced(definition,[new_symbols(naming,[spl44_3])],[avatar_definition]) ).
thf(f5019,plain,
( ( ( omega @ sK91 )
= ( f @ zero_zero_real @ sK91 ) )
| ~ spl44_4
| ~ spl44_6 ),
inference(trivial_inequality_removal,[status(thm)],[f5018]) ).
thf(f5018,plain,
( ( $true = $false )
| ( ( omega @ sK91 )
= ( f @ zero_zero_real @ sK91 ) )
| ~ spl44_4
| ~ spl44_6 ),
inference(superposition,[status(thm)],[f3820,f4916]) ).
thf(f4916,plain,
( ! [X1: variable] :
( ( ( member_variable @ X1 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ u ) ) )
= $true )
| ( ( f @ zero_zero_real @ X1 )
= ( omega @ X1 ) ) )
| ~ spl44_4 ),
inference(backward_demodulation,[status(thm)],[f3876,f4365]) ).
thf(f4365,plain,
( ! [X2: variable,X0: set_variable,X1: variable] :
( ( sup_sup_set_variable @ X0 @ ( insert_variable @ X2 @ ( insert_variable @ X1 @ ( set_option_variable2 @ none_variable ) ) ) )
= ( insert_variable @ X2 @ ( insert_variable @ X1 @ X0 ) ) )
| ~ spl44_4 ),
inference(superposition,[status(thm)],[f1205,f4347]) ).
thf(f4347,plain,
( ! [X0: set_variable,X1: variable] :
( ( insert_variable @ X1 @ X0 )
= ( sup_sup_set_variable @ X0 @ ( insert_variable @ X1 @ ( set_option_variable2 @ none_variable ) ) ) )
| ~ spl44_4 ),
inference(forward_demodulation,[status(thm)],[f3638,f3705]) ).
thf(f3705,plain,
( ( ( these_variable @ bot_bo266290559riable )
= ( set_option_variable2 @ none_variable ) )
| ~ spl44_4 ),
inference(avatar_component_clause,[status(thm)],[f3703]) ).
thf(f3703,definition,
( spl44_4
<=> ( ( these_variable @ bot_bo266290559riable )
= ( set_option_variable2 @ none_variable ) ) ),
introduced(definition,[new_symbols(naming,[spl44_4])],[avatar_definition]) ).
thf(f3638,plain,
! [X0: set_variable,X1: variable] :
( ( insert_variable @ X1 @ X0 )
= ( sup_sup_set_variable @ X0 @ ( insert_variable @ X1 @ ( these_variable @ bot_bo266290559riable ) ) ) ),
inference(superposition,[status(thm)],[f1205,f1567]) ).
thf(f1567,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ X0 @ ( these_variable @ bot_bo266290559riable ) )
= X0 ),
inference(definition_unfolding,[status(thm)],[f1177,f1168]) ).
thf(f1168,plain,
( bot_bot_set_variable
= ( these_variable @ bot_bo266290559riable ) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
thf(f216,axiom,
( bot_bot_set_variable
= ( these_variable @ bot_bo266290559riable ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_215_these__empty) ).
thf(f1177,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ X0 @ bot_bot_set_variable )
= X0 ),
inference(cnf_transformation,[status(thm)],[f827]) ).
thf(f827,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ X0 @ bot_bot_set_variable )
= X0 ),
inference(rectify,[status(thm)],[f143]) ).
thf(f143,axiom,
! [X5: set_variable] :
( ( sup_sup_set_variable @ X5 @ bot_bot_set_variable )
= X5 ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_142_Un__empty__right) ).
thf(f1205,plain,
! [X2: set_variable,X0: variable,X1: set_variable] :
( ( sup_sup_set_variable @ X2 @ ( insert_variable @ X0 @ X1 ) )
= ( insert_variable @ X0 @ ( sup_sup_set_variable @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f837]) ).
thf(f837,plain,
! [X0: variable,X1: set_variable,X2: set_variable] :
( ( sup_sup_set_variable @ X2 @ ( insert_variable @ X0 @ X1 ) )
= ( insert_variable @ X0 @ ( sup_sup_set_variable @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X2: variable,X3: set_variable,X5: set_variable] :
( ( sup_sup_set_variable @ X5 @ ( insert_variable @ X2 @ X3 ) )
= ( insert_variable @ X2 @ ( sup_sup_set_variable @ X5 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_4_Un__insert__right) ).
thf(f3876,plain,
( ! [X1: variable] :
( ( $true
= ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ ( set_option_variable2 @ none_variable ) ) ) ) ) )
| ( ( f @ zero_zero_real @ X1 )
= ( omega @ X1 ) ) )
| ~ spl44_4 ),
inference(forward_demodulation,[status(thm)],[f3875,f3705]) ).
thf(f3875,plain,
! [X1: variable] :
( ( ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
= $true )
| ( ( f @ zero_zero_real @ X1 )
= ( omega @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f2453,f1417]) ).
thf(f1417,plain,
! [X2: variable,X0: variable,X1: set_variable] :
( ( insert_variable @ X0 @ ( insert_variable @ X2 @ X1 ) )
= ( insert_variable @ X2 @ ( insert_variable @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f884]) ).
thf(f884,plain,
! [X0: variable,X1: set_variable,X2: variable] :
( ( insert_variable @ X0 @ ( insert_variable @ X2 @ X1 ) )
= ( insert_variable @ X2 @ ( insert_variable @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f65]) ).
thf(f65,axiom,
! [X6: variable,X5: set_variable,X7: variable] :
( ( insert_variable @ X6 @ ( insert_variable @ X7 @ X5 ) )
= ( insert_variable @ X7 @ ( insert_variable @ X6 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_64_insert__commute) ).
thf(f2453,plain,
! [X1: variable] :
( ( ( f @ zero_zero_real @ X1 )
= ( omega @ X1 ) )
| ( ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f2452]) ).
thf(f2452,plain,
! [X1: variable] :
( ( ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
= $true )
| ( ( ( omega @ X1 )
= ( f @ zero_zero_real @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f2451]) ).
thf(f2451,plain,
! [X1: variable] :
( ( ( ~ ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) ) )
= $false )
| ( ( ( omega @ X1 )
= ( f @ zero_zero_real @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f2450]) ).
thf(f2450,plain,
! [X1: variable] :
( ( ~ ( member_variable @ X1 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
=> ( ( omega @ X1 )
= ( f @ zero_zero_real @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2449]) ).
thf(f2449,plain,
! [X1: variable] :
( $true
= ( ^ [Y0: variable] :
( ~ ( member_variable @ Y0 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
=> ( ( omega @ Y0 )
= ( f @ zero_zero_real @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2448]) ).
thf(f2448,plain,
( ( !! @ variable
@ ^ [Y0: variable] :
( ~ ( member_variable @ Y0 @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
=> ( ( omega @ Y0 )
= ( f @ zero_zero_real @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1647]) ).
thf(f1647,plain,
( ( ^ [Y0: variable > real,Y1: variable > real,Y2: set_variable] :
( !! @ variable
@ ^ [Y3: variable] :
( ~ ( member_variable @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
= ( Y0 @ Y3 ) ) ) )
@ ( f @ zero_zero_real )
@ omega
@ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1410,f1283,f1168]) ).
thf(f1283,plain,
( denota1419872369iation
= ( ^ [Y0: variable > real,Y1: variable > real,Y2: set_variable] :
( !! @ variable
@ ^ [Y3: variable] :
( ~ ( member_variable @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
= ( Y0 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f772]) ).
thf(f772,plain,
( denota1419872369iation
= ( ^ [Y0: variable > real,Y1: variable > real,Y2: set_variable] :
( !! @ variable
@ ^ [Y3: variable] :
( ~ ( member_variable @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
= ( Y0 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f771]) ).
thf(f771,plain,
( ( ^ [X0: variable > real,X1: variable > real,X2: set_variable] :
! [X3: variable] :
( ~ ( member_variable @ X3 @ X2 )
=> ( ( X1 @ X3 )
= ( X0 @ X3 ) ) ) )
= denota1419872369iation ),
inference(rectify,[status(thm)],[f132]) ).
thf(f132,axiom,
( ( ^ [X26: variable > real,X27: variable > real,X28: set_variable] :
! [X29: variable] :
( ~ ( member_variable @ X29 @ X28 )
=> ( ( X26 @ X29 )
= ( X27 @ X29 ) ) ) )
= denota1419872369iation ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_131_Uvariation__def) ).
thf(f1410,plain,
( ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f746]) ).
thf(f746,plain,
( ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f745]) ).
thf(f745,plain,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_0_uv) ).
thf(f3820,plain,
( ( ( member_variable @ sK91 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ u ) ) )
= $false )
| ~ spl44_6 ),
inference(avatar_component_clause,[status(thm)],[f3818]) ).
thf(f3818,definition,
( spl44_6
<=> ( ( member_variable @ sK91 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ u ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl44_6])],[avatar_definition]) ).
thf(f3821,plain,
( spl44_6
| ~ spl44_4 ),
inference(avatar_split_clause,[status(thm)],[f3816,f3703,f3818]) ).
thf(f3816,plain,
( ( ( member_variable @ sK91 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ u ) ) )
= $false )
| ~ spl44_4 ),
inference(forward_demodulation,[status(thm)],[f3815,f3700]) ).
thf(f3700,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ ( set_option_variable2 @ none_variable ) @ X0 )
= X0 ),
inference(backward_demodulation,[status(thm)],[f1602,f1636]) ).
thf(f1636,plain,
( ( these_variable @ bot_bo266290559riable )
= ( set_option_variable2 @ none_variable ) ),
inference(definition_unfolding,[status(thm)],[f1374,f1168]) ).
thf(f1374,plain,
( bot_bot_set_variable
= ( set_option_variable2 @ none_variable ) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
thf(f280,axiom,
( bot_bot_set_variable
= ( set_option_variable2 @ none_variable ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_279_option_Osimps_I14_J) ).
thf(f1602,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ ( these_variable @ bot_bo266290559riable ) @ X0 )
= X0 ),
inference(definition_unfolding,[status(thm)],[f1271,f1168]) ).
thf(f1271,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X0 )
= X0 ),
inference(cnf_transformation,[status(thm)],[f872]) ).
thf(f872,plain,
! [X0: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X0 )
= X0 ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
! [X6: set_variable] :
( ( sup_sup_set_variable @ bot_bot_set_variable @ X6 )
= X6 ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_9_sup__bot__left) ).
thf(f3815,plain,
( ( $false
= ( member_variable @ sK91 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ ( sup_sup_set_variable @ ( set_option_variable2 @ none_variable ) @ u ) ) ) ) )
| ~ spl44_4 ),
inference(forward_demodulation,[status(thm)],[f3814,f3705]) ).
thf(f3814,plain,
( ( member_variable @ sK91 @ ( insert_variable @ ( dVar @ x ) @ ( insert_variable @ ( rVar @ x ) @ ( sup_sup_set_variable @ ( these_variable @ bot_bo266290559riable ) @ u ) ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f3813,f1417]) ).
thf(f3813,plain,
( ( member_variable @ sK91 @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( sup_sup_set_variable @ ( these_variable @ bot_bo266290559riable ) @ u ) ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f3812,f1325]) ).
thf(f1325,plain,
! [X2: set_variable,X0: variable,X1: set_variable] :
( ( insert_variable @ X0 @ ( sup_sup_set_variable @ X2 @ X1 ) )
= ( sup_sup_set_variable @ ( insert_variable @ X0 @ X2 ) @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f954]) ).
thf(f954,plain,
! [X0: variable,X1: set_variable,X2: set_variable] :
( ( insert_variable @ X0 @ ( sup_sup_set_variable @ X2 @ X1 ) )
= ( sup_sup_set_variable @ ( insert_variable @ X0 @ X2 ) @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: variable,X4: set_variable,X3: set_variable] :
( ( sup_sup_set_variable @ ( insert_variable @ X2 @ X3 ) @ X4 )
= ( insert_variable @ X2 @ ( sup_sup_set_variable @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_2_Un__insert__left) ).
thf(f3812,plain,
( ( member_variable @ sK91 @ ( insert_variable @ ( rVar @ x ) @ ( sup_sup_set_variable @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) @ u ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f2880,f1325]) ).
thf(f2880,plain,
( ( member_variable @ sK91 @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f2879]) ).
thf(f2879,plain,
( ( ~ ( member_variable @ sK91 @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2877]) ).
thf(f2877,plain,
( ( ~ ( member_variable @ sK91 @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) )
=> ( ( omega @ sK91 )
= ( f @ zero_zero_real @ sK91 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f2876]) ).
thf(f2876,plain,
( ( ^ [Y0: variable] :
( ~ ( member_variable @ Y0 @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) )
=> ( ( omega @ Y0 )
= ( f @ zero_zero_real @ Y0 ) ) )
@ sK91 )
= $false ),
inference(sigma_clausification,[status(thm)],[f2875]) ).
thf(f2875,plain,
( ( !! @ variable
@ ^ [Y0: variable] :
( ~ ( member_variable @ Y0 @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) )
=> ( ( omega @ Y0 )
= ( f @ zero_zero_real @ Y0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f1578]) ).
thf(f1578,plain,
( ( ^ [Y0: variable > real,Y1: variable > real,Y2: set_variable] :
( !! @ variable
@ ^ [Y3: variable] :
( ~ ( member_variable @ Y3 @ Y2 )
=> ( ( Y1 @ Y3 )
= ( Y0 @ Y3 ) ) ) )
@ ( f @ zero_zero_real )
@ omega
@ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ ( these_variable @ bot_bo266290559riable ) ) ) @ u ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1210,f1283,f1168]) ).
thf(f1210,plain,
( ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f839]) ).
thf(f839,plain,
( ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) )
!= $true ),
inference(flattening,[status(thm)],[f458]) ).
thf(f458,plain,
( ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f457]) ).
thf(f457,plain,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(rectify,[status(thm)],[f358]) ).
thf(f358,negated_conjecture,
~ ( denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ),
inference(negated_conjecture,[status(cth)],[f357]) ).
thf(f357,conjecture,
denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ),
file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',conj_0) ).
thf(f3706,plain,
spl44_4,
inference(avatar_split_clause,[status(thm)],[f1636,f3703]) ).
thf(f3552,plain,
~ spl44_3,
inference(avatar_split_clause,[status(thm)],[f2881,f3549]) ).
thf(f2881,plain,
( ( omega @ sK91 )
!= ( f @ zero_zero_real @ sK91 ) ),
inference(equality_proxy_clausification,[status(thm)],[f2878]) ).
thf(f2878,plain,
( ( ( omega @ sK91 )
= ( f @ zero_zero_real @ sK91 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f2877]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP199^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n025.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 08:30:27 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
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP199^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer USubst problem prob_1246__6349986_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : USubst/prob_1246__6349986_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 462 ( 256 unt; 105 typ; 0 def)
% 0.29/0.46 % Number of atoms : 834 ( 531 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 9 ( 2 avg)
% 0.29/0.46 % Number of connectives : 2475 ( 116 ~; 23 |; 68 &;2092 @)
% 0.29/0.46 % ( 0 <=>; 176 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 18 ( 5 avg)
% 0.29/0.46 % Number of types : 19 ( 18 usr)
% 0.29/0.46 % Number of type conns : 373 ( 373 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 90 ( 87 usr; 22 con; 0-7 aty)
% 0.29/0.46 % Number of variables : 849 ( 54 ^; 774 !; 21 ?; 849 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:46.391
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (18)
% 0.29/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.29/0.46 produc1418842292n_game: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.29/0.46 set_op12188086e_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 option_variable_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 set_variable_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Syntax__Ovariable_J_J,type,
% 0.29/0.46 set_option_variable: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.29/0.46 set_option_trm: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 0.29/0.46 option_variable: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.29/0.46 option_trm: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.29/0.46 denotational_interp: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 set_variable: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_J,type,
% 0.29/0.46 set_trm: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.46 set_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.46 set_nat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Syntax__Ovariable,type,
% 0.29/0.46 variable: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__String__Ochar,type,
% 0.29/0.46 char: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Syntax__Otrm,type,
% 0.29/0.46 trm: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Real__Oreal,type,
% 0.29/0.46 real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (87)
% 0.29/0.46 thf(sy_c_Coincidence_Ostatediff,type,
% 0.29/0.46 statediff: ( variable > real ) > ( variable > real ) > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Coincidence_Ostateinterpol,type,
% 0.29/0.46 stateinterpol: ( variable > real ) > ( variable > real ) > set_variable > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.29/0.46 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_OVagree,type,
% 0.29/0.46 denotational_Vagree: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_Orepv,type,
% 0.29/0.46 denotational_repv: ( variable > real ) > variable > real > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_Osolves__ODE,type,
% 0.29/0.46 denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Denotational__Semantics_Oterm__sem,type,
% 0.29/0.46 denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 0.29/0.46 uminus_uminus_real: real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 uminus430703407e_real: set_variable_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 uminus1851247844riable: set_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.29/0.46 zero_zero_nat: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.29/0.46 zero_zero_real: real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.46 zero_zero_set_nat: set_nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.46 zero_zero_set_real: set_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_If_001t__Real__Oreal,type,
% 0.29/0.46 if_real: $o > real > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 inf_in1556002680e_real: set_variable_real > set_variable_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 sup_sup_set_variable: set_variable > set_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_Osize__class_Osize_001t__Syntax__Ovariable,type,
% 0.29/0.46 size_size_variable: variable > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_ONone_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 none_variable_real: option_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 0.29/0.46 none_trm: option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ovariable,type,
% 0.29/0.46 none_variable: option_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_OSome_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 some_variable_real: ( variable > real ) > option_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 0.29/0.46 some_trm: trm > option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ovariable,type,
% 0.29/0.46 some_variable: variable > option_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Oset__option_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 set_op697949218e_real: option_variable_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Oset__option_001t__Syntax__Otrm,type,
% 0.29/0.46 set_option_trm2: option_trm > set_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Oset__option_001t__Syntax__Ovariable,type,
% 0.29/0.46 set_option_variable2: option_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Othe_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 the_variable_real: option_variable_real > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 0.29/0.46 the_trm: option_trm > trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ovariable,type,
% 0.29/0.46 the_variable: option_variable > variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Othese_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 these_variable_real: set_op12188086e_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Othese_001t__Syntax__Otrm,type,
% 0.29/0.46 these_trm: set_option_trm > set_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Option_Othese_001t__Syntax__Ovariable,type,
% 0.29/0.46 these_variable: set_option_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 0.29/0.46 bot_bo1661475211real_o: ( variable > real ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.29/0.46 bot_bot_variable_o: variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 bot_bo721182586e_real: set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.46 bot_bot_set_nat: set_nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 0.29/0.46 bot_bo1411475018e_real: set_op12188086e_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.29/0.46 bot_bo946428664on_trm: set_option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Syntax__Ovariable_J_J,type,
% 0.29/0.46 bot_bo266290559riable: set_option_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.46 bot_bot_set_real: set_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Otrm_J,type,
% 0.29/0.46 bot_bot_set_trm: set_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 bot_bot_set_variable: set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.29/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.29/0.46 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.29/0.46 collect_variable: ( variable > $o ) > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 insert_variable_real: ( variable > real ) > set_variable_real > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.29/0.46 insert_nat: nat > set_nat > set_nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 insert526581936e_real: option_variable_real > set_op12188086e_real > set_op12188086e_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.29/0.46 insert_option_trm: option_trm > set_option_trm > set_option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 0.29/0.46 insert1340772453riable: option_variable > set_option_variable > set_option_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 0.29/0.46 insert_real: real > set_real > set_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Syntax__Otrm,type,
% 0.29/0.46 insert_trm: trm > set_trm > set_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Oinsert_001t__Syntax__Ovariable,type,
% 0.29/0.46 insert_variable: variable > set_variable > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Ois__empty_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 is_emp227886046e_real: set_variable_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 0.29/0.46 is_empty_variable: set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Ois__singleton_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 is_sin524757308e_real: set_variable_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Ois__singleton_001t__Syntax__Ovariable,type,
% 0.29/0.46 is_sin155454833riable: set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Othe__elem_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 the_el1059226619e_real: set_variable_real > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_Othe__elem_001t__Syntax__Ovariable,type,
% 0.29/0.46 the_elem_variable: set_variable > variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Static__Semantics_OFVT,type,
% 0.29/0.46 static_FVT: trm > set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Static__Semantics_Oselectlike,type,
% 0.29/0.46 static_selectlike: set_variable_real > ( variable > real ) > set_variable > set_variable_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.29/0.46 times: trm > trm > trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Syntax_Ovariable_ODVar,type,
% 0.29/0.46 dVar: char > variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Syntax_Ovariable_ORVar,type,
% 0.29/0.46 rVar: char > variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Syntax_Ovariable_Osize__variable,type,
% 0.29/0.46 size_variable: variable > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 0.29/0.46 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Oadjoint,type,
% 0.29/0.46 uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.29/0.46 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 0.29/0.46 member_variable_real: ( variable > real ) > set_variable_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 0.29/0.46 member523846807e_real: option_variable_real > set_op12188086e_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.29/0.46 member_option_trm: option_trm > set_option_trm > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 0.29/0.46 member814448204riable: option_variable > set_option_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Syntax__Otrm,type,
% 0.29/0.46 member_trm: trm > set_trm > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.29/0.46 member_variable: variable > set_variable > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_F,type,
% 0.29/0.46 f: real > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_I,type,
% 0.29/0.46 i: denotational_interp ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_U,type,
% 0.29/0.46 u: set_variable ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v__092_060omega_062,type,
% 0.29/0.46 omega: variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v__092_060sigma_062,type,
% 0.29/0.46 sigma: produc1418842292n_game ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v__092_060theta_062,type,
% 0.29/0.46 theta: trm ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_rr____,type,
% 0.29/0.46 rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_x,type,
% 0.29/0.46 x: char ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (353)
% 0.29/0.46 thf(fact_0_uv,axiom,
% 0.29/0.46 denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uv
% 0.29/0.46 thf(fact_1_Uvariation__empty,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Nu @ Nu2 @ bot_bot_set_variable )
% 0.29/0.46 = ( Nu = Nu2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_empty
% 0.29/0.46 thf(fact_2_Un__insert__left,axiom,
% 0.29/0.46 ! [A: variable,B: set_variable,C: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( insert_variable @ A @ B ) @ C )
% 0.29/0.46 = ( insert_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_left
% 0.29/0.46 thf(fact_3_Un__insert__left,axiom,
% 0.29/0.46 ! [A: variable > real,B: set_variable_real,C: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( insert_variable_real @ A @ B ) @ C )
% 0.29/0.46 = ( insert_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_left
% 0.29/0.46 thf(fact_4_Un__insert__right,axiom,
% 0.29/0.46 ! [A2: set_variable,A: variable,B: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A2 @ ( insert_variable @ A @ B ) )
% 0.29/0.46 = ( insert_variable @ A @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_right
% 0.29/0.46 thf(fact_5_Un__insert__right,axiom,
% 0.29/0.46 ! [A2: set_variable_real,A: variable > real,B: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A2 @ ( insert_variable_real @ A @ B ) )
% 0.29/0.46 = ( insert_variable_real @ A @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_right
% 0.29/0.46 thf(fact_6_Un__empty,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( ( sup_su1685293586e_real @ A2 @ B )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( ( A2 = bot_bo721182586e_real )
% 0.29/0.46 & ( B = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty
% 0.29/0.46 thf(fact_7_Un__empty,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( ( sup_sup_set_variable @ A2 @ B )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( ( A2 = bot_bot_set_variable )
% 0.29/0.46 & ( B = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty
% 0.29/0.46 thf(fact_8_sup__bot__left,axiom,
% 0.29/0.46 ! [X: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ X )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_left
% 0.29/0.46 thf(fact_9_sup__bot__left,axiom,
% 0.29/0.46 ! [X: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ bot_bot_set_variable @ X )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_left
% 0.29/0.46 thf(fact_10_sup__bot__right,axiom,
% 0.29/0.46 ! [X: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ bot_bo721182586e_real )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_right
% 0.29/0.46 thf(fact_11_sup__bot__right,axiom,
% 0.29/0.46 ! [X: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ bot_bot_set_variable )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_right
% 0.29/0.46 thf(fact_12_bot__eq__sup__iff,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( bot_bo721182586e_real
% 0.29/0.46 = ( sup_su1685293586e_real @ X @ Y ) )
% 0.29/0.46 = ( ( X = bot_bo721182586e_real )
% 0.29/0.46 & ( Y = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_eq_sup_iff
% 0.29/0.46 thf(fact_13_bot__eq__sup__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( bot_bot_set_variable
% 0.29/0.46 = ( sup_sup_set_variable @ X @ Y ) )
% 0.29/0.46 = ( ( X = bot_bot_set_variable )
% 0.29/0.46 & ( Y = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_eq_sup_iff
% 0.29/0.46 thf(fact_14_sup__eq__bot__iff,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( ( sup_su1685293586e_real @ X @ Y )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( ( X = bot_bo721182586e_real )
% 0.29/0.46 & ( Y = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_eq_bot_iff
% 0.29/0.46 thf(fact_15_sup__eq__bot__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( ( sup_sup_set_variable @ X @ Y )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( ( X = bot_bot_set_variable )
% 0.29/0.46 & ( Y = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_eq_bot_iff
% 0.29/0.46 thf(fact_16_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.46 ! [A: set_variable_real,B2: set_variable_real] :
% 0.29/0.46 ( ( ( sup_su1685293586e_real @ A @ B2 )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( ( A = bot_bo721182586e_real )
% 0.29/0.46 & ( B2 = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.eq_neutr_iff
% 0.29/0.46 thf(fact_17_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( ( sup_sup_set_variable @ A @ B2 )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( ( A = bot_bot_set_variable )
% 0.29/0.46 & ( B2 = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.eq_neutr_iff
% 0.29/0.46 thf(fact_18_sup__bot_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ bot_bot_set_variable @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.left_neutral
% 0.29/0.46 thf(fact_19_sup__bot_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.left_neutral
% 0.29/0.46 thf(fact_20_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( bot_bot_set_variable
% 0.29/0.46 = ( sup_sup_set_variable @ A @ B2 ) )
% 0.29/0.46 = ( ( A = bot_bot_set_variable )
% 0.29/0.46 & ( B2 = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.neutr_eq_iff
% 0.29/0.46 thf(fact_21_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.46 ! [A: set_variable_real,B2: set_variable_real] :
% 0.29/0.46 ( ( bot_bo721182586e_real
% 0.29/0.46 = ( sup_su1685293586e_real @ A @ B2 ) )
% 0.29/0.46 = ( ( A = bot_bo721182586e_real )
% 0.29/0.46 & ( B2 = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.neutr_eq_iff
% 0.29/0.46 thf(fact_22_sup__bot_Oright__neutral,axiom,
% 0.29/0.46 ! [A: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A @ bot_bot_set_variable )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.right_neutral
% 0.29/0.46 thf(fact_23_sup__bot_Oright__neutral,axiom,
% 0.29/0.46 ! [A: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A @ bot_bo721182586e_real )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.right_neutral
% 0.29/0.46 thf(fact_24_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P: variable > $o] :
% 0.29/0.46 ( ( bot_bot_set_variable
% 0.29/0.46 = ( collect_variable @ P ) )
% 0.29/0.46 = ( ! [X2: variable] :
% 0.29/0.46 ~ ( P @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % empty_Collect_eq
% 0.29/0.46 thf(fact_25_empty__Collect__eq,axiom,
% 0.29/0.46 ! [P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( bot_bo721182586e_real
% 0.29/0.46 = ( collec633296133e_real @ P ) )
% 0.29/0.46 = ( ! [X2: variable > real] :
% 0.29/0.46 ~ ( P @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % empty_Collect_eq
% 0.29/0.46 thf(fact_26_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P: variable > $o] :
% 0.29/0.46 ( ( ( collect_variable @ P )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( ! [X2: variable] :
% 0.29/0.46 ~ ( P @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_empty_eq
% 0.29/0.46 thf(fact_27_Collect__empty__eq,axiom,
% 0.29/0.46 ! [P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( ( collec633296133e_real @ P )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( ! [X2: variable > real] :
% 0.29/0.46 ~ ( P @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_empty_eq
% 0.29/0.46 thf(fact_28_all__not__in__conv,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( ! [X2: variable] :
% 0.29/0.46 ~ ( member_variable @ X2 @ A2 ) )
% 0.29/0.46 = ( A2 = bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % all_not_in_conv
% 0.29/0.46 thf(fact_29_all__not__in__conv,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( ! [X2: variable > real] :
% 0.29/0.46 ~ ( member_variable_real @ X2 @ A2 ) )
% 0.29/0.46 = ( A2 = bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % all_not_in_conv
% 0.29/0.46 thf(fact_30_empty__iff,axiom,
% 0.29/0.46 ! [C2: variable] :
% 0.29/0.46 ~ ( member_variable @ C2 @ bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % empty_iff
% 0.29/0.46 thf(fact_31_empty__iff,axiom,
% 0.29/0.46 ! [C2: variable > real] :
% 0.29/0.46 ~ ( member_variable_real @ C2 @ bot_bo721182586e_real ) ).
% 0.29/0.46
% 0.29/0.46 % empty_iff
% 0.29/0.46 thf(fact_32_insert__absorb2,axiom,
% 0.29/0.46 ! [X: variable,A2: set_variable] :
% 0.29/0.46 ( ( insert_variable @ X @ ( insert_variable @ X @ A2 ) )
% 0.29/0.46 = ( insert_variable @ X @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_absorb2
% 0.29/0.46 thf(fact_33_insert__absorb2,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( insert_variable_real @ X @ ( insert_variable_real @ X @ A2 ) )
% 0.29/0.46 = ( insert_variable_real @ X @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_absorb2
% 0.29/0.46 thf(fact_34_insert__iff,axiom,
% 0.29/0.46 ! [A: variable,B2: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ A @ ( insert_variable @ B2 @ A2 ) )
% 0.29/0.46 = ( ( A = B2 )
% 0.29/0.46 | ( member_variable @ A @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_iff
% 0.29/0.46 thf(fact_35_insert__iff,axiom,
% 0.29/0.46 ! [A: variable > real,B2: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ A @ ( insert_variable_real @ B2 @ A2 ) )
% 0.29/0.46 = ( ( A = B2 )
% 0.29/0.46 | ( member_variable_real @ A @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_iff
% 0.29/0.46 thf(fact_36_insertCI,axiom,
% 0.29/0.46 ! [A: variable,B: set_variable,B2: variable] :
% 0.29/0.46 ( ( ~ ( member_variable @ A @ B )
% 0.29/0.46 => ( A = B2 ) )
% 0.29/0.46 => ( member_variable @ A @ ( insert_variable @ B2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertCI
% 0.29/0.46 thf(fact_37_insertCI,axiom,
% 0.29/0.46 ! [A: variable > real,B: set_variable_real,B2: variable > real] :
% 0.29/0.46 ( ( ~ ( member_variable_real @ A @ B )
% 0.29/0.46 => ( A = B2 ) )
% 0.29/0.46 => ( member_variable_real @ A @ ( insert_variable_real @ B2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertCI
% 0.29/0.46 thf(fact_38_sup_Oright__idem,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B2 ) @ B2 )
% 0.29/0.46 = ( sup_sup_set_variable @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.right_idem
% 0.29/0.46 thf(fact_39_sup_Oright__idem,axiom,
% 0.29/0.46 ! [A: set_variable_real,B2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A @ B2 ) @ B2 )
% 0.29/0.46 = ( sup_su1685293586e_real @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.right_idem
% 0.29/0.46 thf(fact_40_sup__left__idem,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 0.29/0.46 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_left_idem
% 0.29/0.46 thf(fact_41_sup__left__idem,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ X @ Y ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_left_idem
% 0.29/0.46 thf(fact_42_sup_Oleft__idem,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B2 ) )
% 0.29/0.46 = ( sup_sup_set_variable @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.left_idem
% 0.29/0.46 thf(fact_43_sup_Oleft__idem,axiom,
% 0.29/0.46 ! [A: set_variable_real,B2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ A @ B2 ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.left_idem
% 0.29/0.46 thf(fact_44_sup__idem,axiom,
% 0.29/0.46 ! [X: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ X )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_idem
% 0.29/0.46 thf(fact_45_sup__idem,axiom,
% 0.29/0.46 ! [X: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ X )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % sup_idem
% 0.29/0.46 thf(fact_46_sup_Oidem,axiom,
% 0.29/0.46 ! [A: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup.idem
% 0.29/0.46 thf(fact_47_sup_Oidem,axiom,
% 0.29/0.46 ! [A: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % sup.idem
% 0.29/0.46 thf(fact_48_UnCI,axiom,
% 0.29/0.46 ! [C2: variable,B: set_variable,A2: set_variable] :
% 0.29/0.46 ( ( ~ ( member_variable @ C2 @ B )
% 0.29/0.46 => ( member_variable @ C2 @ A2 ) )
% 0.29/0.46 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnCI
% 0.29/0.46 thf(fact_49_UnCI,axiom,
% 0.29/0.46 ! [C2: variable > real,B: set_variable_real,A2: set_variable_real] :
% 0.29/0.46 ( ( ~ ( member_variable_real @ C2 @ B )
% 0.29/0.46 => ( member_variable_real @ C2 @ A2 ) )
% 0.29/0.46 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnCI
% 0.29/0.46 thf(fact_50_singletonI,axiom,
% 0.29/0.46 ! [A: variable] : ( member_variable @ A @ ( insert_variable @ A @ bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % singletonI
% 0.29/0.46 thf(fact_51_singletonI,axiom,
% 0.29/0.46 ! [A: variable > real] : ( member_variable_real @ A @ ( insert_variable_real @ A @ bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % singletonI
% 0.29/0.46 thf(fact_52_bot__set__def,axiom,
% 0.29/0.46 ( bot_bot_set_variable
% 0.29/0.46 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_set_def
% 0.29/0.46 thf(fact_53_bot__set__def,axiom,
% 0.29/0.46 ( bot_bo721182586e_real
% 0.29/0.46 = ( collec633296133e_real @ bot_bo1661475211real_o ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_set_def
% 0.29/0.46 thf(fact_54_ex__in__conv,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( ? [X2: variable] : ( member_variable @ X2 @ A2 ) )
% 0.29/0.46 = ( A2 != bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % ex_in_conv
% 0.29/0.46 thf(fact_55_ex__in__conv,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( ? [X2: variable > real] : ( member_variable_real @ X2 @ A2 ) )
% 0.29/0.46 = ( A2 != bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % ex_in_conv
% 0.29/0.46 thf(fact_56_equals0I,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ! [Y2: variable] :
% 0.29/0.46 ~ ( member_variable @ Y2 @ A2 )
% 0.29/0.46 => ( A2 = bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % equals0I
% 0.29/0.46 thf(fact_57_equals0I,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ! [Y2: variable > real] :
% 0.29/0.46 ~ ( member_variable_real @ Y2 @ A2 )
% 0.29/0.46 => ( A2 = bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % equals0I
% 0.29/0.46 thf(fact_58_equals0D,axiom,
% 0.29/0.46 ! [A2: set_variable,A: variable] :
% 0.29/0.46 ( ( A2 = bot_bot_set_variable )
% 0.29/0.46 => ~ ( member_variable @ A @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % equals0D
% 0.29/0.46 thf(fact_59_equals0D,axiom,
% 0.29/0.46 ! [A2: set_variable_real,A: variable > real] :
% 0.29/0.46 ( ( A2 = bot_bo721182586e_real )
% 0.29/0.46 => ~ ( member_variable_real @ A @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % equals0D
% 0.29/0.46 thf(fact_60_emptyE,axiom,
% 0.29/0.46 ! [A: variable] :
% 0.29/0.46 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % emptyE
% 0.29/0.46 thf(fact_61_emptyE,axiom,
% 0.29/0.46 ! [A: variable > real] :
% 0.29/0.46 ~ ( member_variable_real @ A @ bot_bo721182586e_real ) ).
% 0.29/0.46
% 0.29/0.46 % emptyE
% 0.29/0.46 thf(fact_62_mk__disjoint__insert,axiom,
% 0.29/0.46 ! [A: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ A @ A2 )
% 0.29/0.46 => ? [B3: set_variable] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable @ A @ B3 ) )
% 0.29/0.46 & ~ ( member_variable @ A @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_disjoint_insert
% 0.29/0.46 thf(fact_63_mk__disjoint__insert,axiom,
% 0.29/0.46 ! [A: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ A @ A2 )
% 0.29/0.46 => ? [B3: set_variable_real] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable_real @ A @ B3 ) )
% 0.29/0.46 & ~ ( member_variable_real @ A @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mk_disjoint_insert
% 0.29/0.46 thf(fact_64_insert__commute,axiom,
% 0.29/0.46 ! [X: variable,Y: variable,A2: set_variable] :
% 0.29/0.46 ( ( insert_variable @ X @ ( insert_variable @ Y @ A2 ) )
% 0.29/0.46 = ( insert_variable @ Y @ ( insert_variable @ X @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_commute
% 0.29/0.46 thf(fact_65_insert__commute,axiom,
% 0.29/0.46 ! [X: variable > real,Y: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( insert_variable_real @ X @ ( insert_variable_real @ Y @ A2 ) )
% 0.29/0.46 = ( insert_variable_real @ Y @ ( insert_variable_real @ X @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_commute
% 0.29/0.46 thf(fact_66_insert__eq__iff,axiom,
% 0.29/0.46 ! [A: variable,A2: set_variable,B2: variable,B: set_variable] :
% 0.29/0.46 ( ~ ( member_variable @ A @ A2 )
% 0.29/0.46 => ( ~ ( member_variable @ B2 @ B )
% 0.29/0.46 => ( ( ( insert_variable @ A @ A2 )
% 0.29/0.46 = ( insert_variable @ B2 @ B ) )
% 0.29/0.46 = ( ( ( A = B2 )
% 0.29/0.46 => ( A2 = B ) )
% 0.29/0.46 & ( ( A != B2 )
% 0.29/0.46 => ? [C3: set_variable] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable @ B2 @ C3 ) )
% 0.29/0.46 & ~ ( member_variable @ B2 @ C3 )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable @ A @ C3 ) )
% 0.29/0.46 & ~ ( member_variable @ A @ C3 ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_eq_iff
% 0.29/0.46 thf(fact_67_insert__eq__iff,axiom,
% 0.29/0.46 ! [A: variable > real,A2: set_variable_real,B2: variable > real,B: set_variable_real] :
% 0.29/0.46 ( ~ ( member_variable_real @ A @ A2 )
% 0.29/0.46 => ( ~ ( member_variable_real @ B2 @ B )
% 0.29/0.46 => ( ( ( insert_variable_real @ A @ A2 )
% 0.29/0.46 = ( insert_variable_real @ B2 @ B ) )
% 0.29/0.46 = ( ( ( A = B2 )
% 0.29/0.46 => ( A2 = B ) )
% 0.29/0.46 & ( ( A != B2 )
% 0.29/0.46 => ? [C3: set_variable_real] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable_real @ B2 @ C3 ) )
% 0.29/0.46 & ~ ( member_variable_real @ B2 @ C3 )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable_real @ A @ C3 ) )
% 0.29/0.46 & ~ ( member_variable_real @ A @ C3 ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_eq_iff
% 0.29/0.46 thf(fact_68_insert__absorb,axiom,
% 0.29/0.46 ! [A: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ A @ A2 )
% 0.29/0.46 => ( ( insert_variable @ A @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_absorb
% 0.29/0.46 thf(fact_69_insert__absorb,axiom,
% 0.29/0.46 ! [A: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ A @ A2 )
% 0.29/0.46 => ( ( insert_variable_real @ A @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_absorb
% 0.29/0.46 thf(fact_70_insert__ident,axiom,
% 0.29/0.46 ! [X: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ~ ( member_variable @ X @ A2 )
% 0.29/0.46 => ( ~ ( member_variable @ X @ B )
% 0.29/0.46 => ( ( ( insert_variable @ X @ A2 )
% 0.29/0.46 = ( insert_variable @ X @ B ) )
% 0.29/0.46 = ( A2 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_ident
% 0.29/0.46 thf(fact_71_insert__ident,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ~ ( member_variable_real @ X @ A2 )
% 0.29/0.46 => ( ~ ( member_variable_real @ X @ B )
% 0.29/0.46 => ( ( ( insert_variable_real @ X @ A2 )
% 0.29/0.46 = ( insert_variable_real @ X @ B ) )
% 0.29/0.46 = ( A2 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_ident
% 0.29/0.46 thf(fact_72_Set_Oset__insert,axiom,
% 0.29/0.46 ! [X: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ X @ A2 )
% 0.29/0.46 => ~ ! [B3: set_variable] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable @ X @ B3 ) )
% 0.29/0.46 => ( member_variable @ X @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Set.set_insert
% 0.29/0.46 thf(fact_73_Set_Oset__insert,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ X @ A2 )
% 0.29/0.46 => ~ ! [B3: set_variable_real] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( insert_variable_real @ X @ B3 ) )
% 0.29/0.46 => ( member_variable_real @ X @ B3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Set.set_insert
% 0.29/0.46 thf(fact_74_insertI2,axiom,
% 0.29/0.46 ! [A: variable,B: set_variable,B2: variable] :
% 0.29/0.46 ( ( member_variable @ A @ B )
% 0.29/0.46 => ( member_variable @ A @ ( insert_variable @ B2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertI2
% 0.29/0.46 thf(fact_75_insertI2,axiom,
% 0.29/0.46 ! [A: variable > real,B: set_variable_real,B2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ A @ B )
% 0.29/0.46 => ( member_variable_real @ A @ ( insert_variable_real @ B2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertI2
% 0.29/0.46 thf(fact_76_insertI1,axiom,
% 0.29/0.46 ! [A: variable,B: set_variable] : ( member_variable @ A @ ( insert_variable @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertI1
% 0.29/0.46 thf(fact_77_insertI1,axiom,
% 0.29/0.46 ! [A: variable > real,B: set_variable_real] : ( member_variable_real @ A @ ( insert_variable_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertI1
% 0.29/0.46 thf(fact_78_insertE,axiom,
% 0.29/0.46 ! [A: variable,B2: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ A @ ( insert_variable @ B2 @ A2 ) )
% 0.29/0.46 => ( ( A != B2 )
% 0.29/0.46 => ( member_variable @ A @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertE
% 0.29/0.46 thf(fact_79_insertE,axiom,
% 0.29/0.46 ! [A: variable > real,B2: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ A @ ( insert_variable_real @ B2 @ A2 ) )
% 0.29/0.46 => ( ( A != B2 )
% 0.29/0.46 => ( member_variable_real @ A @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insertE
% 0.29/0.46 thf(fact_80_sup__left__commute,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 0.29/0.46 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_left_commute
% 0.29/0.46 thf(fact_81_sup__left__commute,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ Y @ ( sup_su1685293586e_real @ X @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_left_commute
% 0.29/0.46 thf(fact_82_sup_Oleft__commute,axiom,
% 0.29/0.46 ! [B2: set_variable,A: set_variable,C2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A @ C2 ) )
% 0.29/0.46 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.left_commute
% 0.29/0.46 thf(fact_83_sup_Oleft__commute,axiom,
% 0.29/0.46 ! [B2: set_variable_real,A: set_variable_real,C2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ B2 @ ( sup_su1685293586e_real @ A @ C2 ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ B2 @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.left_commute
% 0.29/0.46 thf(fact_84_sup__commute,axiom,
% 0.29/0.46 ( sup_sup_set_variable
% 0.29/0.46 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_commute
% 0.29/0.46 thf(fact_85_sup__commute,axiom,
% 0.29/0.46 ( sup_su1685293586e_real
% 0.29/0.46 = ( ^ [X2: set_variable_real,Y3: set_variable_real] : ( sup_su1685293586e_real @ Y3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_commute
% 0.29/0.46 thf(fact_86_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: variable,P: variable > $o] :
% 0.29/0.46 ( ( member_variable @ A @ ( collect_variable @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_87_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: variable > real,P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( member_variable_real @ A @ ( collec633296133e_real @ P ) )
% 0.29/0.46 = ( P @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_88_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( collect_variable
% 0.29/0.46 @ ^ [X2: variable] : ( member_variable @ X2 @ A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_89_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( collec633296133e_real
% 0.29/0.46 @ ^ [X2: variable > real] : ( member_variable_real @ X2 @ A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_90_sup_Ocommute,axiom,
% 0.29/0.46 ( sup_sup_set_variable
% 0.29/0.46 = ( ^ [A3: set_variable,B4: set_variable] : ( sup_sup_set_variable @ B4 @ A3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.commute
% 0.29/0.46 thf(fact_91_sup_Ocommute,axiom,
% 0.29/0.46 ( sup_su1685293586e_real
% 0.29/0.46 = ( ^ [A3: set_variable_real,B4: set_variable_real] : ( sup_su1685293586e_real @ B4 @ A3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.commute
% 0.29/0.46 thf(fact_92_sup__assoc,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.29/0.46 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_assoc
% 0.29/0.46 thf(fact_93_sup__assoc,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 0.29/0.46 = ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_assoc
% 0.29/0.46 thf(fact_94_sup_Oassoc,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable,C2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B2 ) @ C2 )
% 0.29/0.46 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.assoc
% 0.29/0.46 thf(fact_95_sup_Oassoc,axiom,
% 0.29/0.46 ! [A: set_variable_real,B2: set_variable_real,C2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A @ B2 ) @ C2 )
% 0.29/0.46 = ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ B2 @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.assoc
% 0.29/0.46 thf(fact_96_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.46 ! [B: set_variable,K: set_variable,B2: set_variable,A: set_variable] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( sup_sup_set_variable @ K @ B2 ) )
% 0.29/0.46 => ( ( sup_sup_set_variable @ A @ B )
% 0.29/0.46 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.sup2
% 0.29/0.46 thf(fact_97_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.46 ! [B: set_variable_real,K: set_variable_real,B2: set_variable_real,A: set_variable_real] :
% 0.29/0.46 ( ( B
% 0.29/0.46 = ( sup_su1685293586e_real @ K @ B2 ) )
% 0.29/0.46 => ( ( sup_su1685293586e_real @ A @ B )
% 0.29/0.46 = ( sup_su1685293586e_real @ K @ ( sup_su1685293586e_real @ A @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.sup2
% 0.29/0.46 thf(fact_98_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.46 ! [A2: set_variable,K: set_variable,A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( sup_sup_set_variable @ K @ A ) )
% 0.29/0.46 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 0.29/0.46 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.sup1
% 0.29/0.46 thf(fact_99_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.46 ! [A2: set_variable_real,K: set_variable_real,A: set_variable_real,B2: set_variable_real] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 = ( sup_su1685293586e_real @ K @ A ) )
% 0.29/0.46 => ( ( sup_su1685293586e_real @ A2 @ B2 )
% 0.29/0.46 = ( sup_su1685293586e_real @ K @ ( sup_su1685293586e_real @ A @ B2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % boolean_algebra_cancel.sup1
% 0.29/0.46 thf(fact_100_inf__sup__aci_I5_J,axiom,
% 0.29/0.46 ( sup_sup_set_variable
% 0.29/0.46 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(5)
% 0.29/0.46 thf(fact_101_inf__sup__aci_I5_J,axiom,
% 0.29/0.46 ( sup_su1685293586e_real
% 0.29/0.46 = ( ^ [X2: set_variable_real,Y3: set_variable_real] : ( sup_su1685293586e_real @ Y3 @ X2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(5)
% 0.29/0.46 thf(fact_102_inf__sup__aci_I6_J,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.29/0.46 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(6)
% 0.29/0.46 thf(fact_103_inf__sup__aci_I6_J,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 0.29/0.46 = ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(6)
% 0.29/0.46 thf(fact_104_inf__sup__aci_I7_J,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 0.29/0.46 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(7)
% 0.29/0.46 thf(fact_105_inf__sup__aci_I7_J,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ Y @ ( sup_su1685293586e_real @ X @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(7)
% 0.29/0.46 thf(fact_106_inf__sup__aci_I8_J,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 0.29/0.46 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(8)
% 0.29/0.46 thf(fact_107_inf__sup__aci_I8_J,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ X @ Y ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_sup_aci(8)
% 0.29/0.46 thf(fact_108_Un__left__commute,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable,C: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B @ C ) )
% 0.29/0.46 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A2 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_commute
% 0.29/0.46 thf(fact_109_Un__left__commute,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real,C: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ B @ C ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ B @ ( sup_su1685293586e_real @ A2 @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_commute
% 0.29/0.46 thf(fact_110_Un__left__absorb,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 = ( sup_sup_set_variable @ A2 @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_absorb
% 0.29/0.46 thf(fact_111_Un__left__absorb,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 = ( sup_su1685293586e_real @ A2 @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_absorb
% 0.29/0.46 thf(fact_112_Un__commute,axiom,
% 0.29/0.46 ( sup_sup_set_variable
% 0.29/0.46 = ( ^ [A4: set_variable,B5: set_variable] : ( sup_sup_set_variable @ B5 @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_commute
% 0.29/0.46 thf(fact_113_Un__commute,axiom,
% 0.29/0.46 ( sup_su1685293586e_real
% 0.29/0.46 = ( ^ [A4: set_variable_real,B5: set_variable_real] : ( sup_su1685293586e_real @ B5 @ A4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_commute
% 0.29/0.46 thf(fact_114_Un__absorb,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A2 @ A2 )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_absorb
% 0.29/0.46 thf(fact_115_Un__absorb,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A2 @ A2 )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_absorb
% 0.29/0.46 thf(fact_116_Un__assoc,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable,C: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B ) @ C )
% 0.29/0.46 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_assoc
% 0.29/0.46 thf(fact_117_Un__assoc,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real,C: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A2 @ B ) @ C )
% 0.29/0.46 = ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ B @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_assoc
% 0.29/0.46 thf(fact_118_ball__Un,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable,P: variable > $o] :
% 0.29/0.46 ( ( ! [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 => ( P @ X2 ) ) )
% 0.29/0.46 = ( ! [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ A2 )
% 0.29/0.46 => ( P @ X2 ) )
% 0.29/0.46 & ! [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ B )
% 0.29/0.46 => ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_Un
% 0.29/0.46 thf(fact_119_ball__Un,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real,P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( ! [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 => ( P @ X2 ) ) )
% 0.29/0.46 = ( ! [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ A2 )
% 0.29/0.46 => ( P @ X2 ) )
% 0.29/0.46 & ! [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ B )
% 0.29/0.46 => ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_Un
% 0.29/0.46 thf(fact_120_bex__Un,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable,P: variable > $o] :
% 0.29/0.46 ( ( ? [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 & ( P @ X2 ) ) )
% 0.29/0.46 = ( ? [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ A2 )
% 0.29/0.46 & ( P @ X2 ) )
% 0.29/0.46 | ? [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ B )
% 0.29/0.46 & ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_Un
% 0.29/0.46 thf(fact_121_bex__Un,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real,P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( ? [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 & ( P @ X2 ) ) )
% 0.29/0.46 = ( ? [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ A2 )
% 0.29/0.46 & ( P @ X2 ) )
% 0.29/0.46 | ? [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ B )
% 0.29/0.46 & ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_Un
% 0.29/0.46 thf(fact_122_UnI2,axiom,
% 0.29/0.46 ! [C2: variable,B: set_variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ B )
% 0.29/0.46 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI2
% 0.29/0.46 thf(fact_123_UnI2,axiom,
% 0.29/0.46 ! [C2: variable > real,B: set_variable_real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ B )
% 0.29/0.46 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI2
% 0.29/0.46 thf(fact_124_UnI1,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ A2 )
% 0.29/0.46 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI1
% 0.29/0.46 thf(fact_125_UnI1,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI1
% 0.29/0.46 thf(fact_126_UnE,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 => ( ~ ( member_variable @ C2 @ A2 )
% 0.29/0.46 => ( member_variable @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnE
% 0.29/0.46 thf(fact_127_UnE,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 => ( ~ ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 => ( member_variable_real @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnE
% 0.29/0.46 thf(fact_128_Uvariation__sym__rel,axiom,
% 0.29/0.46 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 0.29/0.46 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.29/0.46 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_sym_rel
% 0.29/0.46 thf(fact_129_Uvariation__refl,axiom,
% 0.29/0.46 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_refl
% 0.29/0.46 thf(fact_130_Uvariation__sym,axiom,
% 0.29/0.46 ( denota1419872369iation
% 0.29/0.46 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_sym
% 0.29/0.46 thf(fact_131_Uvariation__def,axiom,
% 0.29/0.46 ( denota1419872369iation
% 0.29/0.46 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 0.29/0.46 ! [I: variable] :
% 0.29/0.46 ( ~ ( member_variable @ I @ U2 )
% 0.29/0.46 => ( ( Nu3 @ I )
% 0.29/0.46 = ( Nu4 @ I ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_def
% 0.29/0.46 thf(fact_132_singleton__inject,axiom,
% 0.29/0.46 ! [A: variable,B2: variable] :
% 0.29/0.46 ( ( ( insert_variable @ A @ bot_bot_set_variable )
% 0.29/0.46 = ( insert_variable @ B2 @ bot_bot_set_variable ) )
% 0.29/0.46 => ( A = B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_inject
% 0.29/0.46 thf(fact_133_singleton__inject,axiom,
% 0.29/0.46 ! [A: variable > real,B2: variable > real] :
% 0.29/0.46 ( ( ( insert_variable_real @ A @ bot_bo721182586e_real )
% 0.29/0.46 = ( insert_variable_real @ B2 @ bot_bo721182586e_real ) )
% 0.29/0.46 => ( A = B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_inject
% 0.29/0.46 thf(fact_134_insert__not__empty,axiom,
% 0.29/0.46 ! [A: variable,A2: set_variable] :
% 0.29/0.46 ( ( insert_variable @ A @ A2 )
% 0.29/0.46 != bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % insert_not_empty
% 0.29/0.46 thf(fact_135_insert__not__empty,axiom,
% 0.29/0.46 ! [A: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( insert_variable_real @ A @ A2 )
% 0.29/0.46 != bot_bo721182586e_real ) ).
% 0.29/0.46
% 0.29/0.46 % insert_not_empty
% 0.29/0.46 thf(fact_136_doubleton__eq__iff,axiom,
% 0.29/0.46 ! [A: variable,B2: variable,C2: variable,D: variable] :
% 0.29/0.46 ( ( ( insert_variable @ A @ ( insert_variable @ B2 @ bot_bot_set_variable ) )
% 0.29/0.46 = ( insert_variable @ C2 @ ( insert_variable @ D @ bot_bot_set_variable ) ) )
% 0.29/0.46 = ( ( ( A = C2 )
% 0.29/0.46 & ( B2 = D ) )
% 0.29/0.46 | ( ( A = D )
% 0.29/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % doubleton_eq_iff
% 0.29/0.46 thf(fact_137_doubleton__eq__iff,axiom,
% 0.29/0.46 ! [A: variable > real,B2: variable > real,C2: variable > real,D: variable > real] :
% 0.29/0.46 ( ( ( insert_variable_real @ A @ ( insert_variable_real @ B2 @ bot_bo721182586e_real ) )
% 0.29/0.46 = ( insert_variable_real @ C2 @ ( insert_variable_real @ D @ bot_bo721182586e_real ) ) )
% 0.29/0.46 = ( ( ( A = C2 )
% 0.29/0.46 & ( B2 = D ) )
% 0.29/0.46 | ( ( A = D )
% 0.29/0.46 & ( B2 = C2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % doubleton_eq_iff
% 0.29/0.46 thf(fact_138_singleton__iff,axiom,
% 0.29/0.46 ! [B2: variable,A: variable] :
% 0.29/0.46 ( ( member_variable @ B2 @ ( insert_variable @ A @ bot_bot_set_variable ) )
% 0.29/0.46 = ( B2 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_iff
% 0.29/0.46 thf(fact_139_singleton__iff,axiom,
% 0.29/0.46 ! [B2: variable > real,A: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ B2 @ ( insert_variable_real @ A @ bot_bo721182586e_real ) )
% 0.29/0.46 = ( B2 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_iff
% 0.29/0.46 thf(fact_140_singletonD,axiom,
% 0.29/0.46 ! [B2: variable,A: variable] :
% 0.29/0.46 ( ( member_variable @ B2 @ ( insert_variable @ A @ bot_bot_set_variable ) )
% 0.29/0.46 => ( B2 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % singletonD
% 0.29/0.46 thf(fact_141_singletonD,axiom,
% 0.29/0.46 ! [B2: variable > real,A: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ B2 @ ( insert_variable_real @ A @ bot_bo721182586e_real ) )
% 0.29/0.46 => ( B2 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % singletonD
% 0.29/0.46 thf(fact_142_Un__empty__right,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ A2 @ bot_bot_set_variable )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_right
% 0.29/0.46 thf(fact_143_Un__empty__right,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ A2 @ bot_bo721182586e_real )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_right
% 0.29/0.46 thf(fact_144_Un__empty__left,axiom,
% 0.29/0.46 ! [B: set_variable] :
% 0.29/0.46 ( ( sup_sup_set_variable @ bot_bot_set_variable @ B )
% 0.29/0.46 = B ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_left
% 0.29/0.46 thf(fact_145_Un__empty__left,axiom,
% 0.29/0.46 ! [B: set_variable_real] :
% 0.29/0.46 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ B )
% 0.29/0.46 = B ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_left
% 0.29/0.46 thf(fact_146_Uvariation__trans,axiom,
% 0.29/0.46 ! [Omega: variable > real,Nu: variable > real,U: set_variable,Mu: variable > real,V: set_variable] :
% 0.29/0.46 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.29/0.46 => ( ( denota1419872369iation @ Nu @ Mu @ V )
% 0.29/0.46 => ( denota1419872369iation @ Omega @ Mu @ ( sup_sup_set_variable @ U @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_trans
% 0.29/0.46 thf(fact_147_singleton__Un__iff,axiom,
% 0.29/0.46 ! [X: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( ( insert_variable @ X @ bot_bot_set_variable )
% 0.29/0.46 = ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 = ( ( ( A2 = bot_bot_set_variable )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 & ( B = bot_bot_set_variable ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_Un_iff
% 0.29/0.46 thf(fact_148_singleton__Un__iff,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( ( insert_variable_real @ X @ bot_bo721182586e_real )
% 0.29/0.46 = ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 = ( ( ( A2 = bot_bo721182586e_real )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 & ( B = bot_bo721182586e_real ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_Un_iff
% 0.29/0.46 thf(fact_149_Un__singleton__iff,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable,X: variable] :
% 0.29/0.46 ( ( ( sup_sup_set_variable @ A2 @ B )
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 = ( ( ( A2 = bot_bot_set_variable )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 & ( B = bot_bot_set_variable ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable @ X @ bot_bot_set_variable ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_singleton_iff
% 0.29/0.46 thf(fact_150_Un__singleton__iff,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real,X: variable > real] :
% 0.29/0.46 ( ( ( sup_su1685293586e_real @ A2 @ B )
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 = ( ( ( A2 = bot_bo721182586e_real )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 & ( B = bot_bo721182586e_real ) )
% 0.29/0.46 | ( ( A2
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 & ( B
% 0.29/0.46 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_singleton_iff
% 0.29/0.46 thf(fact_151_insert__is__Un,axiom,
% 0.29/0.46 ( insert_variable
% 0.29/0.46 = ( ^ [A3: variable] : ( sup_sup_set_variable @ ( insert_variable @ A3 @ bot_bot_set_variable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_is_Un
% 0.29/0.46 thf(fact_152_insert__is__Un,axiom,
% 0.29/0.46 ( insert_variable_real
% 0.29/0.46 = ( ^ [A3: variable > real] : ( sup_su1685293586e_real @ ( insert_variable_real @ A3 @ bot_bo721182586e_real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_is_Un
% 0.29/0.46 thf(fact_153__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.46 ~ ! [Rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
% 0.29/0.46 ~ ! [X0: trm,X1: denotational_interp,X22: trm,X3: denotational_interp,X4: char,X5: real > variable > real] :
% 0.29/0.46 ( ( ? [V6: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ V6 @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 & ( ( denota1863255036rm_sem @ X3 @ X22 @ V6 )
% 0.29/0.46 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 0.29/0.46 = ( ( denota1419872369iation @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 & ( ( denota1863255036rm_sem @ X3 @ X22 @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) )
% 0.29/0.46 != ( denota1863255036rm_sem @ X1 @ X0 @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<And>thesis. (\<And>rr. \<forall>x0 x1 x2 x3 x4 x5. (\<exists>v6. Uvariation v6 (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 v6 \<noteq> term_sem x1 x0 v6) = (Uvariation (rr x0 x1 x2 x3 x4 x5) (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 (rr x0 x1 x2 x3 x4 x5) \<noteq> term_sem x1 x0 (rr x0 x1 x2 x3 x4 x5)) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.46 thf(fact_154_solves__Vagree__trans,axiom,
% 0.29/0.46 ! [F: real > variable > real,Omega: variable > real,U: set_variable,I2: denotational_interp,X: char,Theta: trm,Zeta: real] :
% 0.29/0.46 ( ( denota1419872369iation @ ( F @ zero_zero_real ) @ Omega @ U )
% 0.29/0.46 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 0.29/0.46 => ( denota1419872369iation @ ( F @ Zeta ) @ Omega @ ( sup_sup_set_variable @ U @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % solves_Vagree_trans
% 0.29/0.46 thf(fact_155__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062,axiom,
% 0.29/0.46 ! [X0: trm,X1: denotational_interp,X22: trm,X3: denotational_interp,X4: char,X5: real > variable > real] :
% 0.29/0.46 ( ( ? [V6: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ V6 @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 & ( ( denota1863255036rm_sem @ X3 @ X22 @ V6 )
% 0.29/0.46 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 0.29/0.46 = ( ( denota1419872369iation @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 & ( ( denota1863255036rm_sem @ X3 @ X22 @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) )
% 0.29/0.46 != ( denota1863255036rm_sem @ X1 @ X0 @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>\<forall>x0 x1 x2 x3 x4 x5. (\<exists>v6. Uvariation v6 (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 v6 \<noteq> term_sem x1 x0 v6) = (Uvariation (rr x0 x1 x2 x3 x4 x5) (x5 0) {RVar x4, DVar x4} \<and> term_sem x3 x2 (rr x0 x1 x2 x3 x4 x5) \<noteq> term_sem x1 x0 (rr x0 x1 x2 x3 x4 x5))\<close>
% 0.29/0.46 thf(fact_156_variable_Oinject_I1_J,axiom,
% 0.29/0.46 ! [X12: char,Y1: char] :
% 0.29/0.46 ( ( ( rVar @ X12 )
% 0.29/0.46 = ( rVar @ Y1 ) )
% 0.29/0.46 = ( X12 = Y1 ) ) ).
% 0.29/0.46
% 0.29/0.46 % variable.inject(1)
% 0.29/0.46 thf(fact_157_set__zero,axiom,
% 0.29/0.46 ( zero_zero_set_real
% 0.29/0.46 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_zero
% 0.29/0.46 thf(fact_158_set__zero,axiom,
% 0.29/0.46 ( zero_zero_set_nat
% 0.29/0.46 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_zero
% 0.29/0.46 thf(fact_159_variable_Oinject_I2_J,axiom,
% 0.29/0.46 ! [X23: char,Y22: char] :
% 0.29/0.46 ( ( ( dVar @ X23 )
% 0.29/0.46 = ( dVar @ Y22 ) )
% 0.29/0.46 = ( X23 = Y22 ) ) ).
% 0.29/0.46
% 0.29/0.46 % variable.inject(2)
% 0.29/0.46 thf(fact_160_union__or,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 0.29/0.46 = ( ( member_variable @ C2 @ A2 )
% 0.29/0.46 | ( member_variable @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % union_or
% 0.29/0.46 thf(fact_161_union__or,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 0.29/0.46 = ( ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 | ( member_variable_real @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % union_or
% 0.29/0.46 thf(fact_162_ball__insert,axiom,
% 0.29/0.46 ! [A: variable,B: set_variable,P: variable > $o] :
% 0.29/0.46 ( ( ! [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ ( insert_variable @ A @ B ) )
% 0.29/0.46 => ( P @ X2 ) ) )
% 0.29/0.46 = ( ( P @ A )
% 0.29/0.46 & ! [X2: variable] :
% 0.29/0.46 ( ( member_variable @ X2 @ B )
% 0.29/0.46 => ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_insert
% 0.29/0.46 thf(fact_163_ball__insert,axiom,
% 0.29/0.46 ! [A: variable > real,B: set_variable_real,P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( ! [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ ( insert_variable_real @ A @ B ) )
% 0.29/0.46 => ( P @ X2 ) ) )
% 0.29/0.46 = ( ( P @ A )
% 0.29/0.46 & ! [X2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X2 @ B )
% 0.29/0.46 => ( P @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_insert
% 0.29/0.46 thf(fact_164_the__elem__eq,axiom,
% 0.29/0.46 ! [X: variable] :
% 0.29/0.46 ( ( the_elem_variable @ ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % the_elem_eq
% 0.29/0.46 thf(fact_165_the__elem__eq,axiom,
% 0.29/0.46 ! [X: variable > real] :
% 0.29/0.46 ( ( the_el1059226619e_real @ ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % the_elem_eq
% 0.29/0.46 thf(fact_166_f2,axiom,
% 0.29/0.46 ! [F2: real > variable > real,C4: char,I3: denotational_interp,T: trm,Ia: denotational_interp,Ta: trm] :
% 0.29/0.46 ( ( ( denota1419872369iation @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) @ ( F2 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ C4 ) @ ( insert_variable @ ( dVar @ C4 ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 & ( ( denota1863255036rm_sem @ I3 @ T @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) )
% 0.29/0.46 != ( denota1863255036rm_sem @ Ia @ Ta @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) ) ) )
% 0.29/0.46 | ( ( denota1778088425es_ODE @ I3 @ F2 @ C4 @ T )
% 0.29/0.46 = ( denota1778088425es_ODE @ Ia @ F2 @ C4 @ Ta ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % f2
% 0.29/0.46 thf(fact_167_zero__reorient,axiom,
% 0.29/0.46 ! [X: real] :
% 0.29/0.46 ( ( zero_zero_real = X )
% 0.29/0.46 = ( X = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_reorient
% 0.29/0.46 thf(fact_168_zero__reorient,axiom,
% 0.29/0.46 ! [X: nat] :
% 0.29/0.46 ( ( zero_zero_nat = X )
% 0.29/0.46 = ( X = zero_zero_nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_reorient
% 0.29/0.46 thf(fact_169_not__union__or,axiom,
% 0.29/0.46 ! [X: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( ~ ( member_variable @ X @ ( sup_sup_set_variable @ A2 @ B ) ) )
% 0.29/0.46 = ( ~ ( member_variable @ X @ A2 )
% 0.29/0.46 & ~ ( member_variable @ X @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_union_or
% 0.29/0.46 thf(fact_170_not__union__or,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( ~ ( member_variable_real @ X @ ( sup_su1685293586e_real @ A2 @ B ) ) )
% 0.29/0.46 = ( ~ ( member_variable_real @ X @ A2 )
% 0.29/0.46 & ~ ( member_variable_real @ X @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_union_or
% 0.29/0.46 thf(fact_171_same__ODE__same__sol,axiom,
% 0.29/0.46 ! [F: real > variable > real,X: char,I2: denotational_interp,Theta: trm,J: denotational_interp,Eta: trm] :
% 0.29/0.46 ( ! [Nu5: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Nu5 @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Nu5 )
% 0.29/0.46 = ( denota1863255036rm_sem @ J @ Eta @ Nu5 ) ) )
% 0.29/0.46 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 0.29/0.46 = ( denota1778088425es_ODE @ J @ F @ X @ Eta ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % same_ODE_same_sol
% 0.29/0.46 thf(fact_172_variable_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [X12: char,X23: char] :
% 0.29/0.46 ( ( rVar @ X12 )
% 0.29/0.46 != ( dVar @ X23 ) ) ).
% 0.29/0.46
% 0.29/0.46 % variable.distinct(1)
% 0.29/0.46 thf(fact_173_variable_Oinduct,axiom,
% 0.29/0.46 ! [P: variable > $o,Variable: variable] :
% 0.29/0.46 ( ! [X6: char] : ( P @ ( rVar @ X6 ) )
% 0.29/0.46 => ( ! [X6: char] : ( P @ ( dVar @ X6 ) )
% 0.29/0.46 => ( P @ Variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % variable.induct
% 0.29/0.46 thf(fact_174_variable_Oexhaust,axiom,
% 0.29/0.46 ! [Y: variable] :
% 0.29/0.46 ( ! [X13: char] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( rVar @ X13 ) )
% 0.29/0.46 => ~ ! [X24: char] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( dVar @ X24 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % variable.exhaust
% 0.29/0.46 thf(fact_175_bot__empty__eq,axiom,
% 0.29/0.46 ( bot_bot_variable_o
% 0.29/0.46 = ( ^ [X2: variable] : ( member_variable @ X2 @ bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_empty_eq
% 0.29/0.46 thf(fact_176_bot__empty__eq,axiom,
% 0.29/0.46 ( bot_bo1661475211real_o
% 0.29/0.46 = ( ^ [X2: variable > real] : ( member_variable_real @ X2 @ bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_empty_eq
% 0.29/0.46 thf(fact_177_Collect__empty__eq__bot,axiom,
% 0.29/0.46 ! [P: variable > $o] :
% 0.29/0.46 ( ( ( collect_variable @ P )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( P = bot_bot_variable_o ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_empty_eq_bot
% 0.29/0.46 thf(fact_178_Collect__empty__eq__bot,axiom,
% 0.29/0.46 ! [P: ( variable > real ) > $o] :
% 0.29/0.46 ( ( ( collec633296133e_real @ P )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( P = bot_bo1661475211real_o ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_empty_eq_bot
% 0.29/0.46 thf(fact_179_is__singleton__the__elem,axiom,
% 0.29/0.46 ( is_sin155454833riable
% 0.29/0.46 = ( ^ [A4: set_variable] :
% 0.29/0.46 ( A4
% 0.29/0.46 = ( insert_variable @ ( the_elem_variable @ A4 ) @ bot_bot_set_variable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singleton_the_elem
% 0.29/0.46 thf(fact_180_is__singleton__the__elem,axiom,
% 0.29/0.46 ( is_sin524757308e_real
% 0.29/0.46 = ( ^ [A4: set_variable_real] :
% 0.29/0.46 ( A4
% 0.29/0.46 = ( insert_variable_real @ ( the_el1059226619e_real @ A4 ) @ bot_bo721182586e_real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singleton_the_elem
% 0.29/0.46 thf(fact_181_vaflow2,axiom,
% 0.29/0.46 ! [F: real > variable > real,Theta: trm,Zeta: real] :
% 0.29/0.46 ( ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ F @ x @ Theta )
% 0.29/0.46 => ( denota1419872369iation @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vaflow2
% 0.29/0.46 thf(fact_182_is__singletonI,axiom,
% 0.29/0.46 ! [X: variable] : ( is_sin155454833riable @ ( insert_variable @ X @ bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonI
% 0.29/0.46 thf(fact_183_is__singletonI,axiom,
% 0.29/0.46 ! [X: variable > real] : ( is_sin524757308e_real @ ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonI
% 0.29/0.46 thf(fact_184_a1,axiom,
% 0.29/0.46 denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ f @ x @ theta ).
% 0.29/0.46
% 0.29/0.46 % a1
% 0.29/0.46 thf(fact_185_is__singletonI_H,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( A2 != bot_bot_set_variable )
% 0.29/0.46 => ( ! [X6: variable,Y2: variable] :
% 0.29/0.46 ( ( member_variable @ X6 @ A2 )
% 0.29/0.46 => ( ( member_variable @ Y2 @ A2 )
% 0.29/0.46 => ( X6 = Y2 ) ) )
% 0.29/0.46 => ( is_sin155454833riable @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonI'
% 0.29/0.46 thf(fact_186_is__singletonI_H,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( A2 != bot_bo721182586e_real )
% 0.29/0.46 => ( ! [X6: variable > real,Y2: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X6 @ A2 )
% 0.29/0.46 => ( ( member_variable_real @ Y2 @ A2 )
% 0.29/0.46 => ( X6 = Y2 ) ) )
% 0.29/0.46 => ( is_sin524757308e_real @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonI'
% 0.29/0.46 thf(fact_187_is__singleton__def,axiom,
% 0.29/0.46 ( is_sin155454833riable
% 0.29/0.46 = ( ^ [A4: set_variable] :
% 0.29/0.46 ? [X2: variable] :
% 0.29/0.46 ( A4
% 0.29/0.46 = ( insert_variable @ X2 @ bot_bot_set_variable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singleton_def
% 0.29/0.46 thf(fact_188_is__singleton__def,axiom,
% 0.29/0.46 ( is_sin524757308e_real
% 0.29/0.46 = ( ^ [A4: set_variable_real] :
% 0.29/0.46 ? [X2: variable > real] :
% 0.29/0.46 ( A4
% 0.29/0.46 = ( insert_variable_real @ X2 @ bot_bo721182586e_real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singleton_def
% 0.29/0.46 thf(fact_189_is__singletonE,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( is_sin155454833riable @ A2 )
% 0.29/0.46 => ~ ! [X6: variable] :
% 0.29/0.46 ( A2
% 0.29/0.46 != ( insert_variable @ X6 @ bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonE
% 0.29/0.46 thf(fact_190_is__singletonE,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( is_sin524757308e_real @ A2 )
% 0.29/0.46 => ~ ! [X6: variable > real] :
% 0.29/0.46 ( A2
% 0.29/0.46 != ( insert_variable_real @ X6 @ bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % is_singletonE
% 0.29/0.46 thf(fact_191_vaflow1,axiom,
% 0.29/0.46 ! [F: real > variable > real,Theta: trm,Zeta: real] :
% 0.29/0.46 ( ( denota1778088425es_ODE @ i @ F @ x @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ Theta ) ) )
% 0.29/0.46 => ( denota1419872369iation @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % vaflow1
% 0.29/0.46 thf(fact_192_l2r,axiom,
% 0.29/0.46 ( ( denota1778088425es_ODE @ i @ f @ x @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta ) ) )
% 0.29/0.46 => ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ) ).
% 0.29/0.46
% 0.29/0.46 % l2r
% 0.29/0.46 thf(fact_193_IH,axiom,
% 0.29/0.46 ! [Nu: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Nu @ ( f @ zero_zero_real ) @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ i @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta ) ) @ Nu )
% 0.29/0.46 = ( denota1863255036rm_sem @ ( uSubst1599435252djoint @ sigma @ i @ ( f @ zero_zero_real ) ) @ theta @ Nu ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IH
% 0.29/0.46 thf(fact_194_subdef,axiom,
% 0.29/0.46 ( ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta )
% 0.29/0.46 != none_trm ) ).
% 0.29/0.46
% 0.29/0.46 % subdef
% 0.29/0.46 thf(fact_195_variable_Osize__gen_I1_J,axiom,
% 0.29/0.46 ! [X12: char] :
% 0.29/0.46 ( ( size_variable @ ( rVar @ X12 ) )
% 0.29/0.46 = zero_zero_nat ) ).
% 0.29/0.46
% 0.29/0.46 % variable.size_gen(1)
% 0.29/0.46 thf(fact_196_usubst__term,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real,U: set_variable,Sigma: produc1418842292n_game,Theta: trm,I2: denotational_interp] :
% 0.29/0.46 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 0.29/0.46 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.29/0.46 != none_trm )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ I2 @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ Nu )
% 0.29/0.46 = ( denota1863255036rm_sem @ ( uSubst1599435252djoint @ Sigma @ I2 @ Omega ) @ Theta @ Nu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % usubst_term
% 0.29/0.46 thf(fact_197_usubstappt__det,axiom,
% 0.29/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 0.29/0.46 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.29/0.46 != none_trm )
% 0.29/0.46 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 0.29/0.46 != none_trm )
% 0.29/0.46 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.29/0.46 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % usubstappt_det
% 0.29/0.46 thf(fact_198_undeft__None,axiom,
% 0.29/0.46 none_trm = none_trm ).
% 0.29/0.46
% 0.29/0.46 % undeft_None
% 0.29/0.46 thf(fact_199_usubst__ode,axiom,
% 0.29/0.46 ! [Sigma: produc1418842292n_game,X: char,Theta: trm,I2: denotational_interp,F: real > variable > real] :
% 0.29/0.46 ( ( ( uSubst516392818stappt @ Sigma @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) @ Theta )
% 0.29/0.46 != none_trm )
% 0.29/0.46 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) @ Theta ) ) )
% 0.29/0.46 = ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ Sigma @ I2 @ ( F @ zero_zero_real ) ) @ F @ X @ Theta ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % usubst_ode
% 0.29/0.46 thf(fact_200_variable_Osize__gen_I2_J,axiom,
% 0.29/0.46 ! [X23: char] :
% 0.29/0.46 ( ( size_variable @ ( dVar @ X23 ) )
% 0.29/0.46 = zero_zero_nat ) ).
% 0.29/0.46
% 0.29/0.46 % variable.size_gen(2)
% 0.29/0.46 thf(fact_201_option_Oexpand,axiom,
% 0.29/0.46 ! [Option: option_trm,Option2: option_trm] :
% 0.29/0.46 ( ( ( Option = none_trm )
% 0.29/0.46 = ( Option2 = none_trm ) )
% 0.29/0.46 => ( ( ( Option != none_trm )
% 0.29/0.46 => ( ( Option2 != none_trm )
% 0.29/0.46 => ( ( the_trm @ Option )
% 0.29/0.46 = ( the_trm @ Option2 ) ) ) )
% 0.29/0.46 => ( Option = Option2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.expand
% 0.29/0.46 thf(fact_202_variable_Osize_I3_J,axiom,
% 0.29/0.46 ! [X12: char] :
% 0.29/0.46 ( ( size_size_variable @ ( rVar @ X12 ) )
% 0.29/0.46 = zero_zero_nat ) ).
% 0.29/0.46
% 0.29/0.46 % variable.size(3)
% 0.29/0.46 thf(fact_203_variable_Osize_I4_J,axiom,
% 0.29/0.46 ! [X23: char] :
% 0.29/0.46 ( ( size_size_variable @ ( dVar @ X23 ) )
% 0.29/0.46 = zero_zero_nat ) ).
% 0.29/0.46
% 0.29/0.46 % variable.size(4)
% 0.29/0.46 thf(fact_204_Set_Ois__empty__def,axiom,
% 0.29/0.46 ( is_empty_variable
% 0.29/0.46 = ( ^ [A4: set_variable] : ( A4 = bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Set.is_empty_def
% 0.29/0.46 thf(fact_205_Set_Ois__empty__def,axiom,
% 0.29/0.46 ( is_emp227886046e_real
% 0.29/0.46 = ( ^ [A4: set_variable_real] : ( A4 = bot_bo721182586e_real ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Set.is_empty_def
% 0.29/0.46 thf(fact_206_Uvariation__repv,axiom,
% 0.29/0.46 ! [Omega: variable > real,X: variable,D: real] : ( denota1419872369iation @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert_variable @ X @ bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_repv
% 0.29/0.46 thf(fact_207_these__empty__eq,axiom,
% 0.29/0.46 ! [B: set_option_trm] :
% 0.29/0.46 ( ( ( these_trm @ B )
% 0.29/0.46 = bot_bot_set_trm )
% 0.29/0.46 = ( ( B = bot_bo946428664on_trm )
% 0.29/0.46 | ( B
% 0.29/0.46 = ( insert_option_trm @ none_trm @ bot_bo946428664on_trm ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_empty_eq
% 0.29/0.46 thf(fact_208_these__empty__eq,axiom,
% 0.29/0.46 ! [B: set_option_variable] :
% 0.29/0.46 ( ( ( these_variable @ B )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( ( B = bot_bo266290559riable )
% 0.29/0.46 | ( B
% 0.29/0.46 = ( insert1340772453riable @ none_variable @ bot_bo266290559riable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_empty_eq
% 0.29/0.46 thf(fact_209_these__empty__eq,axiom,
% 0.29/0.46 ! [B: set_op12188086e_real] :
% 0.29/0.46 ( ( ( these_variable_real @ B )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( ( B = bot_bo1411475018e_real )
% 0.29/0.46 | ( B
% 0.29/0.46 = ( insert526581936e_real @ none_variable_real @ bot_bo1411475018e_real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_empty_eq
% 0.29/0.46 thf(fact_210_these__not__empty__eq,axiom,
% 0.29/0.46 ! [B: set_option_trm] :
% 0.29/0.46 ( ( ( these_trm @ B )
% 0.29/0.46 != bot_bot_set_trm )
% 0.29/0.46 = ( ( B != bot_bo946428664on_trm )
% 0.29/0.46 & ( B
% 0.29/0.46 != ( insert_option_trm @ none_trm @ bot_bo946428664on_trm ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_not_empty_eq
% 0.29/0.46 thf(fact_211_these__not__empty__eq,axiom,
% 0.29/0.46 ! [B: set_option_variable] :
% 0.29/0.46 ( ( ( these_variable @ B )
% 0.29/0.46 != bot_bot_set_variable )
% 0.29/0.46 = ( ( B != bot_bo266290559riable )
% 0.29/0.46 & ( B
% 0.29/0.46 != ( insert1340772453riable @ none_variable @ bot_bo266290559riable ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_not_empty_eq
% 0.29/0.46 thf(fact_212_these__not__empty__eq,axiom,
% 0.29/0.46 ! [B: set_op12188086e_real] :
% 0.29/0.46 ( ( ( these_variable_real @ B )
% 0.29/0.46 != bot_bo721182586e_real )
% 0.29/0.46 = ( ( B != bot_bo1411475018e_real )
% 0.29/0.46 & ( B
% 0.29/0.46 != ( insert526581936e_real @ none_variable_real @ bot_bo1411475018e_real ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_not_empty_eq
% 0.29/0.46 thf(fact_213_repv__self,axiom,
% 0.29/0.46 ! [Omega: variable > real,X: variable] :
% 0.29/0.46 ( ( denotational_repv @ Omega @ X @ ( Omega @ X ) )
% 0.29/0.46 = Omega ) ).
% 0.29/0.46
% 0.29/0.46 % repv_self
% 0.29/0.46 thf(fact_214_repv__access,axiom,
% 0.29/0.46 ( denotational_repv
% 0.29/0.46 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if_real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % repv_access
% 0.29/0.46 thf(fact_215_these__empty,axiom,
% 0.29/0.46 ( ( these_variable @ bot_bo266290559riable )
% 0.29/0.46 = bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % these_empty
% 0.29/0.46 thf(fact_216_these__empty,axiom,
% 0.29/0.46 ( ( these_variable_real @ bot_bo1411475018e_real )
% 0.29/0.46 = bot_bo721182586e_real ) ).
% 0.29/0.46
% 0.29/0.46 % these_empty
% 0.29/0.46 thf(fact_217_these__insert__None,axiom,
% 0.29/0.46 ! [A2: set_option_trm] :
% 0.29/0.46 ( ( these_trm @ ( insert_option_trm @ none_trm @ A2 ) )
% 0.29/0.46 = ( these_trm @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_insert_None
% 0.29/0.46 thf(fact_218_repv__def__correct,axiom,
% 0.29/0.46 ( denotational_repv
% 0.29/0.46 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if_real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % repv_def_correct
% 0.29/0.46 thf(fact_219_these__insert__Some,axiom,
% 0.29/0.46 ! [X: variable,A2: set_option_variable] :
% 0.29/0.46 ( ( these_variable @ ( insert1340772453riable @ ( some_variable @ X ) @ A2 ) )
% 0.29/0.46 = ( insert_variable @ X @ ( these_variable @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_insert_Some
% 0.29/0.46 thf(fact_220_these__insert__Some,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_op12188086e_real] :
% 0.29/0.46 ( ( these_variable_real @ ( insert526581936e_real @ ( some_variable_real @ X ) @ A2 ) )
% 0.29/0.46 = ( insert_variable_real @ X @ ( these_variable_real @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_insert_Some
% 0.29/0.46 thf(fact_221_these__insert__Some,axiom,
% 0.29/0.46 ! [X: trm,A2: set_option_trm] :
% 0.29/0.46 ( ( these_trm @ ( insert_option_trm @ ( some_trm @ X ) @ A2 ) )
% 0.29/0.46 = ( insert_trm @ X @ ( these_trm @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % these_insert_Some
% 0.29/0.46 thf(fact_222_repv__selectlike__other__converse,axiom,
% 0.29/0.46 ! [X: variable,Y: variable,Omega: variable > real,D: real,X7: set_variable_real] :
% 0.29/0.46 ( ( X != Y )
% 0.29/0.46 => ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ X7 )
% 0.29/0.46 = ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ Y @ bot_bot_set_variable ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % repv_selectlike_other_converse
% 0.29/0.46 thf(fact_223_repv__selectlike__other,axiom,
% 0.29/0.46 ! [X: variable,Y: variable,Omega: variable > real,D: real,X7: set_variable_real] :
% 0.29/0.46 ( ( X != Y )
% 0.29/0.46 => ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ Y @ bot_bot_set_variable ) ) )
% 0.29/0.46 = ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ X7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % repv_selectlike_other
% 0.29/0.46 thf(fact_224_repv__selectlike__self,axiom,
% 0.29/0.46 ! [Omega: variable > real,X: variable,D: real,X7: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 0.29/0.46 = ( ( D
% 0.29/0.46 = ( Omega @ X ) )
% 0.29/0.46 & ( member_variable_real @ Omega @ X7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % repv_selectlike_self
% 0.29/0.46 thf(fact_225_option_Oinject,axiom,
% 0.29/0.46 ! [X23: trm,Y22: trm] :
% 0.29/0.46 ( ( ( some_trm @ X23 )
% 0.29/0.46 = ( some_trm @ Y22 ) )
% 0.29/0.46 = ( X23 = Y22 ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.inject
% 0.29/0.46 thf(fact_226_selectlike__self,axiom,
% 0.29/0.46 ! [Nu: variable > real,X7: set_variable_real,V: set_variable] :
% 0.29/0.46 ( ( member_variable_real @ Nu @ ( static_selectlike @ X7 @ Nu @ V ) )
% 0.29/0.46 = ( member_variable_real @ Nu @ X7 ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_self
% 0.29/0.46 thf(fact_227_not__None__eq,axiom,
% 0.29/0.46 ! [X: option_trm] :
% 0.29/0.46 ( ( X != none_trm )
% 0.29/0.46 = ( ? [Y3: trm] :
% 0.29/0.46 ( X
% 0.29/0.46 = ( some_trm @ Y3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_None_eq
% 0.29/0.46 thf(fact_228_not__Some__eq,axiom,
% 0.29/0.46 ! [X: option_trm] :
% 0.29/0.46 ( ( ! [Y3: trm] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( some_trm @ Y3 ) ) )
% 0.29/0.46 = ( X = none_trm ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_Some_eq
% 0.29/0.46 thf(fact_229_selectlike__empty,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Nu: variable > real] :
% 0.29/0.46 ( ( static_selectlike @ X7 @ Nu @ bot_bot_set_variable )
% 0.29/0.46 = X7 ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_empty
% 0.29/0.46 thf(fact_230_selectlike__compose,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,W: set_variable] :
% 0.29/0.46 ( ( static_selectlike @ ( static_selectlike @ X7 @ Nu @ V ) @ Nu @ W )
% 0.29/0.46 = ( static_selectlike @ X7 @ Nu @ ( sup_sup_set_variable @ V @ W ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_compose
% 0.29/0.46 thf(fact_231_option_Ocollapse,axiom,
% 0.29/0.46 ! [Option: option_trm] :
% 0.29/0.46 ( ( Option != none_trm )
% 0.29/0.46 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.29/0.46 = Option ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.collapse
% 0.29/0.46 thf(fact_232_in__these__eq,axiom,
% 0.29/0.46 ! [X: variable,A2: set_option_variable] :
% 0.29/0.46 ( ( member_variable @ X @ ( these_variable @ A2 ) )
% 0.29/0.46 = ( member814448204riable @ ( some_variable @ X ) @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % in_these_eq
% 0.29/0.46 thf(fact_233_in__these__eq,axiom,
% 0.29/0.46 ! [X: variable > real,A2: set_op12188086e_real] :
% 0.29/0.46 ( ( member_variable_real @ X @ ( these_variable_real @ A2 ) )
% 0.29/0.46 = ( member523846807e_real @ ( some_variable_real @ X ) @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % in_these_eq
% 0.29/0.46 thf(fact_234_in__these__eq,axiom,
% 0.29/0.46 ! [X: trm,A2: set_option_trm] :
% 0.29/0.46 ( ( member_trm @ X @ ( these_trm @ A2 ) )
% 0.29/0.46 = ( member_option_trm @ ( some_trm @ X ) @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % in_these_eq
% 0.29/0.46 thf(fact_235_selectlike__union,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Y4: set_variable_real,Nu: variable > real,V: set_variable] :
% 0.29/0.46 ( ( static_selectlike @ ( sup_su1685293586e_real @ X7 @ Y4 ) @ Nu @ V )
% 0.29/0.46 = ( sup_su1685293586e_real @ ( static_selectlike @ X7 @ Nu @ V ) @ ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_union
% 0.29/0.46 thf(fact_236_option_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [X23: trm] :
% 0.29/0.46 ( none_trm
% 0.29/0.46 != ( some_trm @ X23 ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.distinct(1)
% 0.29/0.46 thf(fact_237_option_Osel,axiom,
% 0.29/0.46 ! [X23: trm] :
% 0.29/0.46 ( ( the_trm @ ( some_trm @ X23 ) )
% 0.29/0.46 = X23 ) ).
% 0.29/0.46
% 0.29/0.46 % option.sel
% 0.29/0.46 thf(fact_238_option_OdiscI,axiom,
% 0.29/0.46 ! [Option: option_trm,X23: trm] :
% 0.29/0.46 ( ( Option
% 0.29/0.46 = ( some_trm @ X23 ) )
% 0.29/0.46 => ( Option != none_trm ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.discI
% 0.29/0.46 thf(fact_239_option_Oexhaust,axiom,
% 0.29/0.46 ! [Y: option_trm] :
% 0.29/0.46 ( ( Y != none_trm )
% 0.29/0.46 => ~ ! [X24: trm] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( some_trm @ X24 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.exhaust
% 0.29/0.46 thf(fact_240_option_Oinducts,axiom,
% 0.29/0.46 ! [P: option_trm > $o,Option: option_trm] :
% 0.29/0.46 ( ( P @ none_trm )
% 0.29/0.46 => ( ! [X6: trm] : ( P @ ( some_trm @ X6 ) )
% 0.29/0.46 => ( P @ Option ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.inducts
% 0.29/0.46 thf(fact_241_split__option__ex,axiom,
% 0.29/0.46 ( ( ^ [P2: option_trm > $o] :
% 0.29/0.46 ? [X8: option_trm] : ( P2 @ X8 ) )
% 0.29/0.46 = ( ^ [P3: option_trm > $o] :
% 0.29/0.46 ( ( P3 @ none_trm )
% 0.29/0.46 | ? [X2: trm] : ( P3 @ ( some_trm @ X2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % split_option_ex
% 0.29/0.46 thf(fact_242_split__option__all,axiom,
% 0.29/0.46 ( ( ^ [P2: option_trm > $o] :
% 0.29/0.46 ! [X8: option_trm] : ( P2 @ X8 ) )
% 0.29/0.46 = ( ^ [P3: option_trm > $o] :
% 0.29/0.46 ( ( P3 @ none_trm )
% 0.29/0.46 & ! [X2: trm] : ( P3 @ ( some_trm @ X2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % split_option_all
% 0.29/0.46 thf(fact_243_combine__options__cases,axiom,
% 0.29/0.46 ! [X: option_trm,P: option_trm > option_trm > $o,Y: option_trm] :
% 0.29/0.46 ( ( ( X = none_trm )
% 0.29/0.46 => ( P @ X @ Y ) )
% 0.29/0.46 => ( ( ( Y = none_trm )
% 0.29/0.46 => ( P @ X @ Y ) )
% 0.29/0.46 => ( ! [A5: trm,B6: trm] :
% 0.29/0.46 ( ( X
% 0.29/0.46 = ( some_trm @ A5 ) )
% 0.29/0.46 => ( ( Y
% 0.29/0.46 = ( some_trm @ B6 ) )
% 0.29/0.46 => ( P @ X @ Y ) ) )
% 0.29/0.46 => ( P @ X @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % combine_options_cases
% 0.29/0.46 thf(fact_244_ODEo_Oinduct,axiom,
% 0.29/0.46 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.29/0.46 ( ! [X6: char,Theta2: trm] : ( P @ X6 @ ( some_trm @ Theta2 ) )
% 0.29/0.46 => ( ! [X6: char] : ( P @ X6 @ none_trm )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ODEo.induct
% 0.29/0.46 thf(fact_245_undeft__equiv,axiom,
% 0.29/0.46 ! [Theta: option_trm] :
% 0.29/0.46 ( ( Theta != none_trm )
% 0.29/0.46 = ( ? [T2: trm] :
% 0.29/0.46 ( Theta
% 0.29/0.46 = ( some_trm @ T2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % undeft_equiv
% 0.29/0.46 thf(fact_246_Timeso_Oinduct,axiom,
% 0.29/0.46 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.29/0.46 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.29/0.46 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 0.29/0.46 => ( ! [V2: trm] : ( P @ ( some_trm @ V2 ) @ none_trm )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso.induct
% 0.29/0.46 thf(fact_247_Assigno_Oinduct,axiom,
% 0.29/0.46 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.29/0.46 ( ! [X6: variable,Theta2: trm] : ( P @ X6 @ ( some_trm @ Theta2 ) )
% 0.29/0.46 => ( ! [X6: variable] : ( P @ X6 @ none_trm )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Assigno.induct
% 0.29/0.46 thf(fact_248_Differentialo_Ocases,axiom,
% 0.29/0.46 ! [X: option_trm] :
% 0.29/0.46 ( ! [Theta2: trm] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( some_trm @ Theta2 ) )
% 0.29/0.46 => ( X = none_trm ) ) ).
% 0.29/0.46
% 0.29/0.46 % Differentialo.cases
% 0.29/0.46 thf(fact_249_Differentialo_Oinduct,axiom,
% 0.29/0.46 ! [P: option_trm > $o,A0: option_trm] :
% 0.29/0.46 ( ! [Theta2: trm] : ( P @ ( some_trm @ Theta2 ) )
% 0.29/0.46 => ( ( P @ none_trm )
% 0.29/0.46 => ( P @ A0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Differentialo.induct
% 0.29/0.46 thf(fact_250_option_Oexhaust__sel,axiom,
% 0.29/0.46 ! [Option: option_trm] :
% 0.29/0.46 ( ( Option != none_trm )
% 0.29/0.46 => ( Option
% 0.29/0.46 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.exhaust_sel
% 0.29/0.46 thf(fact_251_option_Osimps_I15_J,axiom,
% 0.29/0.46 ! [X23: trm] :
% 0.29/0.46 ( ( set_option_trm2 @ ( some_trm @ X23 ) )
% 0.29/0.46 = ( insert_trm @ X23 @ bot_bot_set_trm ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(15)
% 0.29/0.46 thf(fact_252_option_Osimps_I15_J,axiom,
% 0.29/0.46 ! [X23: variable] :
% 0.29/0.46 ( ( set_option_variable2 @ ( some_variable @ X23 ) )
% 0.29/0.46 = ( insert_variable @ X23 @ bot_bot_set_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(15)
% 0.29/0.46 thf(fact_253_option_Osimps_I15_J,axiom,
% 0.29/0.46 ! [X23: variable > real] :
% 0.29/0.46 ( ( set_op697949218e_real @ ( some_variable_real @ X23 ) )
% 0.29/0.46 = ( insert_variable_real @ X23 @ bot_bo721182586e_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(15)
% 0.29/0.46 thf(fact_254_Vagree__repv__self,axiom,
% 0.29/0.46 ! [Omega: variable > real,X: variable,D: real] :
% 0.29/0.46 ( ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert_variable @ X @ bot_bot_set_variable ) )
% 0.29/0.46 = ( D
% 0.29/0.46 = ( Omega @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_repv_self
% 0.29/0.46 thf(fact_255_elem__set,axiom,
% 0.29/0.46 ! [X: variable,Xo: option_variable] :
% 0.29/0.46 ( ( member_variable @ X @ ( set_option_variable2 @ Xo ) )
% 0.29/0.46 = ( Xo
% 0.29/0.46 = ( some_variable @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % elem_set
% 0.29/0.46 thf(fact_256_elem__set,axiom,
% 0.29/0.46 ! [X: variable > real,Xo: option_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ X @ ( set_op697949218e_real @ Xo ) )
% 0.29/0.46 = ( Xo
% 0.29/0.46 = ( some_variable_real @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % elem_set
% 0.29/0.46 thf(fact_257_elem__set,axiom,
% 0.29/0.46 ! [X: trm,Xo: option_trm] :
% 0.29/0.46 ( ( member_trm @ X @ ( set_option_trm2 @ Xo ) )
% 0.29/0.46 = ( Xo
% 0.29/0.46 = ( some_trm @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % elem_set
% 0.29/0.46 thf(fact_258_Vagree__and,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real,V: set_variable,W: set_variable] :
% 0.29/0.46 ( ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.29/0.46 & ( denotational_Vagree @ Nu @ Nu2 @ W ) )
% 0.29/0.46 = ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup_set_variable @ V @ W ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_and
% 0.29/0.46 thf(fact_259_set__empty__eq,axiom,
% 0.29/0.46 ! [Xo: option_trm] :
% 0.29/0.46 ( ( ( set_option_trm2 @ Xo )
% 0.29/0.46 = bot_bot_set_trm )
% 0.29/0.46 = ( Xo = none_trm ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_empty_eq
% 0.29/0.46 thf(fact_260_set__empty__eq,axiom,
% 0.29/0.46 ! [Xo: option_variable] :
% 0.29/0.46 ( ( ( set_option_variable2 @ Xo )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 = ( Xo = none_variable ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_empty_eq
% 0.29/0.46 thf(fact_261_set__empty__eq,axiom,
% 0.29/0.46 ! [Xo: option_variable_real] :
% 0.29/0.46 ( ( ( set_op697949218e_real @ Xo )
% 0.29/0.46 = bot_bo721182586e_real )
% 0.29/0.46 = ( Xo = none_variable_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % set_empty_eq
% 0.29/0.46 thf(fact_262_similar__selectlike__mem,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real,V: set_variable,X7: set_variable_real] :
% 0.29/0.46 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 0.29/0.46 => ( ( member_variable_real @ Nu @ ( static_selectlike @ X7 @ Omega @ V ) )
% 0.29/0.46 = ( member_variable_real @ Nu @ X7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % similar_selectlike_mem
% 0.29/0.46 thf(fact_263_selectlike__Vagree,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real,V: set_variable,X7: set_variable_real] :
% 0.29/0.46 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 0.29/0.46 => ( ( static_selectlike @ X7 @ Nu @ V )
% 0.29/0.46 = ( static_selectlike @ X7 @ Omega @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_Vagree
% 0.29/0.46 thf(fact_264_Aterm__Some,axiom,
% 0.29/0.46 some_trm = some_trm ).
% 0.29/0.46
% 0.29/0.46 % Aterm_Some
% 0.29/0.46 thf(fact_265_option_Oset__intros,axiom,
% 0.29/0.46 ! [X23: variable] : ( member_variable @ X23 @ ( set_option_variable2 @ ( some_variable @ X23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_intros
% 0.29/0.46 thf(fact_266_option_Oset__intros,axiom,
% 0.29/0.46 ! [X23: variable > real] : ( member_variable_real @ X23 @ ( set_op697949218e_real @ ( some_variable_real @ X23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_intros
% 0.29/0.46 thf(fact_267_option_Oset__intros,axiom,
% 0.29/0.46 ! [X23: trm] : ( member_trm @ X23 @ ( set_option_trm2 @ ( some_trm @ X23 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_intros
% 0.29/0.46 thf(fact_268_option_Oset__cases,axiom,
% 0.29/0.46 ! [E: variable,A: option_variable] :
% 0.29/0.46 ( ( member_variable @ E @ ( set_option_variable2 @ A ) )
% 0.29/0.46 => ( A
% 0.29/0.46 = ( some_variable @ E ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_cases
% 0.29/0.46 thf(fact_269_option_Oset__cases,axiom,
% 0.29/0.46 ! [E: variable > real,A: option_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ E @ ( set_op697949218e_real @ A ) )
% 0.29/0.46 => ( A
% 0.29/0.46 = ( some_variable_real @ E ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_cases
% 0.29/0.46 thf(fact_270_option_Oset__cases,axiom,
% 0.29/0.46 ! [E: trm,A: option_trm] :
% 0.29/0.46 ( ( member_trm @ E @ ( set_option_trm2 @ A ) )
% 0.29/0.46 => ( A
% 0.29/0.46 = ( some_trm @ E ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_cases
% 0.29/0.46 thf(fact_271_ospec,axiom,
% 0.29/0.46 ! [A2: option_trm,P: trm > $o,X: trm] :
% 0.29/0.46 ( ! [X6: trm] :
% 0.29/0.46 ( ( member_trm @ X6 @ ( set_option_trm2 @ A2 ) )
% 0.29/0.46 => ( P @ X6 ) )
% 0.29/0.46 => ( ( A2
% 0.29/0.46 = ( some_trm @ X ) )
% 0.29/0.46 => ( P @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ospec
% 0.29/0.46 thf(fact_272_Vagree__union,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real,V: set_variable,W: set_variable] :
% 0.29/0.46 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.29/0.46 => ( ( denotational_Vagree @ Nu @ Nu2 @ W )
% 0.29/0.46 => ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup_set_variable @ V @ W ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_union
% 0.29/0.46 thf(fact_273_Vagree__def,axiom,
% 0.29/0.46 ( denotational_Vagree
% 0.29/0.46 = ( ^ [Nu3: variable > real,Nu4: variable > real,V3: set_variable] :
% 0.29/0.46 ! [I: variable] :
% 0.29/0.46 ( ( member_variable @ I @ V3 )
% 0.29/0.46 => ( ( Nu3 @ I )
% 0.29/0.46 = ( Nu4 @ I ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_def
% 0.29/0.46 thf(fact_274_Vagree__sym,axiom,
% 0.29/0.46 ( denotational_Vagree
% 0.29/0.46 = ( ^ [Nu3: variable > real,Nu4: variable > real] : ( denotational_Vagree @ Nu4 @ Nu3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_sym
% 0.29/0.46 thf(fact_275_Vagree__refl,axiom,
% 0.29/0.46 ! [Nu: variable > real,V: set_variable] : ( denotational_Vagree @ Nu @ Nu @ V ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_refl
% 0.29/0.46 thf(fact_276_Vagree__sym__rel,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real,V: set_variable] :
% 0.29/0.46 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 0.29/0.46 => ( denotational_Vagree @ Nu2 @ Nu @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_sym_rel
% 0.29/0.46 thf(fact_277_Vagree__empty,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real] : ( denotational_Vagree @ Nu @ Nu2 @ bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_empty
% 0.29/0.46 thf(fact_278_option_Osimps_I14_J,axiom,
% 0.29/0.46 ( ( set_option_trm2 @ none_trm )
% 0.29/0.46 = bot_bot_set_trm ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(14)
% 0.29/0.46 thf(fact_279_option_Osimps_I14_J,axiom,
% 0.29/0.46 ( ( set_option_variable2 @ none_variable )
% 0.29/0.46 = bot_bot_set_variable ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(14)
% 0.29/0.46 thf(fact_280_option_Osimps_I14_J,axiom,
% 0.29/0.46 ( ( set_op697949218e_real @ none_variable_real )
% 0.29/0.46 = bot_bo721182586e_real ) ).
% 0.29/0.46
% 0.29/0.46 % option.simps(14)
% 0.29/0.46 thf(fact_281_option_Oset__sel,axiom,
% 0.29/0.46 ! [A: option_variable] :
% 0.29/0.46 ( ( A != none_variable )
% 0.29/0.46 => ( member_variable @ ( the_variable @ A ) @ ( set_option_variable2 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_sel
% 0.29/0.46 thf(fact_282_option_Oset__sel,axiom,
% 0.29/0.46 ! [A: option_variable_real] :
% 0.29/0.46 ( ( A != none_variable_real )
% 0.29/0.46 => ( member_variable_real @ ( the_variable_real @ A ) @ ( set_op697949218e_real @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_sel
% 0.29/0.46 thf(fact_283_option_Oset__sel,axiom,
% 0.29/0.46 ! [A: option_trm] :
% 0.29/0.46 ( ( A != none_trm )
% 0.29/0.46 => ( member_trm @ ( the_trm @ A ) @ ( set_option_trm2 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % option.set_sel
% 0.29/0.46 thf(fact_284_solves__Vagree,axiom,
% 0.29/0.46 ! [I2: denotational_interp,F: real > variable > real,X: char,Theta: trm,Zeta: real] :
% 0.29/0.46 ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 0.29/0.46 => ( denotational_Vagree @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( uminus1851247844riable @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % solves_Vagree
% 0.29/0.46 thf(fact_285_Vagree__repv,axiom,
% 0.29/0.46 ! [Omega: variable > real,X: variable,D: real] : ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( uminus1851247844riable @ ( insert_variable @ X @ bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_repv
% 0.29/0.46 thf(fact_286_Timeso_Osimps_I3_J,axiom,
% 0.29/0.46 ! [V4: trm] :
% 0.29/0.46 ( ( uSubst918876924Timeso @ ( some_trm @ V4 ) @ none_trm )
% 0.29/0.46 = none_trm ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso.simps(3)
% 0.29/0.46 thf(fact_287_compl__eq__compl__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( ( uminus1851247844riable @ X )
% 0.29/0.46 = ( uminus1851247844riable @ Y ) )
% 0.29/0.46 = ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_eq_compl_iff
% 0.29/0.46 thf(fact_288_compl__eq__compl__iff,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( ( uminus430703407e_real @ X )
% 0.29/0.46 = ( uminus430703407e_real @ Y ) )
% 0.29/0.46 = ( X = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_eq_compl_iff
% 0.29/0.46 thf(fact_289_double__compl,axiom,
% 0.29/0.46 ! [X: set_variable] :
% 0.29/0.46 ( ( uminus1851247844riable @ ( uminus1851247844riable @ X ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % double_compl
% 0.29/0.46 thf(fact_290_double__compl,axiom,
% 0.29/0.46 ! [X: set_variable_real] :
% 0.29/0.46 ( ( uminus430703407e_real @ ( uminus430703407e_real @ X ) )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % double_compl
% 0.29/0.46 thf(fact_291_Compl__eq__Compl__iff,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( ( uminus1851247844riable @ A2 )
% 0.29/0.46 = ( uminus1851247844riable @ B ) )
% 0.29/0.46 = ( A2 = B ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_eq_Compl_iff
% 0.29/0.46 thf(fact_292_Compl__eq__Compl__iff,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( ( uminus430703407e_real @ A2 )
% 0.29/0.46 = ( uminus430703407e_real @ B ) )
% 0.29/0.46 = ( A2 = B ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_eq_Compl_iff
% 0.29/0.46 thf(fact_293_Compl__iff,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) )
% 0.29/0.46 = ( ~ ( member_variable @ C2 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_294_Compl__iff,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) )
% 0.29/0.46 = ( ~ ( member_variable_real @ C2 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Compl_iff
% 0.29/0.46 thf(fact_295_ComplI,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable] :
% 0.29/0.46 ( ~ ( member_variable @ C2 @ A2 )
% 0.29/0.46 => ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_296_ComplI,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ~ ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 => ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplI
% 0.29/0.46 thf(fact_297_add_Oinverse__neutral,axiom,
% 0.29/0.46 ( ( uminus_uminus_real @ zero_zero_real )
% 0.29/0.46 = zero_zero_real ) ).
% 0.29/0.46
% 0.29/0.46 % add.inverse_neutral
% 0.29/0.46 thf(fact_298_neg__0__equal__iff__equal,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( zero_zero_real
% 0.29/0.46 = ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( zero_zero_real = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_0_equal_iff_equal
% 0.29/0.46 thf(fact_299_neg__equal__0__iff__equal,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ( uminus_uminus_real @ A )
% 0.29/0.46 = zero_zero_real )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_equal_0_iff_equal
% 0.29/0.46 thf(fact_300_equal__neg__zero,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( A
% 0.29/0.46 = ( uminus_uminus_real @ A ) )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % equal_neg_zero
% 0.29/0.46 thf(fact_301_neg__equal__zero,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( ( uminus_uminus_real @ A )
% 0.29/0.46 = A )
% 0.29/0.46 = ( A = zero_zero_real ) ) ).
% 0.29/0.46
% 0.29/0.46 % neg_equal_zero
% 0.29/0.46 thf(fact_302_Uvariation__Vagree,axiom,
% 0.29/0.46 ! [Nu: variable > real,Nu2: variable > real,V: set_variable] :
% 0.29/0.46 ( ( denota1419872369iation @ Nu @ Nu2 @ ( uminus1851247844riable @ V ) )
% 0.29/0.46 = ( denotational_Vagree @ Nu @ Nu2 @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % Uvariation_Vagree
% 0.29/0.46 thf(fact_303_double__complement,axiom,
% 0.29/0.46 ! [A2: set_variable] :
% 0.29/0.46 ( ( uminus1851247844riable @ ( uminus1851247844riable @ A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % double_complement
% 0.29/0.46 thf(fact_304_double__complement,axiom,
% 0.29/0.46 ! [A2: set_variable_real] :
% 0.29/0.46 ( ( uminus430703407e_real @ ( uminus430703407e_real @ A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % double_complement
% 0.29/0.46 thf(fact_305_ComplD,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) )
% 0.29/0.46 => ~ ( member_variable @ C2 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplD
% 0.29/0.46 thf(fact_306_ComplD,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) )
% 0.29/0.46 => ~ ( member_variable_real @ C2 @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % ComplD
% 0.29/0.46 thf(fact_307_Timeso_Osimps_I2_J,axiom,
% 0.29/0.46 ! [Eta: option_trm] :
% 0.29/0.46 ( ( uSubst918876924Timeso @ none_trm @ Eta )
% 0.29/0.46 = none_trm ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso.simps(2)
% 0.29/0.46 thf(fact_308_Timeso__undef,axiom,
% 0.29/0.46 ! [Theta: option_trm,Eta: option_trm] :
% 0.29/0.46 ( ( ( uSubst918876924Timeso @ Theta @ Eta )
% 0.29/0.46 = none_trm )
% 0.29/0.46 = ( ( Theta = none_trm )
% 0.29/0.46 | ( Eta = none_trm ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso_undef
% 0.29/0.46 thf(fact_309_selectlike__equal__cocond__corule,axiom,
% 0.29/0.46 ! [Nu: variable > real,V: set_variable,X7: set_variable_real,Y4: set_variable_real] :
% 0.29/0.46 ( ! [Mu2: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Mu2 @ Nu @ V )
% 0.29/0.46 => ( ( member_variable_real @ Mu2 @ X7 )
% 0.29/0.46 = ( member_variable_real @ Mu2 @ Y4 ) ) )
% 0.29/0.46 => ( ( static_selectlike @ X7 @ Nu @ ( uminus1851247844riable @ V ) )
% 0.29/0.46 = ( static_selectlike @ Y4 @ Nu @ ( uminus1851247844riable @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_equal_cocond_corule
% 0.29/0.46 thf(fact_310_selectlike__equal__cocond__rule,axiom,
% 0.29/0.46 ! [Nu: variable > real,V: set_variable,X7: set_variable_real,Y4: set_variable_real] :
% 0.29/0.46 ( ! [Mu2: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Mu2 @ Nu @ ( uminus1851247844riable @ V ) )
% 0.29/0.46 => ( ( member_variable_real @ Mu2 @ X7 )
% 0.29/0.46 = ( member_variable_real @ Mu2 @ Y4 ) ) )
% 0.29/0.46 => ( ( static_selectlike @ X7 @ Nu @ V )
% 0.29/0.46 = ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_equal_cocond_rule
% 0.29/0.46 thf(fact_311_selectlike__equal__cocond,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,Y4: set_variable_real] :
% 0.29/0.46 ( ( ( static_selectlike @ X7 @ Nu @ ( uminus1851247844riable @ V ) )
% 0.29/0.46 = ( static_selectlike @ Y4 @ Nu @ ( uminus1851247844riable @ V ) ) )
% 0.29/0.46 = ( ! [Mu3: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Mu3 @ Nu @ V )
% 0.29/0.46 => ( ( member_variable_real @ Mu3 @ X7 )
% 0.29/0.46 = ( member_variable_real @ Mu3 @ Y4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_equal_cocond
% 0.29/0.46 thf(fact_312_selectlike__equal__cond,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,Y4: set_variable_real] :
% 0.29/0.46 ( ( ( static_selectlike @ X7 @ Nu @ V )
% 0.29/0.46 = ( static_selectlike @ Y4 @ Nu @ V ) )
% 0.29/0.46 = ( ! [Mu3: variable > real] :
% 0.29/0.46 ( ( denota1419872369iation @ Mu3 @ Nu @ ( uminus1851247844riable @ V ) )
% 0.29/0.46 => ( ( member_variable_real @ Mu3 @ X7 )
% 0.29/0.46 = ( member_variable_real @ Mu3 @ Y4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_equal_cond
% 0.29/0.46 thf(fact_313_stateinterpol__insert,axiom,
% 0.29/0.46 ! [V4: variable > real,W2: variable > real,S: set_variable,Z: variable] : ( denotational_Vagree @ ( stateinterpol @ V4 @ W2 @ S ) @ ( stateinterpol @ V4 @ W2 @ ( insert_variable @ Z @ S ) ) @ ( uminus1851247844riable @ ( insert_variable @ Z @ bot_bot_set_variable ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_insert
% 0.29/0.46 thf(fact_314_Timeso_Oelims,axiom,
% 0.29/0.46 ! [X: option_trm,Xa: option_trm,Y: option_trm] :
% 0.29/0.46 ( ( ( uSubst918876924Timeso @ X @ Xa )
% 0.29/0.46 = Y )
% 0.29/0.46 => ( ! [Theta2: trm] :
% 0.29/0.46 ( ( X
% 0.29/0.46 = ( some_trm @ Theta2 ) )
% 0.29/0.46 => ! [Eta2: trm] :
% 0.29/0.46 ( ( Xa
% 0.29/0.46 = ( some_trm @ Eta2 ) )
% 0.29/0.46 => ( Y
% 0.29/0.46 != ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.29/0.46 => ( ( ( X = none_trm )
% 0.29/0.46 => ( Y != none_trm ) )
% 0.29/0.46 => ~ ( ? [V2: trm] :
% 0.29/0.46 ( X
% 0.29/0.46 = ( some_trm @ V2 ) )
% 0.29/0.46 => ( ( Xa = none_trm )
% 0.29/0.46 => ( Y != none_trm ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso.elims
% 0.29/0.46 thf(fact_315_trm_Oinject_I6_J,axiom,
% 0.29/0.46 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.29/0.46 ( ( ( times @ X61 @ X62 )
% 0.29/0.46 = ( times @ Y61 @ Y62 ) )
% 0.29/0.46 = ( ( X61 = Y61 )
% 0.29/0.46 & ( X62 = Y62 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % trm.inject(6)
% 0.29/0.46 thf(fact_316_stateinterpol__left,axiom,
% 0.29/0.46 ! [X: variable,S: set_variable,Nu: variable > real,Omega: variable > real] :
% 0.29/0.46 ( ( member_variable @ X @ S )
% 0.29/0.46 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 0.29/0.46 = ( Nu @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_left
% 0.29/0.46 thf(fact_317_stateinterpol__right,axiom,
% 0.29/0.46 ! [X: variable,S: set_variable,Nu: variable > real,Omega: variable > real] :
% 0.29/0.46 ( ~ ( member_variable @ X @ S )
% 0.29/0.46 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 0.29/0.46 = ( Omega @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_right
% 0.29/0.46 thf(fact_318_selectlike__co__selectlike,axiom,
% 0.29/0.46 ! [X7: set_variable_real,Nu: variable > real,V: set_variable] :
% 0.29/0.46 ( ( static_selectlike @ ( uminus430703407e_real @ ( static_selectlike @ X7 @ Nu @ V ) ) @ Nu @ V )
% 0.29/0.46 = ( static_selectlike @ ( uminus430703407e_real @ X7 ) @ Nu @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % selectlike_co_selectlike
% 0.29/0.46 thf(fact_319_stateinterpol__empty,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real] :
% 0.29/0.46 ( ( stateinterpol @ Nu @ Omega @ bot_bot_set_variable )
% 0.29/0.46 = Omega ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_empty
% 0.29/0.46 thf(fact_320_Vagree__stateinterpol,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real,S: set_variable] : ( denotational_Vagree @ ( stateinterpol @ Nu @ Omega @ S ) @ Nu @ S ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_stateinterpol
% 0.29/0.46 thf(fact_321_stateinterpol__def,axiom,
% 0.29/0.46 ( stateinterpol
% 0.29/0.46 = ( ^ [Nu3: variable > real,Omega2: variable > real,S2: set_variable,X2: variable] : ( if_real @ ( member_variable @ X2 @ S2 ) @ ( Nu3 @ X2 ) @ ( Omega2 @ X2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_def
% 0.29/0.46 thf(fact_322_usubstappt__times__conv,axiom,
% 0.29/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.29/0.46 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.29/0.46 != none_trm )
% 0.29/0.46 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.29/0.46 != none_trm )
% 0.29/0.46 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.29/0.46 != none_trm ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % usubstappt_times_conv
% 0.29/0.46 thf(fact_323_usubstappt_Osimps_I6_J,axiom,
% 0.29/0.46 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.29/0.46 ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.29/0.46 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % usubstappt.simps(6)
% 0.29/0.46 thf(fact_324_Timeso_Osimps_I1_J,axiom,
% 0.29/0.46 ! [Theta: trm,Eta: trm] :
% 0.29/0.46 ( ( uSubst918876924Timeso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.29/0.46 = ( some_trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Timeso.simps(1)
% 0.29/0.46 thf(fact_325_stateinterpol__diff,axiom,
% 0.29/0.46 ! [Nu: variable > real,Omega: variable > real] :
% 0.29/0.46 ( ( stateinterpol @ Nu @ Omega @ ( statediff @ Nu @ Omega ) )
% 0.29/0.46 = Nu ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_diff
% 0.29/0.46 thf(fact_326_stateinterpol__FVT,axiom,
% 0.29/0.46 ! [Z: variable,T3: trm,I2: denotational_interp,Omega: variable > real,Omega3: variable > real,S: set_variable] :
% 0.29/0.46 ( ~ ( member_variable @ Z @ ( static_FVT @ T3 ) )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ S ) )
% 0.29/0.46 = ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ ( insert_variable @ Z @ S ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % stateinterpol_FVT
% 0.29/0.46 thf(fact_327_nostatediff,axiom,
% 0.29/0.46 ! [X: variable,Nu: variable > real,Omega: variable > real] :
% 0.29/0.46 ( ~ ( member_variable @ X @ ( statediff @ Nu @ Omega ) )
% 0.29/0.46 => ( ( Nu @ X )
% 0.29/0.46 = ( Omega @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nostatediff
% 0.29/0.46 thf(fact_328_coincidence__term,axiom,
% 0.29/0.46 ! [Omega: variable > real,Omega3: variable > real,Theta: trm,I2: denotational_interp] :
% 0.29/0.46 ( ( denotational_Vagree @ Omega @ Omega3 @ ( static_FVT @ Theta ) )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 0.29/0.46 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % coincidence_term
% 0.29/0.46 thf(fact_329_coincidence__term__cor,axiom,
% 0.29/0.46 ! [Omega: variable > real,Omega3: variable > real,U: set_variable,Theta: trm,I2: denotational_interp] :
% 0.29/0.46 ( ( denota1419872369iation @ Omega @ Omega3 @ U )
% 0.29/0.46 => ( ( ( inf_inf_set_variable @ ( static_FVT @ Theta ) @ U )
% 0.29/0.46 = bot_bot_set_variable )
% 0.29/0.46 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 0.29/0.46 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % coincidence_term_cor
% 0.29/0.46 thf(fact_330_Vagree__statediff,axiom,
% 0.29/0.46 ! [Omega: variable > real,Omega3: variable > real,S: set_variable] :
% 0.29/0.46 ( ( denotational_Vagree @ Omega @ Omega3 @ S )
% 0.29/0.46 => ( ord_le282106107riable @ ( statediff @ Omega @ Omega3 ) @ ( uminus1851247844riable @ S ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Vagree_statediff
% 0.29/0.46 thf(fact_331_order__refl,axiom,
% 0.29/0.46 ! [X: set_variable] : ( ord_le282106107riable @ X @ X ) ).
% 0.29/0.46
% 0.29/0.46 % order_refl
% 0.29/0.46 thf(fact_332_subsetI,axiom,
% 0.29/0.46 ! [A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ! [X6: variable > real] :
% 0.29/0.46 ( ( member_variable_real @ X6 @ A2 )
% 0.29/0.46 => ( member_variable_real @ X6 @ B ) )
% 0.29/0.46 => ( ord_le1113654598e_real @ A2 @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_333_subsetI,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ! [X6: variable] :
% 0.29/0.46 ( ( member_variable @ X6 @ A2 )
% 0.29/0.46 => ( member_variable @ X6 @ B ) )
% 0.29/0.46 => ( ord_le282106107riable @ A2 @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % subsetI
% 0.29/0.46 thf(fact_334_subset__antisym,axiom,
% 0.29/0.46 ! [A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ A2 @ B )
% 0.29/0.46 => ( ( ord_le282106107riable @ B @ A2 )
% 0.29/0.46 => ( A2 = B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % subset_antisym
% 0.29/0.46 thf(fact_335_inf_Oidem,axiom,
% 0.29/0.46 ! [A: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ A @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % inf.idem
% 0.29/0.46 thf(fact_336_inf__idem,axiom,
% 0.29/0.46 ! [X: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ X @ X )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % inf_idem
% 0.29/0.46 thf(fact_337_inf_Oleft__idem,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B2 ) )
% 0.29/0.46 = ( inf_inf_set_variable @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.left_idem
% 0.29/0.46 thf(fact_338_inf__left__idem,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ X @ ( inf_inf_set_variable @ X @ Y ) )
% 0.29/0.46 = ( inf_inf_set_variable @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_left_idem
% 0.29/0.46 thf(fact_339_inf_Oright__idem,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B2 ) @ B2 )
% 0.29/0.46 = ( inf_inf_set_variable @ A @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.right_idem
% 0.29/0.46 thf(fact_340_inf__right__idem,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X @ Y ) @ Y )
% 0.29/0.46 = ( inf_inf_set_variable @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf_right_idem
% 0.29/0.46 thf(fact_341_IntI,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 => ( ( member_variable_real @ C2 @ B )
% 0.29/0.46 => ( member_variable_real @ C2 @ ( inf_in1556002680e_real @ A2 @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntI
% 0.29/0.46 thf(fact_342_IntI,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ A2 )
% 0.29/0.46 => ( ( member_variable @ C2 @ B )
% 0.29/0.46 => ( member_variable @ C2 @ ( inf_inf_set_variable @ A2 @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IntI
% 0.29/0.46 thf(fact_343_Int__iff,axiom,
% 0.29/0.46 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 0.29/0.46 ( ( member_variable_real @ C2 @ ( inf_in1556002680e_real @ A2 @ B ) )
% 0.29/0.46 = ( ( member_variable_real @ C2 @ A2 )
% 0.29/0.46 & ( member_variable_real @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_iff
% 0.29/0.46 thf(fact_344_Int__iff,axiom,
% 0.29/0.46 ! [C2: variable,A2: set_variable,B: set_variable] :
% 0.29/0.46 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A2 @ B ) )
% 0.29/0.46 = ( ( member_variable @ C2 @ A2 )
% 0.29/0.46 & ( member_variable @ C2 @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Int_iff
% 0.29/0.46 thf(fact_345_le__zero__eq,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.46 = ( N = zero_zero_nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_zero_eq
% 0.29/0.46 thf(fact_346_compl__le__compl__iff,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real] :
% 0.29/0.46 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ X ) @ ( uminus430703407e_real @ Y ) )
% 0.29/0.46 = ( ord_le1113654598e_real @ Y @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_le_compl_iff
% 0.29/0.46 thf(fact_347_compl__le__compl__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ ( uminus1851247844riable @ X ) @ ( uminus1851247844riable @ Y ) )
% 0.29/0.46 = ( ord_le282106107riable @ Y @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_le_compl_iff
% 0.29/0.46 thf(fact_348_le__inf__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ X @ ( inf_inf_set_variable @ Y @ Z ) )
% 0.29/0.46 = ( ( ord_le282106107riable @ X @ Y )
% 0.29/0.46 & ( ord_le282106107riable @ X @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_inf_iff
% 0.29/0.46 thf(fact_349_inf_Obounded__iff,axiom,
% 0.29/0.46 ! [A: set_variable,B2: set_variable,C2: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ A @ ( inf_inf_set_variable @ B2 @ C2 ) )
% 0.29/0.46 = ( ( ord_le282106107riable @ A @ B2 )
% 0.29/0.46 & ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % inf.bounded_iff
% 0.29/0.46 thf(fact_350_le__sup__iff,axiom,
% 0.29/0.46 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 0.29/0.46 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 0.29/0.46 = ( ( ord_le1113654598e_real @ X @ Z )
% 0.29/0.46 & ( ord_le1113654598e_real @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_sup_iff
% 0.29/0.46 thf(fact_351_le__sup__iff,axiom,
% 0.29/0.46 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 0.29/0.46 = ( ( ord_le282106107riable @ X @ Z )
% 0.29/0.46 & ( ord_le282106107riable @ Y @ Z ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_sup_iff
% 0.29/0.46 thf(fact_352_sup_Obounded__iff,axiom,
% 0.29/0.46 ! [B2: set_variable,C2: set_variable,A: set_variable] :
% 0.29/0.46 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A )
% 0.29/0.46 = ( ( ord_le282106107riable @ B2 @ A )
% 0.29/0.46 & ( ord_le282106107riable @ C2 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.bounded_iff
% 0.29/0.46
% 0.29/0.46 % Helper facts (3)
% 0.29/0.46 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.46 ! [P: $o] :
% 0.29/0.46 ( ( P = $true )
% 0.29/0.46 | ( P = $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.46 ! [X: real,Y: real] :
% 0.29/0.46 ( ( if_real @ $false @ X @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.29/0.46 ! [X: real,Y: real] :
% 0.29/0.46 ( ( if_real @ $true @ X @ Y )
% 0.29/0.46 = X ) ).
% 0.29/0.46
% 0.29/0.46 % Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.61/1.49 ---- Embedded in THF ---
% 2.61/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.49 %%% Generated on Tue Feb 24 08:30:28 EST 2026
% 2.61/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.49 %%% Logic specification used:
% 2.61/1.49 %%% thf(spec, logic, $$dhol).
% 2.61/1.49
% 2.61/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2DTF26036.p
% See solution above
% 2.61/1.49 ------------------------
% 2.88/1.51 ---- Cleaned THF ---
% 2.88/1.52 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 2.88/1.52 produc1418842292n_game: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 2.88/1.52 set_op12188086e_real: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 option_variable_real: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 set_variable_real: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Syntax__Ovariable_J_J,type,
% 2.88/1.52 set_option_variable: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.88/1.52 set_option_trm: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 2.88/1.52 option_variable: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.88/1.52 option_trm: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 2.88/1.52 denotational_interp: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 set_variable: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Syntax__Otrm_J,type,
% 2.88/1.52 set_trm: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 2.88/1.52 set_real: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.88/1.52 set_nat: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Syntax__Ovariable,type,
% 2.88/1.52 variable: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__String__Ochar,type,
% 2.88/1.52 char: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Syntax__Otrm,type,
% 2.88/1.52 trm: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Real__Oreal,type,
% 2.88/1.52 real: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(ty_n_t__Nat__Onat,type,
% 2.88/1.52 nat: $tType ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Coincidence_Ostatediff,type,
% 2.88/1.52 statediff: ( variable > real ) > ( variable > real ) > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Coincidence_Ostateinterpol,type,
% 2.88/1.52 stateinterpol: ( variable > real ) > ( variable > real ) > set_variable > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 2.88/1.52 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Denotational__Semantics_OVagree,type,
% 2.88/1.52 denotational_Vagree: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Denotational__Semantics_Orepv,type,
% 2.88/1.52 denotational_repv: ( variable > real ) > variable > real > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Denotational__Semantics_Osolves__ODE,type,
% 2.88/1.52 denota1778088425es_ODE: denotational_interp > ( real > variable > real ) > char > trm > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Denotational__Semantics_Oterm__sem,type,
% 2.88/1.52 denota1863255036rm_sem: denotational_interp > trm > ( variable > real ) > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 2.88/1.52 uminus_uminus_real: real > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 uminus430703407e_real: set_variable_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 uminus1851247844riable: set_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 2.88/1.52 zero_zero_nat: nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 2.88/1.52 zero_zero_real: real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.88/1.52 zero_zero_set_nat: set_nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Groups_Ozero__class_Ozero_001t__Set__Oset_It__Real__Oreal_J,type,
% 2.88/1.52 zero_zero_set_real: set_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_If_001t__Real__Oreal,type,
% 2.88/1.52 if_real: $o > real > real > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 inf_in1556002680e_real: set_variable_real > set_variable_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 sup_sup_set_variable: set_variable > set_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Nat_Osize__class_Osize_001t__Syntax__Ovariable,type,
% 2.88/1.52 size_size_variable: variable > nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_ONone_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 none_variable_real: option_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 2.88/1.52 none_trm: option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ovariable,type,
% 2.88/1.52 none_variable: option_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_OSome_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 some_variable_real: ( variable > real ) > option_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 2.88/1.52 some_trm: trm > option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ovariable,type,
% 2.88/1.52 some_variable: variable > option_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Oset__option_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 set_op697949218e_real: option_variable_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Oset__option_001t__Syntax__Otrm,type,
% 2.88/1.52 set_option_trm2: option_trm > set_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Oset__option_001t__Syntax__Ovariable,type,
% 2.88/1.52 set_option_variable2: option_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Othe_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 the_variable_real: option_variable_real > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 2.88/1.52 the_trm: option_trm > trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ovariable,type,
% 2.88/1.52 the_variable: option_variable > variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Othese_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 these_variable_real: set_op12188086e_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Othese_001t__Syntax__Otrm,type,
% 2.88/1.52 these_trm: set_option_trm > set_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Option_Othese_001t__Syntax__Ovariable,type,
% 2.88/1.52 these_variable: set_option_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_M_Eo_J,type,
% 2.88/1.52 bot_bo1661475211real_o: ( variable > real ) > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 2.88/1.52 bot_bot_variable_o: variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 bot_bo721182586e_real: set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.88/1.52 bot_bot_set_nat: set_nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J_J,type,
% 2.88/1.52 bot_bo1411475018e_real: set_op12188086e_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.88/1.52 bot_bo946428664on_trm: set_option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Syntax__Ovariable_J_J,type,
% 2.88/1.52 bot_bo266290559riable: set_option_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 2.88/1.52 bot_bot_set_real: set_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Otrm_J,type,
% 2.88/1.52 bot_bot_set_trm: set_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 bot_bot_set_variable: set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.88/1.52 ord_less_eq_nat: nat > nat > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.88/1.52 ord_le282106107riable: set_variable > set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_OCollect_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 2.88/1.52 collect_variable: ( variable > $o ) > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 insert_variable_real: ( variable > real ) > set_variable_real > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 2.88/1.52 insert_nat: nat > set_nat > set_nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 insert526581936e_real: option_variable_real > set_op12188086e_real > set_op12188086e_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.88/1.52 insert_option_trm: option_trm > set_option_trm > set_option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 2.88/1.52 insert1340772453riable: option_variable > set_option_variable > set_option_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 2.88/1.52 insert_real: real > set_real > set_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Syntax__Otrm,type,
% 2.88/1.52 insert_trm: trm > set_trm > set_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Oinsert_001t__Syntax__Ovariable,type,
% 2.88/1.52 insert_variable: variable > set_variable > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Ois__empty_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 is_emp227886046e_real: set_variable_real > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 2.88/1.52 is_empty_variable: set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Ois__singleton_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 is_sin524757308e_real: set_variable_real > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Ois__singleton_001t__Syntax__Ovariable,type,
% 2.88/1.52 is_sin155454833riable: set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Othe__elem_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 the_el1059226619e_real: set_variable_real > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Set_Othe__elem_001t__Syntax__Ovariable,type,
% 2.88/1.52 the_elem_variable: set_variable > variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Static__Semantics_OFVT,type,
% 2.88/1.52 static_FVT: trm > set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Static__Semantics_Oselectlike,type,
% 2.88/1.52 static_selectlike: set_variable_real > ( variable > real ) > set_variable > set_variable_real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Syntax_Otrm_OTimes,type,
% 2.88/1.52 times: trm > trm > trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Syntax_Ovariable_ODVar,type,
% 2.88/1.52 dVar: char > variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Syntax_Ovariable_ORVar,type,
% 2.88/1.52 rVar: char > variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_Syntax_Ovariable_Osize__variable,type,
% 2.88/1.52 size_variable: variable > nat ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 2.88/1.52 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Oadjoint,type,
% 2.88/1.52 uSubst1599435252djoint: produc1418842292n_game > denotational_interp > ( variable > real ) > denotational_interp ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 2.88/1.52 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001_062_It__Syntax__Ovariable_Mt__Real__Oreal_J,type,
% 2.88/1.52 member_variable_real: ( variable > real ) > set_variable_real > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001t__Option__Ooption_I_062_It__Syntax__Ovariable_Mt__Real__Oreal_J_J,type,
% 2.88/1.52 member523846807e_real: option_variable_real > set_op12188086e_real > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.88/1.52 member_option_trm: option_trm > set_option_trm > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001t__Option__Ooption_It__Syntax__Ovariable_J,type,
% 2.88/1.52 member814448204riable: option_variable > set_option_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001t__Syntax__Otrm,type,
% 2.88/1.52 member_trm: trm > set_trm > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 2.88/1.52 member_variable: variable > set_variable > $o ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v_F,type,
% 2.88/1.52 f: real > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v_I,type,
% 2.88/1.52 i: denotational_interp ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v_U,type,
% 2.88/1.52 u: set_variable ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v__092_060omega_062,type,
% 2.88/1.52 omega: variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v__092_060sigma_062,type,
% 2.88/1.52 sigma: produc1418842292n_game ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v__092_060theta_062,type,
% 2.88/1.52 theta: trm ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v_rr____,type,
% 2.88/1.52 rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real ).
% 2.88/1.52
% 2.88/1.52 thf(sy_v_x,type,
% 2.88/1.52 x: char ).
% 2.88/1.52
% 2.88/1.52 thf(fact_0_uv,axiom,
% 2.88/1.52 denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_1_Uvariation__empty,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Nu @ Nu2 @ bot_bot_set_variable )
% 2.88/1.52 = ( Nu = Nu2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_2_Un__insert__left,axiom,
% 2.88/1.52 ! [A: variable,B: set_variable,C: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( insert_variable @ A @ B ) @ C )
% 2.88/1.52 = ( insert_variable @ A @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_3_Un__insert__left,axiom,
% 2.88/1.52 ! [A: variable > real,B: set_variable_real,C: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( insert_variable_real @ A @ B ) @ C )
% 2.88/1.52 = ( insert_variable_real @ A @ ( sup_su1685293586e_real @ B @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_4_Un__insert__right,axiom,
% 2.88/1.52 ! [A2: set_variable,A: variable,B: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A2 @ ( insert_variable @ A @ B ) )
% 2.88/1.52 = ( insert_variable @ A @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_5_Un__insert__right,axiom,
% 2.88/1.52 ! [A2: set_variable_real,A: variable > real,B: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A2 @ ( insert_variable_real @ A @ B ) )
% 2.88/1.52 = ( insert_variable_real @ A @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_6_Un__empty,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( ( sup_su1685293586e_real @ A2 @ B )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( ( A2 = bot_bo721182586e_real )
% 2.88/1.52 & ( B = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_7_Un__empty,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( ( sup_sup_set_variable @ A2 @ B )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( ( A2 = bot_bot_set_variable )
% 2.88/1.52 & ( B = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_8_sup__bot__left,axiom,
% 2.88/1.52 ! [X: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ X )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_9_sup__bot__left,axiom,
% 2.88/1.52 ! [X: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ bot_bot_set_variable @ X )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_10_sup__bot__right,axiom,
% 2.88/1.52 ! [X: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ bot_bo721182586e_real )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_11_sup__bot__right,axiom,
% 2.88/1.52 ! [X: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ bot_bot_set_variable )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_12_bot__eq__sup__iff,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( bot_bo721182586e_real
% 2.88/1.52 = ( sup_su1685293586e_real @ X @ Y ) )
% 2.88/1.52 = ( ( X = bot_bo721182586e_real )
% 2.88/1.52 & ( Y = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_13_bot__eq__sup__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( bot_bot_set_variable
% 2.88/1.52 = ( sup_sup_set_variable @ X @ Y ) )
% 2.88/1.52 = ( ( X = bot_bot_set_variable )
% 2.88/1.52 & ( Y = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_14_sup__eq__bot__iff,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( ( sup_su1685293586e_real @ X @ Y )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( ( X = bot_bo721182586e_real )
% 2.88/1.52 & ( Y = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_15_sup__eq__bot__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( ( sup_sup_set_variable @ X @ Y )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( ( X = bot_bot_set_variable )
% 2.88/1.52 & ( Y = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_16_sup__bot_Oeq__neutr__iff,axiom,
% 2.88/1.52 ! [A: set_variable_real,B2: set_variable_real] :
% 2.88/1.52 ( ( ( sup_su1685293586e_real @ A @ B2 )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( ( A = bot_bo721182586e_real )
% 2.88/1.52 & ( B2 = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_17_sup__bot_Oeq__neutr__iff,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( ( sup_sup_set_variable @ A @ B2 )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( ( A = bot_bot_set_variable )
% 2.88/1.52 & ( B2 = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_18_sup__bot_Oleft__neutral,axiom,
% 2.88/1.52 ! [A: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ bot_bot_set_variable @ A )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_19_sup__bot_Oleft__neutral,axiom,
% 2.88/1.52 ! [A: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ A )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_20_sup__bot_Oneutr__eq__iff,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( bot_bot_set_variable
% 2.88/1.52 = ( sup_sup_set_variable @ A @ B2 ) )
% 2.88/1.52 = ( ( A = bot_bot_set_variable )
% 2.88/1.52 & ( B2 = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_21_sup__bot_Oneutr__eq__iff,axiom,
% 2.88/1.52 ! [A: set_variable_real,B2: set_variable_real] :
% 2.88/1.52 ( ( bot_bo721182586e_real
% 2.88/1.52 = ( sup_su1685293586e_real @ A @ B2 ) )
% 2.88/1.52 = ( ( A = bot_bo721182586e_real )
% 2.88/1.52 & ( B2 = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_22_sup__bot_Oright__neutral,axiom,
% 2.88/1.52 ! [A: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A @ bot_bot_set_variable )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_23_sup__bot_Oright__neutral,axiom,
% 2.88/1.52 ! [A: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A @ bot_bo721182586e_real )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_24_empty__Collect__eq,axiom,
% 2.88/1.52 ! [P: variable > $o] :
% 2.88/1.52 ( ( bot_bot_set_variable
% 2.88/1.52 = ( collect_variable @ P ) )
% 2.88/1.52 = ( ! [X2: variable] :
% 2.88/1.52 ~ ( P @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_25_empty__Collect__eq,axiom,
% 2.88/1.52 ! [P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( bot_bo721182586e_real
% 2.88/1.52 = ( collec633296133e_real @ P ) )
% 2.88/1.52 = ( ! [X2: variable > real] :
% 2.88/1.52 ~ ( P @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_26_Collect__empty__eq,axiom,
% 2.88/1.52 ! [P: variable > $o] :
% 2.88/1.52 ( ( ( collect_variable @ P )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( ! [X2: variable] :
% 2.88/1.52 ~ ( P @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_27_Collect__empty__eq,axiom,
% 2.88/1.52 ! [P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( ( collec633296133e_real @ P )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( ! [X2: variable > real] :
% 2.88/1.52 ~ ( P @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_28_all__not__in__conv,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( ! [X2: variable] :
% 2.88/1.52 ~ ( member_variable @ X2 @ A2 ) )
% 2.88/1.52 = ( A2 = bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_29_all__not__in__conv,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( ! [X2: variable > real] :
% 2.88/1.52 ~ ( member_variable_real @ X2 @ A2 ) )
% 2.88/1.52 = ( A2 = bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_30_empty__iff,axiom,
% 2.88/1.52 ! [C2: variable] :
% 2.88/1.52 ~ ( member_variable @ C2 @ bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_31_empty__iff,axiom,
% 2.88/1.52 ! [C2: variable > real] :
% 2.88/1.52 ~ ( member_variable_real @ C2 @ bot_bo721182586e_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_32_insert__absorb2,axiom,
% 2.88/1.52 ! [X: variable,A2: set_variable] :
% 2.88/1.52 ( ( insert_variable @ X @ ( insert_variable @ X @ A2 ) )
% 2.88/1.52 = ( insert_variable @ X @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_33_insert__absorb2,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( insert_variable_real @ X @ ( insert_variable_real @ X @ A2 ) )
% 2.88/1.52 = ( insert_variable_real @ X @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_34_insert__iff,axiom,
% 2.88/1.52 ! [A: variable,B2: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ A @ ( insert_variable @ B2 @ A2 ) )
% 2.88/1.52 = ( ( A = B2 )
% 2.88/1.52 | ( member_variable @ A @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_35_insert__iff,axiom,
% 2.88/1.52 ! [A: variable > real,B2: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ A @ ( insert_variable_real @ B2 @ A2 ) )
% 2.88/1.52 = ( ( A = B2 )
% 2.88/1.52 | ( member_variable_real @ A @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_36_insertCI,axiom,
% 2.88/1.52 ! [A: variable,B: set_variable,B2: variable] :
% 2.88/1.52 ( ( ~ ( member_variable @ A @ B )
% 2.88/1.52 => ( A = B2 ) )
% 2.88/1.52 => ( member_variable @ A @ ( insert_variable @ B2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_37_insertCI,axiom,
% 2.88/1.52 ! [A: variable > real,B: set_variable_real,B2: variable > real] :
% 2.88/1.52 ( ( ~ ( member_variable_real @ A @ B )
% 2.88/1.52 => ( A = B2 ) )
% 2.88/1.52 => ( member_variable_real @ A @ ( insert_variable_real @ B2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_38_sup_Oright__idem,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B2 ) @ B2 )
% 2.88/1.52 = ( sup_sup_set_variable @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_39_sup_Oright__idem,axiom,
% 2.88/1.52 ! [A: set_variable_real,B2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A @ B2 ) @ B2 )
% 2.88/1.52 = ( sup_su1685293586e_real @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_40_sup__left__idem,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 2.88/1.52 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_41_sup__left__idem,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ X @ Y ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_42_sup_Oleft__idem,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ A @ B2 ) )
% 2.88/1.52 = ( sup_sup_set_variable @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_43_sup_Oleft__idem,axiom,
% 2.88/1.52 ! [A: set_variable_real,B2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ A @ B2 ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_44_sup__idem,axiom,
% 2.88/1.52 ! [X: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ X )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_45_sup__idem,axiom,
% 2.88/1.52 ! [X: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ X )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_46_sup_Oidem,axiom,
% 2.88/1.52 ! [A: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A @ A )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_47_sup_Oidem,axiom,
% 2.88/1.52 ! [A: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A @ A )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_48_UnCI,axiom,
% 2.88/1.52 ! [C2: variable,B: set_variable,A2: set_variable] :
% 2.88/1.52 ( ( ~ ( member_variable @ C2 @ B )
% 2.88/1.52 => ( member_variable @ C2 @ A2 ) )
% 2.88/1.52 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_49_UnCI,axiom,
% 2.88/1.52 ! [C2: variable > real,B: set_variable_real,A2: set_variable_real] :
% 2.88/1.52 ( ( ~ ( member_variable_real @ C2 @ B )
% 2.88/1.52 => ( member_variable_real @ C2 @ A2 ) )
% 2.88/1.52 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_50_singletonI,axiom,
% 2.88/1.52 ! [A: variable] : ( member_variable @ A @ ( insert_variable @ A @ bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_51_singletonI,axiom,
% 2.88/1.52 ! [A: variable > real] : ( member_variable_real @ A @ ( insert_variable_real @ A @ bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_52_bot__set__def,axiom,
% 2.88/1.52 ( bot_bot_set_variable
% 2.88/1.52 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_53_bot__set__def,axiom,
% 2.88/1.52 ( bot_bo721182586e_real
% 2.88/1.52 = ( collec633296133e_real @ bot_bo1661475211real_o ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_54_ex__in__conv,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( ? [X2: variable] : ( member_variable @ X2 @ A2 ) )
% 2.88/1.52 = ( A2 != bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_55_ex__in__conv,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( ? [X2: variable > real] : ( member_variable_real @ X2 @ A2 ) )
% 2.88/1.52 = ( A2 != bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_56_equals0I,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ! [Y2: variable] :
% 2.88/1.52 ~ ( member_variable @ Y2 @ A2 )
% 2.88/1.52 => ( A2 = bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_57_equals0I,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ! [Y2: variable > real] :
% 2.88/1.52 ~ ( member_variable_real @ Y2 @ A2 )
% 2.88/1.52 => ( A2 = bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_58_equals0D,axiom,
% 2.88/1.52 ! [A2: set_variable,A: variable] :
% 2.88/1.52 ( ( A2 = bot_bot_set_variable )
% 2.88/1.52 => ~ ( member_variable @ A @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_59_equals0D,axiom,
% 2.88/1.52 ! [A2: set_variable_real,A: variable > real] :
% 2.88/1.52 ( ( A2 = bot_bo721182586e_real )
% 2.88/1.52 => ~ ( member_variable_real @ A @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_60_emptyE,axiom,
% 2.88/1.52 ! [A: variable] :
% 2.88/1.52 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_61_emptyE,axiom,
% 2.88/1.52 ! [A: variable > real] :
% 2.88/1.52 ~ ( member_variable_real @ A @ bot_bo721182586e_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_62_mk__disjoint__insert,axiom,
% 2.88/1.52 ! [A: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ A @ A2 )
% 2.88/1.52 => ? [B3: set_variable] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable @ A @ B3 ) )
% 2.88/1.52 & ~ ( member_variable @ A @ B3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_63_mk__disjoint__insert,axiom,
% 2.88/1.52 ! [A: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ A @ A2 )
% 2.88/1.52 => ? [B3: set_variable_real] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable_real @ A @ B3 ) )
% 2.88/1.52 & ~ ( member_variable_real @ A @ B3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_64_insert__commute,axiom,
% 2.88/1.52 ! [X: variable,Y: variable,A2: set_variable] :
% 2.88/1.52 ( ( insert_variable @ X @ ( insert_variable @ Y @ A2 ) )
% 2.88/1.52 = ( insert_variable @ Y @ ( insert_variable @ X @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_65_insert__commute,axiom,
% 2.88/1.52 ! [X: variable > real,Y: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( insert_variable_real @ X @ ( insert_variable_real @ Y @ A2 ) )
% 2.88/1.52 = ( insert_variable_real @ Y @ ( insert_variable_real @ X @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_66_insert__eq__iff,axiom,
% 2.88/1.52 ! [A: variable,A2: set_variable,B2: variable,B: set_variable] :
% 2.88/1.52 ( ~ ( member_variable @ A @ A2 )
% 2.88/1.52 => ( ~ ( member_variable @ B2 @ B )
% 2.88/1.52 => ( ( ( insert_variable @ A @ A2 )
% 2.88/1.52 = ( insert_variable @ B2 @ B ) )
% 2.88/1.52 = ( ( ( A = B2 )
% 2.88/1.52 => ( A2 = B ) )
% 2.88/1.52 & ( ( A != B2 )
% 2.88/1.52 => ? [C3: set_variable] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable @ B2 @ C3 ) )
% 2.88/1.52 & ~ ( member_variable @ B2 @ C3 )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable @ A @ C3 ) )
% 2.88/1.52 & ~ ( member_variable @ A @ C3 ) ) ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_67_insert__eq__iff,axiom,
% 2.88/1.52 ! [A: variable > real,A2: set_variable_real,B2: variable > real,B: set_variable_real] :
% 2.88/1.52 ( ~ ( member_variable_real @ A @ A2 )
% 2.88/1.52 => ( ~ ( member_variable_real @ B2 @ B )
% 2.88/1.52 => ( ( ( insert_variable_real @ A @ A2 )
% 2.88/1.52 = ( insert_variable_real @ B2 @ B ) )
% 2.88/1.52 = ( ( ( A = B2 )
% 2.88/1.52 => ( A2 = B ) )
% 2.88/1.52 & ( ( A != B2 )
% 2.88/1.52 => ? [C3: set_variable_real] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable_real @ B2 @ C3 ) )
% 2.88/1.52 & ~ ( member_variable_real @ B2 @ C3 )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable_real @ A @ C3 ) )
% 2.88/1.52 & ~ ( member_variable_real @ A @ C3 ) ) ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_68_insert__absorb,axiom,
% 2.88/1.52 ! [A: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ A @ A2 )
% 2.88/1.52 => ( ( insert_variable @ A @ A2 )
% 2.88/1.52 = A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_69_insert__absorb,axiom,
% 2.88/1.52 ! [A: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ A @ A2 )
% 2.88/1.52 => ( ( insert_variable_real @ A @ A2 )
% 2.88/1.52 = A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_70_insert__ident,axiom,
% 2.88/1.52 ! [X: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ~ ( member_variable @ X @ A2 )
% 2.88/1.52 => ( ~ ( member_variable @ X @ B )
% 2.88/1.52 => ( ( ( insert_variable @ X @ A2 )
% 2.88/1.52 = ( insert_variable @ X @ B ) )
% 2.88/1.52 = ( A2 = B ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_71_insert__ident,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ~ ( member_variable_real @ X @ A2 )
% 2.88/1.52 => ( ~ ( member_variable_real @ X @ B )
% 2.88/1.52 => ( ( ( insert_variable_real @ X @ A2 )
% 2.88/1.52 = ( insert_variable_real @ X @ B ) )
% 2.88/1.52 = ( A2 = B ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_72_Set_Oset__insert,axiom,
% 2.88/1.52 ! [X: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ X @ A2 )
% 2.88/1.52 => ~ ! [B3: set_variable] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable @ X @ B3 ) )
% 2.88/1.52 => ( member_variable @ X @ B3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_73_Set_Oset__insert,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ X @ A2 )
% 2.88/1.52 => ~ ! [B3: set_variable_real] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( insert_variable_real @ X @ B3 ) )
% 2.88/1.52 => ( member_variable_real @ X @ B3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_74_insertI2,axiom,
% 2.88/1.52 ! [A: variable,B: set_variable,B2: variable] :
% 2.88/1.52 ( ( member_variable @ A @ B )
% 2.88/1.52 => ( member_variable @ A @ ( insert_variable @ B2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_75_insertI2,axiom,
% 2.88/1.52 ! [A: variable > real,B: set_variable_real,B2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ A @ B )
% 2.88/1.52 => ( member_variable_real @ A @ ( insert_variable_real @ B2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_76_insertI1,axiom,
% 2.88/1.52 ! [A: variable,B: set_variable] : ( member_variable @ A @ ( insert_variable @ A @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_77_insertI1,axiom,
% 2.88/1.52 ! [A: variable > real,B: set_variable_real] : ( member_variable_real @ A @ ( insert_variable_real @ A @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_78_insertE,axiom,
% 2.88/1.52 ! [A: variable,B2: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ A @ ( insert_variable @ B2 @ A2 ) )
% 2.88/1.52 => ( ( A != B2 )
% 2.88/1.52 => ( member_variable @ A @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_79_insertE,axiom,
% 2.88/1.52 ! [A: variable > real,B2: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ A @ ( insert_variable_real @ B2 @ A2 ) )
% 2.88/1.52 => ( ( A != B2 )
% 2.88/1.52 => ( member_variable_real @ A @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_80_sup__left__commute,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 2.88/1.52 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_81_sup__left__commute,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ Y @ ( sup_su1685293586e_real @ X @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_82_sup_Oleft__commute,axiom,
% 2.88/1.52 ! [B2: set_variable,A: set_variable,C2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ B2 @ ( sup_sup_set_variable @ A @ C2 ) )
% 2.88/1.52 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_83_sup_Oleft__commute,axiom,
% 2.88/1.52 ! [B2: set_variable_real,A: set_variable_real,C2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ B2 @ ( sup_su1685293586e_real @ A @ C2 ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ B2 @ C2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_84_sup__commute,axiom,
% 2.88/1.52 ( sup_sup_set_variable
% 2.88/1.52 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_85_sup__commute,axiom,
% 2.88/1.52 ( sup_su1685293586e_real
% 2.88/1.52 = ( ^ [X2: set_variable_real,Y3: set_variable_real] : ( sup_su1685293586e_real @ Y3 @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_86_mem__Collect__eq,axiom,
% 2.88/1.52 ! [A: variable,P: variable > $o] :
% 2.88/1.52 ( ( member_variable @ A @ ( collect_variable @ P ) )
% 2.88/1.52 = ( P @ A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_87_mem__Collect__eq,axiom,
% 2.88/1.52 ! [A: variable > real,P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( member_variable_real @ A @ ( collec633296133e_real @ P ) )
% 2.88/1.52 = ( P @ A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_88_Collect__mem__eq,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( collect_variable
% 2.88/1.52 @ ^ [X2: variable] : ( member_variable @ X2 @ A2 ) )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_89_Collect__mem__eq,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( collec633296133e_real
% 2.88/1.52 @ ^ [X2: variable > real] : ( member_variable_real @ X2 @ A2 ) )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_90_sup_Ocommute,axiom,
% 2.88/1.52 ( sup_sup_set_variable
% 2.88/1.52 = ( ^ [A3: set_variable,B4: set_variable] : ( sup_sup_set_variable @ B4 @ A3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_91_sup_Ocommute,axiom,
% 2.88/1.52 ( sup_su1685293586e_real
% 2.88/1.52 = ( ^ [A3: set_variable_real,B4: set_variable_real] : ( sup_su1685293586e_real @ B4 @ A3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_92_sup__assoc,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.88/1.52 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_93_sup__assoc,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 2.88/1.52 = ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_94_sup_Oassoc,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable,C2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A @ B2 ) @ C2 )
% 2.88/1.52 = ( sup_sup_set_variable @ A @ ( sup_sup_set_variable @ B2 @ C2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_95_sup_Oassoc,axiom,
% 2.88/1.52 ! [A: set_variable_real,B2: set_variable_real,C2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A @ B2 ) @ C2 )
% 2.88/1.52 = ( sup_su1685293586e_real @ A @ ( sup_su1685293586e_real @ B2 @ C2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_96_boolean__algebra__cancel_Osup2,axiom,
% 2.88/1.52 ! [B: set_variable,K: set_variable,B2: set_variable,A: set_variable] :
% 2.88/1.52 ( ( B
% 2.88/1.52 = ( sup_sup_set_variable @ K @ B2 ) )
% 2.88/1.52 => ( ( sup_sup_set_variable @ A @ B )
% 2.88/1.52 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A @ B2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_97_boolean__algebra__cancel_Osup2,axiom,
% 2.88/1.52 ! [B: set_variable_real,K: set_variable_real,B2: set_variable_real,A: set_variable_real] :
% 2.88/1.52 ( ( B
% 2.88/1.52 = ( sup_su1685293586e_real @ K @ B2 ) )
% 2.88/1.52 => ( ( sup_su1685293586e_real @ A @ B )
% 2.88/1.52 = ( sup_su1685293586e_real @ K @ ( sup_su1685293586e_real @ A @ B2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_98_boolean__algebra__cancel_Osup1,axiom,
% 2.88/1.52 ! [A2: set_variable,K: set_variable,A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( sup_sup_set_variable @ K @ A ) )
% 2.88/1.52 => ( ( sup_sup_set_variable @ A2 @ B2 )
% 2.88/1.52 = ( sup_sup_set_variable @ K @ ( sup_sup_set_variable @ A @ B2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_99_boolean__algebra__cancel_Osup1,axiom,
% 2.88/1.52 ! [A2: set_variable_real,K: set_variable_real,A: set_variable_real,B2: set_variable_real] :
% 2.88/1.52 ( ( A2
% 2.88/1.52 = ( sup_su1685293586e_real @ K @ A ) )
% 2.88/1.52 => ( ( sup_su1685293586e_real @ A2 @ B2 )
% 2.88/1.52 = ( sup_su1685293586e_real @ K @ ( sup_su1685293586e_real @ A @ B2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_100_inf__sup__aci_I5_J,axiom,
% 2.88/1.52 ( sup_sup_set_variable
% 2.88/1.52 = ( ^ [X2: set_variable,Y3: set_variable] : ( sup_sup_set_variable @ Y3 @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_101_inf__sup__aci_I5_J,axiom,
% 2.88/1.52 ( sup_su1685293586e_real
% 2.88/1.52 = ( ^ [X2: set_variable_real,Y3: set_variable_real] : ( sup_su1685293586e_real @ Y3 @ X2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_102_inf__sup__aci_I6_J,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.88/1.52 = ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_103_inf__sup__aci_I6_J,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 2.88/1.52 = ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_104_inf__sup__aci_I7_J,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ Y @ Z ) )
% 2.88/1.52 = ( sup_sup_set_variable @ Y @ ( sup_sup_set_variable @ X @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_105_inf__sup__aci_I7_J,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ Y @ Z ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ Y @ ( sup_su1685293586e_real @ X @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_106_inf__sup__aci_I8_J,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ X @ ( sup_sup_set_variable @ X @ Y ) )
% 2.88/1.52 = ( sup_sup_set_variable @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_107_inf__sup__aci_I8_J,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ X @ ( sup_su1685293586e_real @ X @ Y ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_108_Un__left__commute,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable,C: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B @ C ) )
% 2.88/1.52 = ( sup_sup_set_variable @ B @ ( sup_sup_set_variable @ A2 @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_109_Un__left__commute,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real,C: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ B @ C ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ B @ ( sup_su1685293586e_real @ A2 @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_110_Un__left__absorb,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 = ( sup_sup_set_variable @ A2 @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_111_Un__left__absorb,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 = ( sup_su1685293586e_real @ A2 @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_112_Un__commute,axiom,
% 2.88/1.52 ( sup_sup_set_variable
% 2.88/1.52 = ( ^ [A4: set_variable,B5: set_variable] : ( sup_sup_set_variable @ B5 @ A4 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_113_Un__commute,axiom,
% 2.88/1.52 ( sup_su1685293586e_real
% 2.88/1.52 = ( ^ [A4: set_variable_real,B5: set_variable_real] : ( sup_su1685293586e_real @ B5 @ A4 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_114_Un__absorb,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A2 @ A2 )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_115_Un__absorb,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A2 @ A2 )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_116_Un__assoc,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable,C: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ ( sup_sup_set_variable @ A2 @ B ) @ C )
% 2.88/1.52 = ( sup_sup_set_variable @ A2 @ ( sup_sup_set_variable @ B @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_117_Un__assoc,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real,C: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ ( sup_su1685293586e_real @ A2 @ B ) @ C )
% 2.88/1.52 = ( sup_su1685293586e_real @ A2 @ ( sup_su1685293586e_real @ B @ C ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_118_ball__Un,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable,P: variable > $o] :
% 2.88/1.52 ( ( ! [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 => ( P @ X2 ) ) )
% 2.88/1.52 = ( ! [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ A2 )
% 2.88/1.52 => ( P @ X2 ) )
% 2.88/1.52 & ! [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ B )
% 2.88/1.52 => ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_119_ball__Un,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real,P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( ! [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 => ( P @ X2 ) ) )
% 2.88/1.52 = ( ! [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ A2 )
% 2.88/1.52 => ( P @ X2 ) )
% 2.88/1.52 & ! [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ B )
% 2.88/1.52 => ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_120_bex__Un,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable,P: variable > $o] :
% 2.88/1.52 ( ( ? [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 & ( P @ X2 ) ) )
% 2.88/1.52 = ( ? [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ A2 )
% 2.88/1.52 & ( P @ X2 ) )
% 2.88/1.52 | ? [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ B )
% 2.88/1.52 & ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_121_bex__Un,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real,P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( ? [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 & ( P @ X2 ) ) )
% 2.88/1.52 = ( ? [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ A2 )
% 2.88/1.52 & ( P @ X2 ) )
% 2.88/1.52 | ? [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ B )
% 2.88/1.52 & ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_122_UnI2,axiom,
% 2.88/1.52 ! [C2: variable,B: set_variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ B )
% 2.88/1.52 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_123_UnI2,axiom,
% 2.88/1.52 ! [C2: variable > real,B: set_variable_real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ B )
% 2.88/1.52 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_124_UnI1,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ A2 )
% 2.88/1.52 => ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_125_UnI1,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 => ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_126_UnE,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 => ( ~ ( member_variable @ C2 @ A2 )
% 2.88/1.52 => ( member_variable @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_127_UnE,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 => ( ~ ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 => ( member_variable_real @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_128_Uvariation__sym__rel,axiom,
% 2.88/1.52 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 2.88/1.52 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 2.88/1.52 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_129_Uvariation__refl,axiom,
% 2.88/1.52 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_130_Uvariation__sym,axiom,
% 2.88/1.52 ( denota1419872369iation
% 2.88/1.52 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_131_Uvariation__def,axiom,
% 2.88/1.52 ( denota1419872369iation
% 2.88/1.52 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 2.88/1.52 ! [I: variable] :
% 2.88/1.52 ( ~ ( member_variable @ I @ U2 )
% 2.88/1.52 => ( ( Nu3 @ I )
% 2.88/1.52 = ( Nu4 @ I ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_132_singleton__inject,axiom,
% 2.88/1.52 ! [A: variable,B2: variable] :
% 2.88/1.52 ( ( ( insert_variable @ A @ bot_bot_set_variable )
% 2.88/1.52 = ( insert_variable @ B2 @ bot_bot_set_variable ) )
% 2.88/1.52 => ( A = B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_133_singleton__inject,axiom,
% 2.88/1.52 ! [A: variable > real,B2: variable > real] :
% 2.88/1.52 ( ( ( insert_variable_real @ A @ bot_bo721182586e_real )
% 2.88/1.52 = ( insert_variable_real @ B2 @ bot_bo721182586e_real ) )
% 2.88/1.52 => ( A = B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_134_insert__not__empty,axiom,
% 2.88/1.52 ! [A: variable,A2: set_variable] :
% 2.88/1.52 ( ( insert_variable @ A @ A2 )
% 2.88/1.52 != bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_135_insert__not__empty,axiom,
% 2.88/1.52 ! [A: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( insert_variable_real @ A @ A2 )
% 2.88/1.52 != bot_bo721182586e_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_136_doubleton__eq__iff,axiom,
% 2.88/1.52 ! [A: variable,B2: variable,C2: variable,D: variable] :
% 2.88/1.52 ( ( ( insert_variable @ A @ ( insert_variable @ B2 @ bot_bot_set_variable ) )
% 2.88/1.52 = ( insert_variable @ C2 @ ( insert_variable @ D @ bot_bot_set_variable ) ) )
% 2.88/1.52 = ( ( ( A = C2 )
% 2.88/1.52 & ( B2 = D ) )
% 2.88/1.52 | ( ( A = D )
% 2.88/1.52 & ( B2 = C2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_137_doubleton__eq__iff,axiom,
% 2.88/1.52 ! [A: variable > real,B2: variable > real,C2: variable > real,D: variable > real] :
% 2.88/1.52 ( ( ( insert_variable_real @ A @ ( insert_variable_real @ B2 @ bot_bo721182586e_real ) )
% 2.88/1.52 = ( insert_variable_real @ C2 @ ( insert_variable_real @ D @ bot_bo721182586e_real ) ) )
% 2.88/1.52 = ( ( ( A = C2 )
% 2.88/1.52 & ( B2 = D ) )
% 2.88/1.52 | ( ( A = D )
% 2.88/1.52 & ( B2 = C2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_138_singleton__iff,axiom,
% 2.88/1.52 ! [B2: variable,A: variable] :
% 2.88/1.52 ( ( member_variable @ B2 @ ( insert_variable @ A @ bot_bot_set_variable ) )
% 2.88/1.52 = ( B2 = A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_139_singleton__iff,axiom,
% 2.88/1.52 ! [B2: variable > real,A: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ B2 @ ( insert_variable_real @ A @ bot_bo721182586e_real ) )
% 2.88/1.52 = ( B2 = A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_140_singletonD,axiom,
% 2.88/1.52 ! [B2: variable,A: variable] :
% 2.88/1.52 ( ( member_variable @ B2 @ ( insert_variable @ A @ bot_bot_set_variable ) )
% 2.88/1.52 => ( B2 = A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_141_singletonD,axiom,
% 2.88/1.52 ! [B2: variable > real,A: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ B2 @ ( insert_variable_real @ A @ bot_bo721182586e_real ) )
% 2.88/1.52 => ( B2 = A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_142_Un__empty__right,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ A2 @ bot_bot_set_variable )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_143_Un__empty__right,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ A2 @ bot_bo721182586e_real )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_144_Un__empty__left,axiom,
% 2.88/1.52 ! [B: set_variable] :
% 2.88/1.52 ( ( sup_sup_set_variable @ bot_bot_set_variable @ B )
% 2.88/1.52 = B ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_145_Un__empty__left,axiom,
% 2.88/1.52 ! [B: set_variable_real] :
% 2.88/1.52 ( ( sup_su1685293586e_real @ bot_bo721182586e_real @ B )
% 2.88/1.52 = B ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_146_Uvariation__trans,axiom,
% 2.88/1.52 ! [Omega: variable > real,Nu: variable > real,U: set_variable,Mu: variable > real,V: set_variable] :
% 2.88/1.52 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 2.88/1.52 => ( ( denota1419872369iation @ Nu @ Mu @ V )
% 2.88/1.52 => ( denota1419872369iation @ Omega @ Mu @ ( sup_sup_set_variable @ U @ V ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_147_singleton__Un__iff,axiom,
% 2.88/1.52 ! [X: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( ( insert_variable @ X @ bot_bot_set_variable )
% 2.88/1.52 = ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 = ( ( ( A2 = bot_bot_set_variable )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 & ( B = bot_bot_set_variable ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_148_singleton__Un__iff,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( ( insert_variable_real @ X @ bot_bo721182586e_real )
% 2.88/1.52 = ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 = ( ( ( A2 = bot_bo721182586e_real )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 & ( B = bot_bo721182586e_real ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_149_Un__singleton__iff,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable,X: variable] :
% 2.88/1.52 ( ( ( sup_sup_set_variable @ A2 @ B )
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 = ( ( ( A2 = bot_bot_set_variable )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 & ( B = bot_bot_set_variable ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable @ X @ bot_bot_set_variable ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_150_Un__singleton__iff,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real,X: variable > real] :
% 2.88/1.52 ( ( ( sup_su1685293586e_real @ A2 @ B )
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 = ( ( ( A2 = bot_bo721182586e_real )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 & ( B = bot_bo721182586e_real ) )
% 2.88/1.52 | ( ( A2
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 & ( B
% 2.88/1.52 = ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_151_insert__is__Un,axiom,
% 2.88/1.52 ( insert_variable
% 2.88/1.52 = ( ^ [A3: variable] : ( sup_sup_set_variable @ ( insert_variable @ A3 @ bot_bot_set_variable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_152_insert__is__Un,axiom,
% 2.88/1.52 ( insert_variable_real
% 2.88/1.52 = ( ^ [A3: variable > real] : ( sup_su1685293586e_real @ ( insert_variable_real @ A3 @ bot_bo721182586e_real ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_153__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.88/1.52 ~ ! [Rr: trm > denotational_interp > trm > denotational_interp > char > ( real > variable > real ) > variable > real] :
% 2.88/1.52 ~ ! [X0: trm,X1: denotational_interp,X22: trm,X3: denotational_interp,X4: char,X5: real > variable > real] :
% 2.88/1.52 ( ( ? [V6: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ V6 @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 & ( ( denota1863255036rm_sem @ X3 @ X22 @ V6 )
% 2.88/1.52 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 2.88/1.52 = ( ( denota1419872369iation @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 & ( ( denota1863255036rm_sem @ X3 @ X22 @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) )
% 2.88/1.52 != ( denota1863255036rm_sem @ X1 @ X0 @ ( Rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_154_solves__Vagree__trans,axiom,
% 2.88/1.52 ! [F: real > variable > real,Omega: variable > real,U: set_variable,I2: denotational_interp,X: char,Theta: trm,Zeta: real] :
% 2.88/1.52 ( ( denota1419872369iation @ ( F @ zero_zero_real ) @ Omega @ U )
% 2.88/1.52 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 2.88/1.52 => ( denota1419872369iation @ ( F @ Zeta ) @ Omega @ ( sup_sup_set_variable @ U @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_155__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062,axiom,
% 2.88/1.52 ! [X0: trm,X1: denotational_interp,X22: trm,X3: denotational_interp,X4: char,X5: real > variable > real] :
% 2.88/1.52 ( ( ? [V6: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ V6 @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 & ( ( denota1863255036rm_sem @ X3 @ X22 @ V6 )
% 2.88/1.52 != ( denota1863255036rm_sem @ X1 @ X0 @ V6 ) ) ) )
% 2.88/1.52 = ( ( denota1419872369iation @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) @ ( X5 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X4 ) @ ( insert_variable @ ( dVar @ X4 ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 & ( ( denota1863255036rm_sem @ X3 @ X22 @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) )
% 2.88/1.52 != ( denota1863255036rm_sem @ X1 @ X0 @ ( rr @ X0 @ X1 @ X22 @ X3 @ X4 @ X5 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_156_variable_Oinject_I1_J,axiom,
% 2.88/1.52 ! [X12: char,Y1: char] :
% 2.88/1.52 ( ( ( rVar @ X12 )
% 2.88/1.52 = ( rVar @ Y1 ) )
% 2.88/1.52 = ( X12 = Y1 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_157_set__zero,axiom,
% 2.88/1.52 ( zero_zero_set_real
% 2.88/1.52 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_158_set__zero,axiom,
% 2.88/1.52 ( zero_zero_set_nat
% 2.88/1.52 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_159_variable_Oinject_I2_J,axiom,
% 2.88/1.52 ! [X23: char,Y22: char] :
% 2.88/1.52 ( ( ( dVar @ X23 )
% 2.88/1.52 = ( dVar @ Y22 ) )
% 2.88/1.52 = ( X23 = Y22 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_160_union__or,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ ( sup_sup_set_variable @ A2 @ B ) )
% 2.88/1.52 = ( ( member_variable @ C2 @ A2 )
% 2.88/1.52 | ( member_variable @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_161_union__or,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ ( sup_su1685293586e_real @ A2 @ B ) )
% 2.88/1.52 = ( ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 | ( member_variable_real @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_162_ball__insert,axiom,
% 2.88/1.52 ! [A: variable,B: set_variable,P: variable > $o] :
% 2.88/1.52 ( ( ! [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ ( insert_variable @ A @ B ) )
% 2.88/1.52 => ( P @ X2 ) ) )
% 2.88/1.52 = ( ( P @ A )
% 2.88/1.52 & ! [X2: variable] :
% 2.88/1.52 ( ( member_variable @ X2 @ B )
% 2.88/1.52 => ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_163_ball__insert,axiom,
% 2.88/1.52 ! [A: variable > real,B: set_variable_real,P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( ! [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ ( insert_variable_real @ A @ B ) )
% 2.88/1.52 => ( P @ X2 ) ) )
% 2.88/1.52 = ( ( P @ A )
% 2.88/1.52 & ! [X2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X2 @ B )
% 2.88/1.52 => ( P @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_164_the__elem__eq,axiom,
% 2.88/1.52 ! [X: variable] :
% 2.88/1.52 ( ( the_elem_variable @ ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_165_the__elem__eq,axiom,
% 2.88/1.52 ! [X: variable > real] :
% 2.88/1.52 ( ( the_el1059226619e_real @ ( insert_variable_real @ X @ bot_bo721182586e_real ) )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_166_f2,axiom,
% 2.88/1.52 ! [F2: real > variable > real,C4: char,I3: denotational_interp,T: trm,Ia: denotational_interp,Ta: trm] :
% 2.88/1.52 ( ( ( denota1419872369iation @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) @ ( F2 @ zero_zero_real ) @ ( insert_variable @ ( rVar @ C4 ) @ ( insert_variable @ ( dVar @ C4 ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 & ( ( denota1863255036rm_sem @ I3 @ T @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) )
% 2.88/1.52 != ( denota1863255036rm_sem @ Ia @ Ta @ ( rr @ Ta @ Ia @ T @ I3 @ C4 @ F2 ) ) ) )
% 2.88/1.52 | ( ( denota1778088425es_ODE @ I3 @ F2 @ C4 @ T )
% 2.88/1.52 = ( denota1778088425es_ODE @ Ia @ F2 @ C4 @ Ta ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_167_zero__reorient,axiom,
% 2.88/1.52 ! [X: real] :
% 2.88/1.52 ( ( zero_zero_real = X )
% 2.88/1.52 = ( X = zero_zero_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_168_zero__reorient,axiom,
% 2.88/1.52 ! [X: nat] :
% 2.88/1.52 ( ( zero_zero_nat = X )
% 2.88/1.52 = ( X = zero_zero_nat ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_169_not__union__or,axiom,
% 2.88/1.52 ! [X: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( ~ ( member_variable @ X @ ( sup_sup_set_variable @ A2 @ B ) ) )
% 2.88/1.52 = ( ~ ( member_variable @ X @ A2 )
% 2.88/1.52 & ~ ( member_variable @ X @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_170_not__union__or,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( ~ ( member_variable_real @ X @ ( sup_su1685293586e_real @ A2 @ B ) ) )
% 2.88/1.52 = ( ~ ( member_variable_real @ X @ A2 )
% 2.88/1.52 & ~ ( member_variable_real @ X @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_171_same__ODE__same__sol,axiom,
% 2.88/1.52 ! [F: real > variable > real,X: char,I2: denotational_interp,Theta: trm,J: denotational_interp,Eta: trm] :
% 2.88/1.52 ( ! [Nu5: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Nu5 @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Nu5 )
% 2.88/1.52 = ( denota1863255036rm_sem @ J @ Eta @ Nu5 ) ) )
% 2.88/1.52 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 2.88/1.52 = ( denota1778088425es_ODE @ J @ F @ X @ Eta ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_172_variable_Odistinct_I1_J,axiom,
% 2.88/1.52 ! [X12: char,X23: char] :
% 2.88/1.52 ( ( rVar @ X12 )
% 2.88/1.52 != ( dVar @ X23 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_173_variable_Oinduct,axiom,
% 2.88/1.52 ! [P: variable > $o,Variable: variable] :
% 2.88/1.52 ( ! [X6: char] : ( P @ ( rVar @ X6 ) )
% 2.88/1.52 => ( ! [X6: char] : ( P @ ( dVar @ X6 ) )
% 2.88/1.52 => ( P @ Variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_174_variable_Oexhaust,axiom,
% 2.88/1.52 ! [Y: variable] :
% 2.88/1.52 ( ! [X13: char] :
% 2.88/1.52 ( Y
% 2.88/1.52 != ( rVar @ X13 ) )
% 2.88/1.52 => ~ ! [X24: char] :
% 2.88/1.52 ( Y
% 2.88/1.52 != ( dVar @ X24 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_175_bot__empty__eq,axiom,
% 2.88/1.52 ( bot_bot_variable_o
% 2.88/1.52 = ( ^ [X2: variable] : ( member_variable @ X2 @ bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_176_bot__empty__eq,axiom,
% 2.88/1.52 ( bot_bo1661475211real_o
% 2.88/1.52 = ( ^ [X2: variable > real] : ( member_variable_real @ X2 @ bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_177_Collect__empty__eq__bot,axiom,
% 2.88/1.52 ! [P: variable > $o] :
% 2.88/1.52 ( ( ( collect_variable @ P )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( P = bot_bot_variable_o ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_178_Collect__empty__eq__bot,axiom,
% 2.88/1.52 ! [P: ( variable > real ) > $o] :
% 2.88/1.52 ( ( ( collec633296133e_real @ P )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( P = bot_bo1661475211real_o ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_179_is__singleton__the__elem,axiom,
% 2.88/1.52 ( is_sin155454833riable
% 2.88/1.52 = ( ^ [A4: set_variable] :
% 2.88/1.52 ( A4
% 2.88/1.52 = ( insert_variable @ ( the_elem_variable @ A4 ) @ bot_bot_set_variable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_180_is__singleton__the__elem,axiom,
% 2.88/1.52 ( is_sin524757308e_real
% 2.88/1.52 = ( ^ [A4: set_variable_real] :
% 2.88/1.52 ( A4
% 2.88/1.52 = ( insert_variable_real @ ( the_el1059226619e_real @ A4 ) @ bot_bo721182586e_real ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_181_vaflow2,axiom,
% 2.88/1.52 ! [F: real > variable > real,Theta: trm,Zeta: real] :
% 2.88/1.52 ( ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ F @ x @ Theta )
% 2.88/1.52 => ( denota1419872369iation @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_182_is__singletonI,axiom,
% 2.88/1.52 ! [X: variable] : ( is_sin155454833riable @ ( insert_variable @ X @ bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_183_is__singletonI,axiom,
% 2.88/1.52 ! [X: variable > real] : ( is_sin524757308e_real @ ( insert_variable_real @ X @ bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_184_a1,axiom,
% 2.88/1.52 denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ f @ x @ theta ).
% 2.88/1.52
% 2.88/1.52 thf(fact_185_is__singletonI_H,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( A2 != bot_bot_set_variable )
% 2.88/1.52 => ( ! [X6: variable,Y2: variable] :
% 2.88/1.52 ( ( member_variable @ X6 @ A2 )
% 2.88/1.52 => ( ( member_variable @ Y2 @ A2 )
% 2.88/1.52 => ( X6 = Y2 ) ) )
% 2.88/1.52 => ( is_sin155454833riable @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_186_is__singletonI_H,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( A2 != bot_bo721182586e_real )
% 2.88/1.52 => ( ! [X6: variable > real,Y2: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X6 @ A2 )
% 2.88/1.52 => ( ( member_variable_real @ Y2 @ A2 )
% 2.88/1.52 => ( X6 = Y2 ) ) )
% 2.88/1.52 => ( is_sin524757308e_real @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_187_is__singleton__def,axiom,
% 2.88/1.52 ( is_sin155454833riable
% 2.88/1.52 = ( ^ [A4: set_variable] :
% 2.88/1.52 ? [X2: variable] :
% 2.88/1.52 ( A4
% 2.88/1.52 = ( insert_variable @ X2 @ bot_bot_set_variable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_188_is__singleton__def,axiom,
% 2.88/1.52 ( is_sin524757308e_real
% 2.88/1.52 = ( ^ [A4: set_variable_real] :
% 2.88/1.52 ? [X2: variable > real] :
% 2.88/1.52 ( A4
% 2.88/1.52 = ( insert_variable_real @ X2 @ bot_bo721182586e_real ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_189_is__singletonE,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( is_sin155454833riable @ A2 )
% 2.88/1.52 => ~ ! [X6: variable] :
% 2.88/1.52 ( A2
% 2.88/1.52 != ( insert_variable @ X6 @ bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_190_is__singletonE,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( is_sin524757308e_real @ A2 )
% 2.88/1.52 => ~ ! [X6: variable > real] :
% 2.88/1.52 ( A2
% 2.88/1.52 != ( insert_variable_real @ X6 @ bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_191_vaflow1,axiom,
% 2.88/1.52 ! [F: real > variable > real,Theta: trm,Zeta: real] :
% 2.88/1.52 ( ( denota1778088425es_ODE @ i @ F @ x @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ Theta ) ) )
% 2.88/1.52 => ( denota1419872369iation @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_192_l2r,axiom,
% 2.88/1.52 ( ( denota1778088425es_ODE @ i @ f @ x @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta ) ) )
% 2.88/1.52 => ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ sigma @ i @ omega ) @ f @ x @ theta ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_193_IH,axiom,
% 2.88/1.52 ! [Nu: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Nu @ ( f @ zero_zero_real ) @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ i @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta ) ) @ Nu )
% 2.88/1.52 = ( denota1863255036rm_sem @ ( uSubst1599435252djoint @ sigma @ i @ ( f @ zero_zero_real ) ) @ theta @ Nu ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_194_subdef,axiom,
% 2.88/1.52 ( ( uSubst516392818stappt @ sigma @ ( sup_sup_set_variable @ u @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) ) @ theta )
% 2.88/1.52 != none_trm ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_195_variable_Osize__gen_I1_J,axiom,
% 2.88/1.52 ! [X12: char] :
% 2.88/1.52 ( ( size_variable @ ( rVar @ X12 ) )
% 2.88/1.52 = zero_zero_nat ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_196_usubst__term,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real,U: set_variable,Sigma: produc1418842292n_game,Theta: trm,I2: denotational_interp] :
% 2.88/1.52 ( ( denota1419872369iation @ Nu @ Omega @ U )
% 2.88/1.52 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 2.88/1.52 != none_trm )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ I2 @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ Nu )
% 2.88/1.52 = ( denota1863255036rm_sem @ ( uSubst1599435252djoint @ Sigma @ I2 @ Omega ) @ Theta @ Nu ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_197_usubstappt__det,axiom,
% 2.88/1.52 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 2.88/1.52 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 2.88/1.52 != none_trm )
% 2.88/1.52 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 2.88/1.52 != none_trm )
% 2.88/1.52 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 2.88/1.52 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_198_undeft__None,axiom,
% 2.88/1.52 none_trm = none_trm ).
% 2.88/1.52
% 2.88/1.52 thf(fact_199_usubst__ode,axiom,
% 2.88/1.52 ! [Sigma: produc1418842292n_game,X: char,Theta: trm,I2: denotational_interp,F: real > variable > real] :
% 2.88/1.52 ( ( ( uSubst516392818stappt @ Sigma @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) @ Theta )
% 2.88/1.52 != none_trm )
% 2.88/1.52 => ( ( denota1778088425es_ODE @ I2 @ F @ X @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) @ Theta ) ) )
% 2.88/1.52 = ( denota1778088425es_ODE @ ( uSubst1599435252djoint @ Sigma @ I2 @ ( F @ zero_zero_real ) ) @ F @ X @ Theta ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_200_variable_Osize__gen_I2_J,axiom,
% 2.88/1.52 ! [X23: char] :
% 2.88/1.52 ( ( size_variable @ ( dVar @ X23 ) )
% 2.88/1.52 = zero_zero_nat ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_201_option_Oexpand,axiom,
% 2.88/1.52 ! [Option: option_trm,Option2: option_trm] :
% 2.88/1.52 ( ( ( Option = none_trm )
% 2.88/1.52 = ( Option2 = none_trm ) )
% 2.88/1.52 => ( ( ( Option != none_trm )
% 2.88/1.52 => ( ( Option2 != none_trm )
% 2.88/1.52 => ( ( the_trm @ Option )
% 2.88/1.52 = ( the_trm @ Option2 ) ) ) )
% 2.88/1.52 => ( Option = Option2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_202_variable_Osize_I3_J,axiom,
% 2.88/1.52 ! [X12: char] :
% 2.88/1.52 ( ( size_size_variable @ ( rVar @ X12 ) )
% 2.88/1.52 = zero_zero_nat ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_203_variable_Osize_I4_J,axiom,
% 2.88/1.52 ! [X23: char] :
% 2.88/1.52 ( ( size_size_variable @ ( dVar @ X23 ) )
% 2.88/1.52 = zero_zero_nat ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_204_Set_Ois__empty__def,axiom,
% 2.88/1.52 ( is_empty_variable
% 2.88/1.52 = ( ^ [A4: set_variable] : ( A4 = bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_205_Set_Ois__empty__def,axiom,
% 2.88/1.52 ( is_emp227886046e_real
% 2.88/1.52 = ( ^ [A4: set_variable_real] : ( A4 = bot_bo721182586e_real ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_206_Uvariation__repv,axiom,
% 2.88/1.52 ! [Omega: variable > real,X: variable,D: real] : ( denota1419872369iation @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert_variable @ X @ bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_207_these__empty__eq,axiom,
% 2.88/1.52 ! [B: set_option_trm] :
% 2.88/1.52 ( ( ( these_trm @ B )
% 2.88/1.52 = bot_bot_set_trm )
% 2.88/1.52 = ( ( B = bot_bo946428664on_trm )
% 2.88/1.52 | ( B
% 2.88/1.52 = ( insert_option_trm @ none_trm @ bot_bo946428664on_trm ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_208_these__empty__eq,axiom,
% 2.88/1.52 ! [B: set_option_variable] :
% 2.88/1.52 ( ( ( these_variable @ B )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( ( B = bot_bo266290559riable )
% 2.88/1.52 | ( B
% 2.88/1.52 = ( insert1340772453riable @ none_variable @ bot_bo266290559riable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_209_these__empty__eq,axiom,
% 2.88/1.52 ! [B: set_op12188086e_real] :
% 2.88/1.52 ( ( ( these_variable_real @ B )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( ( B = bot_bo1411475018e_real )
% 2.88/1.52 | ( B
% 2.88/1.52 = ( insert526581936e_real @ none_variable_real @ bot_bo1411475018e_real ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_210_these__not__empty__eq,axiom,
% 2.88/1.52 ! [B: set_option_trm] :
% 2.88/1.52 ( ( ( these_trm @ B )
% 2.88/1.52 != bot_bot_set_trm )
% 2.88/1.52 = ( ( B != bot_bo946428664on_trm )
% 2.88/1.52 & ( B
% 2.88/1.52 != ( insert_option_trm @ none_trm @ bot_bo946428664on_trm ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_211_these__not__empty__eq,axiom,
% 2.88/1.52 ! [B: set_option_variable] :
% 2.88/1.52 ( ( ( these_variable @ B )
% 2.88/1.52 != bot_bot_set_variable )
% 2.88/1.52 = ( ( B != bot_bo266290559riable )
% 2.88/1.52 & ( B
% 2.88/1.52 != ( insert1340772453riable @ none_variable @ bot_bo266290559riable ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_212_these__not__empty__eq,axiom,
% 2.88/1.52 ! [B: set_op12188086e_real] :
% 2.88/1.52 ( ( ( these_variable_real @ B )
% 2.88/1.52 != bot_bo721182586e_real )
% 2.88/1.52 = ( ( B != bot_bo1411475018e_real )
% 2.88/1.52 & ( B
% 2.88/1.52 != ( insert526581936e_real @ none_variable_real @ bot_bo1411475018e_real ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_213_repv__self,axiom,
% 2.88/1.52 ! [Omega: variable > real,X: variable] :
% 2.88/1.52 ( ( denotational_repv @ Omega @ X @ ( Omega @ X ) )
% 2.88/1.52 = Omega ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_214_repv__access,axiom,
% 2.88/1.52 ( denotational_repv
% 2.88/1.52 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if_real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_215_these__empty,axiom,
% 2.88/1.52 ( ( these_variable @ bot_bo266290559riable )
% 2.88/1.52 = bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_216_these__empty,axiom,
% 2.88/1.52 ( ( these_variable_real @ bot_bo1411475018e_real )
% 2.88/1.52 = bot_bo721182586e_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_217_these__insert__None,axiom,
% 2.88/1.52 ! [A2: set_option_trm] :
% 2.88/1.52 ( ( these_trm @ ( insert_option_trm @ none_trm @ A2 ) )
% 2.88/1.52 = ( these_trm @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_218_repv__def__correct,axiom,
% 2.88/1.52 ( denotational_repv
% 2.88/1.52 = ( ^ [Omega2: variable > real,X2: variable,R: real,Y3: variable] : ( if_real @ ( X2 = Y3 ) @ R @ ( Omega2 @ Y3 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_219_these__insert__Some,axiom,
% 2.88/1.52 ! [X: variable,A2: set_option_variable] :
% 2.88/1.52 ( ( these_variable @ ( insert1340772453riable @ ( some_variable @ X ) @ A2 ) )
% 2.88/1.52 = ( insert_variable @ X @ ( these_variable @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_220_these__insert__Some,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_op12188086e_real] :
% 2.88/1.52 ( ( these_variable_real @ ( insert526581936e_real @ ( some_variable_real @ X ) @ A2 ) )
% 2.88/1.52 = ( insert_variable_real @ X @ ( these_variable_real @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_221_these__insert__Some,axiom,
% 2.88/1.52 ! [X: trm,A2: set_option_trm] :
% 2.88/1.52 ( ( these_trm @ ( insert_option_trm @ ( some_trm @ X ) @ A2 ) )
% 2.88/1.52 = ( insert_trm @ X @ ( these_trm @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_222_repv__selectlike__other__converse,axiom,
% 2.88/1.52 ! [X: variable,Y: variable,Omega: variable > real,D: real,X7: set_variable_real] :
% 2.88/1.52 ( ( X != Y )
% 2.88/1.52 => ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ X7 )
% 2.88/1.52 = ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ Y @ bot_bot_set_variable ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_223_repv__selectlike__other,axiom,
% 2.88/1.52 ! [X: variable,Y: variable,Omega: variable > real,D: real,X7: set_variable_real] :
% 2.88/1.52 ( ( X != Y )
% 2.88/1.52 => ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ Y @ bot_bot_set_variable ) ) )
% 2.88/1.52 = ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ X7 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_224_repv__selectlike__self,axiom,
% 2.88/1.52 ! [Omega: variable > real,X: variable,D: real,X7: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ ( denotational_repv @ Omega @ X @ D ) @ ( static_selectlike @ X7 @ Omega @ ( insert_variable @ X @ bot_bot_set_variable ) ) )
% 2.88/1.52 = ( ( D
% 2.88/1.52 = ( Omega @ X ) )
% 2.88/1.52 & ( member_variable_real @ Omega @ X7 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_225_option_Oinject,axiom,
% 2.88/1.52 ! [X23: trm,Y22: trm] :
% 2.88/1.52 ( ( ( some_trm @ X23 )
% 2.88/1.52 = ( some_trm @ Y22 ) )
% 2.88/1.52 = ( X23 = Y22 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_226_selectlike__self,axiom,
% 2.88/1.52 ! [Nu: variable > real,X7: set_variable_real,V: set_variable] :
% 2.88/1.52 ( ( member_variable_real @ Nu @ ( static_selectlike @ X7 @ Nu @ V ) )
% 2.88/1.52 = ( member_variable_real @ Nu @ X7 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_227_not__None__eq,axiom,
% 2.88/1.52 ! [X: option_trm] :
% 2.88/1.52 ( ( X != none_trm )
% 2.88/1.52 = ( ? [Y3: trm] :
% 2.88/1.52 ( X
% 2.88/1.52 = ( some_trm @ Y3 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_228_not__Some__eq,axiom,
% 2.88/1.52 ! [X: option_trm] :
% 2.88/1.52 ( ( ! [Y3: trm] :
% 2.88/1.52 ( X
% 2.88/1.52 != ( some_trm @ Y3 ) ) )
% 2.88/1.52 = ( X = none_trm ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_229_selectlike__empty,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Nu: variable > real] :
% 2.88/1.52 ( ( static_selectlike @ X7 @ Nu @ bot_bot_set_variable )
% 2.88/1.52 = X7 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_230_selectlike__compose,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,W: set_variable] :
% 2.88/1.52 ( ( static_selectlike @ ( static_selectlike @ X7 @ Nu @ V ) @ Nu @ W )
% 2.88/1.52 = ( static_selectlike @ X7 @ Nu @ ( sup_sup_set_variable @ V @ W ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_231_option_Ocollapse,axiom,
% 2.88/1.52 ! [Option: option_trm] :
% 2.88/1.52 ( ( Option != none_trm )
% 2.88/1.52 => ( ( some_trm @ ( the_trm @ Option ) )
% 2.88/1.52 = Option ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_232_in__these__eq,axiom,
% 2.88/1.52 ! [X: variable,A2: set_option_variable] :
% 2.88/1.52 ( ( member_variable @ X @ ( these_variable @ A2 ) )
% 2.88/1.52 = ( member814448204riable @ ( some_variable @ X ) @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_233_in__these__eq,axiom,
% 2.88/1.52 ! [X: variable > real,A2: set_op12188086e_real] :
% 2.88/1.52 ( ( member_variable_real @ X @ ( these_variable_real @ A2 ) )
% 2.88/1.52 = ( member523846807e_real @ ( some_variable_real @ X ) @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_234_in__these__eq,axiom,
% 2.88/1.52 ! [X: trm,A2: set_option_trm] :
% 2.88/1.52 ( ( member_trm @ X @ ( these_trm @ A2 ) )
% 2.88/1.52 = ( member_option_trm @ ( some_trm @ X ) @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_235_selectlike__union,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Y4: set_variable_real,Nu: variable > real,V: set_variable] :
% 2.88/1.52 ( ( static_selectlike @ ( sup_su1685293586e_real @ X7 @ Y4 ) @ Nu @ V )
% 2.88/1.52 = ( sup_su1685293586e_real @ ( static_selectlike @ X7 @ Nu @ V ) @ ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_236_option_Odistinct_I1_J,axiom,
% 2.88/1.52 ! [X23: trm] :
% 2.88/1.52 ( none_trm
% 2.88/1.52 != ( some_trm @ X23 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_237_option_Osel,axiom,
% 2.88/1.52 ! [X23: trm] :
% 2.88/1.52 ( ( the_trm @ ( some_trm @ X23 ) )
% 2.88/1.52 = X23 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_238_option_OdiscI,axiom,
% 2.88/1.52 ! [Option: option_trm,X23: trm] :
% 2.88/1.52 ( ( Option
% 2.88/1.52 = ( some_trm @ X23 ) )
% 2.88/1.52 => ( Option != none_trm ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_239_option_Oexhaust,axiom,
% 2.88/1.52 ! [Y: option_trm] :
% 2.88/1.52 ( ( Y != none_trm )
% 2.88/1.52 => ~ ! [X24: trm] :
% 2.88/1.52 ( Y
% 2.88/1.52 != ( some_trm @ X24 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_240_option_Oinducts,axiom,
% 2.88/1.52 ! [P: option_trm > $o,Option: option_trm] :
% 2.88/1.52 ( ( P @ none_trm )
% 2.88/1.52 => ( ! [X6: trm] : ( P @ ( some_trm @ X6 ) )
% 2.88/1.52 => ( P @ Option ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_241_split__option__ex,axiom,
% 2.88/1.52 ( ( ^ [P2: option_trm > $o] :
% 2.88/1.52 ? [X8: option_trm] : ( P2 @ X8 ) )
% 2.88/1.52 = ( ^ [P3: option_trm > $o] :
% 2.88/1.52 ( ( P3 @ none_trm )
% 2.88/1.52 | ? [X2: trm] : ( P3 @ ( some_trm @ X2 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_242_split__option__all,axiom,
% 2.88/1.52 ( ( ^ [P2: option_trm > $o] :
% 2.88/1.52 ! [X8: option_trm] : ( P2 @ X8 ) )
% 2.88/1.52 = ( ^ [P3: option_trm > $o] :
% 2.88/1.52 ( ( P3 @ none_trm )
% 2.88/1.52 & ! [X2: trm] : ( P3 @ ( some_trm @ X2 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_243_combine__options__cases,axiom,
% 2.88/1.52 ! [X: option_trm,P: option_trm > option_trm > $o,Y: option_trm] :
% 2.88/1.52 ( ( ( X = none_trm )
% 2.88/1.52 => ( P @ X @ Y ) )
% 2.88/1.52 => ( ( ( Y = none_trm )
% 2.88/1.52 => ( P @ X @ Y ) )
% 2.88/1.52 => ( ! [A5: trm,B6: trm] :
% 2.88/1.52 ( ( X
% 2.88/1.52 = ( some_trm @ A5 ) )
% 2.88/1.52 => ( ( Y
% 2.88/1.52 = ( some_trm @ B6 ) )
% 2.88/1.52 => ( P @ X @ Y ) ) )
% 2.88/1.52 => ( P @ X @ Y ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_244_ODEo_Oinduct,axiom,
% 2.88/1.52 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 2.88/1.52 ( ! [X6: char,Theta2: trm] : ( P @ X6 @ ( some_trm @ Theta2 ) )
% 2.88/1.52 => ( ! [X6: char] : ( P @ X6 @ none_trm )
% 2.88/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_245_undeft__equiv,axiom,
% 2.88/1.52 ! [Theta: option_trm] :
% 2.88/1.52 ( ( Theta != none_trm )
% 2.88/1.52 = ( ? [T2: trm] :
% 2.88/1.52 ( Theta
% 2.88/1.52 = ( some_trm @ T2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_246_Timeso_Oinduct,axiom,
% 2.88/1.52 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 2.88/1.52 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 2.88/1.52 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 2.88/1.52 => ( ! [V2: trm] : ( P @ ( some_trm @ V2 ) @ none_trm )
% 2.88/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_247_Assigno_Oinduct,axiom,
% 2.88/1.52 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 2.88/1.52 ( ! [X6: variable,Theta2: trm] : ( P @ X6 @ ( some_trm @ Theta2 ) )
% 2.88/1.52 => ( ! [X6: variable] : ( P @ X6 @ none_trm )
% 2.88/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_248_Differentialo_Ocases,axiom,
% 2.88/1.52 ! [X: option_trm] :
% 2.88/1.52 ( ! [Theta2: trm] :
% 2.88/1.52 ( X
% 2.88/1.52 != ( some_trm @ Theta2 ) )
% 2.88/1.52 => ( X = none_trm ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_249_Differentialo_Oinduct,axiom,
% 2.88/1.52 ! [P: option_trm > $o,A0: option_trm] :
% 2.88/1.52 ( ! [Theta2: trm] : ( P @ ( some_trm @ Theta2 ) )
% 2.88/1.52 => ( ( P @ none_trm )
% 2.88/1.52 => ( P @ A0 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_250_option_Oexhaust__sel,axiom,
% 2.88/1.52 ! [Option: option_trm] :
% 2.88/1.52 ( ( Option != none_trm )
% 2.88/1.52 => ( Option
% 2.88/1.52 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_251_option_Osimps_I15_J,axiom,
% 2.88/1.52 ! [X23: trm] :
% 2.88/1.52 ( ( set_option_trm2 @ ( some_trm @ X23 ) )
% 2.88/1.52 = ( insert_trm @ X23 @ bot_bot_set_trm ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_252_option_Osimps_I15_J,axiom,
% 2.88/1.52 ! [X23: variable] :
% 2.88/1.52 ( ( set_option_variable2 @ ( some_variable @ X23 ) )
% 2.88/1.52 = ( insert_variable @ X23 @ bot_bot_set_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_253_option_Osimps_I15_J,axiom,
% 2.88/1.52 ! [X23: variable > real] :
% 2.88/1.52 ( ( set_op697949218e_real @ ( some_variable_real @ X23 ) )
% 2.88/1.52 = ( insert_variable_real @ X23 @ bot_bo721182586e_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_254_Vagree__repv__self,axiom,
% 2.88/1.52 ! [Omega: variable > real,X: variable,D: real] :
% 2.88/1.52 ( ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( insert_variable @ X @ bot_bot_set_variable ) )
% 2.88/1.52 = ( D
% 2.88/1.52 = ( Omega @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_255_elem__set,axiom,
% 2.88/1.52 ! [X: variable,Xo: option_variable] :
% 2.88/1.52 ( ( member_variable @ X @ ( set_option_variable2 @ Xo ) )
% 2.88/1.52 = ( Xo
% 2.88/1.52 = ( some_variable @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_256_elem__set,axiom,
% 2.88/1.52 ! [X: variable > real,Xo: option_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ X @ ( set_op697949218e_real @ Xo ) )
% 2.88/1.52 = ( Xo
% 2.88/1.52 = ( some_variable_real @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_257_elem__set,axiom,
% 2.88/1.52 ! [X: trm,Xo: option_trm] :
% 2.88/1.52 ( ( member_trm @ X @ ( set_option_trm2 @ Xo ) )
% 2.88/1.52 = ( Xo
% 2.88/1.52 = ( some_trm @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_258_Vagree__and,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real,V: set_variable,W: set_variable] :
% 2.88/1.52 ( ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 2.88/1.52 & ( denotational_Vagree @ Nu @ Nu2 @ W ) )
% 2.88/1.52 = ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup_set_variable @ V @ W ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_259_set__empty__eq,axiom,
% 2.88/1.52 ! [Xo: option_trm] :
% 2.88/1.52 ( ( ( set_option_trm2 @ Xo )
% 2.88/1.52 = bot_bot_set_trm )
% 2.88/1.52 = ( Xo = none_trm ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_260_set__empty__eq,axiom,
% 2.88/1.52 ! [Xo: option_variable] :
% 2.88/1.52 ( ( ( set_option_variable2 @ Xo )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 = ( Xo = none_variable ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_261_set__empty__eq,axiom,
% 2.88/1.52 ! [Xo: option_variable_real] :
% 2.88/1.52 ( ( ( set_op697949218e_real @ Xo )
% 2.88/1.52 = bot_bo721182586e_real )
% 2.88/1.52 = ( Xo = none_variable_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_262_similar__selectlike__mem,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real,V: set_variable,X7: set_variable_real] :
% 2.88/1.52 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 2.88/1.52 => ( ( member_variable_real @ Nu @ ( static_selectlike @ X7 @ Omega @ V ) )
% 2.88/1.52 = ( member_variable_real @ Nu @ X7 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_263_selectlike__Vagree,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real,V: set_variable,X7: set_variable_real] :
% 2.88/1.52 ( ( denotational_Vagree @ Nu @ Omega @ V )
% 2.88/1.52 => ( ( static_selectlike @ X7 @ Nu @ V )
% 2.88/1.52 = ( static_selectlike @ X7 @ Omega @ V ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_264_Aterm__Some,axiom,
% 2.88/1.52 some_trm = some_trm ).
% 2.88/1.52
% 2.88/1.52 thf(fact_265_option_Oset__intros,axiom,
% 2.88/1.52 ! [X23: variable] : ( member_variable @ X23 @ ( set_option_variable2 @ ( some_variable @ X23 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_266_option_Oset__intros,axiom,
% 2.88/1.52 ! [X23: variable > real] : ( member_variable_real @ X23 @ ( set_op697949218e_real @ ( some_variable_real @ X23 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_267_option_Oset__intros,axiom,
% 2.88/1.52 ! [X23: trm] : ( member_trm @ X23 @ ( set_option_trm2 @ ( some_trm @ X23 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_268_option_Oset__cases,axiom,
% 2.88/1.52 ! [E: variable,A: option_variable] :
% 2.88/1.52 ( ( member_variable @ E @ ( set_option_variable2 @ A ) )
% 2.88/1.52 => ( A
% 2.88/1.52 = ( some_variable @ E ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_269_option_Oset__cases,axiom,
% 2.88/1.52 ! [E: variable > real,A: option_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ E @ ( set_op697949218e_real @ A ) )
% 2.88/1.52 => ( A
% 2.88/1.52 = ( some_variable_real @ E ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_270_option_Oset__cases,axiom,
% 2.88/1.52 ! [E: trm,A: option_trm] :
% 2.88/1.52 ( ( member_trm @ E @ ( set_option_trm2 @ A ) )
% 2.88/1.52 => ( A
% 2.88/1.52 = ( some_trm @ E ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_271_ospec,axiom,
% 2.88/1.52 ! [A2: option_trm,P: trm > $o,X: trm] :
% 2.88/1.52 ( ! [X6: trm] :
% 2.88/1.52 ( ( member_trm @ X6 @ ( set_option_trm2 @ A2 ) )
% 2.88/1.52 => ( P @ X6 ) )
% 2.88/1.52 => ( ( A2
% 2.88/1.52 = ( some_trm @ X ) )
% 2.88/1.52 => ( P @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_272_Vagree__union,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real,V: set_variable,W: set_variable] :
% 2.88/1.52 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 2.88/1.52 => ( ( denotational_Vagree @ Nu @ Nu2 @ W )
% 2.88/1.52 => ( denotational_Vagree @ Nu @ Nu2 @ ( sup_sup_set_variable @ V @ W ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_273_Vagree__def,axiom,
% 2.88/1.52 ( denotational_Vagree
% 2.88/1.52 = ( ^ [Nu3: variable > real,Nu4: variable > real,V3: set_variable] :
% 2.88/1.52 ! [I: variable] :
% 2.88/1.52 ( ( member_variable @ I @ V3 )
% 2.88/1.52 => ( ( Nu3 @ I )
% 2.88/1.52 = ( Nu4 @ I ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_274_Vagree__sym,axiom,
% 2.88/1.52 ( denotational_Vagree
% 2.88/1.52 = ( ^ [Nu3: variable > real,Nu4: variable > real] : ( denotational_Vagree @ Nu4 @ Nu3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_275_Vagree__refl,axiom,
% 2.88/1.52 ! [Nu: variable > real,V: set_variable] : ( denotational_Vagree @ Nu @ Nu @ V ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_276_Vagree__sym__rel,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real,V: set_variable] :
% 2.88/1.52 ( ( denotational_Vagree @ Nu @ Nu2 @ V )
% 2.88/1.52 => ( denotational_Vagree @ Nu2 @ Nu @ V ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_277_Vagree__empty,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real] : ( denotational_Vagree @ Nu @ Nu2 @ bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_278_option_Osimps_I14_J,axiom,
% 2.88/1.52 ( ( set_option_trm2 @ none_trm )
% 2.88/1.52 = bot_bot_set_trm ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_279_option_Osimps_I14_J,axiom,
% 2.88/1.52 ( ( set_option_variable2 @ none_variable )
% 2.88/1.52 = bot_bot_set_variable ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_280_option_Osimps_I14_J,axiom,
% 2.88/1.52 ( ( set_op697949218e_real @ none_variable_real )
% 2.88/1.52 = bot_bo721182586e_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_281_option_Oset__sel,axiom,
% 2.88/1.52 ! [A: option_variable] :
% 2.88/1.52 ( ( A != none_variable )
% 2.88/1.52 => ( member_variable @ ( the_variable @ A ) @ ( set_option_variable2 @ A ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_282_option_Oset__sel,axiom,
% 2.88/1.52 ! [A: option_variable_real] :
% 2.88/1.52 ( ( A != none_variable_real )
% 2.88/1.52 => ( member_variable_real @ ( the_variable_real @ A ) @ ( set_op697949218e_real @ A ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_283_option_Oset__sel,axiom,
% 2.88/1.52 ! [A: option_trm] :
% 2.88/1.52 ( ( A != none_trm )
% 2.88/1.52 => ( member_trm @ ( the_trm @ A ) @ ( set_option_trm2 @ A ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_284_solves__Vagree,axiom,
% 2.88/1.52 ! [I2: denotational_interp,F: real > variable > real,X: char,Theta: trm,Zeta: real] :
% 2.88/1.52 ( ( denota1778088425es_ODE @ I2 @ F @ X @ Theta )
% 2.88/1.52 => ( denotational_Vagree @ ( F @ Zeta ) @ ( F @ zero_zero_real ) @ ( uminus1851247844riable @ ( insert_variable @ ( rVar @ X ) @ ( insert_variable @ ( dVar @ X ) @ bot_bot_set_variable ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_285_Vagree__repv,axiom,
% 2.88/1.52 ! [Omega: variable > real,X: variable,D: real] : ( denotational_Vagree @ Omega @ ( denotational_repv @ Omega @ X @ D ) @ ( uminus1851247844riable @ ( insert_variable @ X @ bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_286_Timeso_Osimps_I3_J,axiom,
% 2.88/1.52 ! [V4: trm] :
% 2.88/1.52 ( ( uSubst918876924Timeso @ ( some_trm @ V4 ) @ none_trm )
% 2.88/1.52 = none_trm ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_287_compl__eq__compl__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( ( uminus1851247844riable @ X )
% 2.88/1.52 = ( uminus1851247844riable @ Y ) )
% 2.88/1.52 = ( X = Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_288_compl__eq__compl__iff,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( ( uminus430703407e_real @ X )
% 2.88/1.52 = ( uminus430703407e_real @ Y ) )
% 2.88/1.52 = ( X = Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_289_double__compl,axiom,
% 2.88/1.52 ! [X: set_variable] :
% 2.88/1.52 ( ( uminus1851247844riable @ ( uminus1851247844riable @ X ) )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_290_double__compl,axiom,
% 2.88/1.52 ! [X: set_variable_real] :
% 2.88/1.52 ( ( uminus430703407e_real @ ( uminus430703407e_real @ X ) )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_291_Compl__eq__Compl__iff,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( ( uminus1851247844riable @ A2 )
% 2.88/1.52 = ( uminus1851247844riable @ B ) )
% 2.88/1.52 = ( A2 = B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_292_Compl__eq__Compl__iff,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( ( uminus430703407e_real @ A2 )
% 2.88/1.52 = ( uminus430703407e_real @ B ) )
% 2.88/1.52 = ( A2 = B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_293_Compl__iff,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) )
% 2.88/1.52 = ( ~ ( member_variable @ C2 @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_294_Compl__iff,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) )
% 2.88/1.52 = ( ~ ( member_variable_real @ C2 @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_295_ComplI,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable] :
% 2.88/1.52 ( ~ ( member_variable @ C2 @ A2 )
% 2.88/1.52 => ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_296_ComplI,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ~ ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 => ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_297_add_Oinverse__neutral,axiom,
% 2.88/1.52 ( ( uminus_uminus_real @ zero_zero_real )
% 2.88/1.52 = zero_zero_real ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_298_neg__0__equal__iff__equal,axiom,
% 2.88/1.52 ! [A: real] :
% 2.88/1.52 ( ( zero_zero_real
% 2.88/1.52 = ( uminus_uminus_real @ A ) )
% 2.88/1.52 = ( zero_zero_real = A ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_299_neg__equal__0__iff__equal,axiom,
% 2.88/1.52 ! [A: real] :
% 2.88/1.52 ( ( ( uminus_uminus_real @ A )
% 2.88/1.52 = zero_zero_real )
% 2.88/1.52 = ( A = zero_zero_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_300_equal__neg__zero,axiom,
% 2.88/1.52 ! [A: real] :
% 2.88/1.52 ( ( A
% 2.88/1.52 = ( uminus_uminus_real @ A ) )
% 2.88/1.52 = ( A = zero_zero_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_301_neg__equal__zero,axiom,
% 2.88/1.52 ! [A: real] :
% 2.88/1.52 ( ( ( uminus_uminus_real @ A )
% 2.88/1.52 = A )
% 2.88/1.52 = ( A = zero_zero_real ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_302_Uvariation__Vagree,axiom,
% 2.88/1.52 ! [Nu: variable > real,Nu2: variable > real,V: set_variable] :
% 2.88/1.52 ( ( denota1419872369iation @ Nu @ Nu2 @ ( uminus1851247844riable @ V ) )
% 2.88/1.52 = ( denotational_Vagree @ Nu @ Nu2 @ V ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_303_double__complement,axiom,
% 2.88/1.52 ! [A2: set_variable] :
% 2.88/1.52 ( ( uminus1851247844riable @ ( uminus1851247844riable @ A2 ) )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_304_double__complement,axiom,
% 2.88/1.52 ! [A2: set_variable_real] :
% 2.88/1.52 ( ( uminus430703407e_real @ ( uminus430703407e_real @ A2 ) )
% 2.88/1.52 = A2 ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_305_ComplD,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ ( uminus1851247844riable @ A2 ) )
% 2.88/1.52 => ~ ( member_variable @ C2 @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_306_ComplD,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ ( uminus430703407e_real @ A2 ) )
% 2.88/1.52 => ~ ( member_variable_real @ C2 @ A2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_307_Timeso_Osimps_I2_J,axiom,
% 2.88/1.52 ! [Eta: option_trm] :
% 2.88/1.52 ( ( uSubst918876924Timeso @ none_trm @ Eta )
% 2.88/1.52 = none_trm ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_308_Timeso__undef,axiom,
% 2.88/1.52 ! [Theta: option_trm,Eta: option_trm] :
% 2.88/1.52 ( ( ( uSubst918876924Timeso @ Theta @ Eta )
% 2.88/1.52 = none_trm )
% 2.88/1.52 = ( ( Theta = none_trm )
% 2.88/1.52 | ( Eta = none_trm ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_309_selectlike__equal__cocond__corule,axiom,
% 2.88/1.52 ! [Nu: variable > real,V: set_variable,X7: set_variable_real,Y4: set_variable_real] :
% 2.88/1.52 ( ! [Mu2: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Mu2 @ Nu @ V )
% 2.88/1.52 => ( ( member_variable_real @ Mu2 @ X7 )
% 2.88/1.52 = ( member_variable_real @ Mu2 @ Y4 ) ) )
% 2.88/1.52 => ( ( static_selectlike @ X7 @ Nu @ ( uminus1851247844riable @ V ) )
% 2.88/1.52 = ( static_selectlike @ Y4 @ Nu @ ( uminus1851247844riable @ V ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_310_selectlike__equal__cocond__rule,axiom,
% 2.88/1.52 ! [Nu: variable > real,V: set_variable,X7: set_variable_real,Y4: set_variable_real] :
% 2.88/1.52 ( ! [Mu2: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Mu2 @ Nu @ ( uminus1851247844riable @ V ) )
% 2.88/1.52 => ( ( member_variable_real @ Mu2 @ X7 )
% 2.88/1.52 = ( member_variable_real @ Mu2 @ Y4 ) ) )
% 2.88/1.52 => ( ( static_selectlike @ X7 @ Nu @ V )
% 2.88/1.52 = ( static_selectlike @ Y4 @ Nu @ V ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_311_selectlike__equal__cocond,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,Y4: set_variable_real] :
% 2.88/1.52 ( ( ( static_selectlike @ X7 @ Nu @ ( uminus1851247844riable @ V ) )
% 2.88/1.52 = ( static_selectlike @ Y4 @ Nu @ ( uminus1851247844riable @ V ) ) )
% 2.88/1.52 = ( ! [Mu3: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Mu3 @ Nu @ V )
% 2.88/1.52 => ( ( member_variable_real @ Mu3 @ X7 )
% 2.88/1.52 = ( member_variable_real @ Mu3 @ Y4 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_312_selectlike__equal__cond,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Nu: variable > real,V: set_variable,Y4: set_variable_real] :
% 2.88/1.52 ( ( ( static_selectlike @ X7 @ Nu @ V )
% 2.88/1.52 = ( static_selectlike @ Y4 @ Nu @ V ) )
% 2.88/1.52 = ( ! [Mu3: variable > real] :
% 2.88/1.52 ( ( denota1419872369iation @ Mu3 @ Nu @ ( uminus1851247844riable @ V ) )
% 2.88/1.52 => ( ( member_variable_real @ Mu3 @ X7 )
% 2.88/1.52 = ( member_variable_real @ Mu3 @ Y4 ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_313_stateinterpol__insert,axiom,
% 2.88/1.52 ! [V4: variable > real,W2: variable > real,S: set_variable,Z: variable] : ( denotational_Vagree @ ( stateinterpol @ V4 @ W2 @ S ) @ ( stateinterpol @ V4 @ W2 @ ( insert_variable @ Z @ S ) ) @ ( uminus1851247844riable @ ( insert_variable @ Z @ bot_bot_set_variable ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_314_Timeso_Oelims,axiom,
% 2.88/1.52 ! [X: option_trm,Xa: option_trm,Y: option_trm] :
% 2.88/1.52 ( ( ( uSubst918876924Timeso @ X @ Xa )
% 2.88/1.52 = Y )
% 2.88/1.52 => ( ! [Theta2: trm] :
% 2.88/1.52 ( ( X
% 2.88/1.52 = ( some_trm @ Theta2 ) )
% 2.88/1.52 => ! [Eta2: trm] :
% 2.88/1.52 ( ( Xa
% 2.88/1.52 = ( some_trm @ Eta2 ) )
% 2.88/1.52 => ( Y
% 2.88/1.52 != ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 2.88/1.52 => ( ( ( X = none_trm )
% 2.88/1.52 => ( Y != none_trm ) )
% 2.88/1.52 => ~ ( ? [V2: trm] :
% 2.88/1.52 ( X
% 2.88/1.52 = ( some_trm @ V2 ) )
% 2.88/1.52 => ( ( Xa = none_trm )
% 2.88/1.52 => ( Y != none_trm ) ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_315_trm_Oinject_I6_J,axiom,
% 2.88/1.52 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 2.88/1.52 ( ( ( times @ X61 @ X62 )
% 2.88/1.52 = ( times @ Y61 @ Y62 ) )
% 2.88/1.52 = ( ( X61 = Y61 )
% 2.88/1.52 & ( X62 = Y62 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_316_stateinterpol__left,axiom,
% 2.88/1.52 ! [X: variable,S: set_variable,Nu: variable > real,Omega: variable > real] :
% 2.88/1.52 ( ( member_variable @ X @ S )
% 2.88/1.52 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 2.88/1.52 = ( Nu @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_317_stateinterpol__right,axiom,
% 2.88/1.52 ! [X: variable,S: set_variable,Nu: variable > real,Omega: variable > real] :
% 2.88/1.52 ( ~ ( member_variable @ X @ S )
% 2.88/1.52 => ( ( stateinterpol @ Nu @ Omega @ S @ X )
% 2.88/1.52 = ( Omega @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_318_selectlike__co__selectlike,axiom,
% 2.88/1.52 ! [X7: set_variable_real,Nu: variable > real,V: set_variable] :
% 2.88/1.52 ( ( static_selectlike @ ( uminus430703407e_real @ ( static_selectlike @ X7 @ Nu @ V ) ) @ Nu @ V )
% 2.88/1.52 = ( static_selectlike @ ( uminus430703407e_real @ X7 ) @ Nu @ V ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_319_stateinterpol__empty,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real] :
% 2.88/1.52 ( ( stateinterpol @ Nu @ Omega @ bot_bot_set_variable )
% 2.88/1.52 = Omega ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_320_Vagree__stateinterpol,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real,S: set_variable] : ( denotational_Vagree @ ( stateinterpol @ Nu @ Omega @ S ) @ Nu @ S ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_321_stateinterpol__def,axiom,
% 2.88/1.52 ( stateinterpol
% 2.88/1.52 = ( ^ [Nu3: variable > real,Omega2: variable > real,S2: set_variable,X2: variable] : ( if_real @ ( member_variable @ X2 @ S2 ) @ ( Nu3 @ X2 ) @ ( Omega2 @ X2 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_322_usubstappt__times__conv,axiom,
% 2.88/1.52 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 2.88/1.52 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 2.88/1.52 != none_trm )
% 2.88/1.52 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 2.88/1.52 != none_trm )
% 2.88/1.52 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 2.88/1.52 != none_trm ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_323_usubstappt_Osimps_I6_J,axiom,
% 2.88/1.52 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 2.88/1.52 ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 2.88/1.52 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_324_Timeso_Osimps_I1_J,axiom,
% 2.88/1.52 ! [Theta: trm,Eta: trm] :
% 2.88/1.52 ( ( uSubst918876924Timeso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 2.88/1.52 = ( some_trm @ ( times @ Theta @ Eta ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_325_stateinterpol__diff,axiom,
% 2.88/1.52 ! [Nu: variable > real,Omega: variable > real] :
% 2.88/1.52 ( ( stateinterpol @ Nu @ Omega @ ( statediff @ Nu @ Omega ) )
% 2.88/1.52 = Nu ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_326_stateinterpol__FVT,axiom,
% 2.88/1.52 ! [Z: variable,T3: trm,I2: denotational_interp,Omega: variable > real,Omega3: variable > real,S: set_variable] :
% 2.88/1.52 ( ~ ( member_variable @ Z @ ( static_FVT @ T3 ) )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ S ) )
% 2.88/1.52 = ( denota1863255036rm_sem @ I2 @ T3 @ ( stateinterpol @ Omega @ Omega3 @ ( insert_variable @ Z @ S ) ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_327_nostatediff,axiom,
% 2.88/1.52 ! [X: variable,Nu: variable > real,Omega: variable > real] :
% 2.88/1.52 ( ~ ( member_variable @ X @ ( statediff @ Nu @ Omega ) )
% 2.88/1.52 => ( ( Nu @ X )
% 2.88/1.52 = ( Omega @ X ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_328_coincidence__term,axiom,
% 2.88/1.52 ! [Omega: variable > real,Omega3: variable > real,Theta: trm,I2: denotational_interp] :
% 2.88/1.52 ( ( denotational_Vagree @ Omega @ Omega3 @ ( static_FVT @ Theta ) )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 2.88/1.52 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_329_coincidence__term__cor,axiom,
% 2.88/1.52 ! [Omega: variable > real,Omega3: variable > real,U: set_variable,Theta: trm,I2: denotational_interp] :
% 2.88/1.52 ( ( denota1419872369iation @ Omega @ Omega3 @ U )
% 2.88/1.52 => ( ( ( inf_inf_set_variable @ ( static_FVT @ Theta ) @ U )
% 2.88/1.52 = bot_bot_set_variable )
% 2.88/1.52 => ( ( denota1863255036rm_sem @ I2 @ Theta @ Omega )
% 2.88/1.52 = ( denota1863255036rm_sem @ I2 @ Theta @ Omega3 ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_330_Vagree__statediff,axiom,
% 2.88/1.52 ! [Omega: variable > real,Omega3: variable > real,S: set_variable] :
% 2.88/1.52 ( ( denotational_Vagree @ Omega @ Omega3 @ S )
% 2.88/1.52 => ( ord_le282106107riable @ ( statediff @ Omega @ Omega3 ) @ ( uminus1851247844riable @ S ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_331_order__refl,axiom,
% 2.88/1.52 ! [X: set_variable] : ( ord_le282106107riable @ X @ X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_332_subsetI,axiom,
% 2.88/1.52 ! [A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ! [X6: variable > real] :
% 2.88/1.52 ( ( member_variable_real @ X6 @ A2 )
% 2.88/1.52 => ( member_variable_real @ X6 @ B ) )
% 2.88/1.52 => ( ord_le1113654598e_real @ A2 @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_333_subsetI,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ! [X6: variable] :
% 2.88/1.52 ( ( member_variable @ X6 @ A2 )
% 2.88/1.52 => ( member_variable @ X6 @ B ) )
% 2.88/1.52 => ( ord_le282106107riable @ A2 @ B ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_334_subset__antisym,axiom,
% 2.88/1.52 ! [A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ A2 @ B )
% 2.88/1.52 => ( ( ord_le282106107riable @ B @ A2 )
% 2.88/1.52 => ( A2 = B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_335_inf_Oidem,axiom,
% 2.88/1.52 ! [A: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ A @ A )
% 2.88/1.52 = A ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_336_inf__idem,axiom,
% 2.88/1.52 ! [X: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ X @ X )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_337_inf_Oleft__idem,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B2 ) )
% 2.88/1.52 = ( inf_inf_set_variable @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_338_inf__left__idem,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ X @ ( inf_inf_set_variable @ X @ Y ) )
% 2.88/1.52 = ( inf_inf_set_variable @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_339_inf_Oright__idem,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B2 ) @ B2 )
% 2.88/1.52 = ( inf_inf_set_variable @ A @ B2 ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_340_inf__right__idem,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X @ Y ) @ Y )
% 2.88/1.52 = ( inf_inf_set_variable @ X @ Y ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_341_IntI,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 => ( ( member_variable_real @ C2 @ B )
% 2.88/1.52 => ( member_variable_real @ C2 @ ( inf_in1556002680e_real @ A2 @ B ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_342_IntI,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ A2 )
% 2.88/1.52 => ( ( member_variable @ C2 @ B )
% 2.88/1.52 => ( member_variable @ C2 @ ( inf_inf_set_variable @ A2 @ B ) ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_343_Int__iff,axiom,
% 2.88/1.52 ! [C2: variable > real,A2: set_variable_real,B: set_variable_real] :
% 2.88/1.52 ( ( member_variable_real @ C2 @ ( inf_in1556002680e_real @ A2 @ B ) )
% 2.88/1.52 = ( ( member_variable_real @ C2 @ A2 )
% 2.88/1.52 & ( member_variable_real @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_344_Int__iff,axiom,
% 2.88/1.52 ! [C2: variable,A2: set_variable,B: set_variable] :
% 2.88/1.52 ( ( member_variable @ C2 @ ( inf_inf_set_variable @ A2 @ B ) )
% 2.88/1.52 = ( ( member_variable @ C2 @ A2 )
% 2.88/1.52 & ( member_variable @ C2 @ B ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_345_le__zero__eq,axiom,
% 2.88/1.52 ! [N: nat] :
% 2.88/1.52 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.88/1.52 = ( N = zero_zero_nat ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_346_compl__le__compl__iff,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real] :
% 2.88/1.52 ( ( ord_le1113654598e_real @ ( uminus430703407e_real @ X ) @ ( uminus430703407e_real @ Y ) )
% 2.88/1.52 = ( ord_le1113654598e_real @ Y @ X ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_347_compl__le__compl__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ ( uminus1851247844riable @ X ) @ ( uminus1851247844riable @ Y ) )
% 2.88/1.52 = ( ord_le282106107riable @ Y @ X ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_348_le__inf__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ X @ ( inf_inf_set_variable @ Y @ Z ) )
% 2.88/1.52 = ( ( ord_le282106107riable @ X @ Y )
% 2.88/1.52 & ( ord_le282106107riable @ X @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_349_inf_Obounded__iff,axiom,
% 2.88/1.52 ! [A: set_variable,B2: set_variable,C2: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ A @ ( inf_inf_set_variable @ B2 @ C2 ) )
% 2.88/1.52 = ( ( ord_le282106107riable @ A @ B2 )
% 2.88/1.52 & ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_350_le__sup__iff,axiom,
% 2.88/1.52 ! [X: set_variable_real,Y: set_variable_real,Z: set_variable_real] :
% 2.88/1.52 ( ( ord_le1113654598e_real @ ( sup_su1685293586e_real @ X @ Y ) @ Z )
% 2.88/1.52 = ( ( ord_le1113654598e_real @ X @ Z )
% 2.88/1.52 & ( ord_le1113654598e_real @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_351_le__sup__iff,axiom,
% 2.88/1.52 ! [X: set_variable,Y: set_variable,Z: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ X @ Y ) @ Z )
% 2.88/1.52 = ( ( ord_le282106107riable @ X @ Z )
% 2.88/1.52 & ( ord_le282106107riable @ Y @ Z ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(fact_352_sup_Obounded__iff,axiom,
% 2.88/1.52 ! [B2: set_variable,C2: set_variable,A: set_variable] :
% 2.88/1.52 ( ( ord_le282106107riable @ ( sup_sup_set_variable @ B2 @ C2 ) @ A )
% 2.88/1.52 = ( ( ord_le282106107riable @ B2 @ A )
% 2.88/1.52 & ( ord_le282106107riable @ C2 @ A ) ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(help_If_3_1_If_001t__Real__Oreal_T,axiom,
% 2.88/1.52 ! [P: $o] :
% 2.88/1.52 ( ( P = $true )
% 2.88/1.52 | ( P = $false ) ) ).
% 2.88/1.52
% 2.88/1.52 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 2.88/1.52 ! [X: real,Y: real] :
% 2.88/1.52 ( ( if_real @ $false @ X @ Y )
% 2.88/1.52 = Y ) ).
% 2.88/1.52
% 2.88/1.52 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 2.88/1.52 ! [X: real,Y: real] :
% 2.88/1.52 ( ( if_real @ $true @ X @ Y )
% 2.88/1.52 = X ) ).
% 2.88/1.52
% 2.88/1.52 thf(conj_0,conjecture,
% 2.88/1.52 denota1419872369iation @ ( f @ zero_zero_real ) @ omega @ ( sup_sup_set_variable @ ( insert_variable @ ( rVar @ x ) @ ( insert_variable @ ( dVar @ x ) @ bot_bot_set_variable ) ) @ u ) ).
% 2.88/1.52 ------------------------
% 2.88/1.55 % (26135)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/183Mi)
% 2.88/1.55 % (26136)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_26036 for (2999ds/4Mi)
% 2.88/1.55 % (26137)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_26036 for (2999ds/27Mi)
% 2.88/1.56 % (26136)Instruction limit reached!
% 2.88/1.56 % (26136)------------------------------
% 2.88/1.56 % (26136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.56 % (26136)Termination reason: Unknown
% 2.88/1.56 % (26136)Termination phase: shuffling
% 2.88/1.56
% 2.88/1.56 % (26136)Memory used [KB]: 1535
% 2.88/1.56 % (26136)Time elapsed: 0.003 s
% 2.88/1.56 % (26136)Instructions burned: 6 (million)
% 2.88/1.56 % (26136)------------------------------
% 2.88/1.56 % (26136)------------------------------
% 2.88/1.56 % (26138)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/2Mi)
% 2.88/1.56 % (26140)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_26036 for (2999ds/275Mi)
% 2.88/1.56 % (26139)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_26036 for (2999ds/2Mi)
% 2.88/1.56 % (26141)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/18Mi)
% 2.88/1.56 % (26137)Instruction limit reached!
% 2.88/1.56 % (26137)------------------------------
% 2.88/1.56 % (26137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.56 % (26137)Termination reason: Unknown
% 2.88/1.56 % (26137)Termination phase: Property scanning
% 2.88/1.56
% 2.88/1.56 % (26137)Memory used [KB]: 1791
% 2.88/1.56 % (26137)Time elapsed: 0.010 s
% 2.88/1.56 % (26137)Instructions burned: 27 (million)
% 2.88/1.56 % (26137)------------------------------
% 2.88/1.56 % (26137)------------------------------
% 2.88/1.56 % (26138)Instruction limit reached!
% 2.88/1.56 % (26138)------------------------------
% 2.88/1.56 % (26138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.56 % (26138)Termination reason: Unknown
% 2.88/1.56 % (26138)Termination phase: shuffling
% 2.88/1.56
% 2.88/1.56 % (26138)Memory used [KB]: 1407
% 2.88/1.56 % (26139)Instruction limit reached!
% 2.88/1.56 % (26139)------------------------------
% 2.88/1.56 % (26139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.56 % (26139)Termination reason: Unknown
% 2.88/1.56 % (26139)Termination phase: shuffling
% 2.88/1.56
% 2.88/1.56 % (26139)Memory used [KB]: 1407
% 2.88/1.56 % (26139)Time elapsed: 0.004 s
% 2.88/1.56 % (26139)Instructions burned: 3 (million)
% 2.88/1.56 % (26139)------------------------------
% 2.88/1.56 % (26139)------------------------------
% 2.88/1.56 % (26138)Time elapsed: 0.004 s
% 2.88/1.56 % (26138)Instructions burned: 3 (million)
% 2.88/1.56 % (26138)------------------------------
% 2.88/1.56 % (26138)------------------------------
% 2.88/1.56 % (26142)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/3Mi)
% 2.88/1.57 % (26142)Instruction limit reached!
% 2.88/1.57 % (26142)------------------------------
% 2.88/1.57 % (26142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.57 % (26142)Termination reason: Unknown
% 2.88/1.57 % (26142)Termination phase: shuffling
% 2.88/1.57
% 2.88/1.57 % (26142)Memory used [KB]: 1535
% 2.88/1.57 % (26142)Time elapsed: 0.002 s
% 2.88/1.57 % (26142)Instructions burned: 3 (million)
% 2.88/1.57 % (26142)------------------------------
% 2.88/1.57 % (26142)------------------------------
% 2.88/1.57 % (26141)Instruction limit reached!
% 2.88/1.57 % (26141)------------------------------
% 2.88/1.57 % (26141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.57 % (26141)Termination reason: Unknown
% 2.88/1.57 % (26141)Termination phase: shuffling
% 2.88/1.57
% 2.88/1.57 % (26141)Memory used [KB]: 1663
% 2.88/1.57 % (26141)Time elapsed: 0.013 s
% 2.88/1.57 % (26141)Instructions burned: 18 (million)
% 2.88/1.57 % (26141)------------------------------
% 2.88/1.57 % (26141)------------------------------
% 2.88/1.57 % (26143)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_26036 for (2999ds/37Mi)
% 2.88/1.58 % (26146)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_26036 for (2999ds/1041Mi)
% 2.88/1.58 % (26144)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_26036 for (2999ds/15Mi)
% 2.88/1.58 % (26145)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_26036 for (2999ds/3Mi)
% 2.88/1.58 % (26145)Instruction limit reached!
% 2.88/1.58 % (26145)------------------------------
% 2.88/1.58 % (26145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.58 % (26145)Termination reason: Unknown
% 2.88/1.58 % (26145)Termination phase: shuffling
% 2.88/1.58
% 2.88/1.58 % (26145)Memory used [KB]: 1407
% 2.88/1.58 % (26145)Time elapsed: 0.004 s
% 2.88/1.58 % (26145)Instructions burned: 3 (million)
% 2.88/1.58 % (26145)------------------------------
% 2.88/1.58 % (26145)------------------------------
% 2.88/1.58 % (26143)Instruction limit reached!
% 2.88/1.58 % (26143)------------------------------
% 2.88/1.58 % (26143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.58 % (26143)Termination reason: Unknown
% 2.88/1.58 % (26143)Termination phase: shuffling
% 2.88/1.58
% 2.88/1.58 % (26143)Memory used [KB]: 2174
% 2.88/1.58 % (26143)Time elapsed: 0.013 s
% 2.88/1.58 % (26143)Instructions burned: 38 (million)
% 2.88/1.59 % (26143)------------------------------
% 2.88/1.59 % (26143)------------------------------
% 2.88/1.59 % (26144)Instruction limit reached!
% 2.88/1.59 % (26144)------------------------------
% 2.88/1.59 % (26144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.59 % (26144)Termination reason: Unknown
% 2.88/1.59 % (26144)Termination phase: shuffling
% 2.88/1.59
% 2.88/1.59 % (26144)Memory used [KB]: 1663
% 2.88/1.59 % (26144)Time elapsed: 0.011 s
% 2.88/1.59 % (26144)Instructions burned: 15 (million)
% 2.88/1.59 % (26144)------------------------------
% 2.88/1.59 % (26144)------------------------------
% 2.88/1.59 % (26147)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/7Mi)
% 2.88/1.59 % (26147)Instruction limit reached!
% 2.88/1.59 % (26147)------------------------------
% 2.88/1.59 % (26147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.59 % (26147)Termination reason: Unknown
% 2.88/1.59 % (26147)Termination phase: shuffling
% 2.88/1.59
% 2.88/1.59 % (26147)Memory used [KB]: 1535
% 2.88/1.59 % (26147)Time elapsed: 0.006 s
% 2.88/1.59 % (26147)Instructions burned: 7 (million)
% 2.88/1.59 % (26147)------------------------------
% 2.88/1.59 % (26147)------------------------------
% 2.88/1.60 % (26149)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_26036 for (2999ds/3Mi)
% 2.90/1.60 % (26149)Instruction limit reached!
% 2.90/1.60 % (26149)------------------------------
% 2.90/1.60 % (26149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (26149)Termination reason: Unknown
% 2.90/1.60 % (26149)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (26149)Memory used [KB]: 1535
% 2.90/1.60 % (26149)Time elapsed: 0.003 s
% 2.90/1.60 % (26149)Instructions burned: 3 (million)
% 2.90/1.60 % (26149)------------------------------
% 2.90/1.60 % (26149)------------------------------
% 2.90/1.60 % (26140)Refutation not found, incomplete strategy
% 2.90/1.60 % (26140)------------------------------
% 2.90/1.60 % (26140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (26140)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.60
% 2.90/1.60
% 2.90/1.60 % (26140)Memory used [KB]: 6652
% 2.90/1.60 % (26140)Time elapsed: 0.039 s
% 2.90/1.60 % (26140)Instructions burned: 65 (million)
% 2.90/1.60 % (26140)------------------------------
% 2.90/1.60 % (26140)------------------------------
% 2.90/1.60 % (26148)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/16Mi)
% 2.90/1.61 % (26135)Instruction limit reached!
% 2.90/1.61 % (26135)------------------------------
% 2.90/1.61 % (26135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26135)Termination reason: Unknown
% 2.90/1.61 % (26135)Termination phase: Saturation
% 2.90/1.61
% 2.90/1.61 % (26135)Memory used [KB]: 7419
% 2.90/1.61 % (26135)Time elapsed: 0.053 s
% 2.90/1.61 % (26135)Instructions burned: 185 (million)
% 2.90/1.61 % (26135)------------------------------
% 2.90/1.61 % (26135)------------------------------
% 2.90/1.61 % (26150)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_26036 for (2999ds/3Mi)
% 2.90/1.61 % (26152)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/3Mi)
% 2.90/1.61 % (26152)Instruction limit reached!
% 2.90/1.61 % (26152)------------------------------
% 2.90/1.61 % (26152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26152)Termination reason: Unknown
% 2.90/1.61 % (26152)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26152)Memory used [KB]: 1535
% 2.90/1.61 % (26152)Time elapsed: 0.003 s
% 2.90/1.61 % (26152)Instructions burned: 4 (million)
% 2.90/1.61 % (26152)------------------------------
% 2.90/1.61 % (26152)------------------------------
% 2.90/1.61 % (26150)Instruction limit reached!
% 2.90/1.61 % (26150)------------------------------
% 2.90/1.61 % (26150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26150)Termination reason: Unknown
% 2.90/1.61 % (26150)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26150)Memory used [KB]: 1535
% 2.90/1.61 % (26150)Time elapsed: 0.003 s
% 2.90/1.61 % (26150)Instructions burned: 3 (million)
% 2.90/1.61 % (26150)------------------------------
% 2.90/1.61 % (26150)------------------------------
% 2.90/1.61 % (26148)Instruction limit reached!
% 2.90/1.61 % (26148)------------------------------
% 2.90/1.61 % (26148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (26148)Termination reason: Unknown
% 2.90/1.61 % (26148)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (26148)Memory used [KB]: 1791
% 2.90/1.61 % (26148)Time elapsed: 0.010 s
% 2.90/1.61 % (26148)Instructions burned: 17 (million)
% 2.90/1.61 % (26148)------------------------------
% 2.90/1.61 % (26148)------------------------------
% 2.90/1.61 % (26151)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/7Mi)
% 2.90/1.61 % (26153)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/4Mi)
% 2.90/1.61 % (26154)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/18Mi)
% 2.90/1.62 % (26151)Instruction limit reached!
% 2.90/1.62 % (26151)------------------------------
% 2.90/1.62 % (26151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (26151)Termination reason: Unknown
% 2.90/1.62 % (26151)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (26151)Memory used [KB]: 1535
% 2.90/1.62 % (26151)Time elapsed: 0.006 s
% 2.90/1.62 % (26151)Instructions burned: 7 (million)
% 2.90/1.62 % (26151)------------------------------
% 2.90/1.62 % (26151)------------------------------
% 2.90/1.62 % (26153)Instruction limit reached!
% 2.90/1.62 % (26153)------------------------------
% 2.90/1.62 % (26153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (26153)Termination reason: Unknown
% 2.90/1.62 % (26153)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (26153)Memory used [KB]: 1535
% 2.90/1.62 % (26153)Time elapsed: 0.004 s
% 2.90/1.62 % (26153)Instructions burned: 6 (million)
% 2.90/1.62 % (26153)------------------------------
% 2.90/1.62 % (26153)------------------------------
% 2.90/1.62 % (26155)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/710Mi)
% 2.90/1.62 % (26156)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/6Mi)
% 2.90/1.62 % (26156)Instruction limit reached!
% 2.90/1.62 % (26156)------------------------------
% 2.90/1.62 % (26156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (26156)Termination reason: Unknown
% 2.90/1.62 % (26156)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (26156)Memory used [KB]: 1535
% 2.90/1.62 % (26156)Time elapsed: 0.003 s
% 2.90/1.62 % (26156)Instructions burned: 6 (million)
% 2.90/1.62 % (26156)------------------------------
% 2.90/1.62 % (26156)------------------------------
% 2.90/1.62 % (26154)Instruction limit reached!
% 2.90/1.62 % (26154)------------------------------
% 2.90/1.62 % (26154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (26154)Termination reason: Unknown
% 2.90/1.62 % (26154)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (26154)Memory used [KB]: 1791
% 2.90/1.62 % (26154)Time elapsed: 0.007 s
% 2.90/1.62 % (26154)Instructions burned: 20 (million)
% 2.90/1.62 % (26154)------------------------------
% 2.90/1.62 % (26154)------------------------------
% 2.90/1.62 % (26157)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_26036 for (2999ds/902Mi)
% 2.90/1.63 % (26159)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/5Mi)
% 2.90/1.63 % (26159)Instruction limit reached!
% 2.90/1.63 % (26159)------------------------------
% 2.90/1.63 % (26159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (26159)Termination reason: Unknown
% 2.90/1.63 % (26159)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (26159)Memory used [KB]: 1535
% 2.90/1.63 % (26159)Time elapsed: 0.003 s
% 2.90/1.63 % (26159)Instructions burned: 5 (million)
% 2.90/1.63 % (26159)------------------------------
% 2.90/1.63 % (26159)------------------------------
% 2.90/1.63 % (26161)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26036 for (2999ds/377Mi)
% 2.90/1.63 % (26160)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_26036 for (2999ds/6Mi)
% 2.90/1.63 % (26160)Instruction limit reached!
% 2.90/1.63 % (26160)------------------------------
% 2.90/1.63 % (26160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (26160)Termination reason: Unknown
% 2.90/1.63 % (26160)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (26160)Memory used [KB]: 1663
% 2.90/1.63 % (26160)Time elapsed: 0.004 s
% 2.90/1.63 % (26160)Instructions burned: 7 (million)
% 2.90/1.63 % (26160)------------------------------
% 2.90/1.63 % (26160)------------------------------
% 2.90/1.63 % (26158)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_26036 for (2999ds/21Mi)
% 2.90/1.64 % (26162)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_26036 for (2999ds/779Mi)
% 2.90/1.64 % (26158)Instruction limit reached!
% 2.90/1.64 % (26158)------------------------------
% 2.90/1.64 % (26158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.64 % (26158)Termination reason: Unknown
% 2.90/1.64 % (26158)Termination phase: shuffling
% 2.90/1.64
% 2.90/1.64 % (26158)Memory used [KB]: 1791
% 2.90/1.64 % (26158)Time elapsed: 0.012 s
% 2.90/1.64 % (26158)Instructions burned: 21 (million)
% 2.90/1.64 % (26158)------------------------------
% 2.90/1.64 % (26158)------------------------------
% 2.90/1.64 % (26163)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_26036 for (2999ds/19Mi)
% 2.90/1.65 % (26163)Instruction limit reached!
% 2.90/1.65 % (26163)------------------------------
% 2.90/1.65 % (26163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (26163)Termination reason: Unknown
% 2.90/1.65 % (26163)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (26163)Memory used [KB]: 1918
% 2.90/1.65 % (26163)Time elapsed: 0.008 s
% 2.90/1.65 % (26163)Instructions burned: 21 (million)
% 2.90/1.65 % (26163)------------------------------
% 2.90/1.65 % (26163)------------------------------
% 2.90/1.65 % (26164)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26036 for (2998ds/879Mi)
% 2.90/1.66 % (26165)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26036 for (2998ds/17Mi)
% 2.90/1.67 % (26165)Instruction limit reached!
% 2.90/1.67 % (26165)------------------------------
% 2.90/1.67 % (26165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.67 % (26165)Termination reason: Unknown
% 2.90/1.67 % (26165)Termination phase: shuffling
% 2.90/1.67
% 2.90/1.67 % (26165)Memory used [KB]: 1791
% 2.90/1.67 % (26165)Time elapsed: 0.008 s
% 2.90/1.67 % (26165)Instructions burned: 18 (million)
% 2.90/1.67 % (26165)------------------------------
% 2.90/1.67 % (26165)------------------------------
% 2.90/1.68 % (26166)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26036 for (2998ds/3Mi)
% 2.90/1.68 % (26166)Instruction limit reached!
% 2.90/1.68 % (26166)------------------------------
% 2.90/1.68 % (26166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.68 % (26166)Termination reason: Unknown
% 2.90/1.68 % (26166)Termination phase: shuffling
% 2.90/1.68
% 2.90/1.68 % (26166)Memory used [KB]: 1535
% 2.90/1.68 % (26166)Time elapsed: 0.003 s
% 2.90/1.68 % (26166)Instructions burned: 3 (million)
% 2.90/1.68 % (26166)------------------------------
% 2.90/1.68 % (26166)------------------------------
% 2.90/1.69 % (26167)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26036 for (2998ds/30Mi)
% 2.90/1.70 % (26167)Instruction limit reached!
% 2.90/1.70 % (26167)------------------------------
% 2.90/1.70 % (26167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.70 % (26167)Termination reason: Unknown
% 2.90/1.70 % (26167)Termination phase: Property scanning
% 2.90/1.70
% 2.90/1.70 % (26167)Memory used [KB]: 1918
% 2.90/1.70 % (26167)Time elapsed: 0.013 s
% 2.90/1.70 % (26167)Instructions burned: 32 (million)
% 2.90/1.70 % (26167)------------------------------
% 2.90/1.70 % (26167)------------------------------
% 2.90/1.71 % (26168)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26036 for (2998ds/127Mi)
% 2.90/1.74 % (26161)Instruction limit reached!
% 2.90/1.74 % (26161)------------------------------
% 2.90/1.74 % (26161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.74 % (26161)Termination reason: Unknown
% 2.90/1.74 % (26161)Termination phase: Saturation
% 2.90/1.74
% 2.90/1.74 % (26161)Memory used [KB]: 8315
% 2.90/1.74 % (26161)Time elapsed: 0.112 s
% 2.90/1.74 % (26161)Instructions burned: 378 (million)
% 2.90/1.74 % (26161)------------------------------
% 2.90/1.74 % (26161)------------------------------
% 2.90/1.75 % (26168)Instruction limit reached!
% 2.90/1.75 % (26168)------------------------------
% 2.90/1.75 % (26168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.75 % (26168)Termination reason: Unknown
% 2.90/1.75 % (26168)Termination phase: Saturation
% 2.90/1.75
% 2.90/1.75 % (26168)Memory used [KB]: 6908
% 2.90/1.75 % (26168)Time elapsed: 0.040 s
% 2.90/1.75 % (26168)Instructions burned: 127 (million)
% 2.90/1.75 % (26168)------------------------------
% 2.90/1.75 % (26168)------------------------------
% 2.90/1.75 % (26169)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26036 for (2997ds/100Mi)
% 2.90/1.76 % (26170)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_26036 for (2997ds/3Mi)
% 2.90/1.76 % (26170)Instruction limit reached!
% 2.90/1.76 % (26170)------------------------------
% 2.90/1.76 % (26170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.76 % (26170)Termination reason: Unknown
% 2.90/1.76 % (26170)Termination phase: shuffling
% 2.90/1.76
% 2.90/1.76 % (26170)Memory used [KB]: 1535
% 2.90/1.76 % (26170)Time elapsed: 0.002 s
% 2.90/1.76 % (26170)Instructions burned: 3 (million)
% 2.90/1.76 % (26170)------------------------------
% 2.90/1.76 % (26170)------------------------------
% 2.90/1.77 % (26171)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_26036 for (2997ds/20Mi)
% 2.90/1.78 % (26171)Instruction limit reached!
% 2.90/1.78 % (26171)------------------------------
% 2.90/1.78 % (26171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.78 % (26169)Instruction limit reached!
% 2.90/1.78 % (26169)------------------------------
% 2.90/1.78 % (26169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.78 % (26171)Termination reason: Unknown
% 2.90/1.78 % (26171)Termination phase: shuffling
% 2.90/1.78
% 2.90/1.78 % (26171)Memory used [KB]: 1791
% 2.90/1.78 % (26171)Time elapsed: 0.009 s
% 2.90/1.78 % (26171)Instructions burned: 20 (million)
% 2.90/1.78 % (26171)------------------------------
% 2.90/1.78 % (26171)------------------------------
% 2.90/1.78 % (26169)Termination reason: Unknown
% 2.90/1.78 % (26169)Termination phase: Property scanning
% 2.90/1.78
% 2.90/1.78 % (26169)Memory used [KB]: 2430
% 2.90/1.78 % (26169)Time elapsed: 0.027 s
% 2.90/1.78 % (26169)Instructions burned: 101 (million)
% 2.90/1.78 % (26169)------------------------------
% 2.90/1.78 % (26169)------------------------------
% 2.90/1.79 % (26173)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_26036 for (2997ds/107Mi)
% 2.90/1.79 % (26172)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_26036 for (2997ds/86Mi)
% 2.90/1.81 % (26172)Instruction limit reached!
% 2.90/1.81 % (26172)------------------------------
% 2.90/1.81 % (26172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.81 % (26172)Termination reason: Unknown
% 2.90/1.81 % (26172)Termination phase: Property scanning
% 2.90/1.81
% 2.90/1.81 % (26172)Memory used [KB]: 2174
% 2.90/1.81 % (26172)Time elapsed: 0.028 s
% 2.90/1.81 % (26172)Instructions burned: 87 (million)
% 2.90/1.81 % (26172)------------------------------
% 2.90/1.81 % (26172)------------------------------
% 2.90/1.82 % (26173)Instruction limit reached!
% 2.90/1.82 % (26173)------------------------------
% 2.90/1.82 % (26173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.82 % (26173)Termination reason: Unknown
% 2.90/1.82 % (26173)Termination phase: Saturation
% 2.90/1.82
% 2.90/1.82 % (26173)Memory used [KB]: 6780
% 2.90/1.82 % (26173)Time elapsed: 0.031 s
% 2.90/1.82 % (26173)Instructions burned: 107 (million)
% 2.90/1.82 % (26173)------------------------------
% 2.90/1.82 % (26173)------------------------------
% 2.90/1.82 % (26174)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_26036 for (2997ds/39Mi)
% 2.90/1.83 % (26175)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_26036 for (2997ds/448Mi)
% 2.90/1.83 % (26155)Instruction limit reached!
% 2.90/1.83 % (26155)------------------------------
% 2.90/1.83 % (26155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.83 % (26155)Termination reason: Unknown
% 2.90/1.83 % (26155)Termination phase: Saturation
% 2.90/1.83
% 2.90/1.83 % (26155)Memory used [KB]: 7675
% 2.90/1.83 % (26155)Time elapsed: 0.217 s
% 2.90/1.83 % (26155)Instructions burned: 712 (million)
% 2.90/1.83 % (26155)------------------------------
% 2.90/1.83 % (26155)------------------------------
% 2.90/1.84 % (26174)Instruction limit reached!
% 2.90/1.84 % (26174)------------------------------
% 2.90/1.84 % (26174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.84 % (26174)Termination reason: Unknown
% 2.90/1.84 % (26174)Termination phase: shuffling
% 2.90/1.84
% 2.90/1.84 % (26174)Memory used [KB]: 2302
% 2.90/1.84 % (26174)Time elapsed: 0.013 s
% 2.90/1.84 % (26174)Instructions burned: 41 (million)
% 2.90/1.84 % (26174)------------------------------
% 2.90/1.84 % (26174)------------------------------
% 2.90/1.84 % (26176)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/46Mi)
% 2.90/1.85 % (26177)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/98Mi)
% 2.90/1.86 % (26176)Instruction limit reached!
% 2.90/1.86 % (26176)------------------------------
% 2.90/1.86 % (26176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.86 % (26176)Termination reason: Unknown
% 2.90/1.86 % (26176)Termination phase: SInE selection
% 2.90/1.86
% 2.90/1.86 % (26176)Memory used [KB]: 1918
% 2.90/1.86 % (26176)Time elapsed: 0.015 s
% 2.90/1.86 % (26176)Instructions burned: 49 (million)
% 2.90/1.86 % (26176)------------------------------
% 2.90/1.86 % (26176)------------------------------
% 2.90/1.87 % (26178)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/507Mi)
% 2.90/1.87 % (26162)Instruction limit reached!
% 2.90/1.87 % (26162)------------------------------
% 2.90/1.87 % (26162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.87 % (26162)Termination reason: Unknown
% 2.90/1.87 % (26162)Termination phase: Saturation
% 2.90/1.87
% 2.90/1.87 % (26162)Memory used [KB]: 8571
% 2.90/1.87 % (26162)Time elapsed: 0.232 s
% 2.90/1.87 % (26162)Instructions burned: 780 (million)
% 2.90/1.87 % (26162)------------------------------
% 2.90/1.87 % (26162)------------------------------
% 2.90/1.87 % (26177)Instruction limit reached!
% 2.90/1.87 % (26177)------------------------------
% 2.90/1.87 % (26177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.87 % (26177)Termination reason: Unknown
% 2.90/1.87 % (26177)Termination phase: Property scanning
% 2.90/1.87
% 2.90/1.87 % (26177)Memory used [KB]: 2430
% 2.90/1.87 % (26177)Time elapsed: 0.030 s
% 2.90/1.87 % (26177)Instructions burned: 100 (million)
% 2.90/1.87 % (26177)------------------------------
% 2.90/1.87 % (26177)------------------------------
% 2.90/1.88 % (26179)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/149Mi)
% 2.90/1.88 % (26180)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/39Mi)
% 2.90/1.89 % (26146)Instruction limit reached!
% 2.90/1.89 % (26146)------------------------------
% 2.90/1.89 % (26146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.89 % (26146)Termination reason: Unknown
% 2.90/1.89 % (26146)Termination phase: Saturation
% 2.90/1.89
% 2.90/1.89 % (26146)Memory used [KB]: 9978
% 2.90/1.89 % (26146)Time elapsed: 0.317 s
% 2.90/1.89 % (26146)Instructions burned: 1042 (million)
% 2.90/1.89 % (26146)------------------------------
% 2.90/1.89 % (26146)------------------------------
% 2.90/1.90 % (26180)Instruction limit reached!
% 2.90/1.90 % (26180)------------------------------
% 2.90/1.90 % (26180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (26180)Termination reason: Unknown
% 2.90/1.90 % (26180)Termination phase: Preprocessing 1
% 2.90/1.90
% 2.90/1.90 % (26180)Memory used [KB]: 1918
% 2.90/1.90 % (26180)Time elapsed: 0.015 s
% 2.90/1.90 % (26180)Instructions burned: 41 (million)
% 2.90/1.90 % (26180)------------------------------
% 2.90/1.90 % (26180)------------------------------
% 2.90/1.90 % (26181)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/6Mi)
% 2.90/1.90 % (26181)Instruction limit reached!
% 2.90/1.90 % (26181)------------------------------
% 2.90/1.90 % (26181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (26181)Termination reason: Unknown
% 2.90/1.90 % (26181)Termination phase: shuffling
% 2.90/1.90
% 2.90/1.90 % (26181)Memory used [KB]: 1663
% 2.90/1.90 % (26181)Time elapsed: 0.003 s
% 2.90/1.90 % (26181)Instructions burned: 7 (million)
% 2.90/1.90 % (26181)------------------------------
% 2.90/1.90 % (26181)------------------------------
% 2.90/1.91 % (26182)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/1087Mi)
% 2.90/1.91 % (26183)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/47Mi)
% 2.90/1.91 % (26157)Instruction limit reached!
% 2.90/1.91 % (26157)------------------------------
% 2.90/1.91 % (26157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.91 % (26157)Termination reason: Unknown
% 2.90/1.91 % (26157)Termination phase: Saturation
% 2.90/1.91
% 2.90/1.91 % (26157)Memory used [KB]: 8059
% 2.90/1.91 % (26157)Time elapsed: 0.295 s
% 2.90/1.91 % (26157)Instructions burned: 902 (million)
% 2.90/1.91 % (26157)------------------------------
% 2.90/1.91 % (26157)------------------------------
% 2.90/1.92 % (26179)Instruction limit reached!
% 2.90/1.92 % (26179)------------------------------
% 2.90/1.92 % (26179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.92 % (26179)Termination reason: Unknown
% 2.90/1.92 % (26179)Termination phase: Saturation
% 2.90/1.92
% 2.90/1.92 % (26179)Memory used [KB]: 7164
% 2.90/1.92 % (26179)Time elapsed: 0.042 s
% 2.90/1.92 % (26179)Instructions burned: 151 (million)
% 2.90/1.92 % (26179)------------------------------
% 2.90/1.92 % (26179)------------------------------
% 2.90/1.93 % (26184)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/44Mi)
% 2.90/1.93 % (26183)Instruction limit reached!
% 2.90/1.93 % (26183)------------------------------
% 2.90/1.93 % (26183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.93 % (26183)Termination reason: Unknown
% 2.90/1.93 % (26183)Termination phase: Preprocessing 3
% 2.90/1.93
% 2.90/1.93 % (26183)Memory used [KB]: 2046
% 2.90/1.93 % (26183)Time elapsed: 0.015 s
% 2.90/1.93 % (26183)Instructions burned: 48 (million)
% 2.90/1.93 % (26183)------------------------------
% 2.90/1.93 % (26183)------------------------------
% 2.90/1.93 % (26185)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_26036 for (2996ds/432Mi)
% 2.90/1.94 % (26186)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/62Mi)
% 2.90/1.94 % (26164)Instruction limit reached!
% 2.90/1.94 % (26164)------------------------------
% 2.90/1.94 % (26164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (26164)Termination reason: Unknown
% 2.90/1.94 % (26164)Termination phase: Saturation
% 2.90/1.94
% 2.90/1.94 % (26164)Memory used [KB]: 7931
% 2.90/1.94 % (26164)Time elapsed: 0.284 s
% 2.90/1.94 % (26164)Instructions burned: 882 (million)
% 2.90/1.94 % (26164)------------------------------
% 2.90/1.94 % (26164)------------------------------
% 2.90/1.94 % (26184)Instruction limit reached!
% 2.90/1.94 % (26184)------------------------------
% 2.90/1.94 % (26184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (26184)Termination reason: Unknown
% 2.90/1.94 % (26184)Termination phase: shuffling
% 2.90/1.94
% 2.90/1.94 % (26184)Memory used [KB]: 2302
% 2.90/1.94 % (26184)Time elapsed: 0.014 s
% 2.90/1.94 % (26184)Instructions burned: 44 (million)
% 2.90/1.94 % (26184)------------------------------
% 2.90/1.94 % (26184)------------------------------
% 2.90/1.95 % (26187)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/31Mi)
% 2.90/1.95 % (26188)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/96Mi)
% 2.90/1.95 % (26186)Instruction limit reached!
% 2.90/1.95 % (26186)------------------------------
% 2.90/1.95 % (26186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.95 % (26186)Termination reason: Unknown
% 2.90/1.95 % (26186)Termination phase: Property scanning
% 2.90/1.95
% 2.90/1.95 % (26186)Memory used [KB]: 2430
% 2.90/1.95 % (26186)Time elapsed: 0.018 s
% 2.90/1.95 % (26186)Instructions burned: 64 (million)
% 2.90/1.95 % (26175)Instruction limit reached!
% 2.90/1.95 % (26175)------------------------------
% 2.90/1.95 % (26175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.95 % (26175)Termination reason: Unknown
% 2.90/1.95 % (26175)Termination phase: Saturation
% 2.90/1.95
% 2.90/1.95 % (26175)Memory used [KB]: 8955
% 2.90/1.95 % (26175)Time elapsed: 0.128 s
% 2.90/1.95 % (26175)Instructions burned: 449 (million)
% 2.90/1.95 % (26175)------------------------------
% 2.90/1.95 % (26175)------------------------------
% 2.90/1.95 % (26186)------------------------------
% 2.90/1.95 % (26186)------------------------------
% 2.90/1.96 % (26187)Instruction limit reached!
% 2.90/1.96 % (26187)------------------------------
% 2.90/1.96 % (26187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (26187)Termination reason: Unknown
% 2.90/1.96 % (26187)Termination phase: Property scanning
% 2.90/1.96
% 2.90/1.96 % (26187)Memory used [KB]: 1791
% 2.90/1.96 % (26187)Time elapsed: 0.011 s
% 2.90/1.96 % (26187)Instructions burned: 31 (million)
% 2.90/1.96 % (26187)------------------------------
% 2.90/1.96 % (26187)------------------------------
% 2.90/1.96 % (26189)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/453Mi)
% 2.90/1.96 % (26190)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/71Mi)
% 2.90/1.97 % (26191)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/83Mi)
% 2.90/1.98 % (26188)Instruction limit reached!
% 2.90/1.98 % (26188)------------------------------
% 2.90/1.98 % (26188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.98 % (26188)Termination reason: Unknown
% 2.90/1.98 % (26188)Termination phase: Saturation
% 2.90/1.98
% 2.90/1.98 % (26188)Memory used [KB]: 6652
% 2.90/1.98 % (26188)Time elapsed: 0.028 s
% 2.90/1.98 % (26188)Instructions burned: 98 (million)
% 2.90/1.98 % (26188)------------------------------
% 2.90/1.98 % (26188)------------------------------
% 2.90/1.98 % (26190)Instruction limit reached!
% 2.90/1.98 % (26190)------------------------------
% 2.90/1.98 % (26190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.98 % (26190)Termination reason: Unknown
% 2.90/1.98 % (26190)Termination phase: Function definition elimination
% 2.90/1.98
% 2.90/1.98 % (26190)Memory used [KB]: 2174
% 2.90/1.98 % (26190)Time elapsed: 0.021 s
% 2.90/1.98 % (26190)Instructions burned: 71 (million)
% 2.90/1.98 % (26190)------------------------------
% 2.90/1.98 % (26190)------------------------------
% 2.90/1.99 % (26192)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/11Mi)
% 2.90/1.99 % (26192)Instruction limit reached!
% 2.90/1.99 % (26192)------------------------------
% 2.90/1.99 % (26192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.99 % (26192)Termination reason: Unknown
% 2.90/1.99 % (26192)Termination phase: shuffling
% 2.90/1.99
% 2.90/1.99 % (26192)Memory used [KB]: 1663
% 2.90/1.99 % (26192)Time elapsed: 0.004 s
% 2.90/1.99 % (26192)Instructions burned: 11 (million)
% 2.90/1.99 % (26192)------------------------------
% 2.90/1.99 % (26192)------------------------------
% 2.90/1.99 % (26191)Instruction limit reached!
% 2.90/1.99 % (26191)------------------------------
% 2.90/1.99 % (26191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.99 % (26191)Termination reason: Unknown
% 2.90/1.99 % (26191)Termination phase: Saturation
% 2.90/1.99
% 2.90/1.99 % (26191)Memory used [KB]: 6524
% 2.90/1.99 % (26191)Time elapsed: 0.026 s
% 2.90/1.99 % (26191)Instructions burned: 85 (million)
% 2.90/1.99 % (26191)------------------------------
% 2.90/1.99 % (26191)------------------------------
% 2.90/1.99 % (26193)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/41Mi)
% 2.90/2.00 % (26194)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/6Mi)
% 2.90/2.00 % (26194)Instruction limit reached!
% 2.90/2.00 % (26194)------------------------------
% 2.90/2.00 % (26194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (26194)Termination reason: Unknown
% 2.90/2.00 % (26194)Termination phase: shuffling
% 2.90/2.00
% 2.90/2.00 % (26194)Memory used [KB]: 1535
% 2.90/2.00 % (26194)Time elapsed: 0.003 s
% 2.90/2.00 % (26194)Instructions burned: 6 (million)
% 2.90/2.00 % (26194)------------------------------
% 2.90/2.00 % (26194)------------------------------
% 2.90/2.00 % (26195)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/150Mi)
% 2.90/2.00 % (26193)Instruction limit reached!
% 2.90/2.00 % (26193)------------------------------
% 2.90/2.00 % (26193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (26193)Termination reason: Unknown
% 2.90/2.00 % (26193)Termination phase: shuffling
% 2.90/2.00
% 2.90/2.00 % (26193)Memory used [KB]: 2302
% 2.90/2.00 % (26193)Time elapsed: 0.012 s
% 2.90/2.00 % (26193)Instructions burned: 41 (million)
% 2.90/2.00 % (26193)------------------------------
% 2.90/2.00 % (26193)------------------------------
% 6.09/2.01 % (26197)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/109Mi)
% 6.09/2.02 % (26178)Instruction limit reached!
% 6.09/2.02 % (26178)------------------------------
% 6.09/2.02 % (26178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.02 % (26178)Termination reason: Unknown
% 6.09/2.02 % (26178)Termination phase: Saturation
% 6.09/2.02
% 6.09/2.02 % (26178)Memory used [KB]: 8187
% 6.09/2.02 % (26178)Time elapsed: 0.148 s
% 6.09/2.02 % (26178)Instructions burned: 507 (million)
% 6.09/2.02 % (26178)------------------------------
% 6.09/2.02 % (26178)------------------------------
% 6.09/2.02 % (26196)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/343Mi)
% 6.09/2.03 % (26198)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_26036 for (2995ds/253Mi)
% 6.09/2.04 % (26197)Instruction limit reached!
% 6.09/2.04 % (26197)------------------------------
% 6.09/2.04 % (26197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.04 % (26197)Termination reason: Unknown
% 6.09/2.04 % (26197)Termination phase: Saturation
% 6.09/2.04
% 6.09/2.04 % (26197)Memory used [KB]: 6780
% 6.09/2.04 % (26197)Time elapsed: 0.031 s
% 6.09/2.04 % (26197)Instructions burned: 109 (million)
% 6.09/2.04 % (26197)------------------------------
% 6.09/2.04 % (26197)------------------------------
% 6.09/2.04 % (26195)Instruction limit reached!
% 6.09/2.04 % (26195)------------------------------
% 6.09/2.04 % (26195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.04 % (26195)Termination reason: Unknown
% 6.09/2.04 % (26195)Termination phase: Saturation
% 6.09/2.04
% 6.09/2.04 % (26195)Memory used [KB]: 7291
% 6.09/2.04 % (26195)Time elapsed: 0.044 s
% 6.09/2.04 % (26195)Instructions burned: 151 (million)
% 6.09/2.04 % (26195)------------------------------
% 6.09/2.04 % (26195)------------------------------
% 6.09/2.05 % (26199)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/140Mi)
% 6.09/2.05 % (26200)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/614Mi)
% 6.09/2.06 % (26185)Instruction limit reached!
% 6.09/2.06 % (26185)------------------------------
% 6.09/2.06 % (26185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.06 % (26185)Termination reason: Unknown
% 6.09/2.06 % (26185)Termination phase: Saturation
% 6.09/2.06
% 6.09/2.06 % (26185)Memory used [KB]: 3837
% 6.09/2.06 % (26185)Time elapsed: 0.129 s
% 6.09/2.06 % (26185)Instructions burned: 434 (million)
% 6.09/2.06 % (26185)------------------------------
% 6.09/2.06 % (26185)------------------------------
% 6.09/2.07 % (26201)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/202Mi)
% 6.09/2.09 % (26189)Instruction limit reached!
% 6.09/2.09 % (26189)------------------------------
% 6.09/2.09 % (26189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.09 % (26189)Termination reason: Unknown
% 6.09/2.09 % (26189)Termination phase: Saturation
% 6.09/2.09
% 6.09/2.09 % (26189)Memory used [KB]: 7803
% 6.09/2.09 % (26189)Time elapsed: 0.124 s
% 6.09/2.09 % (26189)Instructions burned: 454 (million)
% 6.09/2.09 % (26189)------------------------------
% 6.09/2.09 % (26189)------------------------------
% 6.09/2.09 % (26201)Refutation not found, incomplete strategy
% 6.09/2.09 % (26201)------------------------------
% 6.09/2.09 % (26201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.09 % (26201)Termination reason: Refutation not found, incomplete strategy
% 6.09/2.09
% 6.09/2.09
% 6.09/2.09 % (26201)Memory used [KB]: 6908
% 6.09/2.09 % (26201)Time elapsed: 0.028 s
% 6.09/2.09 % (26201)Instructions burned: 90 (million)
% 6.09/2.09 % (26201)------------------------------
% 6.09/2.09 % (26201)------------------------------
% 6.09/2.09 % (26199)Instruction limit reached!
% 6.09/2.09 % (26199)------------------------------
% 6.09/2.09 % (26199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.10 % (26199)Termination reason: Unknown
% 6.09/2.10 % (26199)Termination phase: Saturation
% 6.09/2.10
% 6.09/2.10 % (26199)Memory used [KB]: 6908
% 6.09/2.10 % (26199)Time elapsed: 0.044 s
% 6.09/2.10 % (26199)Instructions burned: 142 (million)
% 6.09/2.10 % (26199)------------------------------
% 6.09/2.10 % (26199)------------------------------
% 6.09/2.10 % (26202)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/339Mi)
% 6.09/2.10 % (26198)Instruction limit reached!
% 6.09/2.10 % (26198)------------------------------
% 6.09/2.10 % (26198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.10 % (26198)Termination reason: Unknown
% 6.09/2.10 % (26198)Termination phase: Saturation
% 6.09/2.10
% 6.09/2.10 % (26198)Memory used [KB]: 7803
% 6.09/2.10 % (26198)Time elapsed: 0.078 s
% 6.09/2.10 % (26198)Instructions burned: 254 (million)
% 6.09/2.10 % (26198)------------------------------
% 6.09/2.10 % (26198)------------------------------
% 6.09/2.10 % (26203)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=283:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/283Mi)
% 6.09/2.10 % (26204)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/134Mi)
% 6.09/2.11 % (26205)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/298Mi)
% 6.62/2.13 % (26196)Instruction limit reached!
% 6.62/2.13 % (26196)------------------------------
% 6.62/2.13 % (26196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.13 % (26196)Termination reason: Unknown
% 6.62/2.13 % (26196)Termination phase: Saturation
% 6.62/2.13
% 6.62/2.13 % (26196)Memory used [KB]: 7547
% 6.62/2.13 % (26196)Time elapsed: 0.128 s
% 6.62/2.13 % (26196)Instructions burned: 345 (million)
% 6.62/2.13 % (26196)------------------------------
% 6.62/2.13 % (26196)------------------------------
% 6.62/2.14 % (26206)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26036 for (2994ds/192Mi)
% 6.62/2.14 % (26204)Instruction limit reached!
% 6.62/2.14 % (26204)------------------------------
% 6.62/2.14 % (26204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.14 % (26204)Termination reason: Unknown
% 6.62/2.14 % (26204)Termination phase: Saturation
% 6.62/2.14
% 6.62/2.14 % (26204)Memory used [KB]: 7036
% 6.62/2.14 % (26204)Time elapsed: 0.038 s
% 6.62/2.14 % (26204)Instructions burned: 135 (million)
% 6.62/2.14 % (26204)------------------------------
% 6.62/2.14 % (26204)------------------------------
% 6.62/2.15 % (26207)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/258Mi)
% 6.62/2.15 % (26182)Instruction limit reached!
% 6.62/2.15 % (26182)------------------------------
% 6.62/2.15 % (26182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.15 % (26182)Termination reason: Unknown
% 6.62/2.15 % (26182)Termination phase: Saturation
% 6.62/2.15
% 6.62/2.15 % (26182)Memory used [KB]: 7164
% 6.62/2.15 % (26182)Time elapsed: 0.247 s
% 6.62/2.15 % (26182)Instructions burned: 1092 (million)
% 6.62/2.15 % (26182)------------------------------
% 6.62/2.15 % (26182)------------------------------
% 6.62/2.16 % (26208)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/90Mi)
% 6.62/2.18 % (26203)Instruction limit reached!
% 6.62/2.18 % (26203)------------------------------
% 6.62/2.18 % (26203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.18 % (26203)Termination reason: Unknown
% 6.62/2.18 % (26203)Termination phase: Saturation
% 6.62/2.18
% 6.62/2.18 % (26203)Memory used [KB]: 7547
% 6.62/2.18 % (26203)Time elapsed: 0.081 s
% 6.62/2.18 % (26203)Instructions burned: 284 (million)
% 6.62/2.18 % (26203)------------------------------
% 6.62/2.18 % (26203)------------------------------
% 6.62/2.19 % (26208)Instruction limit reached!
% 6.62/2.19 % (26208)------------------------------
% 6.62/2.19 % (26208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.19 % (26208)Termination reason: Unknown
% 6.62/2.19 % (26208)Termination phase: Property scanning
% 6.62/2.19
% 6.62/2.19 % (26208)Memory used [KB]: 2174
% 6.62/2.19 % (26208)Time elapsed: 0.026 s
% 6.62/2.19 % (26208)Instructions burned: 90 (million)
% 6.62/2.19 % (26208)------------------------------
% 6.62/2.19 % (26208)------------------------------
% 6.62/2.19 % (26206)Instruction limit reached!
% 6.62/2.19 % (26206)------------------------------
% 6.62/2.19 % (26206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.19 % (26206)Termination reason: Unknown
% 6.62/2.19 % (26202)Instruction limit reached!
% 6.62/2.19 % (26202)------------------------------
% 6.62/2.19 % (26202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.19 % (26202)Termination reason: Unknown
% 6.62/2.19 % (26202)Termination phase: Saturation
% 6.62/2.19
% 6.62/2.19 % (26202)Memory used [KB]: 7803
% 6.62/2.19 % (26202)Time elapsed: 0.097 s
% 6.62/2.19 % (26202)Instructions burned: 340 (million)
% 6.62/2.19 % (26202)------------------------------
% 6.62/2.19 % (26202)------------------------------
% 6.62/2.19 % (26206)Termination phase: Saturation
% 6.62/2.19
% 6.62/2.19 % (26206)Memory used [KB]: 8315
% 6.62/2.19 % (26206)Time elapsed: 0.057 s
% 6.62/2.19 % (26206)Instructions burned: 193 (million)
% 6.62/2.19 % (26206)------------------------------
% 6.62/2.19 % (26206)------------------------------
% 6.62/2.19 % (26205)Instruction limit reached!
% 6.62/2.19 % (26205)------------------------------
% 6.62/2.19 % (26205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.19 % (26205)Termination reason: Unknown
% 6.62/2.19 % (26205)Termination phase: Saturation
% 6.62/2.19
% 6.62/2.19 % (26205)Memory used [KB]: 7931
% 6.62/2.19 % (26205)Time elapsed: 0.081 s
% 6.62/2.19 % (26205)Instructions burned: 299 (million)
% 6.62/2.19 % (26205)------------------------------
% 6.62/2.19 % (26205)------------------------------
% 6.62/2.19 % (26209)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/231Mi)
% 7.21/2.20 % (26210)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/458Mi)
% 7.21/2.20 % (26211)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/31Mi)
% 7.21/2.20 % (26212)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/297Mi)
% 7.21/2.20 % (26213)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/987Mi)
% 7.21/2.21 % (26211)Instruction limit reached!
% 7.21/2.21 % (26211)------------------------------
% 7.21/2.21 % (26211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.21 % (26211)Termination reason: Unknown
% 7.21/2.21 % (26211)Termination phase: Property scanning
% 7.21/2.21
% 7.21/2.21 % (26211)Memory used [KB]: 1791
% 7.21/2.21 % (26211)Time elapsed: 0.011 s
% 7.21/2.21 % (26211)Instructions burned: 34 (million)
% 7.21/2.21 % (26211)------------------------------
% 7.21/2.21 % (26211)------------------------------
% 7.21/2.22 % (26214)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/182Mi)
% 7.21/2.23 % (26207)Instruction limit reached!
% 7.21/2.23 % (26207)------------------------------
% 7.21/2.23 % (26207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.23 % (26207)Termination reason: Unknown
% 7.21/2.23 % (26207)Termination phase: Saturation
% 7.21/2.23
% 7.21/2.23 % (26207)Memory used [KB]: 7419
% 7.21/2.23 % (26207)Time elapsed: 0.077 s
% 7.21/2.23 % (26207)Instructions burned: 261 (million)
% 7.21/2.23 % (26207)------------------------------
% 7.21/2.23 % (26207)------------------------------
% 7.21/2.23 % (26200)Instruction limit reached!
% 7.21/2.23 % (26200)------------------------------
% 7.21/2.23 % (26200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.23 % (26200)Termination reason: Unknown
% 7.21/2.23 % (26200)Termination phase: Saturation
% 7.21/2.23
% 7.21/2.23 % (26200)Memory used [KB]: 8955
% 7.21/2.23 % (26200)Time elapsed: 0.182 s
% 7.21/2.23 % (26200)Instructions burned: 616 (million)
% 7.21/2.23 % (26200)------------------------------
% 7.21/2.23 % (26200)------------------------------
% 7.21/2.24 % (26215)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/182Mi)
% 7.21/2.24 % (26216)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_26036 for (2993ds/154Mi)
% 7.21/2.26 % (26209)Instruction limit reached!
% 7.21/2.26 % (26209)------------------------------
% 7.21/2.26 % (26209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.26 % (26209)Termination reason: Unknown
% 7.21/2.26 % (26209)Termination phase: Saturation
% 7.21/2.26
% 7.21/2.26 % (26209)Memory used [KB]: 7547
% 7.21/2.26 % (26209)Time elapsed: 0.065 s
% 7.21/2.26 % (26209)Instructions burned: 232 (million)
% 7.21/2.26 % (26209)------------------------------
% 7.21/2.26 % (26209)------------------------------
% 7.21/2.27 % (26217)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/79Mi)
% 7.21/2.27 % (26214)Instruction limit reached!
% 7.21/2.27 % (26214)------------------------------
% 7.21/2.27 % (26214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.27 % (26214)Termination reason: Unknown
% 7.21/2.27 % (26214)Termination phase: Saturation
% 7.21/2.27
% 7.21/2.27 % (26214)Memory used [KB]: 7291
% 7.21/2.27 % (26214)Time elapsed: 0.052 s
% 7.21/2.27 % (26214)Instructions burned: 184 (million)
% 7.21/2.27 % (26214)------------------------------
% 7.21/2.27 % (26214)------------------------------
% 7.21/2.28 % (26218)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/216Mi)
% 7.21/2.29 % (26216)Instruction limit reached!
% 7.21/2.29 % (26216)------------------------------
% 7.21/2.29 % (26216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.29 % (26216)Termination reason: Unknown
% 7.21/2.29 % (26216)Termination phase: Saturation
% 7.21/2.29
% 7.21/2.29 % (26216)Memory used [KB]: 2814
% 7.21/2.29 % (26216)Time elapsed: 0.042 s
% 7.21/2.29 % (26216)Instructions burned: 156 (million)
% 7.21/2.29 % (26216)------------------------------
% 7.21/2.29 % (26216)------------------------------
% 7.21/2.29 % (26217)Instruction limit reached!
% 7.21/2.29 % (26217)------------------------------
% 7.21/2.29 % (26217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.29 % (26215)Instruction limit reached!
% 7.21/2.29 % (26215)------------------------------
% 7.21/2.29 % (26215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.29 % (26215)Termination reason: Unknown
% 7.21/2.29 % (26215)Termination phase: Saturation
% 7.21/2.29
% 7.21/2.29 % (26215)Memory used [KB]: 7419
% 7.21/2.29 % (26215)Time elapsed: 0.055 s
% 7.21/2.29 % (26215)Instructions burned: 182 (million)
% 7.21/2.29 % (26215)------------------------------
% 7.21/2.29 % (26215)------------------------------
% 7.21/2.29 % (26217)Termination reason: Unknown
% 7.21/2.29 % (26217)Termination phase: Property scanning
% 7.21/2.29
% 7.21/2.29 % (26217)Memory used [KB]: 2174
% 7.21/2.29 % (26217)Time elapsed: 0.024 s
% 7.21/2.29 % (26217)Instructions burned: 82 (million)
% 7.21/2.29 % (26217)------------------------------
% 7.21/2.29 % (26217)------------------------------
% 7.21/2.30 % (26219)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/114Mi)
% 7.79/2.30 % (26212)Instruction limit reached!
% 7.79/2.30 % (26212)------------------------------
% 7.79/2.30 % (26212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.30 % (26212)Termination reason: Unknown
% 7.79/2.30 % (26212)Termination phase: Saturation
% 7.79/2.30
% 7.79/2.30 % (26212)Memory used [KB]: 7675
% 7.79/2.30 % (26212)Time elapsed: 0.100 s
% 7.79/2.30 % (26212)Instructions burned: 300 (million)
% 7.79/2.30 % (26212)------------------------------
% 7.79/2.30 % (26212)------------------------------
% 7.79/2.30 % (26220)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/922Mi)
% 7.79/2.30 % (26221)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/182Mi)
% 7.79/2.31 % (26222)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_26036 for (2992ds/164Mi)
% 7.79/2.33 % (26219)Instruction limit reached!
% 7.79/2.33 % (26219)------------------------------
% 7.79/2.33 % (26219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.33 % (26219)Termination reason: Unknown
% 7.79/2.33 % (26219)Termination phase: Saturation
% 7.79/2.33
% 7.79/2.33 % (26219)Memory used [KB]: 6908
% 7.79/2.33 % (26219)Time elapsed: 0.033 s
% 7.79/2.33 % (26219)Instructions burned: 116 (million)
% 7.79/2.33 % (26219)------------------------------
% 7.79/2.33 % (26219)------------------------------
% 7.79/2.33 % (26210)Instruction limit reached!
% 7.79/2.33 % (26210)------------------------------
% 7.79/2.33 % (26210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.33 % (26210)Termination reason: Unknown
% 7.79/2.33 % (26210)Termination phase: Saturation
% 7.79/2.33
% 7.79/2.33 % (26210)Memory used [KB]: 8315
% 7.79/2.33 % (26210)Time elapsed: 0.137 s
% 7.79/2.33 % (26210)Instructions burned: 460 (million)
% 7.79/2.33 % (26210)------------------------------
% 7.79/2.33 % (26210)------------------------------
% 7.79/2.34 % (26223)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/50Mi)
% 7.79/2.34 % (26218)Instruction limit reached!
% 7.79/2.34 % (26218)------------------------------
% 7.79/2.34 % (26218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.34 % (26218)Termination reason: Unknown
% 7.79/2.34 % (26218)Termination phase: Saturation
% 7.79/2.34
% 7.79/2.34 % (26218)Memory used [KB]: 7419
% 7.79/2.34 % (26218)Time elapsed: 0.058 s
% 7.79/2.34 % (26218)Instructions burned: 216 (million)
% 7.79/2.34 % (26218)------------------------------
% 7.79/2.34 % (26218)------------------------------
% 7.79/2.34 % (26224)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/368Mi)
% 7.79/2.35 % (26221)Instruction limit reached!
% 7.79/2.35 % (26221)------------------------------
% 7.79/2.35 % (26221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.35 % (26221)Termination reason: Unknown
% 7.79/2.35 % (26225)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/1021Mi)
% 7.79/2.35 % (26221)Termination phase: Saturation
% 7.79/2.35
% 7.79/2.35 % (26221)Memory used [KB]: 7291
% 7.79/2.35 % (26221)Time elapsed: 0.048 s
% 7.79/2.35 % (26221)Instructions burned: 183 (million)
% 7.79/2.35 % (26221)------------------------------
% 7.79/2.35 % (26221)------------------------------
% 7.79/2.35 % (26223)Instruction limit reached!
% 7.79/2.35 % (26223)------------------------------
% 7.79/2.35 % (26223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.35 % (26223)Termination reason: Unknown
% 7.79/2.35 % (26223)Termination phase: Property scanning
% 7.79/2.35
% 7.79/2.35 % (26223)Memory used [KB]: 2430
% 7.79/2.35 % (26223)Time elapsed: 0.015 s
% 7.79/2.35 % (26223)Instructions burned: 51 (million)
% 7.79/2.35 % (26223)------------------------------
% 7.79/2.35 % (26223)------------------------------
% 7.79/2.35 % (26222)Instruction limit reached!
% 7.79/2.35 % (26222)------------------------------
% 7.79/2.35 % (26222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.35 % (26222)Termination reason: Unknown
% 7.79/2.35 % (26222)Termination phase: Saturation
% 7.79/2.35
% 7.79/2.35 % (26222)Memory used [KB]: 2814
% 7.79/2.35 % (26222)Time elapsed: 0.045 s
% 7.79/2.35 % (26222)Instructions burned: 164 (million)
% 7.79/2.35 % (26222)------------------------------
% 7.79/2.35 % (26222)------------------------------
% 7.79/2.36 % (26226)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/267Mi)
% 7.79/2.36 % (26227)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/204Mi)
% 7.79/2.36 % (26228)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/26Mi)
% 7.79/2.37 % (26228)Instruction limit reached!
% 7.79/2.37 % (26228)------------------------------
% 7.79/2.37 % (26228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.37 % (26228)Termination reason: Unknown
% 7.79/2.37 % (26228)Termination phase: shuffling
% 7.79/2.37
% 7.79/2.37 % (26228)Memory used [KB]: 2046
% 7.79/2.37 % (26228)Time elapsed: 0.009 s
% 7.79/2.37 % (26228)Instructions burned: 29 (million)
% 7.79/2.37 % (26228)------------------------------
% 7.79/2.37 % (26228)------------------------------
% 7.79/2.38 % (26229)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/53Mi)
% 7.79/2.40 % (26229)Instruction limit reached!
% 7.79/2.40 % (26229)------------------------------
% 7.79/2.40 % (26229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.79/2.40 % (26229)Termination reason: Unknown
% 7.79/2.40 % (26229)Termination phase: Property scanning
% 7.79/2.40
% 7.79/2.40 % (26229)Memory used [KB]: 2302
% 7.79/2.40 % (26229)Time elapsed: 0.016 s
% 7.79/2.40 % (26229)Instructions burned: 55 (million)
% 7.79/2.40 % (26229)------------------------------
% 7.79/2.40 % (26229)------------------------------
% 8.30/2.41 % (26230)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/4436Mi)
% 8.30/2.42 % (26227)Instruction limit reached!
% 8.30/2.42 % (26227)------------------------------
% 8.30/2.42 % (26227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.42 % (26227)Termination reason: Unknown
% 8.30/2.42 % (26227)Termination phase: Saturation
% 8.30/2.42
% 8.30/2.42 % (26227)Memory used [KB]: 7419
% 8.30/2.42 % (26227)Time elapsed: 0.059 s
% 8.30/2.42 % (26227)Instructions burned: 206 (million)
% 8.30/2.42 % (26227)------------------------------
% 8.30/2.42 % (26227)------------------------------
% 8.30/2.43 % (26231)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_26036 for (2991ds/1539Mi)
% 8.30/2.43 % (26226)Instruction limit reached!
% 8.30/2.43 % (26226)------------------------------
% 8.30/2.43 % (26226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.43 % (26226)Termination reason: Unknown
% 8.30/2.43 % (26226)Termination phase: Saturation
% 8.30/2.43
% 8.30/2.43 % (26226)Memory used [KB]: 7547
% 8.30/2.43 % (26226)Time elapsed: 0.076 s
% 8.30/2.43 % (26226)Instructions burned: 269 (million)
% 8.30/2.43 % (26226)------------------------------
% 8.30/2.43 % (26226)------------------------------
% 8.30/2.44 % (26232)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_26036 for (2990ds/408Mi)
% 8.30/2.45 % (26224)Instruction limit reached!
% 8.30/2.45 % (26224)------------------------------
% 8.30/2.45 % (26224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.45 % (26224)Termination reason: Unknown
% 8.30/2.45 % (26224)Termination phase: Saturation
% 8.30/2.45
% 8.30/2.45 % (26224)Memory used [KB]: 7931
% 8.30/2.45 % (26224)Time elapsed: 0.110 s
% 8.30/2.45 % (26224)Instructions burned: 369 (million)
% 8.30/2.45 % (26224)------------------------------
% 8.30/2.45 % (26224)------------------------------
% 8.30/2.46 % (26233)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_26036 for (2990ds/5205Mi)
% 8.30/2.49 % (26213)Instruction limit reached!
% 8.30/2.49 % (26213)------------------------------
% 8.30/2.49 % (26213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.49 % (26213)Termination reason: Unknown
% 8.30/2.49 % (26213)Termination phase: Saturation
% 8.30/2.49
% 8.30/2.49 % (26213)Memory used [KB]: 8827
% 8.30/2.49 % (26213)Time elapsed: 0.290 s
% 8.30/2.49 % (26213)Instructions burned: 987 (million)
% 8.30/2.49 % (26213)------------------------------
% 8.30/2.49 % (26213)------------------------------
% 8.89/2.50 % (26234)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_26036 for (2990ds/1913Mi)
% 8.89/2.56 % (26232)Instruction limit reached!
% 8.89/2.56 % (26232)------------------------------
% 8.89/2.56 % (26232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.56 % (26232)Termination reason: Unknown
% 8.89/2.56 % (26232)Termination phase: Saturation
% 8.89/2.56
% 8.89/2.56 % (26232)Memory used [KB]: 8059
% 8.89/2.56 % (26232)Time elapsed: 0.123 s
% 8.89/2.56 % (26232)Instructions burned: 410 (million)
% 8.89/2.56 % (26232)------------------------------
% 8.89/2.56 % (26232)------------------------------
% 8.89/2.57 % (26235)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_26036 for (2989ds/4350Mi)
% 8.89/2.58 % (26220)Instruction limit reached!
% 8.89/2.58 % (26220)------------------------------
% 8.89/2.58 % (26220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.58 % (26220)Termination reason: Unknown
% 8.89/2.58 % (26220)Termination phase: Saturation
% 8.89/2.58
% 8.89/2.58 % (26220)Memory used [KB]: 8059
% 8.89/2.58 % (26220)Time elapsed: 0.308 s
% 8.89/2.58 % (26220)Instructions burned: 924 (million)
% 8.89/2.58 % (26220)------------------------------
% 8.89/2.58 % (26220)------------------------------
% 8.89/2.59 % (26236)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_26036 for (2989ds/68Mi)
% 9.31/2.61 % (26236)Instruction limit reached!
% 9.31/2.61 % (26236)------------------------------
% 9.31/2.61 % (26236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.61 % (26236)Termination reason: Unknown
% 9.31/2.61 % (26236)Termination phase: Property scanning
% 9.31/2.61
% 9.31/2.61 % (26236)Memory used [KB]: 2046
% 9.31/2.61 % (26236)Time elapsed: 0.021 s
% 9.31/2.61 % (26236)Instructions burned: 69 (million)
% 9.31/2.61 % (26236)------------------------------
% 9.31/2.61 % (26236)------------------------------
% 9.31/2.62 % (26237)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_26036 for (2989ds/358Mi)
% 9.31/2.65 % (26225)Instruction limit reached!
% 9.31/2.65 % (26225)------------------------------
% 9.31/2.65 % (26225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.65 % (26225)Termination reason: Unknown
% 9.31/2.65 % (26225)Termination phase: Saturation
% 9.31/2.65
% 9.31/2.65 % (26225)Memory used [KB]: 8571
% 9.31/2.65 % (26225)Time elapsed: 0.308 s
% 9.31/2.65 % (26225)Instructions burned: 1021 (million)
% 9.31/2.65 % (26225)------------------------------
% 9.31/2.65 % (26225)------------------------------
% 9.31/2.66 % (26238)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_26036 for (2988ds/31Mi)
% 9.31/2.67 % (26231)First to succeed.
% 9.31/2.67 % (26238)Instruction limit reached!
% 9.31/2.67 % (26238)------------------------------
% 9.31/2.67 % (26238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.67 % (26238)Termination reason: Unknown
% 9.31/2.67 % (26238)Termination phase: Property scanning
% 9.31/2.67
% 9.31/2.67 % (26238)Memory used [KB]: 1791
% 9.31/2.67 % (26238)Time elapsed: 0.011 s
% 9.31/2.67 % (26231)Refutation found. Thanks to Tanya!
% 9.31/2.67 % SZS status Theorem for DTF2THF_26036
% 9.31/2.67 % SZS output start Proof for DTF2THF_26036
% 9.31/2.67 thf(type_def_5, type, variable: $tType).
% 9.31/2.67 thf(type_def_6, type, real: $tType).
% 9.31/2.67 thf(type_def_8, type, set_variable: $tType).
% 9.31/2.67 thf(type_def_9, type, denotational_interp: $tType).
% 9.31/2.67 thf(type_def_10, type, char: $tType).
% 9.31/2.67 thf(type_def_11, type, trm: $tType).
% 9.31/2.67 thf(type_def_12, type, set_variable_real: $tType).
% 9.31/2.67 thf(type_def_13, type, nat: $tType).
% 9.31/2.67 thf(type_def_14, type, set_nat: $tType).
% 9.31/2.67 thf(type_def_15, type, set_real: $tType).
% 9.31/2.67 thf(type_def_16, type, option_variable_real: $tType).
% 9.31/2.67 thf(type_def_17, type, option_trm: $tType).
% 9.31/2.67 thf(type_def_18, type, option_variable: $tType).
% 9.31/2.67 thf(type_def_19, type, set_trm: $tType).
% 9.31/2.67 thf(type_def_20, type, set_op12188086e_real: $tType).
% 9.31/2.67 thf(type_def_21, type, set_option_trm: $tType).
% 9.31/2.67 thf(type_def_22, type, set_option_variable: $tType).
% 9.31/2.67 thf(type_def_23, type, produc1418842292n_game: $tType).
% 9.31/2.67 thf(func_def_0, type, produc1418842292n_game: $tType).
% 9.31/2.67 thf(func_def_1, type, set_op12188086e_real: $tType).
% 9.31/2.68 thf(func_def_2, type, option_variable_real: $tType).
% 9.31/2.68 thf(func_def_3, type, set_variable_real: $tType).
% 9.31/2.68 thf(func_def_4, type, set_option_variable: $tType).
% 9.31/2.68 thf(func_def_5, type, set_option_trm: $tType).
% 9.31/2.68 thf(func_def_6, type, option_variable: $tType).
% 9.31/2.68 thf(func_def_7, type, option_trm: $tType).
% 9.31/2.68 thf(func_def_8, type, denotational_interp: $tType).
% 9.31/2.68 thf(func_def_9, type, set_variable: $tType).
% 9.31/2.68 thf(func_def_10, type, set_trm: $tType).
% 9.31/2.68 thf(func_def_11, type, set_real: $tType).
% 9.31/2.68 thf(func_def_12, type, set_nat: $tType).
% 9.31/2.68 thf(func_def_13, type, variable: $tType).
% 9.31/2.68 thf(func_def_14, type, char: $tType).
% 9.31/2.68 thf(func_def_15, type, trm: $tType).
% 9.31/2.68 thf(func_def_16, type, real: $tType).
% 9.31/2.68 thf(func_def_17, type, nat: $tType).
% 9.31/2.68 thf(func_def_18, type, statediff: (variable > real) > (variable > real) > set_variable).
% 9.31/2.68 thf(func_def_19, type, stateinterpol: (variable > real) > (variable > real) > set_variable > variable > real).
% 9.31/2.68 thf(func_def_20, type, denota1419872369iation: (variable > real) > (variable > real) > set_variable > $o).
% 9.31/2.68 thf(func_def_21, type, denotational_Vagree: (variable > real) > (variable > real) > set_variable > $o).
% 9.31/2.68 thf(func_def_22, type, denotational_repv: (variable > real) > variable > real > variable > real).
% 9.31/2.68 thf(func_def_23, type, denota1778088425es_ODE: denotational_interp > (real > variable > real) > char > trm > $o).
% 9.31/2.68 thf(func_def_24, type, denota1863255036rm_sem: denotational_interp > trm > (variable > real) > real).
% 9.31/2.68 thf(func_def_25, type, uminus_uminus_real: real > real).
% 9.31/2.68 thf(func_def_26, type, uminus430703407e_real: set_variable_real > set_variable_real).
% 9.31/2.68 thf(func_def_27, type, uminus1851247844riable: set_variable > set_variable).
% 9.31/2.68 thf(func_def_28, type, zero_zero_nat: nat).
% 9.31/2.68 thf(func_def_29, type, zero_zero_real: real).
% 9.31/2.68 thf(func_def_30, type, zero_zero_set_nat: set_nat).
% 9.31/2.68 thf(func_def_31, type, zero_zero_set_real: set_real).
% 9.31/2.68 thf(func_def_32, type, if_real: $o > real > real > real).
% 9.31/2.68 thf(func_def_33, type, inf_in1556002680e_real: set_variable_real > set_variable_real > set_variable_real).
% 9.31/2.68 thf(func_def_34, type, inf_inf_set_variable: set_variable > set_variable > set_variable).
% 9.31/2.68 thf(func_def_35, type, sup_su1685293586e_real: set_variable_real > set_variable_real > set_variable_real).
% 9.31/2.68 thf(func_def_36, type, sup_sup_set_variable: set_variable > set_variable > set_variable).
% 9.31/2.68 thf(func_def_37, type, size_size_variable: variable > nat).
% 9.31/2.68 thf(func_def_38, type, none_variable_real: option_variable_real).
% 9.31/2.68 thf(func_def_39, type, none_trm: option_trm).
% 9.31/2.68 thf(func_def_40, type, none_variable: option_variable).
% 9.31/2.68 thf(func_def_41, type, some_variable_real: (variable > real) > option_variable_real).
% 9.31/2.68 thf(func_def_42, type, some_trm: trm > option_trm).
% 9.31/2.68 thf(func_def_43, type, some_variable: variable > option_variable).
% 9.31/2.68 thf(func_def_44, type, set_op697949218e_real: option_variable_real > set_variable_real).
% 9.31/2.68 thf(func_def_45, type, set_option_trm2: option_trm > set_trm).
% 9.31/2.68 thf(func_def_46, type, set_option_variable2: option_variable > set_variable).
% 9.31/2.68 thf(func_def_47, type, the_variable_real: option_variable_real > variable > real).
% 9.31/2.68 thf(func_def_48, type, the_trm: option_trm > trm).
% 9.31/2.68 thf(func_def_49, type, the_variable: option_variable > variable).
% 9.31/2.68 thf(func_def_50, type, these_variable_real: set_op12188086e_real > set_variable_real).
% 9.31/2.68 thf(func_def_51, type, these_trm: set_option_trm > set_trm).
% 9.31/2.68 thf(func_def_52, type, these_variable: set_option_variable > set_variable).
% 9.31/2.68 thf(func_def_53, type, bot_bo1661475211real_o: (variable > real) > $o).
% 9.31/2.68 thf(func_def_54, type, bot_bot_variable_o: variable > $o).
% 9.31/2.68 thf(func_def_55, type, bot_bo721182586e_real: set_variable_real).
% 9.31/2.68 thf(func_def_56, type, bot_bot_set_nat: set_nat).
% 9.31/2.68 thf(func_def_57, type, bot_bo1411475018e_real: set_op12188086e_real).
% 9.31/2.68 thf(func_def_58, type, bot_bo946428664on_trm: set_option_trm).
% 9.31/2.68 thf(func_def_59, type, bot_bo266290559riable: set_option_variable).
% 9.31/2.68 thf(func_def_60, type, bot_bot_set_real: set_real).
% 9.31/2.68 thf(func_def_61, type, bot_bot_set_trm: set_trm).
% 9.31/2.68 thf(func_def_62, type, bot_bot_set_variable: set_variable).
% 9.31/2.68 thf(func_def_63, type, ord_less_eq_nat: nat > nat > $o).
% 9.31/2.68 thf(func_def_64, type, ord_le1113654598e_real: set_variable_real > set_variable_real > $o).
% 9.31/2.68 thf(func_def_65, type, ord_le282106107riable: set_variable > set_variable > $o).
% 9.31/2.68 thf(func_def_66, type, collec633296133e_real: ((variable > real) > $o) > set_variable_real).
% 9.31/2.68 thf(func_def_67, type, collect_variable: (variable > $o) > set_variable).
% 9.31/2.68 thf(func_def_68, type, insert_variable_real: (variable > real) > set_variable_real > set_variable_real).
% 9.31/2.68 thf(func_def_69, type, insert_nat: nat > set_nat > set_nat).
% 9.31/2.68 thf(func_def_70, type, insert526581936e_real: option_variable_real > set_op12188086e_real > set_op12188086e_real).
% 9.31/2.68 thf(func_def_71, type, insert_option_trm: option_trm > set_option_trm > set_option_trm).
% 9.31/2.68 thf(func_def_72, type, insert1340772453riable: option_variable > set_option_variable > set_option_variable).
% 9.31/2.68 thf(func_def_73, type, insert_real: real > set_real > set_real).
% 9.31/2.68 thf(func_def_74, type, insert_trm: trm > set_trm > set_trm).
% 9.31/2.68 thf(func_def_75, type, insert_variable: variable > set_variable > set_variable).
% 9.31/2.68 thf(func_def_76, type, is_emp227886046e_real: set_variable_real > $o).
% 9.31/2.68 thf(func_def_77, type, is_empty_variable: set_variable > $o).
% 9.31/2.68 thf(func_def_78, type, is_sin524757308e_real: set_variable_real > $o).
% 9.31/2.68 thf(func_def_79, type, is_sin155454833riable: set_variable > $o).
% 9.31/2.68 thf(func_def_80, type, the_el1059226619e_real: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_81, type, the_elem_variable: set_variable > variable).
% 9.31/2.68 thf(func_def_82, type, static_FVT: trm > set_variable).
% 9.31/2.68 thf(func_def_83, type, static_selectlike: set_variable_real > (variable > real) > set_variable > set_variable_real).
% 9.31/2.68 thf(func_def_84, type, times: trm > trm > trm).
% 9.31/2.68 thf(func_def_85, type, dVar: char > variable).
% 9.31/2.68 thf(func_def_86, type, rVar: char > variable).
% 9.31/2.68 thf(func_def_87, type, size_variable: variable > nat).
% 9.31/2.68 thf(func_def_88, type, uSubst918876924Timeso: option_trm > option_trm > option_trm).
% 9.31/2.68 thf(func_def_89, type, uSubst1599435252djoint: produc1418842292n_game > denotational_interp > (variable > real) > denotational_interp).
% 9.31/2.68 thf(func_def_90, type, uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm).
% 9.31/2.68 thf(func_def_91, type, member_variable_real: (variable > real) > set_variable_real > $o).
% 9.31/2.68 thf(func_def_92, type, member523846807e_real: option_variable_real > set_op12188086e_real > $o).
% 9.31/2.68 thf(func_def_93, type, member_option_trm: option_trm > set_option_trm > $o).
% 9.31/2.68 thf(func_def_94, type, member814448204riable: option_variable > set_option_variable > $o).
% 9.31/2.68 thf(func_def_95, type, member_trm: trm > set_trm > $o).
% 9.31/2.68 thf(func_def_96, type, member_variable: variable > set_variable > $o).
% 9.31/2.68 thf(func_def_97, type, f: real > variable > real).
% 9.31/2.68 thf(func_def_98, type, i: denotational_interp).
% 9.31/2.68 thf(func_def_99, type, u: set_variable).
% 9.31/2.68 thf(func_def_100, type, omega: variable > real).
% 9.31/2.68 thf(func_def_101, type, sigma: produc1418842292n_game).
% 9.31/2.68 thf(func_def_102, type, theta: trm).
% 9.31/2.68 thf(func_def_103, type, rr: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 9.31/2.68 thf(func_def_104, type, x: char).
% 9.31/2.68 thf(func_def_120, type, sP0: (option_trm > option_trm > $o) > option_trm > option_trm > $o).
% 9.31/2.68 thf(func_def_121, type, sP1: option_trm > option_trm > option_trm > $o).
% 9.31/2.68 thf(func_def_122, type, sK2: char > (real > variable > real) > trm > trm > denotational_interp > denotational_interp > variable > real).
% 9.31/2.68 thf(func_def_123, type, sK3: set_variable > variable).
% 9.31/2.68 thf(func_def_124, type, sK4: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_125, type, sK5: set_variable > variable > set_variable).
% 9.31/2.68 thf(func_def_126, type, sK6: set_variable_real > set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_127, type, sK7: (option_trm > option_trm > $o) > option_trm > option_trm > trm).
% 9.31/2.68 thf(func_def_128, type, sK8: (option_trm > option_trm > $o) > option_trm > option_trm > trm).
% 9.31/2.68 thf(func_def_129, type, sK9: set_variable_real > (variable > real) > set_variable_real).
% 9.31/2.68 thf(func_def_130, type, sK10: set_variable > variable).
% 9.31/2.68 thf(func_def_131, type, sK11: set_variable > variable).
% 9.31/2.68 thf(func_def_132, type, sK12: option_trm > trm).
% 9.31/2.68 thf(func_def_133, type, sK13: set_variable > variable > set_variable).
% 9.31/2.68 thf(func_def_134, type, sK14: set_variable_real > (variable > real) > set_variable_real > set_variable > variable > real).
% 9.31/2.68 thf(func_def_135, type, sK15: trm > denotational_interp > trm > denotational_interp > char > (real > variable > real) > variable > real).
% 9.31/2.68 thf(func_def_136, type, sK16: (variable > $o) > char).
% 9.31/2.68 thf(func_def_137, type, sK17: (variable > $o) > char).
% 9.31/2.68 thf(func_def_138, type, sK18: (trm > $o) > option_trm > trm).
% 9.31/2.68 thf(func_def_139, type, sK19: (option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_140, type, sK20: set_variable_real > (variable > real) > set_variable > set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_141, type, sK21: option_trm > option_trm > option_trm > trm).
% 9.31/2.68 thf(func_def_142, type, sK22: option_trm > option_trm > option_trm > trm).
% 9.31/2.68 thf(func_def_143, type, sK23: option_trm > trm).
% 9.31/2.68 thf(func_def_144, type, sK24: (variable > option_trm > $o) > variable).
% 9.31/2.68 thf(func_def_145, type, sK25: (variable > option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_146, type, sK26: (variable > option_trm > $o) > variable).
% 9.31/2.68 thf(func_def_147, type, sK27: variable > char).
% 9.31/2.68 thf(func_def_148, type, sK28: variable > char).
% 9.31/2.68 thf(func_def_149, type, sK29: option_trm > trm).
% 9.31/2.68 thf(func_def_150, type, sK30: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_151, type, sK31: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_152, type, sK32: set_variable > variable).
% 9.31/2.68 thf(func_def_153, type, sK33: (option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_154, type, sK34: set_variable_real > (variable > real) > set_variable_real).
% 9.31/2.68 thf(func_def_155, type, sK35: set_variable > set_variable > variable).
% 9.31/2.68 thf(func_def_156, type, sK36: (option_trm > option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_157, type, sK37: (option_trm > option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_158, type, sK38: (option_trm > option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_159, type, sK39: (option_trm > option_trm > $o) > option_trm).
% 9.31/2.68 thf(func_def_160, type, sK40: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_161, type, sK41: (char > option_trm > $o) > char).
% 9.31/2.68 thf(func_def_162, type, sK42: (char > option_trm > $o) > trm).
% 9.31/2.68 thf(func_def_163, type, sK43: (char > option_trm > $o) > char).
% 9.31/2.68 thf(func_def_165, type, sK45: set_variable > variable).
% 9.31/2.68 thf(func_def_166, type, sK46: (variable > real) > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_167, type, sK47: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_168, type, sK48: set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_169, type, sK49: set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_170, type, sK50: set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_171, type, sK51: set_variable_real > set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_172, type, sK52: set_variable_real > set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_173, type, sK53: set_variable > set_variable_real > set_variable_real > (variable > real) > variable > real).
% 9.31/2.68 thf(func_def_174, type, sK54: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_175, type, sK55: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_176, type, sK56: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_177, type, sK57: (variable > real) > set_variable > (variable > real) > variable).
% 9.31/2.68 thf(func_def_178, type, sK58: (variable > real) > real > variable > variable).
% 9.31/2.68 thf(func_def_179, type, sK59: variable > variable).
% 9.31/2.68 thf(func_def_180, type, sK60: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_181, type, sK61: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_182, type, sK62: (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_183, type, sK63: option_trm > trm).
% 9.31/2.68 thf(func_def_184, type, sK64: ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_185, type, sK65: set_variable > variable).
% 9.31/2.68 thf(func_def_186, type, sK66: ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_187, type, sK67: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_188, type, sK68: (variable > real) > set_variable > (variable > real) > variable).
% 9.31/2.68 thf(func_def_189, type, sK69: (variable > real) > set_variable > (variable > real) > variable).
% 9.31/2.68 thf(func_def_190, type, sK70: (variable > $o) > variable).
% 9.31/2.68 thf(func_def_191, type, sK71: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_192, type, sK72: (variable > real) > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_193, type, sK73: (variable > real) > trm > (variable > real) > variable).
% 9.31/2.68 thf(func_def_194, type, sK74: (variable > real) > variable > real).
% 9.31/2.68 thf(func_def_195, type, sK75: (variable > real) > variable).
% 9.31/2.68 thf(func_def_196, type, sK76: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_197, type, sK77: option_trm > trm).
% 9.31/2.68 thf(func_def_198, type, sK78: trm > char > denotational_interp > trm > denotational_interp > (real > variable > real) > variable).
% 9.31/2.68 thf(func_def_199, type, sK79: trm > denotational_interp > denotational_interp > (real > variable > real) > trm > char > variable > real).
% 9.31/2.68 thf(func_def_200, type, sK80: char > (real > variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_201, type, sK81: char > (real > variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_202, type, sK82: (variable > $o) > variable).
% 9.31/2.68 thf(func_def_203, type, sK83: set_variable > (variable > real) > (real > variable > real) > variable).
% 9.31/2.68 thf(func_def_204, type, sK84: set_variable_real > set_variable_real > (variable > real) > (variable > real) > set_variable_real).
% 9.31/2.68 thf(func_def_205, type, sK85: option_trm > trm).
% 9.31/2.68 thf(func_def_206, type, sK86: (variable > real) > set_variable > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_207, type, sK87: (variable > real) > set_variable > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_208, type, sK88: (variable > real) > set_variable > (variable > real) > variable).
% 9.31/2.68 thf(func_def_209, type, sK89: (variable > real) > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_210, type, sK90: (variable > real) > (variable > real) > set_variable > variable).
% 9.31/2.68 thf(func_def_211, type, sK91: variable).
% 9.31/2.68 thf(func_def_212, type, sK92: set_variable > variable).
% 9.31/2.68 thf(func_def_213, type, sK93: set_variable_real > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_214, type, sK94: set_variable_real > (variable > real) > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_215, type, sK95: set_variable_real > (variable > real) > ((variable > real) > $o) > variable > real).
% 9.31/2.68 thf(func_def_216, type, sK96: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_217, type, sK97: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_218, type, sK98: char > (variable > real) > (real > variable > real) > variable).
% 9.31/2.68 thf(func_def_219, type, sK99: char > (variable > real) > (real > variable > real) > variable).
% 9.31/2.68 thf(func_def_220, type, sK100: char > trm > denotational_interp > (real > variable > real) > denotational_interp > trm > variable > real).
% 9.31/2.68 thf(func_def_221, type, sK101: char > trm > (real > variable > real) > denotational_interp > denotational_interp > trm > variable).
% 9.31/2.68 thf(func_def_222, type, sK102: char > trm > (real > variable > real) > denotational_interp > denotational_interp > trm > variable).
% 9.31/2.68 thf(func_def_223, type, sK103: set_variable > (variable > $o) > set_variable > variable).
% 9.31/2.68 thf(func_def_224, type, sK104: set_variable > (variable > $o) > variable).
% 9.31/2.68 thf(func_def_225, type, sK105: set_variable > (variable > $o) > variable).
% 9.31/2.68 thf(func_def_226, type, sK106: set_variable > (variable > $o) > variable).
% 9.31/2.68 thf(func_def_227, type, sK107: ((variable > real) > $o) > set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_228, type, sK108: ((variable > real) > $o) > set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_229, type, sK109: ((variable > real) > $o) > set_variable_real > set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_230, type, sK110: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_231, type, sK111: (variable > real) > set_variable > (variable > real) > variable).
% 9.31/2.68 thf(func_def_232, type, sK112: set_variable_real > variable > real).
% 9.31/2.68 thf(func_def_233, type, sK113: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_234, type, sK114: variable > variable > set_variable > set_variable > set_variable).
% 9.31/2.68 thf(func_def_235, type, sK115: set_variable > (variable > real) > (variable > real) > variable).
% 9.31/2.68 thf(func_def_236, type, sK116: set_variable_real > set_variable > set_variable_real > (variable > real) > variable > real).
% 9.31/2.68 thf(func_def_237, type, sK117: set_variable > variable).
% 9.31/2.68 thf(func_def_238, type, sK118: variable > set_variable > (variable > $o) > variable).
% 9.31/2.68 thf(func_def_239, type, sK119: variable > set_variable > (variable > $o) > variable).
% 9.31/2.68 thf(func_def_240, type, sK120: (variable > $o) > set_variable > variable).
% 9.31/2.68 thf(func_def_241, type, sK121: (variable > $o) > set_variable > set_variable > variable).
% 9.31/2.68 thf(func_def_242, type, sK122: (variable > $o) > set_variable > variable).
% 9.31/2.68 thf(func_def_243, type, sK123: (variable > $o) > set_variable > variable).
% 9.31/2.68 thf(func_def_244, type, sK124: set_variable > variable).
% 9.31/2.68 thf(func_def_245, type, ph125: !>[X0: $tType]:(X0)).
% 9.31/2.68 thf(f5025,plain,(
% 9.31/2.68 $false),
% 9.31/2.68 inference(avatar_sat_refutation,[status(thm)],[f3552,f3706,f3821,f5024])).
% 9.31/2.68 thf(f5024,plain,(
% 9.31/2.68 spl44_3 | ~spl44_4 | ~spl44_6),
% 9.31/2.68 inference(avatar_contradiction_clause,[status(thm)],[f5023])).
% 9.31/2.68 thf(f5023,plain,(
% 9.31/2.68 $false | (spl44_3 | ~spl44_4 | ~spl44_6)),
% 9.31/2.68 inference(subsumption_resolution,[status(thm)],[f5019,f3551])).
% 9.31/2.68 thf(f3551,plain,(
% 9.31/2.68 ((omega @ sK91) != (f @ zero_zero_real @ sK91)) | spl44_3),
% 9.31/2.68 inference(avatar_component_clause,[status(thm)],[f3549])).
% 9.31/2.68 thf(f3549,definition,(
% 9.31/2.68 spl44_3 <=> ((omega @ sK91) = (f @ zero_zero_real @ sK91))),
% 9.31/2.68 introduced(definition,[new_symbols(naming,[spl44_3])],[avatar_definition])).
% 9.31/2.68 thf(f5019,plain,(
% 9.31/2.68 ((omega @ sK91) = (f @ zero_zero_real @ sK91)) | (~spl44_4 | ~spl44_6)),
% 9.31/2.68 inference(trivial_inequality_removal,[status(thm)],[f5018])).
% 9.31/2.68 thf(f5018,plain,(
% 9.31/2.68 ($true = $false) | ((omega @ sK91) = (f @ zero_zero_real @ sK91)) | (~spl44_4 | ~spl44_6)),
% 9.31/2.68 inference(superposition,[status(thm)],[f3820,f4916])).
% 9.31/2.68 thf(f4916,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (((member_variable @ X1 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ u))) = $true) | ((f @ zero_zero_real @ X1) = (omega @ X1))) ) | ~spl44_4),
% 9.31/2.68 inference(backward_demodulation,[status(thm)],[f3876,f4365])).
% 9.31/2.68 thf(f4365,plain,(
% 9.31/2.68 ( ! [X2 : variable,X0 : set_variable,X1 : variable] : (((sup_sup_set_variable @ X0 @ (insert_variable @ X2 @ (insert_variable @ X1 @ (set_option_variable2 @ none_variable)))) = (insert_variable @ X2 @ (insert_variable @ X1 @ X0)))) ) | ~spl44_4),
% 9.31/2.68 inference(superposition,[status(thm)],[f1205,f4347])).
% 9.31/2.68 thf(f4347,plain,(
% 9.31/2.68 ( ! [X0 : set_variable,X1 : variable] : (((insert_variable @ X1 @ X0) = (sup_sup_set_variable @ X0 @ (insert_variable @ X1 @ (set_option_variable2 @ none_variable))))) ) | ~spl44_4),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3638,f3705])).
% 9.31/2.68 thf(f3705,plain,(
% 9.31/2.68 ((these_variable @ bot_bo266290559riable) = (set_option_variable2 @ none_variable)) | ~spl44_4),
% 9.31/2.68 inference(avatar_component_clause,[status(thm)],[f3703])).
% 9.31/2.68 thf(f3703,definition,(
% 9.31/2.68 spl44_4 <=> ((these_variable @ bot_bo266290559riable) = (set_option_variable2 @ none_variable))),
% 9.31/2.68 introduced(definition,[new_symbols(naming,[spl44_4])],[avatar_definition])).
% 9.31/2.68 thf(f3638,plain,(
% 9.31/2.68 ( ! [X0 : set_variable,X1 : variable] : (((insert_variable @ X1 @ X0) = (sup_sup_set_variable @ X0 @ (insert_variable @ X1 @ (these_variable @ bot_bo266290559riable))))) )),
% 9.31/2.68 inference(superposition,[status(thm)],[f1205,f1567])).
% 9.31/2.68 thf(f1567,plain,(
% 9.31/2.68 ( ! [X0 : set_variable] : (((sup_sup_set_variable @ X0 @ (these_variable @ bot_bo266290559riable)) = X0)) )),
% 9.31/2.68 inference(definition_unfolding,[status(thm)],[f1177,f1168])).
% 9.31/2.68 thf(f1168,plain,(
% 9.31/2.68 (bot_bot_set_variable = (these_variable @ bot_bo266290559riable))),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f216])).
% 9.31/2.68 thf(f216,axiom,(
% 9.31/2.68 (bot_bot_set_variable = (these_variable @ bot_bo266290559riable))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_215_these__empty)).
% 9.31/2.68 thf(f1177,plain,(
% 9.31/2.68 ( ! [X0 : set_variable] : (((sup_sup_set_variable @ X0 @ bot_bot_set_variable) = X0)) )),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f827])).
% 9.31/2.68 thf(f827,plain,(
% 9.31/2.68 ! [X0 : set_variable] : ((sup_sup_set_variable @ X0 @ bot_bot_set_variable) = X0)),
% 9.31/2.68 inference(rectify,[status(thm)],[f143])).
% 9.31/2.68 thf(f143,axiom,(
% 9.31/2.68 ! [X5 : set_variable] : ((sup_sup_set_variable @ X5 @ bot_bot_set_variable) = X5)),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_142_Un__empty__right)).
% 9.31/2.68 thf(f1205,plain,(
% 9.31/2.68 ( ! [X2 : set_variable,X0 : variable,X1 : set_variable] : (((sup_sup_set_variable @ X2 @ (insert_variable @ X0 @ X1)) = (insert_variable @ X0 @ (sup_sup_set_variable @ X2 @ X1)))) )),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f837])).
% 9.31/2.68 thf(f837,plain,(
% 9.31/2.68 ! [X0 : variable,X1 : set_variable,X2 : set_variable] : ((sup_sup_set_variable @ X2 @ (insert_variable @ X0 @ X1)) = (insert_variable @ X0 @ (sup_sup_set_variable @ X2 @ X1)))),
% 9.31/2.68 inference(rectify,[status(thm)],[f5])).
% 9.31/2.68 thf(f5,axiom,(
% 9.31/2.68 ! [X2 : variable,X3 : set_variable,X5 : set_variable] : ((sup_sup_set_variable @ X5 @ (insert_variable @ X2 @ X3)) = (insert_variable @ X2 @ (sup_sup_set_variable @ X5 @ X3)))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_4_Un__insert__right)).
% 9.31/2.68 thf(f3876,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (($true = (member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ none_variable)))))) | ((f @ zero_zero_real @ X1) = (omega @ X1))) ) | ~spl44_4),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3875,f3705])).
% 9.31/2.68 thf(f3875,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (((member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ (these_variable @ bot_bo266290559riable))))) = $true) | ((f @ zero_zero_real @ X1) = (omega @ X1))) )),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f2453,f1417])).
% 9.31/2.68 thf(f1417,plain,(
% 9.31/2.68 ( ! [X2 : variable,X0 : variable,X1 : set_variable] : (((insert_variable @ X0 @ (insert_variable @ X2 @ X1)) = (insert_variable @ X2 @ (insert_variable @ X0 @ X1)))) )),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f884])).
% 9.31/2.68 thf(f884,plain,(
% 9.31/2.68 ! [X0 : variable,X1 : set_variable,X2 : variable] : ((insert_variable @ X0 @ (insert_variable @ X2 @ X1)) = (insert_variable @ X2 @ (insert_variable @ X0 @ X1)))),
% 9.31/2.68 inference(rectify,[status(thm)],[f65])).
% 9.31/2.68 thf(f65,axiom,(
% 9.31/2.68 ! [X6 : variable,X5 : set_variable,X7 : variable] : ((insert_variable @ X6 @ (insert_variable @ X7 @ X5)) = (insert_variable @ X7 @ (insert_variable @ X6 @ X5)))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_64_insert__commute)).
% 9.31/2.68 thf(f2453,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (((f @ zero_zero_real @ X1) = (omega @ X1)) | ((member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))))) = $true)) )),
% 9.31/2.68 inference(equality_proxy_clausification,[status(thm)],[f2452])).
% 9.31/2.68 thf(f2452,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (((member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))))) = $true) | (((omega @ X1) = (f @ zero_zero_real @ X1)) = $true)) )),
% 9.31/2.68 inference(not_proxy_clausification,[status(thm)],[f2451])).
% 9.31/2.68 thf(f2451,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (((~ (member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable)))))) = $false) | (((omega @ X1) = (f @ zero_zero_real @ X1)) = $true)) )),
% 9.31/2.68 inference(binary_proxy_clausification,[status(thm)],[f2450])).
% 9.31/2.68 thf(f2450,plain,(
% 9.31/2.68 ( ! [X1 : variable] : ((((~ (member_variable @ X1 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable)))))) => ((omega @ X1) = (f @ zero_zero_real @ X1))) = $true)) )),
% 9.31/2.68 inference(beta_eta_normalization,[status(thm)],[f2449])).
% 9.31/2.68 thf(f2449,plain,(
% 9.31/2.68 ( ! [X1 : variable] : (($true = ((^[Y0 : variable]: ((~ (member_variable @ Y0 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable)))))) => ((omega @ Y0) = (f @ zero_zero_real @ Y0)))) @ X1))) )),
% 9.31/2.68 inference(pi_clausification,[status(thm)],[f2448])).
% 9.31/2.68 thf(f2448,plain,(
% 9.31/2.68 ((!! @ variable @ (^[Y0 : variable]: ((~ (member_variable @ Y0 @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable)))))) => ((omega @ Y0) = (f @ zero_zero_real @ Y0))))) = $true)),
% 9.31/2.68 inference(beta_eta_normalization,[status(thm)],[f1647])).
% 9.31/2.68 thf(f1647,plain,(
% 9.31/2.68 (((^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set_variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member_variable @ Y3 @ Y2)) => ((Y1 @ Y3) = (Y0 @ Y3)))))))))) @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))))) = $true)),
% 9.31/2.68 inference(definition_unfolding,[status(thm)],[f1410,f1283,f1168])).
% 9.31/2.68 thf(f1283,plain,(
% 9.31/2.68 (denota1419872369iation = (^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set_variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member_variable @ Y3 @ Y2)) => ((Y1 @ Y3) = (Y0 @ Y3)))))))))))),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f772])).
% 9.31/2.68 thf(f772,plain,(
% 9.31/2.68 (denota1419872369iation = (^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set_variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member_variable @ Y3 @ Y2)) => ((Y1 @ Y3) = (Y0 @ Y3)))))))))))),
% 9.31/2.68 inference(fool_elimination,[status(thm)],[f771])).
% 9.31/2.68 thf(f771,plain,(
% 9.31/2.68 ((^[X0 : variable > real, X1 : variable > real, X2 : set_variable] : (! [X3 : variable] : (~(member_variable @ X3 @ X2) => ((X1 @ X3) = (X0 @ X3))))) = denota1419872369iation)),
% 9.31/2.68 inference(rectify,[status(thm)],[f132])).
% 9.31/2.68 thf(f132,axiom,(
% 9.31/2.68 ((^[X26 : variable > real, X27 : variable > real, X28 : set_variable] : (! [X29 : variable] : (~(member_variable @ X29 @ X28) => ((X26 @ X29) = (X27 @ X29))))) = denota1419872369iation)),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_131_Uvariation__def)).
% 9.31/2.68 thf(f1410,plain,(
% 9.31/2.68 ((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) = $true)),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f746])).
% 9.31/2.68 thf(f746,plain,(
% 9.31/2.68 ((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) = $true)),
% 9.31/2.68 inference(fool_elimination,[status(thm)],[f745])).
% 9.31/2.68 thf(f745,plain,(
% 9.31/2.68 (denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),
% 9.31/2.68 inference(rectify,[status(thm)],[f1])).
% 9.31/2.68 thf(f1,axiom,(
% 9.31/2.68 (denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_0_uv)).
% 9.31/2.68 thf(f3820,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ u))) = $false) | ~spl44_6),
% 9.31/2.68 inference(avatar_component_clause,[status(thm)],[f3818])).
% 9.31/2.68 thf(f3818,definition,(
% 9.31/2.68 spl44_6 <=> ((member_variable @ sK91 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ u))) = $false)),
% 9.31/2.68 introduced(definition,[new_symbols(naming,[spl44_6])],[avatar_definition])).
% 9.31/2.68 thf(f3821,plain,(
% 9.31/2.68 spl44_6 | ~spl44_4),
% 9.31/2.68 inference(avatar_split_clause,[status(thm)],[f3816,f3703,f3818])).
% 9.31/2.68 thf(f3816,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ u))) = $false) | ~spl44_4),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3815,f3700])).
% 9.31/2.68 thf(f3700,plain,(
% 9.31/2.68 ( ! [X0 : set_variable] : (((sup_sup_set_variable @ (set_option_variable2 @ none_variable) @ X0) = X0)) )),
% 9.31/2.68 inference(backward_demodulation,[status(thm)],[f1602,f1636])).
% 9.31/2.68 thf(f1636,plain,(
% 9.31/2.68 ((these_variable @ bot_bo266290559riable) = (set_option_variable2 @ none_variable))),
% 9.31/2.68 inference(definition_unfolding,[status(thm)],[f1374,f1168])).
% 9.31/2.68 thf(f1374,plain,(
% 9.31/2.68 (bot_bot_set_variable = (set_option_variable2 @ none_variable))),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f280])).
% 9.31/2.68 thf(f280,axiom,(
% 9.31/2.68 (bot_bot_set_variable = (set_option_variable2 @ none_variable))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_279_option_Osimps_I14_J)).
% 9.31/2.68 thf(f1602,plain,(
% 9.31/2.68 ( ! [X0 : set_variable] : (((sup_sup_set_variable @ (these_variable @ bot_bo266290559riable) @ X0) = X0)) )),
% 9.31/2.68 inference(definition_unfolding,[status(thm)],[f1271,f1168])).
% 9.31/2.68 thf(f1271,plain,(
% 9.31/2.68 ( ! [X0 : set_variable] : (((sup_sup_set_variable @ bot_bot_set_variable @ X0) = X0)) )),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f872])).
% 9.31/2.68 thf(f872,plain,(
% 9.31/2.68 ! [X0 : set_variable] : ((sup_sup_set_variable @ bot_bot_set_variable @ X0) = X0)),
% 9.31/2.68 inference(rectify,[status(thm)],[f10])).
% 9.31/2.68 thf(f10,axiom,(
% 9.31/2.68 ! [X6 : set_variable] : ((sup_sup_set_variable @ bot_bot_set_variable @ X6) = X6)),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_9_sup__bot__left)).
% 9.31/2.68 thf(f3815,plain,(
% 9.31/2.68 ($false = (member_variable @ sK91 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ (sup_sup_set_variable @ (set_option_variable2 @ none_variable) @ u))))) | ~spl44_4),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3814,f3705])).
% 9.31/2.68 thf(f3814,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (insert_variable @ (dVar @ x) @ (insert_variable @ (rVar @ x) @ (sup_sup_set_variable @ (these_variable @ bot_bo266290559riable) @ u)))) = $false)),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3813,f1417])).
% 9.31/2.68 thf(f3813,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (sup_sup_set_variable @ (these_variable @ bot_bo266290559riable) @ u)))) = $false)),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f3812,f1325])).
% 9.31/2.68 thf(f1325,plain,(
% 9.31/2.68 ( ! [X2 : set_variable,X0 : variable,X1 : set_variable] : (((insert_variable @ X0 @ (sup_sup_set_variable @ X2 @ X1)) = (sup_sup_set_variable @ (insert_variable @ X0 @ X2) @ X1))) )),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f954])).
% 9.31/2.68 thf(f954,plain,(
% 9.31/2.68 ! [X0 : variable,X1 : set_variable,X2 : set_variable] : ((insert_variable @ X0 @ (sup_sup_set_variable @ X2 @ X1)) = (sup_sup_set_variable @ (insert_variable @ X0 @ X2) @ X1))),
% 9.31/2.68 inference(rectify,[status(thm)],[f3])).
% 9.31/2.68 thf(f3,axiom,(
% 9.31/2.68 ! [X2 : variable,X4 : set_variable,X3 : set_variable] : ((sup_sup_set_variable @ (insert_variable @ X2 @ X3) @ X4) = (insert_variable @ X2 @ (sup_sup_set_variable @ X3 @ X4)))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',fact_2_Un__insert__left)).
% 9.31/2.68 thf(f3812,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (insert_variable @ (rVar @ x) @ (sup_sup_set_variable @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable)) @ u))) = $false)),
% 9.31/2.68 inference(forward_demodulation,[status(thm)],[f2880,f1325])).
% 9.31/2.68 thf(f2880,plain,(
% 9.31/2.68 ((member_variable @ sK91 @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u)) = $false)),
% 9.31/2.68 inference(not_proxy_clausification,[status(thm)],[f2879])).
% 9.31/2.68 thf(f2879,plain,(
% 9.31/2.68 ((~ (member_variable @ sK91 @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u))) = $true)),
% 9.31/2.68 inference(binary_proxy_clausification,[status(thm)],[f2877])).
% 9.31/2.68 thf(f2877,plain,(
% 9.31/2.68 (((~ (member_variable @ sK91 @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u))) => ((omega @ sK91) = (f @ zero_zero_real @ sK91))) = $false)),
% 9.31/2.68 inference(beta_eta_normalization,[status(thm)],[f2876])).
% 9.31/2.68 thf(f2876,plain,(
% 9.31/2.68 (((^[Y0 : variable]: ((~ (member_variable @ Y0 @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u))) => ((omega @ Y0) = (f @ zero_zero_real @ Y0)))) @ sK91) = $false)),
% 9.31/2.68 inference(sigma_clausification,[status(thm)],[f2875])).
% 9.31/2.68 thf(f2875,plain,(
% 9.31/2.68 ((!! @ variable @ (^[Y0 : variable]: ((~ (member_variable @ Y0 @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u))) => ((omega @ Y0) = (f @ zero_zero_real @ Y0))))) != $true)),
% 9.31/2.68 inference(beta_eta_normalization,[status(thm)],[f1578])).
% 9.31/2.68 thf(f1578,plain,(
% 9.31/2.68 (((^[Y0 : variable > real]: ((^[Y1 : variable > real]: ((^[Y2 : set_variable]: (!! @ variable @ (^[Y3 : variable]: ((~ (member_variable @ Y3 @ Y2)) => ((Y1 @ Y3) = (Y0 @ Y3)))))))))) @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ (these_variable @ bot_bo266290559riable))) @ u)) != $true)),
% 9.31/2.68 inference(definition_unfolding,[status(thm)],[f1210,f1283,f1168])).
% 9.31/2.68 thf(f1210,plain,(
% 9.31/2.68 ((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)) != $true)),
% 9.31/2.68 inference(cnf_transformation,[status(thm)],[f839])).
% 9.31/2.68 thf(f839,plain,(
% 9.31/2.68 ((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)) != $true)),
% 9.31/2.68 inference(flattening,[status(thm)],[f458])).
% 9.31/2.68 thf(f458,plain,(
% 9.31/2.68 ~((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)) = $true)),
% 9.31/2.68 inference(fool_elimination,[status(thm)],[f457])).
% 9.31/2.68 thf(f457,plain,(
% 9.31/2.68 ~(denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u))),
% 9.31/2.68 inference(rectify,[status(thm)],[f358])).
% 9.31/2.68 thf(f358,negated_conjecture,(
% 9.31/2.68 ~(denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u))),
% 9.31/2.68 inference(negated_conjecture,[status(cth)],[f357])).
% 9.31/2.68 thf(f357,conjecture,(
% 9.31/2.68 (denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u))),
% 9.31/2.68 file('/export/starexec/sandbox2/tmp/tmp.eBWM3imTOx/DTF2THF_26036.p',conj_0)).
% 9.31/2.68 thf(f3706,plain,(
% 9.31/2.68 spl44_4),
% 9.31/2.68 inference(avatar_split_clause,[status(thm)],[f1636,f3703])).
% 9.31/2.68 thf(f3552,plain,(
% 9.31/2.68 ~spl44_3),
% 9.31/2.68 inference(avatar_split_clause,[status(thm)],[f2881,f3549])).
% 9.31/2.68 thf(f2881,plain,(
% 9.31/2.68 ((omega @ sK91) != (f @ zero_zero_real @ sK91))),
% 9.31/2.68 inference(equality_proxy_clausification,[status(thm)],[f2878])).
% 9.31/2.68 thf(f2878,plain,(
% 9.31/2.68 (((omega @ sK91) = (f @ zero_zero_real @ sK91)) = $false)),
% 9.31/2.68 inference(binary_proxy_clausification,[status(thm)],[f2877])).
% 9.31/2.68 % SZS output end Proof for DTF2THF_26036
% 9.31/2.68 % (26231)------------------------------
% 9.31/2.68 % (26231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.68 % (26231)Termination reason: Refutation
% 9.31/2.68
% 9.31/2.68 % (26231)Memory used [KB]: 8571
% 9.31/2.68 % (26231)Time elapsed: 0.246 s
% 9.31/2.68 % (26231)Instructions burned: 821 (million)
% 9.31/2.68 % (26231)------------------------------
% 9.31/2.68 % (26231)------------------------------
% 9.31/2.68 % (26134)Success in time 1.149 s
%------------------------------------------------------------------------------