%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP203^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 08:56:23 AM UTC 2026
% Result : Theorem 27.42s 5.14s
% Output : Refutation 27.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 106 ( 78 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 542 ( 37 ~; 40 |; 13 &; 442 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 148 ( 148 >; 0 *; 0 +; 0 <<)
% Number of symbols : 392 ( 390 usr; 19 con; 0-8 aty)
% Number of variables : 201 ( 148 ^; 48 !; 5 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
option_fml: $tType ).
thf(type_def_7,type,
option_trm: $tType ).
thf(type_def_8,type,
char: $tType ).
thf(type_def_9,type,
option_game: $tType ).
thf(type_def_10,type,
produc799602994n_game: $tType ).
thf(type_def_11,type,
produc62062515n_game: $tType ).
thf(type_def_12,type,
set_variable: $tType ).
thf(type_def_13,type,
trm: $tType ).
thf(type_def_14,type,
variable: $tType ).
thf(type_def_15,type,
set_Pr79606376n_game: $tType ).
thf(type_def_16,type,
set_Pr739694057n_game: $tType ).
thf(type_def_17,type,
set_Pr720454634n_game: $tType ).
thf(type_def_18,type,
set_Pr1235432374le_trm: $tType ).
thf(type_def_19,type,
set_Pr943832262on_trm: $tType ).
thf(type_def_20,type,
fml: $tType ).
thf(type_def_21,type,
game: $tType ).
thf(type_def_22,type,
produc1418842292n_game: $tType ).
thf(type_def_23,type,
produc46605351on_fml: $tType ).
thf(type_def_24,type,
produc1739631244on_fml: $tType ).
thf(type_def_25,type,
produc1016592119n_game: $tType ).
thf(type_def_26,type,
produc1072747943on_trm: $tType ).
thf(type_def_27,type,
produc1367888000le_trm: $tType ).
thf(type_def_28,type,
produc1699626005le_trm: $tType ).
thf(type_def_29,type,
produc464795408on_trm: $tType ).
thf(type_def_30,type,
produc1408538418on_fml: $tType ).
thf(type_def_31,type,
produc1024976764on_trm: $tType ).
thf(type_def_32,type,
real: $tType ).
thf(func_def_0,type,
produc1699626005le_trm: $tType ).
thf(func_def_1,type,
set_Pr720454634n_game: $tType ).
thf(func_def_2,type,
produc1418842292n_game: $tType ).
thf(func_def_3,type,
set_Pr739694057n_game: $tType ).
thf(func_def_4,type,
produc62062515n_game: $tType ).
thf(func_def_5,type,
set_Pr79606376n_game: $tType ).
thf(func_def_6,type,
produc799602994n_game: $tType ).
thf(func_def_7,type,
produc1016592119n_game: $tType ).
thf(func_def_8,type,
produc1739631244on_fml: $tType ).
thf(func_def_9,type,
produc1072747943on_trm: $tType ).
thf(func_def_10,type,
produc46605351on_fml: $tType ).
thf(func_def_11,type,
set_Pr943832262on_trm: $tType ).
thf(func_def_12,type,
set_Pr1235432374le_trm: $tType ).
thf(func_def_13,type,
produc1024976764on_trm: $tType ).
thf(func_def_14,type,
produc1408538418on_fml: $tType ).
thf(func_def_15,type,
produc464795408on_trm: $tType ).
thf(func_def_16,type,
produc1367888000le_trm: $tType ).
thf(func_def_17,type,
option_game: $tType ).
thf(func_def_18,type,
option_trm: $tType ).
thf(func_def_19,type,
option_fml: $tType ).
thf(func_def_20,type,
set_variable: $tType ).
thf(func_def_21,type,
variable: $tType ).
thf(func_def_22,type,
game: $tType ).
thf(func_def_23,type,
char: $tType ).
thf(func_def_24,type,
trm: $tType ).
thf(func_def_25,type,
fml: $tType ).
thf(func_def_26,type,
real: $tType ).
thf(func_def_27,type,
if_option_fml: $o > option_fml > option_fml > option_fml ).
thf(func_def_28,type,
if_option_trm: $o > option_trm > option_trm > option_trm ).
thf(func_def_29,type,
inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
thf(func_def_30,type,
inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
thf(func_def_31,type,
inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
thf(func_def_32,type,
inf_in185389155_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > set_variable > trm > $o ).
thf(func_def_33,type,
inf_in605351507_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > char > option_trm > $o ).
thf(func_def_34,type,
inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
thf(func_def_35,type,
inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game ).
thf(func_def_36,type,
inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game ).
thf(func_def_37,type,
inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game ).
thf(func_def_38,type,
inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm ).
thf(func_def_39,type,
inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm ).
thf(func_def_40,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(func_def_41,type,
none_fml: option_fml ).
thf(func_def_42,type,
none_game: option_game ).
thf(func_def_43,type,
none_trm: option_trm ).
thf(func_def_44,type,
some_fml: fml > option_fml ).
thf(func_def_45,type,
some_game: game > option_game ).
thf(func_def_46,type,
some_trm: trm > option_trm ).
thf(func_def_47,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_48,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_49,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_50,type,
case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
thf(func_def_51,type,
case_o325794063ml_trm: option_fml > ( trm > option_fml ) > option_trm > option_fml ).
thf(func_def_52,type,
case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
thf(func_def_53,type,
the_fml: option_fml > fml ).
thf(func_def_54,type,
the_game: option_game > game ).
thf(func_def_55,type,
the_trm: option_trm > trm ).
thf(func_def_56,type,
bot_bo1895715589game_o: ( char > option_fml ) > ( char > option_game ) > $o ).
thf(func_def_57,type,
bot_bo1417568964game_o: ( char > option_trm ) > produc799602994n_game > $o ).
thf(func_def_58,type,
bot_bo849148163game_o: ( char > option_trm ) > produc62062515n_game > $o ).
thf(func_def_59,type,
bot_bo512610661_trm_o: set_variable > trm > $o ).
thf(func_def_60,type,
bot_bo102862421_trm_o: char > option_trm > $o ).
thf(func_def_61,type,
bot_bot_variable_o: variable > $o ).
thf(func_def_62,type,
bot_bo456479484n_game: set_Pr79606376n_game ).
thf(func_def_63,type,
bot_bo1302831229n_game: set_Pr739694057n_game ).
thf(func_def_64,type,
bot_bo1453406334n_game: set_Pr720454634n_game ).
thf(func_def_65,type,
bot_bo896421962le_trm: set_Pr1235432374le_trm ).
thf(func_def_66,type,
bot_bo18861914on_trm: set_Pr943832262on_trm ).
thf(func_def_67,type,
bot_bot_set_variable: set_variable ).
thf(func_def_68,type,
produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
thf(func_def_69,type,
produc1048060077n_game: ( char > option_trm ) > produc799602994n_game > produc62062515n_game ).
thf(func_def_70,type,
produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
thf(func_def_71,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(func_def_72,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_73,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_74,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(func_def_75,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(func_def_76,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(func_def_77,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(func_def_78,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(func_def_79,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(func_def_80,type,
produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_81,type,
produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_82,type,
produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
thf(func_def_83,type,
produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
thf(func_def_84,type,
produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_85,type,
produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_86,type,
produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
thf(func_def_87,type,
produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
thf(func_def_88,type,
produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_89,type,
produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
thf(func_def_90,type,
produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(func_def_91,type,
produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
thf(func_def_92,type,
produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
thf(func_def_93,type,
produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
thf(func_def_94,type,
produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
thf(func_def_95,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(func_def_96,type,
produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
thf(func_def_97,type,
produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
thf(func_def_98,type,
produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
thf(func_def_99,type,
produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
thf(func_def_100,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(func_def_101,type,
produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
thf(func_def_102,type,
produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
thf(func_def_103,type,
produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
thf(func_def_104,type,
produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
thf(func_def_105,type,
produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
thf(func_def_106,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_107,type,
is_empty_variable: set_variable > $o ).
thf(func_def_108,type,
static_FVF: fml > set_variable ).
thf(func_def_109,type,
static_FVT: trm > set_variable ).
thf(func_def_110,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(func_def_111,type,
geq: trm > trm > fml ).
thf(func_def_112,type,
pred: char > trm > fml ).
thf(func_def_113,type,
const: char > trm ).
thf(func_def_114,type,
differential: trm > trm ).
thf(func_def_115,type,
func: char > trm > trm ).
thf(func_def_116,type,
number: real > trm ).
thf(func_def_117,type,
plus: trm > trm > trm ).
thf(func_def_118,type,
times: trm > trm > trm ).
thf(func_def_119,type,
var: variable > trm ).
thf(func_def_120,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(func_def_121,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_122,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(func_def_123,type,
uSubst1367128042_Testo: option_fml > option_game ).
thf(func_def_124,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_125,type,
uSubst_Mirabelle_dot: trm ).
thf(func_def_126,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(func_def_127,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_128,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_129,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_130,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(func_def_131,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(func_def_132,type,
member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
thf(func_def_133,type,
member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
thf(func_def_134,type,
member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o ).
thf(func_def_135,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_136,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_137,type,
member_variable: variable > set_variable > $o ).
thf(func_def_138,type,
ua: set_variable ).
thf(func_def_139,type,
va: set_variable ).
thf(func_def_140,type,
sigma: produc1418842292n_game ).
thf(func_def_141,type,
theta: trm ).
thf(func_def_142,type,
p: char ).
thf(func_def_157,type,
sP0: ( option_trm > option_fml > $o ) > option_trm > option_fml > $o ).
thf(func_def_158,type,
sP1: ( option_fml > option_fml > $o ) > option_fml > option_fml > $o ).
thf(func_def_159,type,
sP2: ( option_fml > option_game > $o ) > option_fml > option_game > $o ).
thf(func_def_160,type,
sP3: option_trm > option_trm > option_fml > $o ).
thf(func_def_161,type,
sP4: ( option_game > option_fml > $o ) > option_fml > option_game > $o ).
thf(func_def_162,type,
sP5: ( option_trm > option_trm > $o ) > option_trm > option_trm > $o ).
thf(func_def_163,type,
sP6: ( option_game > option_trm > $o ) > option_game > option_trm > $o ).
thf(func_def_164,type,
sP7: ( option_fml > option_trm > $o ) > option_fml > option_trm > $o ).
thf(func_def_165,type,
sP8: ( trm > $o ) > $o ).
thf(func_def_166,type,
sP9: ( trm > $o ) > $o ).
thf(func_def_167,type,
sP10: ( option_trm > option_game > $o ) > option_trm > option_game > $o ).
thf(func_def_168,type,
sP11: ( option_game > option_game > $o ) > option_game > option_game > $o ).
thf(func_def_169,type,
sP12: trm > produc1418842292n_game > set_variable > option_trm > $o ).
thf(func_def_170,type,
sP13: trm > produc1418842292n_game > set_variable > option_trm > $o ).
thf(func_def_171,type,
sP14: trm > produc1418842292n_game > set_variable > option_trm > $o ).
thf(func_def_172,type,
sP15: trm > produc1418842292n_game > set_variable > option_trm > $o ).
thf(func_def_173,type,
sP16: trm > option_trm > produc1418842292n_game > set_variable > $o ).
thf(func_def_174,type,
sP17: trm > option_trm > produc1418842292n_game > set_variable > $o ).
thf(func_def_175,type,
sP18: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_176,type,
sP19: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_177,type,
sP20: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_178,type,
sP21: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_179,type,
sP22: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_180,type,
sP23: ( produc1418842292n_game > set_variable > trm > $o ) > $o ).
thf(func_def_181,type,
sK24: ( trm > $o ) > ( trm > option_fml ) > ( option_fml > $o ) > trm ).
thf(func_def_182,type,
sK25: ( option_trm > option_fml > $o ) > option_trm > option_fml > trm ).
thf(func_def_183,type,
sK26: ( option_trm > option_fml > $o ) > option_trm > option_fml > fml ).
thf(func_def_184,type,
sK27: produc799602994n_game > ( ( char > option_fml ) > ( char > option_game ) > $o ) > char > option_fml ).
thf(func_def_185,type,
sK28: produc799602994n_game > ( ( char > option_fml ) > ( char > option_game ) > $o ) > char > option_game ).
thf(func_def_186,type,
sK29: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_187,type,
sK30: ( option_fml > option_fml > $o ) > option_fml > option_fml > fml ).
thf(func_def_188,type,
sK31: ( option_fml > option_game > $o ) > option_fml > option_game > game ).
thf(func_def_189,type,
sK32: ( option_fml > option_game > $o ) > option_fml > option_game > fml ).
thf(func_def_190,type,
sK33: produc1016592119n_game > game ).
thf(func_def_191,type,
sK34: produc1016592119n_game > game ).
thf(func_def_192,type,
sK35: produc1016592119n_game > game ).
thf(func_def_193,type,
sK36: produc1016592119n_game > option_game ).
thf(func_def_194,type,
sK37: option_fml > fml ).
thf(func_def_195,type,
sK38: set_variable > char > produc1418842292n_game > trm ).
thf(func_def_196,type,
sK39: set_variable > set_variable > variable ).
thf(func_def_197,type,
sK40: ( variable > $o ) > variable ).
thf(func_def_198,type,
sK41: option_trm > trm ).
thf(func_def_199,type,
sK42: option_fml > option_trm > option_trm > trm ).
thf(func_def_200,type,
sK43: option_fml > option_trm > option_trm > trm ).
thf(func_def_201,type,
sK44: option_trm > trm ).
thf(func_def_202,type,
sK45: ( set_variable > trm > $o ) > produc1367888000le_trm > trm ).
thf(func_def_203,type,
sK46: ( set_variable > trm > $o ) > produc1367888000le_trm > set_variable ).
thf(func_def_204,type,
sK47: ( char > option_trm > $o ) > char ).
thf(func_def_205,type,
sK48: ( char > option_trm > $o ) > char ).
thf(func_def_206,type,
sK49: ( char > option_trm > $o ) > trm ).
thf(func_def_207,type,
sK50: ( produc799602994n_game > char > option_fml ) > ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > char > option_fml ).
thf(func_def_208,type,
sK51: ( produc799602994n_game > char > option_fml ) > ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > char > option_game ).
thf(func_def_209,type,
sK52: ( option_game > $o ) > game ).
thf(func_def_210,type,
sK53: produc1418842292n_game > char > set_variable > trm ).
thf(func_def_211,type,
sK54: option_game > ( game > $o ) > game ).
thf(func_def_212,type,
sK55: option_game > game ).
thf(func_def_213,type,
sK56: ( variable > option_fml > $o ) > variable ).
thf(func_def_214,type,
sK57: ( variable > option_fml > $o ) > variable ).
thf(func_def_215,type,
sK58: ( variable > option_fml > $o ) > fml ).
thf(func_def_216,type,
sK59: set_variable > set_variable > variable ).
thf(func_def_217,type,
sK60: set_variable > set_variable > variable ).
thf(func_def_218,type,
sK61: ( option_game > option_fml > $o ) > game ).
thf(func_def_219,type,
sK62: ( option_game > option_fml > $o ) > option_fml ).
thf(func_def_220,type,
sK63: ( option_game > option_fml > $o ) > fml ).
thf(func_def_221,type,
sK64: ( option_game > option_fml > $o ) > game ).
thf(func_def_222,type,
sK65: ( option_game > option_fml > $o ) > option_fml > option_game > fml ).
thf(func_def_223,type,
sK66: ( option_game > option_fml > $o ) > option_fml > option_game > game ).
thf(func_def_224,type,
sK67: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > char > option_trm ).
thf(func_def_225,type,
sK68: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > produc62062515n_game ).
thf(func_def_226,type,
sK69: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > ( produc799602994n_game > option_fml ) > char > option_game ).
thf(func_def_227,type,
sK70: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > ( produc799602994n_game > option_fml ) > char > option_fml ).
thf(func_def_228,type,
sK71: option_game > game ).
thf(func_def_229,type,
sK72: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_230,type,
sK73: ( option_trm > option_trm > $o ) > option_trm > option_trm > trm ).
thf(func_def_231,type,
sK74: set_variable > set_variable > variable ).
thf(func_def_232,type,
sK75: ( variable > $o ) > ( variable > $o ) > variable ).
thf(func_def_233,type,
sK76: ( produc799602994n_game > char > option_trm ) > ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > char > option_fml ).
thf(func_def_234,type,
sK77: ( produc799602994n_game > char > option_trm ) > ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > char > option_game ).
thf(func_def_235,type,
sK78: ( option_game > option_trm > $o ) > option_game > option_trm > game ).
thf(func_def_236,type,
sK79: ( option_game > option_trm > $o ) > option_game > option_trm > trm ).
thf(func_def_237,type,
sK80: option_game > game ).
thf(func_def_238,type,
sK81: trm > trm ).
thf(func_def_239,type,
sK82: trm > trm ).
thf(func_def_240,type,
sK83: trm > char ).
thf(func_def_241,type,
sK84: trm > trm ).
thf(func_def_242,type,
sK85: trm > trm ).
thf(func_def_243,type,
sK86: trm > trm ).
thf(func_def_244,type,
sK87: trm > variable ).
thf(func_def_245,type,
sK88: trm > real ).
thf(func_def_246,type,
sK89: trm > char ).
thf(func_def_247,type,
sK90: trm > trm ).
thf(func_def_248,type,
sK91: option_fml > fml ).
thf(func_def_249,type,
sK92: produc1024976764on_trm > variable ).
thf(func_def_250,type,
sK93: produc1024976764on_trm > trm ).
thf(func_def_251,type,
sK94: produc1024976764on_trm > variable ).
thf(func_def_252,type,
sK95: option_fml > ( fml > $o ) > fml ).
thf(func_def_253,type,
sK96: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > ( produc1418842292n_game > char > option_fml ) > produc62062515n_game ).
thf(func_def_254,type,
sK97: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > ( produc1418842292n_game > char > option_fml ) > char > option_trm ).
thf(func_def_255,type,
sK98: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > ( produc1418842292n_game > option_fml ) > char > option_trm ).
thf(func_def_256,type,
sK99: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > ( produc1418842292n_game > option_fml ) > produc62062515n_game ).
thf(func_def_257,type,
sK100: ( option_fml > option_trm > $o ) > option_fml > option_trm > trm ).
thf(func_def_258,type,
sK101: ( option_fml > option_trm > $o ) > option_fml > option_trm > fml ).
thf(func_def_259,type,
sK102: option_fml > fml ).
thf(func_def_260,type,
sK103: ( trm > $o ) > trm ).
thf(func_def_261,type,
sK104: ( trm > $o ) > trm ).
thf(func_def_262,type,
sK105: ( trm > $o ) > trm ).
thf(func_def_263,type,
sK106: ( trm > $o ) > trm ).
thf(func_def_264,type,
sK107: ( trm > $o ) > char ).
thf(func_def_265,type,
sK108: ( trm > $o ) > trm ).
thf(func_def_266,type,
sK109: ( trm > $o ) > trm ).
thf(func_def_267,type,
sK110: ( trm > $o ) > variable ).
thf(func_def_268,type,
sK111: ( trm > $o ) > char ).
thf(func_def_269,type,
sK112: ( trm > $o ) > real ).
thf(func_def_270,type,
sK113: produc46605351on_fml > option_fml ).
thf(func_def_271,type,
sK114: produc46605351on_fml > fml ).
thf(func_def_272,type,
sK115: produc46605351on_fml > fml ).
thf(func_def_273,type,
sK116: produc46605351on_fml > fml ).
thf(func_def_274,type,
sK117: produc1408538418on_fml > variable ).
thf(func_def_275,type,
sK118: produc1408538418on_fml > fml ).
thf(func_def_276,type,
sK119: produc1408538418on_fml > variable ).
thf(func_def_277,type,
sK120: ( char > option_trm > $o ) > produc464795408on_trm > option_trm ).
thf(func_def_278,type,
sK121: ( char > option_trm > $o ) > produc464795408on_trm > char ).
thf(func_def_279,type,
sK122: produc1699626005le_trm > set_variable ).
thf(func_def_280,type,
sK123: produc1699626005le_trm > real ).
thf(func_def_281,type,
sK124: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_282,type,
sK125: produc1699626005le_trm > trm ).
thf(func_def_283,type,
sK126: produc1699626005le_trm > trm ).
thf(func_def_284,type,
sK127: produc1699626005le_trm > set_variable ).
thf(func_def_285,type,
sK128: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_286,type,
sK129: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_287,type,
sK130: produc1699626005le_trm > char ).
thf(func_def_288,type,
sK131: produc1699626005le_trm > trm ).
thf(func_def_289,type,
sK132: produc1699626005le_trm > set_variable ).
thf(func_def_290,type,
sK133: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_291,type,
sK134: produc1699626005le_trm > set_variable ).
thf(func_def_292,type,
sK135: produc1699626005le_trm > trm ).
thf(func_def_293,type,
sK136: produc1699626005le_trm > trm ).
thf(func_def_294,type,
sK137: produc1699626005le_trm > trm ).
thf(func_def_295,type,
sK138: produc1699626005le_trm > set_variable ).
thf(func_def_296,type,
sK139: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_297,type,
sK140: produc1699626005le_trm > set_variable ).
thf(func_def_298,type,
sK141: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_299,type,
sK142: produc1699626005le_trm > char ).
thf(func_def_300,type,
sK143: produc1699626005le_trm > set_variable ).
thf(func_def_301,type,
sK144: produc1699626005le_trm > variable ).
thf(func_def_302,type,
sK145: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_303,type,
sK146: ( variable > option_trm > $o ) > variable ).
thf(func_def_304,type,
sK147: ( variable > option_trm > $o ) > variable ).
thf(func_def_305,type,
sK148: ( variable > option_trm > $o ) > trm ).
thf(func_def_306,type,
sK149: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > ( produc62062515n_game > option_trm ) > char > option_trm ).
thf(func_def_307,type,
sK150: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > ( produc62062515n_game > option_trm ) > produc799602994n_game ).
thf(func_def_308,type,
sK151: option_trm > trm ).
thf(func_def_309,type,
sK152: ( option_game > $o ) > game ).
thf(func_def_310,type,
sK153: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > ( produc799602994n_game > option_trm ) > char > option_fml ).
thf(func_def_311,type,
sK154: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > ( produc799602994n_game > option_trm ) > char > option_game ).
thf(func_def_312,type,
sK155: ( produc62062515n_game > char > option_trm ) > ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > char > option_trm ).
thf(func_def_313,type,
sK156: ( produc62062515n_game > char > option_trm ) > ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc799602994n_game ).
thf(func_def_314,type,
sK157: set_variable > variable ).
thf(func_def_315,type,
sK158: ( variable > $o ) > variable ).
thf(func_def_316,type,
sK159: ( fml > $o ) > ( option_fml > $o ) > ( fml > option_fml ) > fml ).
thf(func_def_317,type,
sK160: produc1739631244on_fml > fml ).
thf(func_def_318,type,
sK161: produc1739631244on_fml > game ).
thf(func_def_319,type,
sK162: produc1739631244on_fml > option_fml ).
thf(func_def_320,type,
sK163: produc1739631244on_fml > game ).
thf(func_def_321,type,
sK164: ( produc62062515n_game > char > option_fml ) > ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > char > option_trm ).
thf(func_def_322,type,
sK165: ( produc62062515n_game > char > option_fml ) > ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc799602994n_game ).
thf(func_def_323,type,
sK166: produc1418842292n_game > char > set_variable > fml ).
thf(func_def_324,type,
sK167: option_game > game ).
thf(func_def_325,type,
sK168: option_trm > trm ).
thf(func_def_326,type,
sK169: ( trm > $o ) > option_trm > trm ).
thf(func_def_327,type,
sK170: ( option_trm > option_game > $o ) > option_trm > option_game > game ).
thf(func_def_328,type,
sK171: ( option_trm > option_game > $o ) > option_trm > option_game > trm ).
thf(func_def_329,type,
sK172: ( option_game > option_game > $o ) > option_game ).
thf(func_def_330,type,
sK173: ( option_game > option_game > $o ) > game ).
thf(func_def_331,type,
sK174: ( option_game > option_game > $o ) > game ).
thf(func_def_332,type,
sK175: ( option_game > option_game > $o ) > game ).
thf(func_def_333,type,
sK176: set_variable > variable ).
thf(func_def_334,type,
sK177: produc464795408on_trm > char ).
thf(func_def_335,type,
sK178: produc464795408on_trm > trm ).
thf(func_def_336,type,
sK179: produc464795408on_trm > char ).
thf(func_def_337,type,
sK180: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_338,type,
sK181: ( option_game > option_game > $o ) > option_game > option_game > game ).
thf(func_def_339,type,
sK182: option_fml > fml ).
thf(func_def_340,type,
sK183: produc1072747943on_trm > trm ).
thf(func_def_341,type,
sK184: produc1072747943on_trm > trm ).
thf(func_def_342,type,
sK185: produc1072747943on_trm > trm ).
thf(func_def_343,type,
sK186: produc1072747943on_trm > option_trm ).
thf(func_def_344,type,
sK187: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > ( produc62062515n_game > option_fml ) > char > option_trm ).
thf(func_def_345,type,
sK188: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > ( produc62062515n_game > option_fml ) > produc799602994n_game ).
thf(func_def_346,type,
sK189: ( option_trm > $o ) > trm ).
thf(func_def_347,type,
sK190: option_trm > trm ).
thf(func_def_348,type,
sK191: ( option_trm > option_trm > $o ) > option_trm ).
thf(func_def_349,type,
sK192: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_350,type,
sK193: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_351,type,
sK194: ( option_trm > option_trm > $o ) > trm ).
thf(func_def_352,type,
sK195: set_variable > variable ).
thf(func_def_353,type,
sK196: option_fml > fml ).
thf(func_def_354,type,
sK197: produc1418842292n_game > set_variable > char > trm ).
thf(func_def_355,type,
sK198: option_game > game ).
thf(func_def_356,type,
sK199: ( option_fml > $o ) > produc1418842292n_game > ( ( char > option_trm ) > produc62062515n_game > option_fml ) > char > option_trm ).
thf(func_def_357,type,
sK200: ( option_fml > $o ) > produc1418842292n_game > ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc62062515n_game ).
thf(func_def_358,type,
sK201: ( option_fml > $o ) > fml ).
thf(func_def_359,type,
sK202: ( option_trm > $o ) > trm ).
thf(func_def_360,type,
sK203: ( trm > $o ) > ( trm > option_trm ) > ( option_trm > $o ) > trm ).
thf(func_def_361,type,
sK204: option_trm > trm ).
thf(func_def_362,type,
sK205: trm > option_trm > produc1418842292n_game > set_variable > trm ).
thf(func_def_363,type,
sK206: trm > option_trm > produc1418842292n_game > set_variable > trm ).
thf(func_def_364,type,
sK207: trm > option_trm > produc1418842292n_game > set_variable > trm ).
thf(func_def_365,type,
sK208: trm > produc1418842292n_game > set_variable > option_trm > char ).
thf(func_def_366,type,
sK209: trm > produc1418842292n_game > set_variable > option_trm > char ).
thf(func_def_367,type,
sK210: trm > produc1418842292n_game > set_variable > option_trm > trm ).
thf(func_def_368,type,
sK211: trm > produc1418842292n_game > set_variable > option_trm > variable ).
thf(func_def_369,type,
sK212: trm > produc1418842292n_game > set_variable > option_trm > real ).
thf(func_def_370,type,
sK213: option_trm > set_variable > produc1418842292n_game > trm > trm ).
thf(func_def_371,type,
sK214: option_trm > set_variable > produc1418842292n_game > trm > trm ).
thf(func_def_372,type,
sK215: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_373,type,
sK216: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_374,type,
sK217: ( option_fml > option_fml > $o ) > fml ).
thf(func_def_375,type,
sK218: ( option_fml > option_fml > $o ) > option_fml ).
thf(func_def_376,type,
sK219: ( option_fml > $o ) > fml ).
thf(func_def_377,type,
sK220: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_378,type,
sK221: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_379,type,
sK222: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_380,type,
sK223: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_381,type,
sK224: ( produc1418842292n_game > set_variable > trm > $o ) > char ).
thf(func_def_382,type,
sK225: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_383,type,
sK226: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_384,type,
sK227: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_385,type,
sK228: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_386,type,
sK229: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_387,type,
sK230: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_388,type,
sK231: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_389,type,
sK232: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_390,type,
sK233: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_391,type,
sK234: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_392,type,
sK235: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_393,type,
sK236: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_394,type,
sK237: ( produc1418842292n_game > set_variable > trm > $o ) > variable ).
thf(func_def_395,type,
sK238: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_396,type,
sK239: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_397,type,
sK240: ( produc1418842292n_game > set_variable > trm > $o ) > char ).
thf(func_def_398,type,
sK241: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_399,type,
sK242: ( produc1418842292n_game > set_variable > trm > $o ) > real ).
thf(func_def_400,type,
sK243: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_401,type,
sK244: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > produc799602994n_game ).
thf(func_def_402,type,
sK245: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > char > option_trm ).
thf(func_def_403,type,
sK246: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_404,type,
sK247: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_405,type,
sK248: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_406,type,
sK249: ( produc1418842292n_game > set_variable > trm > $o ) > char ).
thf(func_def_407,type,
sK250: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_408,type,
sK251: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_409,type,
sK252: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_410,type,
sK253: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_411,type,
sK254: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_412,type,
sK255: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_413,type,
sK256: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_414,type,
sK257: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_415,type,
sK258: ( produc1418842292n_game > set_variable > trm > $o ) > trm ).
thf(func_def_416,type,
sK259: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_417,type,
sK260: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_418,type,
sK261: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_419,type,
sK262: ( produc1418842292n_game > set_variable > trm > $o ) > char ).
thf(func_def_420,type,
sK263: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_421,type,
sK264: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_422,type,
sK265: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_423,type,
sK266: ( produc1418842292n_game > set_variable > trm > $o ) > real ).
thf(func_def_424,type,
sK267: ( produc1418842292n_game > set_variable > trm > $o ) > produc1418842292n_game ).
thf(func_def_425,type,
sK268: ( produc1418842292n_game > set_variable > trm > $o ) > set_variable ).
thf(func_def_426,type,
sK269: ( produc1418842292n_game > set_variable > trm > $o ) > variable ).
thf(func_def_429,type,
ph271:
!>[X0: $tType] : X0 ).
thf(f12225,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2401,f2409,f5857,f12213]) ).
thf(f12213,plain,
~ spl270_37,
inference(avatar_contradiction_clause,[status(thm)],[f12212]) ).
thf(f12212,plain,
( $false
| ~ spl270_37 ),
inference(trivial_inequality_removal,[status(thm)],[f12211]) ).
thf(f12211,plain,
( ( none_fml != none_fml )
| ~ spl270_37 ),
inference(superposition,[status(thm)],[f1777,f5850]) ).
thf(f5850,plain,
( ! [X1: trm] :
( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) ) )
| ~ spl270_37 ),
inference(avatar_component_clause,[status(thm)],[f5849]) ).
thf(f5849,definition,
( spl270_37
<=> ! [X1: trm] :
( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl270_37])],[avatar_definition]) ).
thf(f1777,plain,
( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
( none_fml
!= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_1_Pred_Oprems_I2_J) ).
thf(f5857,plain,
( spl270_37
| spl270_37
| spl270_2
| spl270_4 ),
inference(avatar_split_clause,[status(thm)],[f5856,f2385,f2375,f5849,f5849]) ).
thf(f2375,definition,
( spl270_2
<=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ) ),
introduced(definition,[new_symbols(naming,[spl270_2])],[avatar_definition]) ).
thf(f2385,definition,
( spl270_4
<=> ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ),
introduced(definition,[new_symbols(naming,[spl270_4])],[avatar_definition]) ).
thf(f5856,plain,
( ! [X0: trm,X1: trm] :
( ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X0 ) ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) ) ) )
| spl270_2
| spl270_4 ),
inference(subsumption_resolution,[status(thm)],[f5844,f2386]) ).
thf(f2386,plain,
( ( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) )
| spl270_4 ),
inference(avatar_component_clause,[status(thm)],[f2385]) ).
thf(f5844,plain,
( ! [X0: trm,X1: trm] :
( ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X0 ) ) ) )
| spl270_2
| spl270_4 ),
inference(trivial_inequality_removal,[status(thm)],[f5843]) ).
thf(f5843,plain,
( ! [X0: trm,X1: trm] :
( ( bot_bot_set_variable != bot_bot_set_variable )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X0 ) ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
| spl270_2
| spl270_4 ),
inference(superposition,[status(thm)],[f2705,f2026]) ).
thf(f2026,plain,
! [X2: char,X3: produc1418842292n_game,X0: set_variable,X1: trm] :
( ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) )
| ( none_fml
= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
| ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ ( sK166 @ X3 @ X2 @ X0 ) ) @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1418]) ).
thf(f1418,plain,
! [X0: set_variable,X1: trm,X2: char,X3: produc1418842292n_game] :
( ( none_fml
= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
| ( ( none_trm
!= ( uSubst516392818stappt @ X3 @ X0 @ X1 ) )
& ( ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) )
| ( ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ ( sK166 @ X3 @ X2 @ X0 ) ) @ X0 ) )
& ( ( some_fml @ ( sK166 @ X3 @ X2 @ X0 ) )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f1061,f1417]) ).
thf(f1417,plain,
! [X0: set_variable,X2: char,X3: produc1418842292n_game] :
( ? [X4: fml] :
( ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ X4 ) @ X0 ) )
& ( ( some_fml @ X4 )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) )
=> ( ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ ( sK166 @ X3 @ X2 @ X0 ) ) @ X0 ) )
& ( ( some_fml @ ( sK166 @ X3 @ X2 @ X0 ) )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1061,plain,
! [X0: set_variable,X1: trm,X2: char,X3: produc1418842292n_game] :
( ( none_fml
= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
| ( ( none_trm
!= ( uSubst516392818stappt @ X3 @ X0 @ X1 ) )
& ( ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) )
| ? [X4: fml] :
( ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ X4 ) @ X0 ) )
& ( ( some_fml @ X4 )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f488]) ).
thf(f488,plain,
! [X0: set_variable,X1: trm,X2: char,X3: produc1418842292n_game] :
( ( none_fml
!= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X3 @ X0 @ X1 ) )
& ( ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) )
| ? [X4: fml] :
( ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ X4 ) @ X0 ) )
& ( ( some_fml @ X4 )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f487]) ).
thf(f487,plain,
! [X0: set_variable,X1: trm,X2: char,X3: produc1418842292n_game] :
( ( none_fml
!= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X3 @ X0 @ X1 ) )
& ( ? [X4: fml] :
( ( ( produc1250175341on_fml
@ ^ [X5: char > option_trm] :
( produc1615133358on_fml
@ ^ [X6: char > option_trm] :
( produc1420172399on_fml
@ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
@ X3
@ X2 )
= ( some_fml @ X4 ) )
& ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ X4 ) @ X0 ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [X9: char > option_trm] :
( produc1615133358on_fml
@ ^ [X10: char > option_trm] :
( produc1420172399on_fml
@ ^ [X11: char > option_fml,X12: char > option_game] : X11 ) )
@ X3
@ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f140]) ).
thf(f140,axiom,
! [X30: set_variable,X31: trm,X28: char,X27: produc1418842292n_game] :
( ( none_fml
!= ( uSubst516392804stappf @ X27 @ X30 @ ( pred @ X28 @ X31 ) ) )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X27 @ X30 @ X31 ) )
& ( ? [X63: fml] :
( ( ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ X27
@ X28 )
= ( some_fml @ X63 ) )
& ( bot_bot_set_variable
= ( inf_inf_set_variable @ ( static_FVF @ X63 ) @ X30 ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ X27
@ X28 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_139_usubstappf__pred__conv) ).
thf(f2705,plain,
( ! [X0: set_variable,X1: trm] :
( ( bot_bot_set_variable
!= ( inf_inf_set_variable @ ( static_FVF @ ( sK166 @ sigma @ p @ X0 ) ) @ va ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ X0 @ ( pred @ p @ X1 ) ) ) )
| spl270_2
| spl270_4 ),
inference(forward_demodulation,[status(thm)],[f2704,f1593]) ).
thf(f1593,plain,
! [X0: fml] :
( ( the_fml @ ( some_fml @ X0 ) )
= X0 ),
inference(cnf_transformation,[status(thm)],[f797]) ).
thf(f797,plain,
! [X0: fml] :
( ( the_fml @ ( some_fml @ X0 ) )
= X0 ),
inference(rectify,[status(thm)],[f131]) ).
thf(f131,axiom,
! [X40: fml] :
( ( the_fml @ ( some_fml @ X40 ) )
= X40 ),
file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_130_option_Osel) ).
thf(f2704,plain,
( ! [X0: set_variable,X1: trm] :
( ( bot_bot_set_variable
!= ( inf_inf_set_variable @ ( static_FVF @ ( the_fml @ ( some_fml @ ( sK166 @ sigma @ p @ X0 ) ) ) ) @ va ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ X0 @ ( pred @ p @ X1 ) ) ) )
| spl270_2
| spl270_4 ),
inference(subsumption_resolution,[status(thm)],[f2688,f2386]) ).
thf(f2688,plain,
( ! [X0: set_variable,X1: trm] :
( ( bot_bot_set_variable
!= ( inf_inf_set_variable @ ( static_FVF @ ( the_fml @ ( some_fml @ ( sK166 @ sigma @ p @ X0 ) ) ) ) @ va ) )
| ( none_fml
= ( uSubst516392804stappf @ sigma @ X0 @ ( pred @ p @ X1 ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
| spl270_2 ),
inference(superposition,[status(thm)],[f2376,f2025]) ).
thf(f2025,plain,
! [X2: char,X3: produc1418842292n_game,X0: set_variable,X1: trm] :
( ( ( some_fml @ ( sK166 @ X3 @ X2 @ X0 ) )
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) )
| ( none_fml
= ( uSubst516392804stappf @ X3 @ X0 @ ( pred @ X2 @ X1 ) ) )
| ( none_fml
= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ X3
@ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1418]) ).
thf(f2376,plain,
( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
| spl270_2 ),
inference(avatar_component_clause,[status(thm)],[f2375]) ).
thf(f2409,plain,
~ spl270_4,
inference(avatar_split_clause,[status(thm)],[f1873,f2385]) ).
thf(f1873,plain,
( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ),
inference(cnf_transformation,[status(thm)],[f862]) ).
thf(f862,plain,
( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ),
inference(flattening,[status(thm)],[f528]) ).
thf(f528,plain,
( none_fml
!= ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ),
inference(fool_elimination,[status(thm)],[f527]) ).
thf(f527,plain,
( ( produc1250175341on_fml
@ ^ [X0: char > option_trm] :
( produc1615133358on_fml
@ ^ [X1: char > option_trm] :
( produc1420172399on_fml
@ ^ [X2: char > option_fml,X3: char > option_game] : X2 ) )
@ sigma
@ p )
!= none_fml ),
inference(rectify,[status(thm)],[f359]) ).
thf(f359,negated_conjecture,
( ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ sigma
@ p )
!= none_fml ),
inference(negated_conjecture,[status(cth)],[f358]) ).
thf(f358,conjecture,
( ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ sigma
@ p )
= none_fml ),
file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',conj_0) ).
thf(f2401,plain,
~ spl270_2,
inference(avatar_split_clause,[status(thm)],[f1936,f2375]) ).
thf(f1936,plain,
( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ),
inference(cnf_transformation,[status(thm)],[f957]) ).
thf(f957,plain,
( ( none_fml
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) )
& ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) ) ),
inference(ennf_transformation,[status(thm)],[f771]) ).
thf(f771,plain,
~ ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( none_fml
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [Y0: char > option_trm] :
( produc1615133358on_fml
@ ^ [Y1: char > option_trm] :
( produc1420172399on_fml
@ ^ [Y2: char > option_fml,Y3: char > option_game] : Y2 ) )
@ sigma
@ p ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f770]) ).
thf(f770,plain,
~ ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X0: char > option_trm] :
( produc1615133358on_fml
@ ^ [X1: char > option_trm] :
( produc1420172399on_fml
@ ^ [X2: char > option_fml,X3: char > option_game] : X2 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ p ) ) )
= none_fml ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
~ ( ( bot_bot_set_variable
!= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ sigma
@ p ) ) )
@ va ) )
=> ( ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X8: char > option_trm] :
( produc1615133358on_fml
@ ^ [X9: char > option_trm] :
( produc1420172399on_fml
@ ^ [X10: char > option_fml,X11: char > option_game] : X10 ) )
@ sigma
@ p ) ) )
= none_fml ) ),
file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP203^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:29:55 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : ITP203^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.47 % Domain : Interactive Theorem Proving
% 0.20/0.47 % Problem : Sledgehammer USubst problem prob_534__6335794_1
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Des21]
% 0.20/0.47 % Names : USubst/prob_534__6335794_1 [Des21]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0
% 0.20/0.47 % Syntax : Number of formulae : 501 ( 247 unt; 143 typ; 0 def)
% 0.20/0.47 % Number of atoms : 842 ( 658 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 31 ( 2 avg)
% 0.20/0.47 % Number of connectives : 3409 ( 189 ~; 14 |; 44 &;2816 @)
% 0.20/0.47 % ( 0 <=>; 346 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 26 ( 5 avg)
% 0.20/0.47 % Number of types : 28 ( 27 usr)
% 0.20/0.47 % Number of type conns : 993 ( 993 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 119 ( 116 usr; 17 con; 0-8 aty)
% 0.20/0.47 % Number of variables : 1376 ( 387 ^; 971 !; 18 ?;1376 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:41.418
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % Could-be-implicit typings (27)
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1699626005le_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__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_J,type,
% 0.20/0.47 set_Pr720454634n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 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,
% 0.20/0.47 produc1418842292n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__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,
% 0.20/0.47 set_Pr739694057n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 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__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J,type,
% 0.20/0.47 produc62062515n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__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,type,
% 0.20/0.47 set_Pr79606376n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__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,type,
% 0.20/0.47 produc799602994n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.20/0.47 produc1016592119n_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1739631244on_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1072747943on_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc46605351on_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.20/0.47 set_Pr943832262on_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.20/0.47 set_Pr1235432374le_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1024976764on_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1408538418on_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc464795408on_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.20/0.47 produc1367888000le_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.20/0.47 option_game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 option_trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 option_fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.20/0.47 set_variable: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ovariable,type,
% 0.20/0.47 variable: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ogame,type,
% 0.20/0.47 game: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__String__Ochar,type,
% 0.20/0.47 char: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Otrm,type,
% 0.20/0.47 trm: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Syntax__Ofml,type,
% 0.20/0.47 fml: $tType ).
% 0.20/0.47
% 0.20/0.47 thf(ty_n_t__Real__Oreal,type,
% 0.20/0.47 real: $tType ).
% 0.20/0.47
% 0.20/0.47 % Explicit typings (116)
% 0.20/0.47 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 if_option_fml: $o > option_fml > option_fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 0.20/0.47 inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 0.20/0.47 inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
% 0.20/0.47
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% 0.20/0.47 inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
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% 0.20/0.47
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
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% 0.20/0.47
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% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
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% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
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% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
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% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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_J,type,
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% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
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% 0.20/0.47 produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
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% 0.20/0.47 thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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,type,
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% 0.20/0.47
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% 0.20/0.47 produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
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% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.20/0.47 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__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_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.20/0.47 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_Eo,type,
% 0.20/0.47 produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_Eo,type,
% 0.20/0.47 produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.20/0.47 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.20/0.47 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.20/0.47 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_Eo,type,
% 0.20/0.47 produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.20/0.47 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001_Eo,type,
% 0.20/0.47 produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001_Eo,type,
% 0.20/0.47 produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.20/0.47 collect_variable: ( variable > $o ) > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_c_Static__Semantics_OFVF,type,
% 0.20/0.47 static_FVF: fml > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Static__Semantics_OFVT,type,
% 0.20/0.47 static_FVT: trm > set_variable ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_String_Ochar_OChar,type,
% 0.20/0.47 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.20/0.47 geq: trm > trm > fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Ofml_OPred,type,
% 0.20/0.47 pred: char > trm > fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.20/0.47 const: char > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.20/0.47 differential: trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.20/0.47 func: char > trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.20/0.47 number: real > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.20/0.47 plus: trm > trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.20/0.47 times: trm > trm > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.20/0.47 var: variable > trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 0.20/0.47 uSubst716837505ntialo: option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 0.20/0.47 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 0.20/0.47 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto,type,
% 0.20/0.47 uSubst1367128042_Testo: option_fml > option_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 0.20/0.47 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odot,type,
% 0.20/0.47 uSubst_Mirabelle_dot: trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 0.20/0.47 uSubst1408967625substt: trm > produc1418842292n_game ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 0.20/0.47 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 0.20/0.47 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.20/0.47 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 0.20/0.47 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.20/0.47 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__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,type,
% 0.20/0.47 member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
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% 0.20/0.47 thf(sy_c_member_001t__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,type,
% 0.20/0.47 member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
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% 0.20/0.47 thf(sy_c_member_001t__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,
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% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
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% 0.20/0.47 thf(sy_c_member_001t__Syntax__Ovariable,type,
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% 0.20/0.47 thf(sy_v_Ua____,type,
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% 0.20/0.47 thf(sy_v_Va____,type,
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% 0.20/0.47 thf(sy_v__092_060sigma_062,type,
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% 0.20/0.47
% 0.20/0.47 thf(sy_v__092_060theta_062____,type,
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% 0.20/0.47 thf(sy_v_p____,type,
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% 0.20/0.47
% 0.20/0.47 % Relevant facts (352)
% 0.20/0.47 thf(fact_0_f7,axiom,
% 0.20/0.47 ! [Z: option_fml,F: fml > option_fml,Za: option_fml] :
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% 0.20/0.47 => ( ( case_o209804997ml_fml @ Z @ F @ Za )
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% 0.20/0.47 => ( ( case_o209804997ml_fml @ Z @ F @ Za )
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% 0.20/0.47
% 0.20/0.47 % f7
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% 0.20/0.47 % Pred.prems(2)
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% 0.20/0.47 % case_prod_app
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% 0.20/0.47 ( produc692578258on_trm
% 0.20/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_4_case__prod__app,axiom,
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 0.20/0.47 ( produc154833544on_fml
% 0.20/0.47 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_5_case__prod__app,axiom,
% 0.20/0.47 ( produc1036610745on_trm
% 0.20/0.47 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 0.20/0.47 ( produc885547027on_trm
% 0.20/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_6_case__prod__app,axiom,
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 0.20/0.47 ( produc347802313on_fml
% 0.20/0.47 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 0.20/0.47 @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % case_prod_app
% 0.20/0.47 thf(fact_7_Pred_Oprems_I1_J,axiom,
% 0.20/0.47 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 != none_fml ) ).
% 0.20/0.47
% 0.20/0.47 % Pred.prems(1)
% 0.20/0.47 thf(fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,axiom,
% 0.20/0.47 ~ ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 => ( none_fml
% 0.20/0.47 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>(if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff) \<noteq> usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p))\<close>
% 0.20/0.47 thf(fact_9_f9,axiom,
% 0.20/0.47 ( ( ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p )
% 0.20/0.47 = none_fml )
% 0.20/0.47 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % f9
% 0.20/0.47 thf(fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,axiom,
% 0.20/0.47 ~ ( ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 => ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 0.20/0.47 @ ^ [F2: fml] :
% 0.20/0.47 ( if_option_fml
% 0.20/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.20/0.47 @ none_fml )
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) )
% 0.20/0.47 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 => ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 0.20/0.47 @ ^ [F2: fml] :
% 0.20/0.47 ( if_option_fml
% 0.20/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.20/0.47 @ none_fml )
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) )
% 0.20/0.47 = none_fml ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>(case SPreds \<sigma> p of None \<Rightarrow> Afml (Pred p (the (usubstappt \<sigma> V \<theta>))) | Some f \<Rightarrow> if FVF f \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} f else undeff) \<noteq> (if FVF (the (SPreds \<sigma> p)) \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} (the (SPreds \<sigma> p)) else undeff)\<close>
% 0.20/0.47 thf(fact_11_Ando_Oinduct,axiom,
% 0.20/0.47 ! [P2: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 0.20/0.47 ( ! [Phi: fml,Psi: fml] : ( P2 @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) )
% 0.20/0.47 => ( ! [X_1: option_fml] : ( P2 @ none_fml @ X_1 )
% 0.20/0.47 => ( ! [V: fml] : ( P2 @ ( some_fml @ V ) @ none_fml )
% 0.20/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Ando.induct
% 0.20/0.47 thf(fact_12_Testo_Ocases,axiom,
% 0.20/0.47 ! [X2: option_fml] :
% 0.20/0.47 ( ! [Phi: fml] :
% 0.20/0.47 ( X2
% 0.20/0.47 != ( some_fml @ Phi ) )
% 0.20/0.47 => ( X2 = none_fml ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.cases
% 0.20/0.47 thf(fact_13_Testo_Oinduct,axiom,
% 0.20/0.47 ! [P2: option_fml > $o,A0: option_fml] :
% 0.20/0.47 ( ! [Phi: fml] : ( P2 @ ( some_fml @ Phi ) )
% 0.20/0.47 => ( ( P2 @ none_fml )
% 0.20/0.47 => ( P2 @ A0 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Testo.induct
% 0.20/0.47 thf(fact_14_undeff__equiv,axiom,
% 0.20/0.47 ! [Phi2: option_fml] :
% 0.20/0.47 ( ( Phi2 != none_fml )
% 0.20/0.47 = ( ? [F2: fml] :
% 0.20/0.47 ( Phi2
% 0.20/0.47 = ( some_fml @ F2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % undeff_equiv
% 0.20/0.47 thf(fact_15_Existso_Oinduct,axiom,
% 0.20/0.47 ! [P2: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 0.20/0.47 ( ! [X3: variable,Phi: fml] : ( P2 @ X3 @ ( some_fml @ Phi ) )
% 0.20/0.47 => ( ! [X3: variable] : ( P2 @ X3 @ none_fml )
% 0.20/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Existso.induct
% 0.20/0.47 thf(fact_16_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_17_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_18_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc885547027on_trm @ F3 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_19_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_trm > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc885547027on_trm @ F3 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_20_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_trm ) > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_21_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_trm ) > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_22_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_fml ) > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc347802313on_fml
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_23_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: ( char > option_fml ) > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc885547027on_trm
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_24_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc1036610745on_trm
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_25_prod_Ocase__distrib,axiom,
% 0.20/0.47 ! [H: option_fml > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 0.20/0.47 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 0.20/0.47 = ( produc1420172399on_fml
% 0.20/0.47 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 0.20/0.47 @ Prod ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.case_distrib
% 0.20/0.47 thf(fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
% 0.20/0.47 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 != ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>usubstappf \<sigma> U (Pred p \<theta>) \<noteq> usubstappf \<sigma> V (Pred p \<theta>)\<close>
% 0.20/0.47 thf(fact_27_f5,axiom,
% 0.20/0.47 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 0.20/0.47 = ( uSubst516392818stappt @ sigma @ va @ theta ) ) ).
% 0.20/0.47
% 0.20/0.47 % f5
% 0.20/0.47 thf(fact_28_calculation_I1_J,axiom,
% 0.20/0.47 ~ ( ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 = bot_bot_set_variable )
% 0.20/0.47 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) ) ) )
% 0.20/0.47 & ( ( ( inf_inf_set_variable
% 0.20/0.47 @ ( static_FVF
% 0.20/0.47 @ ( the_fml
% 0.20/0.47 @ ( produc1250175341on_fml
% 0.20/0.47 @ ^ [Uu: char > option_trm] :
% 0.20/0.47 ( produc1615133358on_fml
% 0.20/0.47 @ ^ [Uv: char > option_trm] :
% 0.20/0.47 ( produc1420172399on_fml
% 0.20/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.20/0.47 @ sigma
% 0.20/0.47 @ p ) ) )
% 0.20/0.47 @ va )
% 0.20/0.47 != bot_bot_set_variable )
% 0.20/0.47 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 = none_fml ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % calculation(1)
% 0.20/0.47 thf(fact_29_calculation_I2_J,axiom,
% 0.20/0.47 ( ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.20/0.47 != ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 0.32/0.47 @ ( the_fml
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) ) ) )
% 0.32/0.47 => ( ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p )
% 0.32/0.47 = none_fml ) ) ).
% 0.32/0.47
% 0.32/0.47 % calculation(2)
% 0.32/0.47 thf(fact_30_f6,axiom,
% 0.32/0.47 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.32/0.47 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % f6
% 0.32/0.47 thf(fact_31__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_A_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_092_060close_062,axiom,
% 0.32/0.47 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 0.32/0.47 != ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<open>usubstappf \<sigma> U (Pred p \<theta>) \<noteq> (case SPreds \<sigma> p of None \<Rightarrow> Afml (Pred p (the (usubstappt \<sigma> V \<theta>))) | Some f \<Rightarrow> if FVF f \<inter> V = {} then usubstappf (dotsubstt (the (usubstappt \<sigma> V \<theta>))) {} f else undeff)\<close>
% 0.32/0.47 thf(fact_32_usubstappf__pred2,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,P3: char,R2: fml,U: set_variable,Theta: trm] :
% 0.32/0.47 ( ( ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ Sigma
% 0.32/0.47 @ P3 )
% 0.32/0.47 = ( some_fml @ R2 ) )
% 0.32/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 0.32/0.47 != bot_bot_set_variable )
% 0.32/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.32/0.47 = none_fml ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_pred2
% 0.32/0.47 thf(fact_33_f3,axiom,
% 0.32/0.47 ( ( case_o325794063ml_trm @ none_fml
% 0.32/0.47 @ ^ [T: trm] :
% 0.32/0.47 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) )
% 0.32/0.47 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 0.32/0.47 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % f3
% 0.32/0.47 thf(fact_34_f8,axiom,
% 0.32/0.47 ( ( case_o325794063ml_trm @ none_fml
% 0.32/0.47 @ ^ [T: trm] :
% 0.32/0.47 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) )
% 0.32/0.47 @ ( uSubst516392818stappt @ sigma @ va @ theta ) )
% 0.32/0.47 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % f8
% 0.32/0.47 thf(fact_35_f1,axiom,
% 0.32/0.47 ( ( case_o325794063ml_trm @ none_fml
% 0.32/0.47 @ ^ [T: trm] :
% 0.32/0.47 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) )
% 0.32/0.47 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 0.32/0.47 != none_fml ) ).
% 0.32/0.47
% 0.32/0.47 % f1
% 0.32/0.47 thf(fact_36_f4,axiom,
% 0.32/0.47 ( ( case_o325794063ml_trm @ none_fml
% 0.32/0.47 @ ^ [T: trm] :
% 0.32/0.47 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 0.32/0.47 @ ^ [F2: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ sigma
% 0.32/0.47 @ p ) )
% 0.32/0.47 @ ( uSubst516392818stappt @ sigma @ va @ theta ) )
% 0.32/0.47 != none_fml ) ).
% 0.32/0.47
% 0.32/0.47 % f4
% 0.32/0.47 thf(fact_37_option_Ocollapse,axiom,
% 0.32/0.47 ! [Option: option_fml] :
% 0.32/0.47 ( ( Option != none_fml )
% 0.32/0.47 => ( ( some_fml @ ( the_fml @ Option ) )
% 0.32/0.47 = Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.collapse
% 0.32/0.47 thf(fact_38_option_Ocollapse,axiom,
% 0.32/0.47 ! [Option: option_trm] :
% 0.32/0.47 ( ( Option != none_trm )
% 0.32/0.47 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.32/0.47 = Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.collapse
% 0.32/0.47 thf(fact_39_option_Ocollapse,axiom,
% 0.32/0.47 ! [Option: option_game] :
% 0.32/0.47 ( ( Option != none_game )
% 0.32/0.47 => ( ( some_game @ ( the_game @ Option ) )
% 0.32/0.47 = Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.collapse
% 0.32/0.47 thf(fact_40_not__Some__eq,axiom,
% 0.32/0.47 ! [X2: option_fml] :
% 0.32/0.47 ( ( ! [Y: fml] :
% 0.32/0.47 ( X2
% 0.32/0.47 != ( some_fml @ Y ) ) )
% 0.32/0.47 = ( X2 = none_fml ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_Some_eq
% 0.32/0.47 thf(fact_41_not__Some__eq,axiom,
% 0.32/0.47 ! [X2: option_trm] :
% 0.32/0.47 ( ( ! [Y: trm] :
% 0.32/0.47 ( X2
% 0.32/0.47 != ( some_trm @ Y ) ) )
% 0.32/0.47 = ( X2 = none_trm ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_Some_eq
% 0.32/0.47 thf(fact_42_not__Some__eq,axiom,
% 0.32/0.47 ! [X2: option_game] :
% 0.32/0.47 ( ( ! [Y: game] :
% 0.32/0.47 ( X2
% 0.32/0.47 != ( some_game @ Y ) ) )
% 0.32/0.47 = ( X2 = none_game ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_Some_eq
% 0.32/0.47 thf(fact_43_not__None__eq,axiom,
% 0.32/0.47 ! [X2: option_fml] :
% 0.32/0.47 ( ( X2 != none_fml )
% 0.32/0.47 = ( ? [Y: fml] :
% 0.32/0.47 ( X2
% 0.32/0.47 = ( some_fml @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_None_eq
% 0.32/0.47 thf(fact_44_not__None__eq,axiom,
% 0.32/0.47 ! [X2: option_trm] :
% 0.32/0.47 ( ( X2 != none_trm )
% 0.32/0.47 = ( ? [Y: trm] :
% 0.32/0.47 ( X2
% 0.32/0.47 = ( some_trm @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_None_eq
% 0.32/0.47 thf(fact_45_not__None__eq,axiom,
% 0.32/0.47 ! [X2: option_game] :
% 0.32/0.47 ( ( X2 != none_game )
% 0.32/0.47 = ( ? [Y: game] :
% 0.32/0.47 ( X2
% 0.32/0.47 = ( some_game @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_None_eq
% 0.32/0.47 thf(fact_46_usubstappf_Osimps_I1_J,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,P3: char,Theta: trm] :
% 0.32/0.47 ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.32/0.47 = ( case_o325794063ml_trm @ none_fml
% 0.32/0.47 @ ^ [Sigma_theta: trm] :
% 0.32/0.47 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ P3 @ Sigma_theta ) )
% 0.32/0.47 @ ^ [R: fml] :
% 0.32/0.47 ( if_option_fml
% 0.32/0.47 @ ( ( inf_inf_set_variable @ ( static_FVF @ R ) @ U )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.32/0.47 @ none_fml )
% 0.32/0.47 @ ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ Sigma
% 0.32/0.47 @ P3 ) )
% 0.32/0.47 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf.simps(1)
% 0.32/0.47 thf(fact_47_inf__bot__left,axiom,
% 0.32/0.47 ! [X2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X2 )
% 0.32/0.47 = bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % inf_bot_left
% 0.32/0.47 thf(fact_48_inf__bot__right,axiom,
% 0.32/0.47 ! [X2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ bot_bot_set_variable )
% 0.32/0.47 = bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % inf_bot_right
% 0.32/0.47 thf(fact_49_option_Osplit__sel__asm,axiom,
% 0.32/0.47 ! [P2: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.32/0.47 ( ( P2 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ~ ( ( ( Option = none_fml )
% 0.32/0.47 & ~ ( P2 @ F1 ) )
% 0.32/0.47 | ( ( Option
% 0.32/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.32/0.47 & ~ ( P2 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel_asm
% 0.32/0.47 thf(fact_50_option_Osplit__sel__asm,axiom,
% 0.32/0.47 ! [P2: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.32/0.47 ( ( P2 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.32/0.47 & ~ ( P2 @ F1 ) )
% 0.32/0.47 | ( ( Option
% 0.32/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.32/0.47 & ~ ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel_asm
% 0.32/0.47 thf(fact_51_option_Osplit__sel__asm,axiom,
% 0.32/0.47 ! [P2: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.32/0.47 ( ( P2 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ~ ( ( ( Option = none_trm )
% 0.32/0.47 & ~ ( P2 @ F1 ) )
% 0.32/0.47 | ( ( Option
% 0.32/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.32/0.47 & ~ ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel_asm
% 0.32/0.47 thf(fact_52_f2,axiom,
% 0.32/0.47 ! [Z: option_fml,F: trm > option_fml,Za: option_trm] :
% 0.32/0.47 ( ( ( Za = none_trm )
% 0.32/0.47 => ( ( case_o325794063ml_trm @ Z @ F @ Za )
% 0.32/0.47 = Z ) )
% 0.32/0.47 & ( ( Za != none_trm )
% 0.32/0.47 => ( ( case_o325794063ml_trm @ Z @ F @ Za )
% 0.32/0.47 = ( F @ ( the_trm @ Za ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % f2
% 0.32/0.47 thf(fact_53_inf__right__idem,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Y2 )
% 0.32/0.47 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_right_idem
% 0.32/0.47 thf(fact_54_inf_Oright__idem,axiom,
% 0.32/0.47 ! [A: set_variable,B: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ B )
% 0.32/0.47 = ( inf_inf_set_variable @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.right_idem
% 0.32/0.47 thf(fact_55_inf__left__idem,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ X2 @ Y2 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_left_idem
% 0.32/0.47 thf(fact_56_inf_Oleft__idem,axiom,
% 0.32/0.47 ! [A: set_variable,B: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B ) )
% 0.32/0.47 = ( inf_inf_set_variable @ A @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.left_idem
% 0.32/0.47 thf(fact_57_inf__idem,axiom,
% 0.32/0.47 ! [X2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ X2 )
% 0.32/0.47 = X2 ) ).
% 0.32/0.47
% 0.32/0.47 % inf_idem
% 0.32/0.47 thf(fact_58_inf_Oidem,axiom,
% 0.32/0.47 ! [A: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A @ A )
% 0.32/0.47 = A ) ).
% 0.32/0.47
% 0.32/0.47 % inf.idem
% 0.32/0.47 thf(fact_59_option_Oinject,axiom,
% 0.32/0.47 ! [X23: fml,Y22: fml] :
% 0.32/0.47 ( ( ( some_fml @ X23 )
% 0.32/0.47 = ( some_fml @ Y22 ) )
% 0.32/0.47 = ( X23 = Y22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inject
% 0.32/0.47 thf(fact_60_option_Oinject,axiom,
% 0.32/0.47 ! [X23: trm,Y22: trm] :
% 0.32/0.47 ( ( ( some_trm @ X23 )
% 0.32/0.47 = ( some_trm @ Y22 ) )
% 0.32/0.47 = ( X23 = Y22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inject
% 0.32/0.47 thf(fact_61_option_Oinject,axiom,
% 0.32/0.47 ! [X23: game,Y22: game] :
% 0.32/0.47 ( ( ( some_game @ X23 )
% 0.32/0.47 = ( some_game @ Y22 ) )
% 0.32/0.47 = ( X23 = Y22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inject
% 0.32/0.47 thf(fact_62_usubstappf__pred,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,P3: char,R2: fml,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 0.32/0.47 ( ( ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ Sigma
% 0.32/0.47 @ P3 )
% 0.32/0.47 = ( some_fml @ R2 ) )
% 0.32/0.47 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 = ( some_trm @ Sigma_theta2 ) )
% 0.32/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.32/0.47 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_pred
% 0.32/0.47 thf(fact_63_Diamondo_Oinduct,axiom,
% 0.32/0.47 ! [P2: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 0.32/0.47 ( ! [Alpha: game,Phi: fml] : ( P2 @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) )
% 0.32/0.47 => ( ! [X_1: option_fml] : ( P2 @ none_game @ X_1 )
% 0.32/0.47 => ( ! [V: game] : ( P2 @ ( some_game @ V ) @ none_fml )
% 0.32/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Diamondo.induct
% 0.32/0.47 thf(fact_64_option_Odisc__eq__case_I2_J,axiom,
% 0.32/0.47 ! [Option: option_fml] :
% 0.32/0.47 ( ( Option != none_fml )
% 0.32/0.47 = ( case_option_o_fml @ $false
% 0.32/0.47 @ ^ [Uu: fml] : $true
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(2)
% 0.32/0.47 thf(fact_65_option_Odisc__eq__case_I2_J,axiom,
% 0.32/0.47 ! [Option: option_trm] :
% 0.32/0.47 ( ( Option != none_trm )
% 0.32/0.47 = ( case_option_o_trm @ $false
% 0.32/0.47 @ ^ [Uu: trm] : $true
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(2)
% 0.32/0.47 thf(fact_66_option_Odisc__eq__case_I2_J,axiom,
% 0.32/0.47 ! [Option: option_game] :
% 0.32/0.47 ( ( Option != none_game )
% 0.32/0.47 = ( case_option_o_game @ $false
% 0.32/0.47 @ ^ [Uu: game] : $true
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(2)
% 0.32/0.47 thf(fact_67_option_Odisc__eq__case_I1_J,axiom,
% 0.32/0.47 ! [Option: option_fml] :
% 0.32/0.47 ( ( Option = none_fml )
% 0.32/0.47 = ( case_option_o_fml @ $true
% 0.32/0.47 @ ^ [Uu: fml] : $false
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(1)
% 0.32/0.47 thf(fact_68_option_Odisc__eq__case_I1_J,axiom,
% 0.32/0.47 ! [Option: option_trm] :
% 0.32/0.47 ( ( Option = none_trm )
% 0.32/0.47 = ( case_option_o_trm @ $true
% 0.32/0.47 @ ^ [Uu: trm] : $false
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(1)
% 0.32/0.47 thf(fact_69_option_Odisc__eq__case_I1_J,axiom,
% 0.32/0.47 ! [Option: option_game] :
% 0.32/0.47 ( ( Option = none_game )
% 0.32/0.47 = ( case_option_o_game @ $true
% 0.32/0.47 @ ^ [Uu: game] : $false
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.disc_eq_case(1)
% 0.32/0.47 thf(fact_70_usubstappt__det,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V2: set_variable] :
% 0.32/0.47 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 != none_trm )
% 0.32/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ V2 @ Theta )
% 0.32/0.47 != none_trm )
% 0.32/0.47 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 = ( uSubst516392818stappt @ Sigma @ V2 @ Theta ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappt_det
% 0.32/0.47 thf(fact_71_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: variable,P2: variable > $o] :
% 0.32/0.47 ( ( member_variable @ A @ ( collect_variable @ P2 ) )
% 0.32/0.47 = ( P2 @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_72_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ( collect_variable
% 0.32/0.47 @ ^ [X: variable] : ( member_variable @ X @ A2 ) )
% 0.32/0.47 = A2 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_73_Collect__cong,axiom,
% 0.32/0.47 ! [P2: variable > $o,Q: variable > $o] :
% 0.32/0.47 ( ! [X3: variable] :
% 0.32/0.47 ( ( P2 @ X3 )
% 0.32/0.47 = ( Q @ X3 ) )
% 0.32/0.47 => ( ( collect_variable @ P2 )
% 0.32/0.47 = ( collect_variable @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_74_case__optionE,axiom,
% 0.32/0.47 ! [P2: $o,Q: fml > $o,X2: option_fml] :
% 0.32/0.47 ( ( case_option_o_fml @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( ( X2 = none_fml )
% 0.32/0.47 => ~ P2 )
% 0.32/0.47 => ~ ! [Y3: fml] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_fml @ Y3 ) )
% 0.32/0.47 => ~ ( Q @ Y3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % case_optionE
% 0.32/0.47 thf(fact_75_case__optionE,axiom,
% 0.32/0.47 ! [P2: $o,Q: trm > $o,X2: option_trm] :
% 0.32/0.47 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( ( X2 = none_trm )
% 0.32/0.47 => ~ P2 )
% 0.32/0.47 => ~ ! [Y3: trm] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_trm @ Y3 ) )
% 0.32/0.47 => ~ ( Q @ Y3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % case_optionE
% 0.32/0.47 thf(fact_76_case__optionE,axiom,
% 0.32/0.47 ! [P2: $o,Q: game > $o,X2: option_game] :
% 0.32/0.47 ( ( case_option_o_game @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( ( X2 = none_game )
% 0.32/0.47 => ~ P2 )
% 0.32/0.47 => ~ ! [Y3: game] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_game @ Y3 ) )
% 0.32/0.47 => ~ ( Q @ Y3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % case_optionE
% 0.32/0.47 thf(fact_77_inf__left__commute,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_left_commute
% 0.32/0.47 thf(fact_78_inf_Oleft__commute,axiom,
% 0.32/0.47 ! [B: set_variable,A: set_variable,C: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ B @ ( inf_inf_set_variable @ A @ C ) )
% 0.32/0.47 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.left_commute
% 0.32/0.47 thf(fact_79_inf__commute,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_commute
% 0.32/0.47 thf(fact_80_inf_Ocommute,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [A3: set_variable,B2: set_variable] : ( inf_inf_set_variable @ B2 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.commute
% 0.32/0.47 thf(fact_81_inf__assoc,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Z2 )
% 0.32/0.47 = ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_assoc
% 0.32/0.47 thf(fact_82_inf_Oassoc,axiom,
% 0.32/0.47 ! [A: set_variable,B: set_variable,C: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ C )
% 0.32/0.47 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf.assoc
% 0.32/0.47 thf(fact_83_boolean__algebra__cancel_Oinf2,axiom,
% 0.32/0.47 ! [B3: set_variable,K: set_variable,B: set_variable,A: set_variable] :
% 0.32/0.47 ( ( B3
% 0.32/0.47 = ( inf_inf_set_variable @ K @ B ) )
% 0.32/0.47 => ( ( inf_inf_set_variable @ A @ B3 )
% 0.32/0.47 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % boolean_algebra_cancel.inf2
% 0.32/0.47 thf(fact_84_boolean__algebra__cancel_Oinf1,axiom,
% 0.32/0.47 ! [A2: set_variable,K: set_variable,A: set_variable,B: set_variable] :
% 0.32/0.47 ( ( A2
% 0.32/0.47 = ( inf_inf_set_variable @ K @ A ) )
% 0.32/0.47 => ( ( inf_inf_set_variable @ A2 @ B )
% 0.32/0.47 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % boolean_algebra_cancel.inf1
% 0.32/0.47 thf(fact_85_inf__sup__aci_I1_J,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_sup_aci(1)
% 0.32/0.47 thf(fact_86_inf__sup__aci_I2_J,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Z2 )
% 0.32/0.47 = ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_sup_aci(2)
% 0.32/0.47 thf(fact_87_inf__sup__aci_I3_J,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X2 @ Z2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_sup_aci(3)
% 0.32/0.47 thf(fact_88_inf__sup__aci_I4_J,axiom,
% 0.32/0.47 ! [X2: set_variable,Y2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ X2 @ Y2 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_sup_aci(4)
% 0.32/0.47 thf(fact_89_option_Ocase__distrib,axiom,
% 0.32/0.47 ! [H: option_fml > option_fml,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.32/0.47 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( case_o209804997ml_fml @ ( H @ F1 )
% 0.32/0.47 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_distrib
% 0.32/0.47 thf(fact_90_option_Ocase__distrib,axiom,
% 0.32/0.47 ! [H: option_fml > option_fml,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.32/0.47 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( case_o325794063ml_trm @ ( H @ F1 )
% 0.32/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_distrib
% 0.32/0.47 thf(fact_91_option_Ocase__distrib,axiom,
% 0.32/0.47 ! [H: option_fml > option_trm,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.32/0.47 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( case_o487727941rm_trm @ ( H @ F1 )
% 0.32/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_distrib
% 0.32/0.47 thf(fact_92_option_Ocase__distrib,axiom,
% 0.32/0.47 ! [H: option_trm > option_fml,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.32/0.47 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( case_o325794063ml_trm @ ( H @ F1 )
% 0.32/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_distrib
% 0.32/0.47 thf(fact_93_option_Ocase__distrib,axiom,
% 0.32/0.47 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.32/0.47 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( case_o487727941rm_trm @ ( H @ F1 )
% 0.32/0.47 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 0.32/0.47 @ Option ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_distrib
% 0.32/0.47 thf(fact_94_option_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X23: fml] :
% 0.32/0.47 ( none_fml
% 0.32/0.47 != ( some_fml @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.distinct(1)
% 0.32/0.47 thf(fact_95_option_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X23: trm] :
% 0.32/0.47 ( none_trm
% 0.32/0.47 != ( some_trm @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.distinct(1)
% 0.32/0.47 thf(fact_96_option_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X23: game] :
% 0.32/0.47 ( none_game
% 0.32/0.47 != ( some_game @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.distinct(1)
% 0.32/0.47 thf(fact_97_option_OdiscI,axiom,
% 0.32/0.47 ! [Option: option_fml,X23: fml] :
% 0.32/0.47 ( ( Option
% 0.32/0.47 = ( some_fml @ X23 ) )
% 0.32/0.47 => ( Option != none_fml ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.discI
% 0.32/0.47 thf(fact_98_option_OdiscI,axiom,
% 0.32/0.47 ! [Option: option_trm,X23: trm] :
% 0.32/0.47 ( ( Option
% 0.32/0.47 = ( some_trm @ X23 ) )
% 0.32/0.47 => ( Option != none_trm ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.discI
% 0.32/0.47 thf(fact_99_option_OdiscI,axiom,
% 0.32/0.47 ! [Option: option_game,X23: game] :
% 0.32/0.47 ( ( Option
% 0.32/0.47 = ( some_game @ X23 ) )
% 0.32/0.47 => ( Option != none_game ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.discI
% 0.32/0.47 thf(fact_100_option_Oexhaust,axiom,
% 0.32/0.47 ! [Y2: option_fml] :
% 0.32/0.47 ( ( Y2 != none_fml )
% 0.32/0.47 => ~ ! [X24: fml] :
% 0.32/0.47 ( Y2
% 0.32/0.47 != ( some_fml @ X24 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust
% 0.32/0.47 thf(fact_101_option_Oexhaust,axiom,
% 0.32/0.47 ! [Y2: option_trm] :
% 0.32/0.47 ( ( Y2 != none_trm )
% 0.32/0.47 => ~ ! [X24: trm] :
% 0.32/0.47 ( Y2
% 0.32/0.47 != ( some_trm @ X24 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust
% 0.32/0.47 thf(fact_102_option_Oexhaust,axiom,
% 0.32/0.47 ! [Y2: option_game] :
% 0.32/0.47 ( ( Y2 != none_game )
% 0.32/0.47 => ~ ! [X24: game] :
% 0.32/0.47 ( Y2
% 0.32/0.47 != ( some_game @ X24 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust
% 0.32/0.47 thf(fact_103_option_Oinducts,axiom,
% 0.32/0.47 ! [P2: option_fml > $o,Option: option_fml] :
% 0.32/0.47 ( ( P2 @ none_fml )
% 0.32/0.47 => ( ! [X3: fml] : ( P2 @ ( some_fml @ X3 ) )
% 0.32/0.47 => ( P2 @ Option ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inducts
% 0.32/0.47 thf(fact_104_option_Oinducts,axiom,
% 0.32/0.47 ! [P2: option_trm > $o,Option: option_trm] :
% 0.32/0.47 ( ( P2 @ none_trm )
% 0.32/0.47 => ( ! [X3: trm] : ( P2 @ ( some_trm @ X3 ) )
% 0.32/0.47 => ( P2 @ Option ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inducts
% 0.32/0.47 thf(fact_105_option_Oinducts,axiom,
% 0.32/0.47 ! [P2: option_game > $o,Option: option_game] :
% 0.32/0.47 ( ( P2 @ none_game )
% 0.32/0.47 => ( ! [X3: game] : ( P2 @ ( some_game @ X3 ) )
% 0.32/0.47 => ( P2 @ Option ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.inducts
% 0.32/0.47 thf(fact_106_split__option__ex,axiom,
% 0.32/0.47 ( ( ^ [P4: option_fml > $o] :
% 0.32/0.47 ? [X4: option_fml] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_fml > $o] :
% 0.32/0.47 ( ( P @ none_fml )
% 0.32/0.47 | ? [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_ex
% 0.32/0.47 thf(fact_107_split__option__ex,axiom,
% 0.32/0.47 ( ( ^ [P4: option_trm > $o] :
% 0.32/0.47 ? [X4: option_trm] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_trm > $o] :
% 0.32/0.47 ( ( P @ none_trm )
% 0.32/0.47 | ? [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_ex
% 0.32/0.47 thf(fact_108_split__option__ex,axiom,
% 0.32/0.47 ( ( ^ [P4: option_game > $o] :
% 0.32/0.47 ? [X4: option_game] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_game > $o] :
% 0.32/0.47 ( ( P @ none_game )
% 0.32/0.47 | ? [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_ex
% 0.32/0.47 thf(fact_109_split__option__all,axiom,
% 0.32/0.47 ( ( ^ [P4: option_fml > $o] :
% 0.32/0.47 ! [X4: option_fml] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_fml > $o] :
% 0.32/0.47 ( ( P @ none_fml )
% 0.32/0.47 & ! [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_all
% 0.32/0.47 thf(fact_110_split__option__all,axiom,
% 0.32/0.47 ( ( ^ [P4: option_trm > $o] :
% 0.32/0.47 ! [X4: option_trm] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_trm > $o] :
% 0.32/0.47 ( ( P @ none_trm )
% 0.32/0.47 & ! [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_all
% 0.32/0.47 thf(fact_111_split__option__all,axiom,
% 0.32/0.47 ( ( ^ [P4: option_game > $o] :
% 0.32/0.47 ! [X4: option_game] : ( P4 @ X4 ) )
% 0.32/0.47 = ( ^ [P: option_game > $o] :
% 0.32/0.47 ( ( P @ none_game )
% 0.32/0.47 & ! [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % split_option_all
% 0.32/0.47 thf(fact_112_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_fml,P2: option_fml > option_fml > $o,Y2: option_fml] :
% 0.32/0.47 ( ( ( X2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: fml,B4: fml] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_fml @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_fml @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_113_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_fml,P2: option_fml > option_trm > $o,Y2: option_trm] :
% 0.32/0.47 ( ( ( X2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: fml,B4: trm] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_fml @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_trm @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_114_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_fml,P2: option_fml > option_game > $o,Y2: option_game] :
% 0.32/0.47 ( ( ( X2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: fml,B4: game] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_fml @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_game @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_115_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_trm,P2: option_trm > option_fml > $o,Y2: option_fml] :
% 0.32/0.47 ( ( ( X2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: trm,B4: fml] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_trm @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_fml @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_116_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_trm,P2: option_trm > option_trm > $o,Y2: option_trm] :
% 0.32/0.47 ( ( ( X2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: trm,B4: trm] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_trm @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_trm @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_117_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_trm,P2: option_trm > option_game > $o,Y2: option_game] :
% 0.32/0.47 ( ( ( X2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: trm,B4: game] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_trm @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_game @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_118_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_game,P2: option_game > option_fml > $o,Y2: option_fml] :
% 0.32/0.47 ( ( ( X2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_fml )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: game,B4: fml] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_game @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_fml @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_119_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_game,P2: option_game > option_trm > $o,Y2: option_trm] :
% 0.32/0.47 ( ( ( X2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_trm )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: game,B4: trm] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_game @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_trm @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_120_combine__options__cases,axiom,
% 0.32/0.47 ! [X2: option_game,P2: option_game > option_game > $o,Y2: option_game] :
% 0.32/0.47 ( ( ( X2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ( ( Y2 = none_game )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) )
% 0.32/0.47 => ( ! [A4: game,B4: game] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_game @ A4 ) )
% 0.32/0.47 => ( ( Y2
% 0.32/0.47 = ( some_game @ B4 ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) )
% 0.32/0.47 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % combine_options_cases
% 0.32/0.47 thf(fact_121_option_Osimps_I4_J,axiom,
% 0.32/0.47 ! [F1: option_fml,F22: fml > option_fml] :
% 0.32/0.47 ( ( case_o209804997ml_fml @ F1 @ F22 @ none_fml )
% 0.32/0.47 = F1 ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(4)
% 0.32/0.47 thf(fact_122_option_Osimps_I4_J,axiom,
% 0.32/0.47 ! [F1: option_fml,F22: trm > option_fml] :
% 0.32/0.47 ( ( case_o325794063ml_trm @ F1 @ F22 @ none_trm )
% 0.32/0.47 = F1 ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(4)
% 0.32/0.47 thf(fact_123_option_Osimps_I4_J,axiom,
% 0.32/0.47 ! [F1: option_trm,F22: trm > option_trm] :
% 0.32/0.47 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 0.32/0.47 = F1 ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(4)
% 0.32/0.47 thf(fact_124_option_Oexpand,axiom,
% 0.32/0.47 ! [Option: option_fml,Option2: option_fml] :
% 0.32/0.47 ( ( ( Option = none_fml )
% 0.32/0.47 = ( Option2 = none_fml ) )
% 0.32/0.47 => ( ( ( Option != none_fml )
% 0.32/0.47 => ( ( Option2 != none_fml )
% 0.32/0.47 => ( ( the_fml @ Option )
% 0.32/0.47 = ( the_fml @ Option2 ) ) ) )
% 0.32/0.47 => ( Option = Option2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.expand
% 0.32/0.47 thf(fact_125_option_Oexpand,axiom,
% 0.32/0.47 ! [Option: option_trm,Option2: option_trm] :
% 0.32/0.47 ( ( ( Option = none_trm )
% 0.32/0.47 = ( Option2 = none_trm ) )
% 0.32/0.47 => ( ( ( Option != none_trm )
% 0.32/0.47 => ( ( Option2 != none_trm )
% 0.32/0.47 => ( ( the_trm @ Option )
% 0.32/0.47 = ( the_trm @ Option2 ) ) ) )
% 0.32/0.47 => ( Option = Option2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.expand
% 0.32/0.47 thf(fact_126_option_Oexpand,axiom,
% 0.32/0.47 ! [Option: option_game,Option2: option_game] :
% 0.32/0.47 ( ( ( Option = none_game )
% 0.32/0.47 = ( Option2 = none_game ) )
% 0.32/0.47 => ( ( ( Option != none_game )
% 0.32/0.47 => ( ( Option2 != none_game )
% 0.32/0.47 => ( ( the_game @ Option )
% 0.32/0.47 = ( the_game @ Option2 ) ) ) )
% 0.32/0.47 => ( Option = Option2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.expand
% 0.32/0.47 thf(fact_127_option_Osimps_I5_J,axiom,
% 0.32/0.47 ! [F1: option_fml,F22: fml > option_fml,X23: fml] :
% 0.32/0.47 ( ( case_o209804997ml_fml @ F1 @ F22 @ ( some_fml @ X23 ) )
% 0.32/0.47 = ( F22 @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(5)
% 0.32/0.47 thf(fact_128_option_Osimps_I5_J,axiom,
% 0.32/0.47 ! [F1: option_fml,F22: trm > option_fml,X23: trm] :
% 0.32/0.47 ( ( case_o325794063ml_trm @ F1 @ F22 @ ( some_trm @ X23 ) )
% 0.32/0.47 = ( F22 @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(5)
% 0.32/0.47 thf(fact_129_option_Osimps_I5_J,axiom,
% 0.32/0.47 ! [F1: option_trm,F22: trm > option_trm,X23: trm] :
% 0.32/0.47 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X23 ) )
% 0.32/0.47 = ( F22 @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.simps(5)
% 0.32/0.47 thf(fact_130_option_Osel,axiom,
% 0.32/0.47 ! [X23: fml] :
% 0.32/0.47 ( ( the_fml @ ( some_fml @ X23 ) )
% 0.32/0.47 = X23 ) ).
% 0.32/0.47
% 0.32/0.47 % option.sel
% 0.32/0.47 thf(fact_131_option_Osel,axiom,
% 0.32/0.47 ! [X23: trm] :
% 0.32/0.47 ( ( the_trm @ ( some_trm @ X23 ) )
% 0.32/0.47 = X23 ) ).
% 0.32/0.47
% 0.32/0.47 % option.sel
% 0.32/0.47 thf(fact_132_option_Osel,axiom,
% 0.32/0.47 ! [X23: game] :
% 0.32/0.47 ( ( the_game @ ( some_game @ X23 ) )
% 0.32/0.47 = X23 ) ).
% 0.32/0.47
% 0.32/0.47 % option.sel
% 0.32/0.47 thf(fact_133_option_Oexhaust__sel,axiom,
% 0.32/0.47 ! [Option: option_fml] :
% 0.32/0.47 ( ( Option != none_fml )
% 0.32/0.47 => ( Option
% 0.32/0.47 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust_sel
% 0.32/0.47 thf(fact_134_option_Oexhaust__sel,axiom,
% 0.32/0.47 ! [Option: option_trm] :
% 0.32/0.47 ( ( Option != none_trm )
% 0.32/0.47 => ( Option
% 0.32/0.47 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust_sel
% 0.32/0.47 thf(fact_135_option_Oexhaust__sel,axiom,
% 0.32/0.47 ! [Option: option_game] :
% 0.32/0.47 ( ( Option != none_game )
% 0.32/0.47 => ( Option
% 0.32/0.47 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.exhaust_sel
% 0.32/0.47 thf(fact_136_option_Ocase__eq__if,axiom,
% 0.32/0.47 ( case_o209804997ml_fml
% 0.32/0.47 = ( ^ [F12: option_fml,F23: fml > option_fml,Option3: option_fml] : ( if_option_fml @ ( Option3 = none_fml ) @ F12 @ ( F23 @ ( the_fml @ Option3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_eq_if
% 0.32/0.47 thf(fact_137_option_Ocase__eq__if,axiom,
% 0.32/0.47 ( case_o325794063ml_trm
% 0.32/0.47 = ( ^ [F12: option_fml,F23: trm > option_fml,Option3: option_trm] : ( if_option_fml @ ( Option3 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_eq_if
% 0.32/0.47 thf(fact_138_option_Ocase__eq__if,axiom,
% 0.32/0.47 ( case_o487727941rm_trm
% 0.32/0.47 = ( ^ [F12: option_trm,F23: trm > option_trm,Option3: option_trm] : ( if_option_trm @ ( Option3 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.case_eq_if
% 0.32/0.47 thf(fact_139_usubstappf__pred__conv,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,P3: char,Theta: trm] :
% 0.32/0.47 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 0.32/0.47 != none_fml )
% 0.32/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 != none_trm )
% 0.32/0.47 & ( ( ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ Sigma
% 0.32/0.47 @ P3 )
% 0.32/0.47 = none_fml )
% 0.32/0.47 | ? [R3: fml] :
% 0.32/0.47 ( ( ( produc1250175341on_fml
% 0.32/0.47 @ ^ [Uu: char > option_trm] :
% 0.32/0.47 ( produc1615133358on_fml
% 0.32/0.47 @ ^ [Uv: char > option_trm] :
% 0.32/0.47 ( produc1420172399on_fml
% 0.32/0.47 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.47 @ Sigma
% 0.32/0.47 @ P3 )
% 0.32/0.47 = ( some_fml @ R3 ) )
% 0.32/0.47 & ( ( inf_inf_set_variable @ ( static_FVF @ R3 ) @ U )
% 0.32/0.47 = bot_bot_set_variable ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_pred_conv
% 0.32/0.47 thf(fact_140_option_Osplit__sel,axiom,
% 0.32/0.47 ! [P2: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 0.32/0.47 ( ( P2 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ( ( Option = none_fml )
% 0.32/0.47 => ( P2 @ F1 ) )
% 0.32/0.47 & ( ( Option
% 0.32/0.47 = ( some_fml @ ( the_fml @ Option ) ) )
% 0.32/0.47 => ( P2 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel
% 0.32/0.47 thf(fact_141_option_Osplit__sel,axiom,
% 0.32/0.47 ! [P2: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 0.32/0.47 ( ( P2 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ( ( Option = none_trm )
% 0.32/0.47 => ( P2 @ F1 ) )
% 0.32/0.47 & ( ( Option
% 0.32/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.32/0.47 => ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel
% 0.32/0.47 thf(fact_142_option_Osplit__sel,axiom,
% 0.32/0.47 ! [P2: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 0.32/0.47 ( ( P2 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 0.32/0.47 = ( ( ( Option = none_trm )
% 0.32/0.47 => ( P2 @ F1 ) )
% 0.32/0.47 & ( ( Option
% 0.32/0.47 = ( some_trm @ ( the_trm @ Option ) ) )
% 0.32/0.47 => ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % option.split_sel
% 0.32/0.47 thf(fact_143_fml_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 0.32/0.47 ( ( ( pred @ X11 @ X12 )
% 0.32/0.47 = ( pred @ Y11 @ Y12 ) )
% 0.32/0.47 = ( ( X11 = Y11 )
% 0.32/0.47 & ( X12 = Y12 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fml.inject(1)
% 0.32/0.47 thf(fact_144_Int__iff,axiom,
% 0.32/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.32/0.47 = ( ( member_variable @ C @ A2 )
% 0.32/0.47 & ( member_variable @ C @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_iff
% 0.32/0.47 thf(fact_145_IntI,axiom,
% 0.32/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( member_variable @ C @ A2 )
% 0.32/0.47 => ( ( member_variable @ C @ B3 )
% 0.32/0.47 => ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntI
% 0.32/0.47 thf(fact_146_empty__Collect__eq,axiom,
% 0.32/0.47 ! [P2: variable > $o] :
% 0.32/0.47 ( ( bot_bot_set_variable
% 0.32/0.47 = ( collect_variable @ P2 ) )
% 0.32/0.47 = ( ! [X: variable] :
% 0.32/0.47 ~ ( P2 @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_Collect_eq
% 0.32/0.47 thf(fact_147_Collect__empty__eq,axiom,
% 0.32/0.47 ! [P2: variable > $o] :
% 0.32/0.47 ( ( ( collect_variable @ P2 )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 = ( ! [X: variable] :
% 0.32/0.47 ~ ( P2 @ X ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_empty_eq
% 0.32/0.47 thf(fact_148_all__not__in__conv,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ( ! [X: variable] :
% 0.32/0.47 ~ ( member_variable @ X @ A2 ) )
% 0.32/0.47 = ( A2 = bot_bot_set_variable ) ) ).
% 0.32/0.47
% 0.32/0.47 % all_not_in_conv
% 0.32/0.47 thf(fact_149_empty__iff,axiom,
% 0.32/0.47 ! [C: variable] :
% 0.32/0.47 ~ ( member_variable @ C @ bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % empty_iff
% 0.32/0.47 thf(fact_150_disjoint__iff__not__equal,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 = ( ! [X: variable] :
% 0.32/0.47 ( ( member_variable @ X @ A2 )
% 0.32/0.47 => ! [Y: variable] :
% 0.32/0.47 ( ( member_variable @ Y @ B3 )
% 0.32/0.47 => ( X != Y ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % disjoint_iff_not_equal
% 0.32/0.47 thf(fact_151_Aterm__Some,axiom,
% 0.32/0.47 some_trm = some_trm ).
% 0.32/0.47
% 0.32/0.47 % Aterm_Some
% 0.32/0.47 thf(fact_152_Loopo_Ocases,axiom,
% 0.32/0.47 ! [X2: option_game] :
% 0.32/0.47 ( ! [Alpha: game] :
% 0.32/0.47 ( X2
% 0.32/0.47 != ( some_game @ Alpha ) )
% 0.32/0.47 => ( X2 = none_game ) ) ).
% 0.32/0.47
% 0.32/0.47 % Loopo.cases
% 0.32/0.47 thf(fact_153_ODEo_Oinduct,axiom,
% 0.32/0.47 ! [P2: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.32/0.47 ( ! [X3: char,Theta2: trm] : ( P2 @ X3 @ ( some_trm @ Theta2 ) )
% 0.32/0.47 => ( ! [X3: char] : ( P2 @ X3 @ none_trm )
% 0.32/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ODEo.induct
% 0.32/0.47 thf(fact_154_Loopo_Oinduct,axiom,
% 0.32/0.47 ! [P2: option_game > $o,A0: option_game] :
% 0.32/0.47 ( ! [Alpha: game] : ( P2 @ ( some_game @ Alpha ) )
% 0.32/0.47 => ( ( P2 @ none_game )
% 0.32/0.47 => ( P2 @ A0 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Loopo.induct
% 0.32/0.47 thf(fact_155_undefg__equiv,axiom,
% 0.32/0.47 ! [Alpha2: option_game] :
% 0.32/0.47 ( ( Alpha2 != none_game )
% 0.32/0.47 = ( ? [G: game] :
% 0.32/0.47 ( Alpha2
% 0.32/0.47 = ( some_game @ G ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % undefg_equiv
% 0.32/0.47 thf(fact_156_undeft__equiv,axiom,
% 0.32/0.47 ! [Theta: option_trm] :
% 0.32/0.47 ( ( Theta != none_trm )
% 0.32/0.47 = ( ? [T: trm] :
% 0.32/0.47 ( Theta
% 0.32/0.47 = ( some_trm @ T ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % undeft_equiv
% 0.32/0.47 thf(fact_157_Timeso_Oinduct,axiom,
% 0.32/0.47 ! [P2: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.32/0.47 ( ! [Theta2: trm,Eta: trm] : ( P2 @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) )
% 0.32/0.47 => ( ! [X_1: option_trm] : ( P2 @ none_trm @ X_1 )
% 0.32/0.47 => ( ! [V: trm] : ( P2 @ ( some_trm @ V ) @ none_trm )
% 0.32/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Timeso.induct
% 0.32/0.47 thf(fact_158_Assigno_Oinduct,axiom,
% 0.32/0.47 ! [P2: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.32/0.47 ( ! [X3: variable,Theta2: trm] : ( P2 @ X3 @ ( some_trm @ Theta2 ) )
% 0.32/0.47 => ( ! [X3: variable] : ( P2 @ X3 @ none_trm )
% 0.32/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Assigno.induct
% 0.32/0.47 thf(fact_159_Composeo_Oinduct,axiom,
% 0.32/0.47 ! [P2: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 0.32/0.47 ( ! [Alpha: game,Beta: game] : ( P2 @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.32/0.47 => ( ! [Alpha: option_game] : ( P2 @ Alpha @ none_game )
% 0.32/0.47 => ( ! [V: game] : ( P2 @ none_game @ ( some_game @ V ) )
% 0.32/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Composeo.induct
% 0.32/0.47 thf(fact_160_Differentialo_Ocases,axiom,
% 0.32/0.47 ! [X2: option_trm] :
% 0.32/0.47 ( ! [Theta2: trm] :
% 0.32/0.47 ( X2
% 0.32/0.47 != ( some_trm @ Theta2 ) )
% 0.32/0.47 => ( X2 = none_trm ) ) ).
% 0.32/0.47
% 0.32/0.47 % Differentialo.cases
% 0.32/0.47 thf(fact_161_Differentialo_Oinduct,axiom,
% 0.32/0.47 ! [P2: option_trm > $o,A0: option_trm] :
% 0.32/0.47 ( ! [Theta2: trm] : ( P2 @ ( some_trm @ Theta2 ) )
% 0.32/0.47 => ( ( P2 @ none_trm )
% 0.32/0.47 => ( P2 @ A0 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Differentialo.induct
% 0.32/0.47 thf(fact_162_undeft__None,axiom,
% 0.32/0.47 none_trm = none_trm ).
% 0.32/0.47
% 0.32/0.47 % undeft_None
% 0.32/0.47 thf(fact_163_emptyE,axiom,
% 0.32/0.47 ! [A: variable] :
% 0.32/0.47 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % emptyE
% 0.32/0.47 thf(fact_164_equals0D,axiom,
% 0.32/0.47 ! [A2: set_variable,A: variable] :
% 0.32/0.47 ( ( A2 = bot_bot_set_variable )
% 0.32/0.47 => ~ ( member_variable @ A @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % equals0D
% 0.32/0.47 thf(fact_165_equals0I,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ! [Y3: variable] :
% 0.32/0.47 ~ ( member_variable @ Y3 @ A2 )
% 0.32/0.47 => ( A2 = bot_bot_set_variable ) ) ).
% 0.32/0.47
% 0.32/0.47 % equals0I
% 0.32/0.47 thf(fact_166_ex__in__conv,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ( ? [X: variable] : ( member_variable @ X @ A2 ) )
% 0.32/0.47 = ( A2 != bot_bot_set_variable ) ) ).
% 0.32/0.47
% 0.32/0.47 % ex_in_conv
% 0.32/0.47 thf(fact_167_bot__set__def,axiom,
% 0.32/0.47 ( bot_bot_set_variable
% 0.32/0.47 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 0.32/0.47
% 0.32/0.47 % bot_set_def
% 0.32/0.47 thf(fact_168_IntE,axiom,
% 0.32/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.32/0.47 => ~ ( ( member_variable @ C @ A2 )
% 0.32/0.47 => ~ ( member_variable @ C @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntE
% 0.32/0.47 thf(fact_169_IntD1,axiom,
% 0.32/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.32/0.47 => ( member_variable @ C @ A2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD1
% 0.32/0.47 thf(fact_170_IntD2,axiom,
% 0.32/0.47 ! [C: variable,A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.32/0.47 => ( member_variable @ C @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % IntD2
% 0.32/0.47 thf(fact_171_Int__assoc,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 0.32/0.47 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_assoc
% 0.32/0.47 thf(fact_172_Int__absorb,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A2 @ A2 )
% 0.32/0.47 = A2 ) ).
% 0.32/0.47
% 0.32/0.47 % Int_absorb
% 0.32/0.47 thf(fact_173_Int__commute,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_commute
% 0.32/0.47 thf(fact_174_Int__left__absorb,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_left_absorb
% 0.32/0.47 thf(fact_175_Int__left__commute,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 0.32/0.47 = ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_left_commute
% 0.32/0.47 thf(fact_176_empty__def,axiom,
% 0.32/0.47 ( bot_bot_set_variable
% 0.32/0.47 = ( collect_variable
% 0.32/0.47 @ ^ [X: variable] : $false ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_def
% 0.32/0.47 thf(fact_177_Collect__conj__eq,axiom,
% 0.32/0.47 ! [P2: variable > $o,Q: variable > $o] :
% 0.32/0.47 ( ( collect_variable
% 0.32/0.47 @ ^ [X: variable] :
% 0.32/0.47 ( ( P2 @ X )
% 0.32/0.47 & ( Q @ X ) ) )
% 0.32/0.47 = ( inf_inf_set_variable @ ( collect_variable @ P2 ) @ ( collect_variable @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_conj_eq
% 0.32/0.47 thf(fact_178_Int__Collect,axiom,
% 0.32/0.47 ! [X2: variable,A2: set_variable,P2: variable > $o] :
% 0.32/0.47 ( ( member_variable @ X2 @ ( inf_inf_set_variable @ A2 @ ( collect_variable @ P2 ) ) )
% 0.32/0.47 = ( ( member_variable @ X2 @ A2 )
% 0.32/0.47 & ( P2 @ X2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_Collect
% 0.32/0.47 thf(fact_179_Int__def,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.32/0.47 ( collect_variable
% 0.32/0.47 @ ^ [X: variable] :
% 0.32/0.47 ( ( member_variable @ X @ A5 )
% 0.32/0.47 & ( member_variable @ X @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_def
% 0.32/0.47 thf(fact_180_inf__set__def,axiom,
% 0.32/0.47 ( inf_inf_set_variable
% 0.32/0.47 = ( ^ [A5: set_variable,B5: set_variable] :
% 0.32/0.47 ( collect_variable
% 0.32/0.47 @ ( inf_inf_variable_o
% 0.32/0.47 @ ^ [X: variable] : ( member_variable @ X @ A5 )
% 0.32/0.47 @ ^ [X: variable] : ( member_variable @ X @ B5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_set_def
% 0.32/0.47 thf(fact_181_Int__emptyI,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ! [X3: variable] :
% 0.32/0.47 ( ( member_variable @ X3 @ A2 )
% 0.32/0.47 => ~ ( member_variable @ X3 @ B3 ) )
% 0.32/0.47 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.32/0.47 = bot_bot_set_variable ) ) ).
% 0.32/0.47
% 0.32/0.47 % Int_emptyI
% 0.32/0.47 thf(fact_182_disjoint__iff,axiom,
% 0.32/0.47 ! [A2: set_variable,B3: set_variable] :
% 0.32/0.47 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 = ( ! [X: variable] :
% 0.32/0.47 ( ( member_variable @ X @ A2 )
% 0.32/0.47 => ~ ( member_variable @ X @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % disjoint_iff
% 0.32/0.47 thf(fact_183_Int__empty__left,axiom,
% 0.32/0.47 ! [B3: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B3 )
% 0.32/0.47 = bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % Int_empty_left
% 0.32/0.47 thf(fact_184_Int__empty__right,axiom,
% 0.32/0.47 ! [A2: set_variable] :
% 0.32/0.47 ( ( inf_inf_set_variable @ A2 @ bot_bot_set_variable )
% 0.32/0.47 = bot_bot_set_variable ) ).
% 0.32/0.47
% 0.32/0.47 % Int_empty_right
% 0.32/0.47 thf(fact_185_disjE__realizer2,axiom,
% 0.32/0.47 ! [P2: $o,Q: fml > $o,X2: option_fml,R4: option_fml > $o,F3: option_fml,G2: fml > option_fml] :
% 0.32/0.47 ( ( case_option_o_fml @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( P2
% 0.32/0.47 => ( R4 @ F3 ) )
% 0.32/0.47 => ( ! [Q2: fml] :
% 0.32/0.47 ( ( Q @ Q2 )
% 0.32/0.47 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.32/0.47 => ( R4 @ ( case_o209804997ml_fml @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % disjE_realizer2
% 0.32/0.47 thf(fact_186_disjE__realizer2,axiom,
% 0.32/0.47 ! [P2: $o,Q: trm > $o,X2: option_trm,R4: option_fml > $o,F3: option_fml,G2: trm > option_fml] :
% 0.32/0.47 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( P2
% 0.32/0.47 => ( R4 @ F3 ) )
% 0.32/0.47 => ( ! [Q2: trm] :
% 0.32/0.47 ( ( Q @ Q2 )
% 0.32/0.47 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.32/0.47 => ( R4 @ ( case_o325794063ml_trm @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % disjE_realizer2
% 0.32/0.47 thf(fact_187_disjE__realizer2,axiom,
% 0.32/0.47 ! [P2: $o,Q: trm > $o,X2: option_trm,R4: option_trm > $o,F3: option_trm,G2: trm > option_trm] :
% 0.32/0.47 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 0.32/0.47 => ( ( P2
% 0.32/0.47 => ( R4 @ F3 ) )
% 0.32/0.47 => ( ! [Q2: trm] :
% 0.32/0.47 ( ( Q @ Q2 )
% 0.32/0.47 => ( R4 @ ( G2 @ Q2 ) ) )
% 0.32/0.47 => ( R4 @ ( case_o487727941rm_trm @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % disjE_realizer2
% 0.32/0.47 thf(fact_188_usubstappf__geqr,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.47 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.32/0.47 != none_fml )
% 0.32/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.32/0.47 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_geqr
% 0.32/0.47 thf(fact_189_usubstappf__geq,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.47 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 != none_trm )
% 0.32/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.32/0.47 != none_trm )
% 0.32/0.47 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.32/0.47 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_geq
% 0.32/0.47 thf(fact_190_Geqo_Osimps_I3_J,axiom,
% 0.32/0.47 ! [V3: trm] :
% 0.32/0.47 ( ( uSubst152838031e_Geqo @ ( some_trm @ V3 ) @ none_trm )
% 0.32/0.47 = none_fml ) ).
% 0.32/0.47
% 0.32/0.47 % Geqo.simps(3)
% 0.32/0.47 thf(fact_191_Set_Ois__empty__def,axiom,
% 0.32/0.47 ( is_empty_variable
% 0.32/0.47 = ( ^ [A5: set_variable] : ( A5 = bot_bot_set_variable ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Set.is_empty_def
% 0.32/0.47 thf(fact_192_usubstappf__geq__conv,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.47 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.32/0.47 != none_fml )
% 0.32/0.47 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.47 != none_trm )
% 0.32/0.47 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.32/0.47 != none_trm ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf_geq_conv
% 0.32/0.47 thf(fact_193_fml_Oinject_I2_J,axiom,
% 0.32/0.47 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 0.32/0.47 ( ( ( geq @ X21 @ X222 )
% 0.32/0.47 = ( geq @ Y21 @ Y222 ) )
% 0.32/0.47 = ( ( X21 = Y21 )
% 0.32/0.47 & ( X222 = Y222 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % fml.inject(2)
% 0.32/0.47 thf(fact_194_fml_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 0.32/0.47 ( ( pred @ X11 @ X12 )
% 0.32/0.47 != ( geq @ X21 @ X222 ) ) ).
% 0.32/0.47
% 0.32/0.47 % fml.distinct(1)
% 0.32/0.47 thf(fact_195_usubstappf_Osimps_I2_J,axiom,
% 0.32/0.47 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.47 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 0.32/0.47 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % usubstappf.simps(2)
% 0.32/0.47 thf(fact_196_Geqo_Osimps_I1_J,axiom,
% 0.32/0.47 ! [Theta: trm,Eta2: trm] :
% 0.32/0.47 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta2 ) )
% 0.32/0.47 = ( some_fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Geqo.simps(1)
% 0.32/0.47 thf(fact_197_Geqo_Oelims,axiom,
% 0.32/0.47 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.32/0.47 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 0.32/0.47 = Y2 )
% 0.32/0.47 => ( ! [Theta2: trm] :
% 0.32/0.47 ( ( X2
% 0.32/0.47 = ( some_trm @ Theta2 ) )
% 0.32/0.47 => ! [Eta: trm] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( some_trm @ Eta ) )
% 0.32/0.47 => ( Y2
% 0.32/0.47 != ( some_fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 0.32/0.47 => ( ( ( X2 = none_trm )
% 0.32/0.47 => ( Y2 != none_fml ) )
% 0.32/0.47 => ~ ( ? [V: trm] :
% 0.32/0.47 ( X2
% 0.32/0.47 = ( some_trm @ V ) )
% 0.32/0.47 => ( ( Xa = none_trm )
% 0.32/0.47 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Geqo.elims
% 0.32/0.47 thf(fact_198_Geqo_Osimps_I2_J,axiom,
% 0.32/0.47 ! [Eta2: option_trm] :
% 0.32/0.47 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 0.32/0.47 = none_fml ) ).
% 0.32/0.47
% 0.32/0.47 % Geqo.simps(2)
% 0.32/0.47 thf(fact_199_Geqo__undef,axiom,
% 0.32/0.47 ! [Theta: option_trm,Eta2: option_trm] :
% 0.32/0.47 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta2 )
% 0.32/0.47 = none_fml )
% 0.32/0.47 = ( ( Theta = none_trm )
% 0.32/0.47 | ( Eta2 = none_trm ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Geqo_undef
% 0.32/0.47 thf(fact_200_inf__Int__eq,axiom,
% 0.32/0.47 ! [R4: set_variable,S: set_variable] :
% 0.32/0.47 ( ( inf_inf_variable_o
% 0.32/0.47 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 0.32/0.47 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 0.32/0.47 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % inf_Int_eq
% 0.32/0.47 thf(fact_201_Collect__empty__eq__bot,axiom,
% 0.32/0.47 ! [P2: variable > $o] :
% 0.32/0.47 ( ( ( collect_variable @ P2 )
% 0.32/0.47 = bot_bot_set_variable )
% 0.32/0.47 = ( P2 = bot_bot_variable_o ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_empty_eq_bot
% 0.32/0.47 thf(fact_202_bot__empty__eq,axiom,
% 0.32/0.47 ( bot_bot_variable_o
% 0.32/0.47 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % bot_empty_eq
% 0.32/0.47 thf(fact_203_internal__case__prod__def,axiom,
% 0.32/0.47 produc1278328899on_fml = produc1250175341on_fml ).
% 0.32/0.47
% 0.32/0.47 % internal_case_prod_def
% 0.32/0.47 thf(fact_204_internal__case__prod__def,axiom,
% 0.32/0.47 produc2141841102on_trm = produc1231571704on_trm ).
% 0.32/0.47
% 0.32/0.47 % internal_case_prod_def
% 0.32/0.47 thf(fact_205_internal__case__prod__def,axiom,
% 0.32/0.47 produc377919108on_fml = produc1615133358on_fml ).
% 0.32/0.47
% 0.32/0.47 % internal_case_prod_def
% 0.32/0.47 thf(fact_206_internal__case__prod__def,axiom,
% 0.32/0.47 produc1214549391on_trm = produc1036610745on_trm ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_207_internal__case__prod__def,axiom,
% 0.32/0.48 produc1598111045on_fml = produc1420172399on_fml ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_208_internal__case__prod__def,axiom,
% 0.32/0.48 produc1591622303on_fml = produc347802313on_fml ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_209_internal__case__prod__def,axiom,
% 0.32/0.48 produc2129367017on_trm = produc885547027on_trm ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_210_internal__case__prod__def,axiom,
% 0.32/0.48 produc1903410526on_fml = produc154833544on_fml ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_211_internal__case__prod__def,axiom,
% 0.32/0.48 produc293671592on_trm = produc692578258on_trm ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_212_internal__case__prod__def,axiom,
% 0.32/0.48 produc724717725on_fml = produc1499310791on_fml ).
% 0.32/0.48
% 0.32/0.48 % internal_case_prod_def
% 0.32/0.48 thf(fact_213_usubstappt_Osimps_I4_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 0.32/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.32/0.48 = ( case_o487727941rm_trm @ none_trm
% 0.32/0.48 @ ^ [Sigma_theta: trm] :
% 0.32/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta ) )
% 0.32/0.48 @ ^ [R: trm] :
% 0.32/0.48 ( if_option_trm
% 0.32/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.32/0.48 @ none_trm )
% 0.32/0.48 @ ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 ) )
% 0.32/0.48 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.simps(4)
% 0.32/0.48 thf(fact_214_Diamondo_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1739631244on_fml] :
% 0.32/0.48 ( ! [Alpha: game,Phi: fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) ) )
% 0.32/0.48 => ( ! [Phi: option_fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2124676926on_fml @ none_game @ Phi ) )
% 0.32/0.48 => ~ ! [V: game] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2124676926on_fml @ ( some_game @ V ) @ none_fml ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Diamondo.cases
% 0.32/0.48 thf(fact_215_Testo__undef,axiom,
% 0.32/0.48 ! [Phi2: option_fml] :
% 0.32/0.48 ( ( ( uSubst1367128042_Testo @ Phi2 )
% 0.32/0.48 = none_game )
% 0.32/0.48 = ( Phi2 = none_fml ) ) ).
% 0.32/0.48
% 0.32/0.48 % Testo_undef
% 0.32/0.48 thf(fact_216_prod_Oinject,axiom,
% 0.32/0.48 ! [X13: char,X23: option_trm,Y1: char,Y22: option_trm] :
% 0.32/0.48 ( ( ( produc1500300866on_trm @ X13 @ X23 )
% 0.32/0.48 = ( produc1500300866on_trm @ Y1 @ Y22 ) )
% 0.32/0.48 = ( ( X13 = Y1 )
% 0.32/0.48 & ( X23 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_217_prod_Oinject,axiom,
% 0.32/0.48 ! [X13: set_variable,X23: trm,Y1: set_variable,Y22: trm] :
% 0.32/0.48 ( ( ( produc1482344242le_trm @ X13 @ X23 )
% 0.32/0.48 = ( produc1482344242le_trm @ Y1 @ Y22 ) )
% 0.32/0.48 = ( ( X13 = Y1 )
% 0.32/0.48 & ( X23 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_218_prod_Oinject,axiom,
% 0.32/0.48 ! [X13: char > option_trm,X23: produc62062515n_game,Y1: char > option_trm,Y22: produc62062515n_game] :
% 0.32/0.48 ( ( ( produc1618635950n_game @ X13 @ X23 )
% 0.32/0.48 = ( produc1618635950n_game @ Y1 @ Y22 ) )
% 0.32/0.48 = ( ( X13 = Y1 )
% 0.32/0.48 & ( X23 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_219_prod_Oinject,axiom,
% 0.32/0.48 ! [X13: char > option_trm,X23: produc799602994n_game,Y1: char > option_trm,Y22: produc799602994n_game] :
% 0.32/0.48 ( ( ( produc1048060077n_game @ X13 @ X23 )
% 0.32/0.48 = ( produc1048060077n_game @ Y1 @ Y22 ) )
% 0.32/0.48 = ( ( X13 = Y1 )
% 0.32/0.48 & ( X23 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_220_prod_Oinject,axiom,
% 0.32/0.48 ! [X13: char > option_fml,X23: char > option_game,Y1: char > option_fml,Y22: char > option_game] :
% 0.32/0.48 ( ( ( produc123610156n_game @ X13 @ X23 )
% 0.32/0.48 = ( produc123610156n_game @ Y1 @ Y22 ) )
% 0.32/0.48 = ( ( X13 = Y1 )
% 0.32/0.48 & ( X23 = Y22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % prod.inject
% 0.32/0.48 thf(fact_221_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: char,B: option_trm,A6: char,B6: option_trm] :
% 0.32/0.48 ( ( ( produc1500300866on_trm @ A @ B )
% 0.32/0.48 = ( produc1500300866on_trm @ A6 @ B6 ) )
% 0.32/0.48 = ( ( A = A6 )
% 0.32/0.48 & ( B = B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_222_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: set_variable,B: trm,A6: set_variable,B6: trm] :
% 0.32/0.48 ( ( ( produc1482344242le_trm @ A @ B )
% 0.32/0.48 = ( produc1482344242le_trm @ A6 @ B6 ) )
% 0.32/0.48 = ( ( A = A6 )
% 0.32/0.48 & ( B = B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_223_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: char > option_trm,B: produc62062515n_game,A6: char > option_trm,B6: produc62062515n_game] :
% 0.32/0.48 ( ( ( produc1618635950n_game @ A @ B )
% 0.32/0.48 = ( produc1618635950n_game @ A6 @ B6 ) )
% 0.32/0.48 = ( ( A = A6 )
% 0.32/0.48 & ( B = B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_224_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: char > option_trm,B: produc799602994n_game,A6: char > option_trm,B6: produc799602994n_game] :
% 0.32/0.48 ( ( ( produc1048060077n_game @ A @ B )
% 0.32/0.48 = ( produc1048060077n_game @ A6 @ B6 ) )
% 0.32/0.48 = ( ( A = A6 )
% 0.32/0.48 & ( B = B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_225_old_Oprod_Oinject,axiom,
% 0.32/0.48 ! [A: char > option_fml,B: char > option_game,A6: char > option_fml,B6: char > option_game] :
% 0.32/0.48 ( ( ( produc123610156n_game @ A @ B )
% 0.32/0.48 = ( produc123610156n_game @ A6 @ B6 ) )
% 0.32/0.48 = ( ( A = A6 )
% 0.32/0.48 & ( B = B6 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % old.prod.inject
% 0.32/0.48 thf(fact_226_trm_Oinject_I4_J,axiom,
% 0.32/0.48 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.32/0.48 ( ( ( func @ X41 @ X42 )
% 0.32/0.48 = ( func @ Y41 @ Y42 ) )
% 0.32/0.48 = ( ( X41 = Y41 )
% 0.32/0.48 & ( X42 = Y42 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(4)
% 0.32/0.48 thf(fact_227_case__prodI,axiom,
% 0.32/0.48 ! [F3: char > option_trm > $o,A: char,B: option_trm] :
% 0.32/0.48 ( ( F3 @ A @ B )
% 0.32/0.48 => ( produc584666985_trm_o @ F3 @ ( produc1500300866on_trm @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI
% 0.32/0.48 thf(fact_228_case__prodI,axiom,
% 0.32/0.48 ! [F3: set_variable > trm > $o,A: set_variable,B: trm] :
% 0.32/0.48 ( ( F3 @ A @ B )
% 0.32/0.48 => ( produc82209913_trm_o @ F3 @ ( produc1482344242le_trm @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI
% 0.32/0.48 thf(fact_229_case__prodI,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc62062515n_game > $o,A: char > option_trm,B: produc62062515n_game] :
% 0.32/0.48 ( ( F3 @ A @ B )
% 0.32/0.48 => ( produc1707653117game_o @ F3 @ ( produc1618635950n_game @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI
% 0.32/0.48 thf(fact_230_case__prodI,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > $o,A: char > option_trm,B: produc799602994n_game] :
% 0.32/0.48 ( ( F3 @ A @ B )
% 0.32/0.48 => ( produc1868740670game_o @ F3 @ ( produc1048060077n_game @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI
% 0.32/0.48 thf(fact_231_case__prodI,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > $o,A: char > option_fml,B: char > option_game] :
% 0.32/0.48 ( ( F3 @ A @ B )
% 0.32/0.48 => ( produc159680767game_o @ F3 @ ( produc123610156n_game @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI
% 0.32/0.48 thf(fact_232_case__prodI2,axiom,
% 0.32/0.48 ! [P3: produc464795408on_trm,C: char > option_trm > $o] :
% 0.32/0.48 ( ! [A4: char,B4: option_trm] :
% 0.32/0.48 ( ( P3
% 0.32/0.48 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 0.32/0.48 => ( C @ A4 @ B4 ) )
% 0.32/0.48 => ( produc584666985_trm_o @ C @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI2
% 0.32/0.48 thf(fact_233_case__prodI2,axiom,
% 0.32/0.48 ! [P3: produc1367888000le_trm,C: set_variable > trm > $o] :
% 0.32/0.48 ( ! [A4: set_variable,B4: trm] :
% 0.32/0.48 ( ( P3
% 0.32/0.48 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 0.32/0.48 => ( C @ A4 @ B4 ) )
% 0.32/0.48 => ( produc82209913_trm_o @ C @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI2
% 0.32/0.48 thf(fact_234_case__prodI2,axiom,
% 0.32/0.48 ! [P3: produc1418842292n_game,C: ( char > option_trm ) > produc62062515n_game > $o] :
% 0.32/0.48 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 0.32/0.48 ( ( P3
% 0.32/0.48 = ( produc1618635950n_game @ A4 @ B4 ) )
% 0.32/0.48 => ( C @ A4 @ B4 ) )
% 0.32/0.48 => ( produc1707653117game_o @ C @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI2
% 0.32/0.48 thf(fact_235_case__prodI2,axiom,
% 0.32/0.48 ! [P3: produc62062515n_game,C: ( char > option_trm ) > produc799602994n_game > $o] :
% 0.32/0.48 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 0.32/0.48 ( ( P3
% 0.32/0.48 = ( produc1048060077n_game @ A4 @ B4 ) )
% 0.32/0.48 => ( C @ A4 @ B4 ) )
% 0.32/0.48 => ( produc1868740670game_o @ C @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI2
% 0.32/0.48 thf(fact_236_case__prodI2,axiom,
% 0.32/0.48 ! [P3: produc799602994n_game,C: ( char > option_fml ) > ( char > option_game ) > $o] :
% 0.32/0.48 ( ! [A4: char > option_fml,B4: char > option_game] :
% 0.32/0.48 ( ( P3
% 0.32/0.48 = ( produc123610156n_game @ A4 @ B4 ) )
% 0.32/0.48 => ( C @ A4 @ B4 ) )
% 0.32/0.48 => ( produc159680767game_o @ C @ P3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodI2
% 0.32/0.48 thf(fact_237_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 0.32/0.48 ( ( produc1250175341on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_238_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 0.32/0.48 ( ( produc1231571704on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_239_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 0.32/0.48 ( ( produc1615133358on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_240_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,A: char > option_fml,B: char > option_game] :
% 0.32/0.48 ( ( produc1036610745on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_241_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,A: char > option_fml,B: char > option_game] :
% 0.32/0.48 ( ( produc1420172399on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_242_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_fml,A: char > option_fml,B: char > option_game] :
% 0.32/0.48 ( ( produc347802313on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_243_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_trm,A: char > option_fml,B: char > option_game] :
% 0.32/0.48 ( ( produc885547027on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_244_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 0.32/0.48 ( ( produc154833544on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_245_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 0.32/0.48 ( ( produc692578258on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_246_case__prod__conv,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc62062515n_game > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 0.32/0.48 ( ( produc1499310791on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 0.32/0.48 = ( F3 @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_conv
% 0.32/0.48 thf(fact_247_usubstappt__func2,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable,Theta: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R2 ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.32/0.48 != bot_bot_set_variable )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.32/0.48 = none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_func2
% 0.32/0.48 thf(fact_248_usubstappt__func,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R2 ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.48 = ( some_trm @ Sigma_theta2 ) )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.32/0.48 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_func
% 0.32/0.48 thf(fact_249_inf__Int__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.32/0.48 ( ( inf_in605351507_trm_o
% 0.32/0.48 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 )
% 0.32/0.48 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) )
% 0.32/0.48 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ ( inf_in1243659096on_trm @ R4 @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_Int_eq2
% 0.32/0.48 thf(fact_250_inf__Int__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.32/0.48 ( ( inf_in185389155_trm_o
% 0.32/0.48 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 )
% 0.32/0.48 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) )
% 0.32/0.48 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ ( inf_in906025800le_trm @ R4 @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_Int_eq2
% 0.32/0.48 thf(fact_251_inf__Int__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 0.32/0.48 ( ( inf_in1920662529game_o
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 )
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) )
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ ( inf_in360367996n_game @ R4 @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_Int_eq2
% 0.32/0.48 thf(fact_252_inf__Int__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 0.32/0.48 ( ( inf_in1072207554game_o
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 )
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) )
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ ( inf_in69689467n_game @ R4 @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_Int_eq2
% 0.32/0.48 thf(fact_253_inf__Int__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 0.32/0.48 ( ( inf_in243546115game_o
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 )
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) )
% 0.32/0.48 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ ( inf_in1391117306n_game @ R4 @ S ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % inf_Int_eq2
% 0.32/0.48 thf(fact_254_bot__empty__eq2,axiom,
% 0.32/0.48 ( bot_bo102862421_trm_o
% 0.32/0.48 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ bot_bo18861914on_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq2
% 0.32/0.48 thf(fact_255_bot__empty__eq2,axiom,
% 0.32/0.48 ( bot_bo512610661_trm_o
% 0.32/0.48 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ bot_bo896421962le_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq2
% 0.32/0.48 thf(fact_256_bot__empty__eq2,axiom,
% 0.32/0.48 ( bot_bo849148163game_o
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ bot_bo1453406334n_game ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq2
% 0.32/0.48 thf(fact_257_bot__empty__eq2,axiom,
% 0.32/0.48 ( bot_bo1417568964game_o
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ bot_bo1302831229n_game ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq2
% 0.32/0.48 thf(fact_258_bot__empty__eq2,axiom,
% 0.32/0.48 ( bot_bo1895715589game_o
% 0.32/0.48 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ bot_bo456479484n_game ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bot_empty_eq2
% 0.32/0.48 thf(fact_259_pred__equals__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.32/0.48 ( ( ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 ) )
% 0.32/0.48 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) ) )
% 0.32/0.48 = ( R4 = S ) ) ).
% 0.32/0.48
% 0.32/0.48 % pred_equals_eq2
% 0.32/0.48 thf(fact_260_pred__equals__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.32/0.48 ( ( ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 ) )
% 0.32/0.48 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) ) )
% 0.32/0.48 = ( R4 = S ) ) ).
% 0.32/0.48
% 0.32/0.48 % pred_equals_eq2
% 0.32/0.48 thf(fact_261_pred__equals__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 0.32/0.48 ( ( ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 ) )
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) ) )
% 0.32/0.48 = ( R4 = S ) ) ).
% 0.32/0.48
% 0.32/0.48 % pred_equals_eq2
% 0.32/0.48 thf(fact_262_pred__equals__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 0.32/0.48 ( ( ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 ) )
% 0.32/0.48 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) ) )
% 0.32/0.48 = ( R4 = S ) ) ).
% 0.32/0.48
% 0.32/0.48 % pred_equals_eq2
% 0.32/0.48 thf(fact_263_pred__equals__eq2,axiom,
% 0.32/0.48 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 0.32/0.48 ( ( ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 ) )
% 0.32/0.48 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) ) )
% 0.32/0.48 = ( R4 = S ) ) ).
% 0.32/0.48
% 0.32/0.48 % pred_equals_eq2
% 0.32/0.48 thf(fact_264_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,G2: produc1418842292n_game > char > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1618635950n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1250175341on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_265_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,G2: produc62062515n_game > char > option_trm] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1231571704on_trm @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_266_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,G2: produc62062515n_game > char > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1615133358on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_267_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,G2: produc799602994n_game > char > option_trm] :
% 0.32/0.48 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1036610745on_trm @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_268_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,G2: produc799602994n_game > char > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1420172399on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_269_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_fml,G2: produc799602994n_game > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc347802313on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_270_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_trm,G2: produc799602994n_game > option_trm] :
% 0.32/0.48 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc885547027on_trm @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_271_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > option_fml,G2: produc62062515n_game > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc154833544on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_272_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc799602994n_game > option_trm,G2: produc62062515n_game > option_trm] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc692578258on_trm @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_273_cond__case__prod__eta,axiom,
% 0.32/0.48 ! [F3: ( char > option_trm ) > produc62062515n_game > option_fml,G2: produc1418842292n_game > option_fml] :
% 0.32/0.48 ( ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 0.32/0.48 ( ( F3 @ X3 @ Y3 )
% 0.32/0.48 = ( G2 @ ( produc1618635950n_game @ X3 @ Y3 ) ) )
% 0.32/0.48 => ( ( produc1499310791on_fml @ F3 )
% 0.32/0.48 = G2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % cond_case_prod_eta
% 0.32/0.48 thf(fact_274_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc1418842292n_game > char > option_fml] :
% 0.32/0.48 ( ( produc1250175341on_fml
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_275_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc62062515n_game > char > option_trm] :
% 0.32/0.48 ( ( produc1231571704on_trm
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_276_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc62062515n_game > char > option_fml] :
% 0.32/0.48 ( ( produc1615133358on_fml
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_277_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc799602994n_game > char > option_trm] :
% 0.32/0.48 ( ( produc1036610745on_trm
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_278_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc799602994n_game > char > option_fml] :
% 0.32/0.48 ( ( produc1420172399on_fml
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_279_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc799602994n_game > option_fml] :
% 0.32/0.48 ( ( produc347802313on_fml
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_280_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc799602994n_game > option_trm] :
% 0.32/0.48 ( ( produc885547027on_trm
% 0.32/0.48 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_281_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc62062515n_game > option_fml] :
% 0.32/0.48 ( ( produc154833544on_fml
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_282_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc62062515n_game > option_trm] :
% 0.32/0.48 ( ( produc692578258on_trm
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_283_case__prod__eta,axiom,
% 0.32/0.48 ! [F3: produc1418842292n_game > option_fml] :
% 0.32/0.48 ( ( produc1499310791on_fml
% 0.32/0.48 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 0.32/0.48 = F3 ) ).
% 0.32/0.48
% 0.32/0.48 % case_prod_eta
% 0.32/0.48 thf(fact_284_case__prodE2,axiom,
% 0.32/0.48 ! [Q: option_fml > $o,P2: ( char > option_trm ) > produc62062515n_game > option_fml,Z2: produc1418842292n_game] :
% 0.32/0.48 ( ( Q @ ( produc1499310791on_fml @ P2 @ Z2 ) )
% 0.32/0.48 => ~ ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 0.32/0.48 ( ( Z2
% 0.32/0.48 = ( produc1618635950n_game @ X3 @ Y3 ) )
% 0.32/0.48 => ~ ( Q @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % case_prodE2
% 0.32/0.48 thf(fact_285_usubstappt__func__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.48 != none_trm )
% 0.32/0.48 & ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = none_trm )
% 0.32/0.48 | ? [R3: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R3 ) )
% 0.32/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.32/0.48 = bot_bot_set_variable ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_func_conv
% 0.32/0.48 thf(fact_286_Testo_Osimps_I2_J,axiom,
% 0.32/0.48 ( ( uSubst1367128042_Testo @ none_fml )
% 0.32/0.48 = none_game ) ).
% 0.32/0.48
% 0.32/0.48 % Testo.simps(2)
% 0.32/0.48 thf(fact_287_usappconst__simp,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R2 ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 => ( ( uSubst1559070963pconst @ Sigma @ U @ F3 )
% 0.32/0.48 = ( some_trm @ R2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usappconst_simp
% 0.32/0.48 thf(fact_288_usappconst__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 0.32/0.48 ( ( ( uSubst1559070963pconst @ Sigma @ U @ F3 )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = none_trm )
% 0.32/0.48 | ? [R3: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R3 ) )
% 0.32/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.32/0.48 = bot_bot_set_variable ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usappconst_conv
% 0.32/0.48 thf(fact_289_usubstappt__const,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R2 ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.32/0.48 = ( some_trm @ R2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_const
% 0.32/0.48 thf(fact_290_trm_Oinject_I3_J,axiom,
% 0.32/0.48 ! [X32: char,Y32: char] :
% 0.32/0.48 ( ( ( const @ X32 )
% 0.32/0.48 = ( const @ Y32 ) )
% 0.32/0.48 = ( X32 = Y32 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(3)
% 0.32/0.48 thf(fact_291_trm_Odistinct_I23_J,axiom,
% 0.32/0.48 ! [X32: char,X41: char,X42: trm] :
% 0.32/0.48 ( ( const @ X32 )
% 0.32/0.48 != ( func @ X41 @ X42 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(23)
% 0.32/0.48 thf(fact_292_usubstappt_Osimps_I3_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 0.32/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.32/0.48 = ( uSubst1559070963pconst @ Sigma @ U @ F3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.simps(3)
% 0.32/0.48 thf(fact_293_ODEo_Ocases,axiom,
% 0.32/0.48 ! [X2: produc464795408on_trm] :
% 0.32/0.48 ( ! [X3: char,Theta2: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1500300866on_trm @ X3 @ ( some_trm @ Theta2 ) ) )
% 0.32/0.48 => ~ ! [X3: char] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1500300866on_trm @ X3 @ none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ODEo.cases
% 0.32/0.48 thf(fact_294_Assigno_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1024976764on_trm] :
% 0.32/0.48 ( ! [X3: variable,Theta2: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1743721902on_trm @ X3 @ ( some_trm @ Theta2 ) ) )
% 0.32/0.48 => ~ ! [X3: variable] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1743721902on_trm @ X3 @ none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Assigno.cases
% 0.32/0.48 thf(fact_295_Timeso_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1072747943on_trm] :
% 0.32/0.48 ( ! [Theta2: trm,Eta: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) ) )
% 0.32/0.48 => ( ! [Eta: option_trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc709594775on_trm @ none_trm @ Eta ) )
% 0.32/0.48 => ~ ! [V: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Timeso.cases
% 0.32/0.48 thf(fact_296_Existso_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1408538418on_fml] :
% 0.32/0.48 ( ! [X3: variable,Phi: fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1205977188on_fml @ X3 @ ( some_fml @ Phi ) ) )
% 0.32/0.48 => ~ ! [X3: variable] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1205977188on_fml @ X3 @ none_fml ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Existso.cases
% 0.32/0.48 thf(fact_297_Ando_Ocases,axiom,
% 0.32/0.48 ! [X2: produc46605351on_fml] :
% 0.32/0.48 ( ! [Phi: fml,Psi: fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc909629463on_fml @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) ) )
% 0.32/0.48 => ( ! [Psi: option_fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 0.32/0.48 => ~ ! [V: fml] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc909629463on_fml @ ( some_fml @ V ) @ none_fml ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Ando.cases
% 0.32/0.48 thf(fact_298_Composeo_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1016592119n_game] :
% 0.32/0.48 ( ! [Alpha: game,Beta: game] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 0.32/0.48 => ( ! [Alpha: option_game] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 0.32/0.48 => ~ ! [V: game] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc1111617711n_game @ none_game @ ( some_game @ V ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Composeo.cases
% 0.32/0.48 thf(fact_299_usappconst__def,axiom,
% 0.32/0.48 ( uSubst1559070963pconst
% 0.32/0.48 = ( ^ [Sigma2: produc1418842292n_game,U2: set_variable,F2: char] :
% 0.32/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F2 ) )
% 0.32/0.48 @ ^ [R: trm] :
% 0.32/0.48 ( if_option_trm
% 0.32/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 @ ( some_trm @ R )
% 0.32/0.48 @ none_trm )
% 0.32/0.48 @ ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma2
% 0.32/0.48 @ F2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usappconst_def
% 0.32/0.48 thf(fact_300_usubstappt__const__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = none_trm )
% 0.32/0.48 | ? [R3: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [F0: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 )
% 0.32/0.48 = ( some_trm @ R3 ) )
% 0.32/0.48 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 0.32/0.48 = bot_bot_set_variable ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_const_conv
% 0.32/0.48 thf(fact_301_usubstappt_Opsimps_I4_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( func @ F3 @ Theta ) ) ) )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 0.32/0.48 = ( case_o487727941rm_trm @ none_trm
% 0.32/0.48 @ ^ [Sigma_theta: trm] :
% 0.32/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta ) )
% 0.32/0.48 @ ^ [R: trm] :
% 0.32/0.48 ( if_option_trm
% 0.32/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.32/0.48 @ none_trm )
% 0.32/0.48 @ ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma
% 0.32/0.48 @ F3 ) )
% 0.32/0.48 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.psimps(4)
% 0.32/0.48 thf(fact_302_usubstappt_Opsimps_I3_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( const @ F3 ) ) ) )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 0.32/0.48 = ( uSubst1559070963pconst @ Sigma @ U @ F3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.psimps(3)
% 0.32/0.48 thf(fact_303_usubstappt_Opsimps_I1_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( var @ X2 ) ) ) )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.32/0.48 = ( some_trm @ ( var @ X2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.psimps(1)
% 0.32/0.48 thf(fact_304_usubstappt_Opsimps_I2_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,R2: real] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( number @ R2 ) ) ) )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R2 ) )
% 0.32/0.48 = ( some_trm @ ( number @ R2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.psimps(2)
% 0.32/0.48 thf(fact_305_trm_Oinject_I2_J,axiom,
% 0.32/0.48 ! [X23: real,Y22: real] :
% 0.32/0.48 ( ( ( number @ X23 )
% 0.32/0.48 = ( number @ Y22 ) )
% 0.32/0.48 = ( X23 = Y22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(2)
% 0.32/0.48 thf(fact_306_trm_Oinject_I1_J,axiom,
% 0.32/0.48 ! [X13: variable,Y1: variable] :
% 0.32/0.48 ( ( ( var @ X13 )
% 0.32/0.48 = ( var @ Y1 ) )
% 0.32/0.48 = ( X13 = Y1 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(1)
% 0.32/0.48 thf(fact_307_trm_Odistinct_I15_J,axiom,
% 0.32/0.48 ! [X23: real,X41: char,X42: trm] :
% 0.32/0.48 ( ( number @ X23 )
% 0.32/0.48 != ( func @ X41 @ X42 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(15)
% 0.32/0.48 thf(fact_308_trm_Odistinct_I5_J,axiom,
% 0.32/0.48 ! [X13: variable,X41: char,X42: trm] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( func @ X41 @ X42 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(5)
% 0.32/0.48 thf(fact_309_trm_Odistinct_I1_J,axiom,
% 0.32/0.48 ! [X13: variable,X23: real] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( number @ X23 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(1)
% 0.32/0.48 thf(fact_310_trm_Odistinct_I13_J,axiom,
% 0.32/0.48 ! [X23: real,X32: char] :
% 0.32/0.48 ( ( number @ X23 )
% 0.32/0.48 != ( const @ X32 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(13)
% 0.32/0.48 thf(fact_311_trm_Odistinct_I3_J,axiom,
% 0.32/0.48 ! [X13: variable,X32: char] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( const @ X32 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(3)
% 0.32/0.48 thf(fact_312_usubstappt_Osimps_I2_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,R2: real] :
% 0.32/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R2 ) )
% 0.32/0.48 = ( some_trm @ ( number @ R2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.simps(2)
% 0.32/0.48 thf(fact_313_usubstappt_Osimps_I1_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.32/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.32/0.48 = ( some_trm @ ( var @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.simps(1)
% 0.32/0.48 thf(fact_314_usubstappt_Opinduct,axiom,
% 0.32/0.48 ! [A0: produc1418842292n_game,A1: set_variable,A22: trm,P2: produc1418842292n_game > set_variable > trm > $o] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A0 @ ( produc1482344242le_trm @ A1 @ A22 ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X3 ) ) ) )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 0.32/0.48 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ( ! [X25: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 = ( some_trm @ X25 ) )
% 0.32/0.48 => ! [X2a: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma3
% 0.32/0.48 @ F5 )
% 0.32/0.48 = ( some_trm @ X2a ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 => ( P2 @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( func @ F5 @ Theta2 ) ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.32/0.48 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) )
% 0.32/0.48 => ( ( P2 @ Sigma3
% 0.32/0.48 @ ( collect_variable
% 0.32/0.48 @ ^ [X: variable] : $true )
% 0.32/0.48 @ Theta2 )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) ) )
% 0.32/0.48 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.pinduct
% 0.32/0.48 thf(fact_315_dotsubstt__def,axiom,
% 0.32/0.48 ( uSubst1408967625substt
% 0.32/0.48 = ( ^ [Theta3: trm] :
% 0.32/0.48 ( produc1618635950n_game
% 0.32/0.48 @ ^ [F2: char] :
% 0.32/0.48 ( if_option_trm
% 0.32/0.48 @ ( F2
% 0.32/0.48 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 0.32/0.48 @ ( some_trm @ Theta3 )
% 0.32/0.48 @ none_trm )
% 0.32/0.48 @ ( produc1048060077n_game
% 0.32/0.48 @ ^ [Uu: char] : none_trm
% 0.32/0.48 @ ( produc123610156n_game
% 0.32/0.48 @ ^ [Uu: char] : none_fml
% 0.32/0.48 @ ^ [Uu: char] : none_game ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dotsubstt_def
% 0.32/0.48 thf(fact_316_trm_Oinject_I6_J,axiom,
% 0.32/0.48 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.32/0.48 ( ( ( times @ X61 @ X62 )
% 0.32/0.48 = ( times @ Y61 @ Y62 ) )
% 0.32/0.48 = ( ( X61 = Y61 )
% 0.32/0.48 & ( X62 = Y62 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(6)
% 0.32/0.48 thf(fact_317_trm_Oinject_I5_J,axiom,
% 0.32/0.48 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.32/0.48 ( ( ( plus @ X51 @ X52 )
% 0.32/0.48 = ( plus @ Y51 @ Y52 ) )
% 0.32/0.48 = ( ( X51 = Y51 )
% 0.32/0.48 & ( X52 = Y52 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(5)
% 0.32/0.48 thf(fact_318_trm_Oinject_I7_J,axiom,
% 0.32/0.48 ! [X7: trm,Y7: trm] :
% 0.32/0.48 ( ( ( differential @ X7 )
% 0.32/0.48 = ( differential @ Y7 ) )
% 0.32/0.48 = ( X7 = Y7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.inject(7)
% 0.32/0.48 thf(fact_319_trm_Odistinct_I7_J,axiom,
% 0.32/0.48 ! [X13: variable,X51: trm,X52: trm] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( plus @ X51 @ X52 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(7)
% 0.32/0.48 thf(fact_320_trm_Odistinct_I9_J,axiom,
% 0.32/0.48 ! [X13: variable,X61: trm,X62: trm] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( times @ X61 @ X62 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(9)
% 0.32/0.48 thf(fact_321_trm_Odistinct_I11_J,axiom,
% 0.32/0.48 ! [X13: variable,X7: trm] :
% 0.32/0.48 ( ( var @ X13 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(11)
% 0.32/0.48 thf(fact_322_trm_Odistinct_I17_J,axiom,
% 0.32/0.48 ! [X23: real,X51: trm,X52: trm] :
% 0.32/0.48 ( ( number @ X23 )
% 0.32/0.48 != ( plus @ X51 @ X52 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(17)
% 0.32/0.48 thf(fact_323_trm_Odistinct_I19_J,axiom,
% 0.32/0.48 ! [X23: real,X61: trm,X62: trm] :
% 0.32/0.48 ( ( number @ X23 )
% 0.32/0.48 != ( times @ X61 @ X62 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(19)
% 0.32/0.48 thf(fact_324_trm_Odistinct_I21_J,axiom,
% 0.32/0.48 ! [X23: real,X7: trm] :
% 0.32/0.48 ( ( number @ X23 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(21)
% 0.32/0.48 thf(fact_325_trm_Oexhaust,axiom,
% 0.32/0.48 ! [Y2: trm] :
% 0.32/0.48 ( ! [X14: variable] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( var @ X14 ) )
% 0.32/0.48 => ( ! [X24: real] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( number @ X24 ) )
% 0.32/0.48 => ( ! [X33: char] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( const @ X33 ) )
% 0.32/0.48 => ( ! [X412: char,X422: trm] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( func @ X412 @ X422 ) )
% 0.32/0.48 => ( ! [X512: trm,X522: trm] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( plus @ X512 @ X522 ) )
% 0.32/0.48 => ( ! [X612: trm,X622: trm] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( times @ X612 @ X622 ) )
% 0.32/0.48 => ~ ! [X72: trm] :
% 0.32/0.48 ( Y2
% 0.32/0.48 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.exhaust
% 0.32/0.48 thf(fact_326_trm_Oinduct,axiom,
% 0.32/0.48 ! [P2: trm > $o,Trm: trm] :
% 0.32/0.48 ( ! [X3: variable] : ( P2 @ ( var @ X3 ) )
% 0.32/0.48 => ( ! [X3: real] : ( P2 @ ( number @ X3 ) )
% 0.32/0.48 => ( ! [X3: char] : ( P2 @ ( const @ X3 ) )
% 0.32/0.48 => ( ! [X1a: char,X2a2: trm] :
% 0.32/0.48 ( ( P2 @ X2a2 )
% 0.32/0.48 => ( P2 @ ( func @ X1a @ X2a2 ) ) )
% 0.32/0.48 => ( ! [X1a: trm,X2a2: trm] :
% 0.32/0.48 ( ( P2 @ X1a )
% 0.32/0.48 => ( ( P2 @ X2a2 )
% 0.32/0.48 => ( P2 @ ( plus @ X1a @ X2a2 ) ) ) )
% 0.32/0.48 => ( ! [X1a: trm,X2a2: trm] :
% 0.32/0.48 ( ( P2 @ X1a )
% 0.32/0.48 => ( ( P2 @ X2a2 )
% 0.32/0.48 => ( P2 @ ( times @ X1a @ X2a2 ) ) ) )
% 0.32/0.48 => ( ! [X3: trm] :
% 0.32/0.48 ( ( P2 @ X3 )
% 0.32/0.48 => ( P2 @ ( differential @ X3 ) ) )
% 0.32/0.48 => ( P2 @ Trm ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.induct
% 0.32/0.48 thf(fact_327_trm_Odistinct_I25_J,axiom,
% 0.32/0.48 ! [X32: char,X51: trm,X52: trm] :
% 0.32/0.48 ( ( const @ X32 )
% 0.32/0.48 != ( plus @ X51 @ X52 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(25)
% 0.32/0.48 thf(fact_328_trm_Odistinct_I27_J,axiom,
% 0.32/0.48 ! [X32: char,X61: trm,X62: trm] :
% 0.32/0.48 ( ( const @ X32 )
% 0.32/0.48 != ( times @ X61 @ X62 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(27)
% 0.32/0.48 thf(fact_329_trm_Odistinct_I29_J,axiom,
% 0.32/0.48 ! [X32: char,X7: trm] :
% 0.32/0.48 ( ( const @ X32 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(29)
% 0.32/0.48 thf(fact_330_trm_Odistinct_I41_J,axiom,
% 0.32/0.48 ! [X61: trm,X62: trm,X7: trm] :
% 0.32/0.48 ( ( times @ X61 @ X62 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(41)
% 0.32/0.48 thf(fact_331_trm_Odistinct_I39_J,axiom,
% 0.32/0.48 ! [X51: trm,X52: trm,X7: trm] :
% 0.32/0.48 ( ( plus @ X51 @ X52 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(39)
% 0.32/0.48 thf(fact_332_trm_Odistinct_I37_J,axiom,
% 0.32/0.48 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.32/0.48 ( ( plus @ X51 @ X52 )
% 0.32/0.48 != ( times @ X61 @ X62 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(37)
% 0.32/0.48 thf(fact_333_trm_Odistinct_I31_J,axiom,
% 0.32/0.48 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.32/0.48 ( ( func @ X41 @ X42 )
% 0.32/0.48 != ( plus @ X51 @ X52 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(31)
% 0.32/0.48 thf(fact_334_trm_Odistinct_I33_J,axiom,
% 0.32/0.48 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.32/0.48 ( ( func @ X41 @ X42 )
% 0.32/0.48 != ( times @ X61 @ X62 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(33)
% 0.32/0.48 thf(fact_335_trm_Odistinct_I35_J,axiom,
% 0.32/0.48 ! [X41: char,X42: trm,X7: trm] :
% 0.32/0.48 ( ( func @ X41 @ X42 )
% 0.32/0.48 != ( differential @ X7 ) ) ).
% 0.32/0.48
% 0.32/0.48 % trm.distinct(35)
% 0.32/0.48 thf(fact_336_usubstappt_Ocases,axiom,
% 0.32/0.48 ! [X2: produc1699626005le_trm] :
% 0.32/0.48 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X3 ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ~ ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.32/0.48 ( X2
% 0.32/0.48 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.cases
% 0.32/0.48 thf(fact_337_usubstappt__times__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta2 ) )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.48 != none_trm )
% 0.32/0.48 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.32/0.48 != none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_times_conv
% 0.32/0.48 thf(fact_338_usubstappt__plus__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.32/0.48 != none_trm )
% 0.32/0.48 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 0.32/0.48 != none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_plus_conv
% 0.32/0.48 thf(fact_339_usubstappt__differential__conv,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.32/0.48 != none_trm )
% 0.32/0.48 => ( ( uSubst516392818stappt @ Sigma
% 0.32/0.48 @ ( collect_variable
% 0.32/0.48 @ ^ [X: variable] : $true )
% 0.32/0.48 @ Theta )
% 0.32/0.48 != none_trm ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_differential_conv
% 0.32/0.48 thf(fact_340_usubstappt__induct,axiom,
% 0.32/0.48 ! [P2: produc1418842292n_game > set_variable > trm > $o,A0: produc1418842292n_game,A1: set_variable,A22: trm] :
% 0.32/0.48 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] : ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] : ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] : ( P2 @ Sigma3 @ U3 @ ( const @ F5 ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ( ! [X25: trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 = ( some_trm @ X25 ) )
% 0.32/0.48 => ! [X2a: trm] :
% 0.32/0.48 ( ( ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ Sigma3
% 0.32/0.48 @ F5 )
% 0.32/0.48 = ( some_trm @ X2a ) )
% 0.32/0.48 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 => ( P2 @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ! [Eta: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 0.32/0.48 => ! [Eta: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 0.32/0.48 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.32/0.48 ( ( P2 @ Sigma3
% 0.32/0.48 @ ( collect_variable
% 0.32/0.48 @ ^ [X: variable] : $true )
% 0.32/0.48 @ Theta2 )
% 0.32/0.48 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) )
% 0.32/0.48 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt_induct
% 0.32/0.48 thf(fact_341_dot__def,axiom,
% 0.32/0.48 ( uSubst_Mirabelle_dot
% 0.32/0.48 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % dot_def
% 0.32/0.48 thf(fact_342_usubstappt_Opelims,axiom,
% 0.32/0.48 ! [X2: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 0.32/0.48 ( ( ( uSubst516392818stappt @ X2 @ Xa @ Xb )
% 0.32/0.48 = Y2 )
% 0.32/0.48 => ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ Xb ) ) )
% 0.32/0.48 => ( ! [X3: variable] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( var @ X3 ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( some_trm @ ( var @ X3 ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( var @ X3 ) ) ) ) ) )
% 0.32/0.48 => ( ! [R3: real] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( number @ R3 ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( some_trm @ ( number @ R3 ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 0.32/0.48 => ( ! [F5: char] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( const @ F5 ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( uSubst1559070963pconst @ X2 @ Xa @ F5 ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 0.32/0.48 => ( ! [F5: char,Theta2: trm] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( func @ F5 @ Theta2 ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( case_o487727941rm_trm @ none_trm
% 0.32/0.48 @ ^ [Sigma_theta: trm] :
% 0.32/0.48 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta ) )
% 0.32/0.48 @ ^ [R: trm] :
% 0.32/0.48 ( if_option_trm
% 0.32/0.48 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 0.32/0.48 = bot_bot_set_variable )
% 0.32/0.48 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 0.32/0.48 @ none_trm )
% 0.32/0.48 @ ( produc866613687on_trm
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1231571704on_trm
% 0.32/0.48 @ ^ [F4: char > option_trm] :
% 0.32/0.48 ( produc1036610745on_trm
% 0.32/0.48 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 0.32/0.48 @ X2
% 0.32/0.48 @ F5 ) )
% 0.32/0.48 @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( func @ F5 @ Theta2 ) ) ) ) ) )
% 0.32/0.48 => ( ! [Theta2: trm,Eta: trm] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( plus @ Theta2 @ Eta ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst516392818stappt @ X2 @ Xa @ Eta ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( plus @ Theta2 @ Eta ) ) ) ) ) )
% 0.32/0.48 => ( ! [Theta2: trm,Eta: trm] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( times @ Theta2 @ Eta ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst516392818stappt @ X2 @ Xa @ Eta ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( times @ Theta2 @ Eta ) ) ) ) ) )
% 0.32/0.48 => ~ ! [Theta2: trm] :
% 0.32/0.48 ( ( Xb
% 0.32/0.48 = ( differential @ Theta2 ) )
% 0.32/0.48 => ( ( Y2
% 0.32/0.48 = ( uSubst716837505ntialo
% 0.32/0.48 @ ( uSubst516392818stappt @ X2
% 0.32/0.48 @ ( collect_variable
% 0.32/0.48 @ ^ [X: variable] : $true )
% 0.32/0.48 @ Theta2 ) ) )
% 0.32/0.48 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.pelims
% 0.32/0.48 thf(fact_343_Differentialo_Osimps_I2_J,axiom,
% 0.32/0.48 ( ( uSubst716837505ntialo @ none_trm )
% 0.32/0.48 = none_trm ) ).
% 0.32/0.48
% 0.32/0.48 % Differentialo.simps(2)
% 0.32/0.48 thf(fact_344_Differentialo__undef,axiom,
% 0.32/0.48 ! [Theta: option_trm] :
% 0.32/0.48 ( ( ( uSubst716837505ntialo @ Theta )
% 0.32/0.48 = none_trm )
% 0.32/0.48 = ( Theta = none_trm ) ) ).
% 0.32/0.48
% 0.32/0.48 % Differentialo_undef
% 0.32/0.48 thf(fact_345_Pluso_Osimps_I2_J,axiom,
% 0.32/0.48 ! [Eta2: option_trm] :
% 0.32/0.48 ( ( uSubst141955042_Pluso @ none_trm @ Eta2 )
% 0.32/0.48 = none_trm ) ).
% 0.32/0.48
% 0.32/0.48 % Pluso.simps(2)
% 0.32/0.48 thf(fact_346_Timeso_Osimps_I2_J,axiom,
% 0.32/0.48 ! [Eta2: option_trm] :
% 0.32/0.48 ( ( uSubst918876924Timeso @ none_trm @ Eta2 )
% 0.32/0.48 = none_trm ) ).
% 0.32/0.48
% 0.32/0.48 % Timeso.simps(2)
% 0.32/0.48 thf(fact_347_Pluso__undef,axiom,
% 0.32/0.48 ! [Theta: option_trm,Eta2: option_trm] :
% 0.32/0.48 ( ( ( uSubst141955042_Pluso @ Theta @ Eta2 )
% 0.32/0.48 = none_trm )
% 0.32/0.48 = ( ( Theta = none_trm )
% 0.32/0.48 | ( Eta2 = none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Pluso_undef
% 0.32/0.48 thf(fact_348_Timeso__undef,axiom,
% 0.32/0.48 ! [Theta: option_trm,Eta2: option_trm] :
% 0.32/0.48 ( ( ( uSubst918876924Timeso @ Theta @ Eta2 )
% 0.32/0.48 = none_trm )
% 0.32/0.48 = ( ( Theta = none_trm )
% 0.32/0.48 | ( Eta2 = none_trm ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Timeso_undef
% 0.32/0.48 thf(fact_349_Pluso_Osimps_I3_J,axiom,
% 0.32/0.48 ! [V3: trm] :
% 0.32/0.48 ( ( uSubst141955042_Pluso @ ( some_trm @ V3 ) @ none_trm )
% 0.32/0.48 = none_trm ) ).
% 0.32/0.48
% 0.32/0.48 % Pluso.simps(3)
% 0.32/0.48 thf(fact_350_Timeso_Osimps_I3_J,axiom,
% 0.32/0.48 ! [V3: trm] :
% 0.32/0.48 ( ( uSubst918876924Timeso @ ( some_trm @ V3 ) @ none_trm )
% 0.32/0.48 = none_trm ) ).
% 0.32/0.48
% 0.32/0.48 % Timeso.simps(3)
% 0.32/0.48 thf(fact_351_usubstappt_Osimps_I5_J,axiom,
% 0.32/0.48 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 0.32/0.48 ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 0.32/0.48 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % usubstappt.simps(5)
% 0.32/0.48
% 0.32/0.48 % Helper facts (5)
% 0.32/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 0.32/0.48 ! [X2: option_fml,Y2: option_fml] :
% 0.32/0.48 ( ( if_option_fml @ $false @ X2 @ Y2 )
% 0.32/0.48 = Y2 ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 0.32/0.48 ! [X2: option_fml,Y2: option_fml] :
% 0.32/0.48 ( ( if_option_fml @ $true @ X2 @ Y2 )
% 0.32/0.48 = X2 ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.32/0.48 ! [P2: $o] :
% 0.32/0.48 ( ( P2 = $true )
% 0.32/0.48 | ( P2 = $false ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.32/0.48 ! [X2: option_trm,Y2: option_trm] :
% 0.32/0.48 ( ( if_option_trm @ $false @ X2 @ Y2 )
% 0.32/0.48 = Y2 ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 0.32/0.48 ! [X2: option_trm,Y2: option_trm] :
% 0.32/0.48 ( ( if_option_trm @ $true @ X2 @ Y2 )
% 0.32/0.48 = X2 ) ).
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 ( ( produc1250175341on_fml
% 0.32/0.48 @ ^ [Uu: char > option_trm] :
% 0.32/0.48 ( produc1615133358on_fml
% 0.32/0.48 @ ^ [Uv: char > option_trm] :
% 0.32/0.48 ( produc1420172399on_fml
% 0.32/0.48 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 0.32/0.48 @ sigma
% 0.32/0.48 @ p )
% 0.32/0.48 = none_fml ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 2.91/1.55 ---- Embedded in THF ---
% 2.91/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.91/1.56 %%% Generated on Tue Feb 24 08:29:56 EST 2026
% 2.91/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.91/1.56 %%% Logic specification used:
% 2.91/1.56 %%% thf(spec, logic, $$dhol).
% 2.91/1.56
% 2.91/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2DTF16880.p
% See solution above
% 2.91/1.56 ------------------------
% 2.91/1.59 ---- Cleaned THF ---
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1699626005le_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__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_J,type,
% 2.91/1.59 set_Pr720454634n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 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,
% 2.91/1.59 produc1418842292n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__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,
% 2.91/1.59 set_Pr739694057n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 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__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J,type,
% 2.91/1.59 produc62062515n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__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,type,
% 2.91/1.59 set_Pr79606376n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__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,type,
% 2.91/1.59 produc799602994n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.91/1.59 produc1016592119n_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1739631244on_fml: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1072747943on_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc46605351on_fml: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 2.91/1.59 set_Pr943832262on_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 2.91/1.59 set_Pr1235432374le_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1024976764on_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1408538418on_fml: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc464795408on_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 2.91/1.59 produc1367888000le_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.91/1.59 option_game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 option_trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 option_fml: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.91/1.59 set_variable: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Syntax__Ovariable,type,
% 2.91/1.59 variable: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Syntax__Ogame,type,
% 2.91/1.59 game: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__String__Ochar,type,
% 2.91/1.59 char: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Syntax__Otrm,type,
% 2.91/1.59 trm: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Syntax__Ofml,type,
% 2.91/1.59 fml: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(ty_n_t__Real__Oreal,type,
% 2.91/1.59 real: $tType ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 if_option_fml: $o > option_fml > option_fml > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_If_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 if_option_trm: $o > option_trm > option_trm > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 2.91/1.59 inf_in243546115game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( ( char > option_fml ) > ( char > option_game ) > $o ) > ( char > option_fml ) > ( char > option_game ) > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 2.91/1.59 inf_in1072207554game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > ( ( char > option_trm ) > produc799602994n_game > $o ) > ( char > option_trm ) > produc799602994n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 2.91/1.59 inf_in1920662529game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > ( ( char > option_trm ) > produc62062515n_game > $o ) > ( char > option_trm ) > produc62062515n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 2.91/1.59 inf_in185389155_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > set_variable > trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 2.91/1.59 inf_in605351507_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > char > option_trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 2.91/1.59 inf_inf_variable_o: ( variable > $o ) > ( variable > $o ) > variable > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,type,
% 2.91/1.59 inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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,
% 2.91/1.59 inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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_J,type,
% 2.91/1.59 inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 2.91/1.59 inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 2.91/1.59 inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.91/1.59 inf_inf_set_variable: set_variable > set_variable > set_variable ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 2.91/1.59 none_fml: option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 2.91/1.59 none_game: option_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 2.91/1.59 none_trm: option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 2.91/1.59 some_fml: fml > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 2.91/1.59 some_game: game > option_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 2.91/1.59 some_trm: trm > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 2.91/1.59 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 2.91/1.59 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 2.91/1.59 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Ofml,type,
% 2.91/1.59 case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Syntax__Otrm,type,
% 2.91/1.59 case_o325794063ml_trm: option_fml > ( trm > option_fml ) > option_trm > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Syntax__Otrm,type,
% 2.91/1.59 case_o487727941rm_trm: option_trm > ( trm > option_trm ) > option_trm > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 2.91/1.59 the_fml: option_fml > fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 2.91/1.59 the_game: option_game > game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 2.91/1.59 the_trm: option_trm > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_M_Eo_J_J,type,
% 2.91/1.59 bot_bo1895715589game_o: ( char > option_fml ) > ( char > option_game ) > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 2.91/1.59 bot_bo1417568964game_o: ( char > option_trm ) > produc799602994n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__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_M_Eo_J_J,type,
% 2.91/1.59 bot_bo849148163game_o: ( char > option_trm ) > produc62062515n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 2.91/1.59 bot_bo512610661_trm_o: set_variable > trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 2.91/1.59 bot_bo102862421_trm_o: char > option_trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 2.91/1.59 bot_bot_variable_o: variable > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,type,
% 2.91/1.59 bot_bo456479484n_game: set_Pr79606376n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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,
% 2.91/1.59 bot_bo1302831229n_game: set_Pr739694057n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__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_J,type,
% 2.91/1.59 bot_bo1453406334n_game: set_Pr720454634n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 2.91/1.59 bot_bo896421962le_trm: set_Pr1235432374le_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 2.91/1.59 bot_bo18861914on_trm: set_Pr943832262on_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 2.91/1.59 bot_bot_set_variable: set_variable ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 2.91/1.59 produc123610156n_game: ( char > option_fml ) > ( char > option_game ) > produc799602994n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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,type,
% 2.91/1.59 produc1048060077n_game: ( char > option_trm ) > produc799602994n_game > produc62062515n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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,type,
% 2.91/1.59 produc1618635950n_game: ( char > option_trm ) > produc62062515n_game > produc1418842292n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 2.91/1.59 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__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_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 2.91/1.59 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 2.91/1.59 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1598111045on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1214549391on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc1591622303on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc2129367017on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc377919108on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc2141841102on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc1903410526on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc293671592on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1278328899on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Ointernal__case__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc724717725on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1036610745on_trm: ( ( char > option_fml ) > ( char > option_game ) > char > option_trm ) > produc799602994n_game > char > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001_Eo,type,
% 2.91/1.59 produc159680767game_o: ( ( char > option_fml ) > ( char > option_game ) > $o ) > produc799602994n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc347802313on_fml: ( ( char > option_fml ) > ( char > option_game ) > option_fml ) > produc799602994n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc885547027on_trm: ( ( char > option_fml ) > ( char > option_game ) > option_trm ) > produc799602994n_game > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc1231571704on_trm: ( ( char > option_trm ) > produc799602994n_game > char > option_trm ) > produc62062515n_game > char > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_Eo,type,
% 2.91/1.59 produc1868740670game_o: ( ( char > option_trm ) > produc799602994n_game > $o ) > produc62062515n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc154833544on_fml: ( ( char > option_trm ) > produc799602994n_game > option_fml ) > produc62062515n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 2.91/1.59 produc692578258on_trm: ( ( char > option_trm ) > produc799602994n_game > option_trm ) > produc62062515n_game > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 2.91/1.59 produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.59 produc866613687on_trm: ( ( char > option_trm ) > produc62062515n_game > char > option_trm ) > produc1418842292n_game > char > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001_Eo,type,
% 2.91/1.59 produc1707653117game_o: ( ( char > option_trm ) > produc62062515n_game > $o ) > produc1418842292n_game > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__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_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 2.91/1.59 produc1499310791on_fml: ( ( char > option_trm ) > produc62062515n_game > option_fml ) > produc1418842292n_game > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm_001_Eo,type,
% 2.91/1.59 produc82209913_trm_o: ( set_variable > trm > $o ) > produc1367888000le_trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001_Eo,type,
% 2.91/1.59 produc584666985_trm_o: ( char > option_trm > $o ) > produc464795408on_trm > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 2.91/1.59 collect_variable: ( variable > $o ) > set_variable ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Set_Ois__empty_001t__Syntax__Ovariable,type,
% 2.91/1.59 is_empty_variable: set_variable > $o ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Static__Semantics_OFVF,type,
% 2.91/1.59 static_FVF: fml > set_variable ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Static__Semantics_OFVT,type,
% 2.91/1.59 static_FVT: trm > set_variable ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_String_Ochar_OChar,type,
% 2.91/1.59 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Ofml_OGeq,type,
% 2.91/1.59 geq: trm > trm > fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Ofml_OPred,type,
% 2.91/1.59 pred: char > trm > fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_OConst,type,
% 2.91/1.59 const: char > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 2.91/1.59 differential: trm > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_OFunc,type,
% 2.91/1.59 func: char > trm > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_ONumber,type,
% 2.91/1.59 number: real > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_OPlus,type,
% 2.91/1.59 plus: trm > trm > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_OTimes,type,
% 2.91/1.59 times: trm > trm > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_Syntax_Otrm_OVar,type,
% 2.91/1.59 var: variable > trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 2.91/1.59 uSubst716837505ntialo: option_trm > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 2.91/1.59 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 2.91/1.59 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto,type,
% 2.91/1.59 uSubst1367128042_Testo: option_fml > option_game ).
% 2.91/1.59
% 2.91/1.59 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 2.91/1.59 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odot,type,
% 2.91/1.60 uSubst_Mirabelle_dot: trm ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Odotsubstt,type,
% 2.91/1.60 uSubst1408967625substt: trm > produc1418842292n_game ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 2.91/1.60 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 2.91/1.60 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 2.91/1.60 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 2.91/1.60 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__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_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 2.91/1.60 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__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,type,
% 2.91/1.60 member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__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,type,
% 2.91/1.60 member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__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,
% 2.91/1.60 member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 2.91/1.60 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 2.91/1.60 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 2.91/1.60 member_variable: variable > set_variable > $o ).
% 2.91/1.60
% 2.91/1.60 thf(sy_v_Ua____,type,
% 2.91/1.60 ua: set_variable ).
% 2.91/1.60
% 2.91/1.60 thf(sy_v_Va____,type,
% 2.91/1.60 va: set_variable ).
% 2.91/1.60
% 2.91/1.60 thf(sy_v__092_060sigma_062,type,
% 2.91/1.60 sigma: produc1418842292n_game ).
% 2.91/1.60
% 2.91/1.60 thf(sy_v__092_060theta_062____,type,
% 2.91/1.60 theta: trm ).
% 2.91/1.60
% 2.91/1.60 thf(sy_v_p____,type,
% 2.91/1.60 p: char ).
% 2.91/1.60
% 2.91/1.60 thf(fact_0_f7,axiom,
% 2.91/1.60 ! [Z: option_fml,F: fml > option_fml,Za: option_fml] :
% 2.91/1.60 ( ( ( Za = none_fml )
% 2.91/1.60 => ( ( case_o209804997ml_fml @ Z @ F @ Za )
% 2.91/1.60 = Z ) )
% 2.91/1.60 & ( ( Za != none_fml )
% 2.91/1.60 => ( ( case_o209804997ml_fml @ Z @ F @ Za )
% 2.91/1.60 = ( F @ ( the_fml @ Za ) ) ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_1_Pred_Oprems_I2_J,axiom,
% 2.91/1.60 ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
% 2.91/1.60 != none_fml ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_2_case__prod__app,axiom,
% 2.91/1.60 ( produc1250175341on_fml
% 2.91/1.60 = ( ^ [F2: ( char > option_trm ) > produc62062515n_game > char > option_fml,X: produc1418842292n_game,Y: char] :
% 2.91/1.60 ( produc1499310791on_fml
% 2.91/1.60 @ ^ [L: char > option_trm,R: produc62062515n_game] : ( F2 @ L @ R @ Y )
% 2.91/1.60 @ X ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_3_case__prod__app,axiom,
% 2.91/1.60 ( produc1231571704on_trm
% 2.91/1.60 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_trm,X: produc62062515n_game,Y: char] :
% 2.91/1.60 ( produc692578258on_trm
% 2.91/1.60 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 2.91/1.60 @ X ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_4_case__prod__app,axiom,
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 = ( ^ [F2: ( char > option_trm ) > produc799602994n_game > char > option_fml,X: produc62062515n_game,Y: char] :
% 2.91/1.60 ( produc154833544on_fml
% 2.91/1.60 @ ^ [L: char > option_trm,R: produc799602994n_game] : ( F2 @ L @ R @ Y )
% 2.91/1.60 @ X ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_5_case__prod__app,axiom,
% 2.91/1.60 ( produc1036610745on_trm
% 2.91/1.60 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_trm,X: produc799602994n_game,Y: char] :
% 2.91/1.60 ( produc885547027on_trm
% 2.91/1.60 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 2.91/1.60 @ X ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_6_case__prod__app,axiom,
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 = ( ^ [F2: ( char > option_fml ) > ( char > option_game ) > char > option_fml,X: produc799602994n_game,Y: char] :
% 2.91/1.60 ( produc347802313on_fml
% 2.91/1.60 @ ^ [L: char > option_fml,R: char > option_game] : ( F2 @ L @ R @ Y )
% 2.91/1.60 @ X ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_7_Pred_Oprems_I1_J,axiom,
% 2.91/1.60 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 != none_fml ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,axiom,
% 2.91/1.60 ~ ( ( ( inf_inf_set_variable
% 2.91/1.60 @ ( static_FVF
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) )
% 2.91/1.60 @ va )
% 2.91/1.60 != bot_bot_set_variable )
% 2.91/1.60 => ( none_fml
% 2.91/1.60 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_9_f9,axiom,
% 2.91/1.60 ( ( ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p )
% 2.91/1.60 = none_fml )
% 2.91/1.60 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 = ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,axiom,
% 2.91/1.60 ~ ( ( ( ( inf_inf_set_variable
% 2.91/1.60 @ ( static_FVF
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) )
% 2.91/1.60 @ va )
% 2.91/1.60 = bot_bot_set_variable )
% 2.91/1.60 => ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 2.91/1.60 @ ^ [F2: fml] :
% 2.91/1.60 ( if_option_fml
% 2.91/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 2.91/1.60 = bot_bot_set_variable )
% 2.91/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 2.91/1.60 @ none_fml )
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) )
% 2.91/1.60 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) ) ) )
% 2.91/1.60 & ( ( ( inf_inf_set_variable
% 2.91/1.60 @ ( static_FVF
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) )
% 2.91/1.60 @ va )
% 2.91/1.60 != bot_bot_set_variable )
% 2.91/1.60 => ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 2.91/1.60 @ ^ [F2: fml] :
% 2.91/1.60 ( if_option_fml
% 2.91/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 2.91/1.60 = bot_bot_set_variable )
% 2.91/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 2.91/1.60 @ none_fml )
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) )
% 2.91/1.60 = none_fml ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_11_Ando_Oinduct,axiom,
% 2.91/1.60 ! [P2: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 2.91/1.60 ( ! [Phi: fml,Psi: fml] : ( P2 @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) )
% 2.91/1.60 => ( ! [X_1: option_fml] : ( P2 @ none_fml @ X_1 )
% 2.91/1.60 => ( ! [V: fml] : ( P2 @ ( some_fml @ V ) @ none_fml )
% 2.91/1.60 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_12_Testo_Ocases,axiom,
% 2.91/1.60 ! [X2: option_fml] :
% 2.91/1.60 ( ! [Phi: fml] :
% 2.91/1.60 ( X2
% 2.91/1.60 != ( some_fml @ Phi ) )
% 2.91/1.60 => ( X2 = none_fml ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_13_Testo_Oinduct,axiom,
% 2.91/1.60 ! [P2: option_fml > $o,A0: option_fml] :
% 2.91/1.60 ( ! [Phi: fml] : ( P2 @ ( some_fml @ Phi ) )
% 2.91/1.60 => ( ( P2 @ none_fml )
% 2.91/1.60 => ( P2 @ A0 ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_14_undeff__equiv,axiom,
% 2.91/1.60 ! [Phi2: option_fml] :
% 2.91/1.60 ( ( Phi2 != none_fml )
% 2.91/1.60 = ( ? [F2: fml] :
% 2.91/1.60 ( Phi2
% 2.91/1.60 = ( some_fml @ F2 ) ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_15_Existso_Oinduct,axiom,
% 2.91/1.60 ! [P2: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 2.91/1.60 ( ! [X3: variable,Phi: fml] : ( P2 @ X3 @ ( some_fml @ Phi ) )
% 2.91/1.60 => ( ! [X3: variable] : ( P2 @ X3 @ none_fml )
% 2.91/1.60 => ( P2 @ A0 @ A1 ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_16_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_fml > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc347802313on_fml
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_17_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_fml > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc885547027on_trm
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_18_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_trm > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc885547027on_trm @ F3 @ Prod ) )
% 2.91/1.60 = ( produc347802313on_fml
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_19_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_trm > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_trm,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc885547027on_trm @ F3 @ Prod ) )
% 2.91/1.60 = ( produc885547027on_trm
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_20_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: ( char > option_trm ) > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 2.91/1.60 = ( produc347802313on_fml
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_21_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: ( char > option_trm ) > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc1036610745on_trm @ F3 @ Prod ) )
% 2.91/1.60 = ( produc885547027on_trm
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_22_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: ( char > option_fml ) > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc347802313on_fml
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_23_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: ( char > option_fml ) > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc1420172399on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc885547027on_trm
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_24_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_fml > char > option_trm,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc1036610745on_trm
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_25_prod_Ocase__distrib,axiom,
% 2.91/1.60 ! [H: option_fml > char > option_fml,F3: ( char > option_fml ) > ( char > option_game ) > option_fml,Prod: produc799602994n_game] :
% 2.91/1.60 ( ( H @ ( produc347802313on_fml @ F3 @ Prod ) )
% 2.91/1.60 = ( produc1420172399on_fml
% 2.91/1.60 @ ^ [X1: char > option_fml,X22: char > option_game] : ( H @ ( F3 @ X1 @ X22 ) )
% 2.91/1.60 @ Prod ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
% 2.91/1.60 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 != ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_27_f5,axiom,
% 2.91/1.60 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 2.91/1.60 = ( uSubst516392818stappt @ sigma @ va @ theta ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_28_calculation_I1_J,axiom,
% 2.91/1.60 ~ ( ( ( ( inf_inf_set_variable
% 2.91/1.60 @ ( static_FVF
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) )
% 2.91/1.60 @ va )
% 2.91/1.60 = bot_bot_set_variable )
% 2.91/1.60 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) ) ) )
% 2.91/1.60 & ( ( ( inf_inf_set_variable
% 2.91/1.60 @ ( static_FVF
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) )
% 2.91/1.60 @ va )
% 2.91/1.60 != bot_bot_set_variable )
% 2.91/1.60 => ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 = none_fml ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_29_calculation_I2_J,axiom,
% 2.91/1.60 ( ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 != ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
% 2.91/1.60 @ ( the_fml
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) ) )
% 2.91/1.60 => ( ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p )
% 2.91/1.60 = none_fml ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_30_f6,axiom,
% 2.91/1.60 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 2.91/1.60 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 2.91/1.60 @ ^ [F2: fml] :
% 2.91/1.60 ( if_option_fml
% 2.91/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 2.91/1.60 = bot_bot_set_variable )
% 2.91/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 2.91/1.60 @ none_fml )
% 2.91/1.60 @ ( produc1250175341on_fml
% 2.91/1.60 @ ^ [Uu: char > option_trm] :
% 2.91/1.60 ( produc1615133358on_fml
% 2.91/1.60 @ ^ [Uv: char > option_trm] :
% 2.91/1.60 ( produc1420172399on_fml
% 2.91/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 2.91/1.60 @ sigma
% 2.91/1.60 @ p ) ) ) ).
% 2.91/1.60
% 2.91/1.60 thf(fact_31__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_A_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_092_060close_062,axiom,
% 3.05/1.60 ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
% 3.05/1.60 != ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_32_usubstappf__pred2,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,P3: char,R2: fml,U: set_variable,Theta: trm] :
% 3.05/1.60 ( ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ P3 )
% 3.05/1.60 = ( some_fml @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 3.05/1.60 != bot_bot_set_variable )
% 3.05/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.05/1.60 = none_fml ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_33_f3,axiom,
% 3.05/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.05/1.60 @ ^ [T: trm] :
% 3.05/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 3.05/1.60 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_34_f8,axiom,
% 3.05/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.05/1.60 @ ^ [T: trm] :
% 3.05/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ sigma @ va @ theta ) )
% 3.05/1.60 = ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_35_f1,axiom,
% 3.05/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.05/1.60 @ ^ [T: trm] :
% 3.05/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ ua )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ sigma @ ua @ theta ) )
% 3.05/1.60 != none_fml ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_36_f4,axiom,
% 3.05/1.60 ( ( case_o325794063ml_trm @ none_fml
% 3.05/1.60 @ ^ [T: trm] :
% 3.05/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ T ) )
% 3.05/1.60 @ ^ [F2: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ F2 ) @ va )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ T ) @ bot_bot_set_variable @ F2 )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ sigma @ va @ theta ) )
% 3.05/1.60 != none_fml ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_37_option_Ocollapse,axiom,
% 3.05/1.60 ! [Option: option_fml] :
% 3.05/1.60 ( ( Option != none_fml )
% 3.05/1.60 => ( ( some_fml @ ( the_fml @ Option ) )
% 3.05/1.60 = Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_38_option_Ocollapse,axiom,
% 3.05/1.60 ! [Option: option_trm] :
% 3.05/1.60 ( ( Option != none_trm )
% 3.05/1.60 => ( ( some_trm @ ( the_trm @ Option ) )
% 3.05/1.60 = Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_39_option_Ocollapse,axiom,
% 3.05/1.60 ! [Option: option_game] :
% 3.05/1.60 ( ( Option != none_game )
% 3.05/1.60 => ( ( some_game @ ( the_game @ Option ) )
% 3.05/1.60 = Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_40_not__Some__eq,axiom,
% 3.05/1.60 ! [X2: option_fml] :
% 3.05/1.60 ( ( ! [Y: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( some_fml @ Y ) ) )
% 3.05/1.60 = ( X2 = none_fml ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_41_not__Some__eq,axiom,
% 3.05/1.60 ! [X2: option_trm] :
% 3.05/1.60 ( ( ! [Y: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( some_trm @ Y ) ) )
% 3.05/1.60 = ( X2 = none_trm ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_42_not__Some__eq,axiom,
% 3.05/1.60 ! [X2: option_game] :
% 3.05/1.60 ( ( ! [Y: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( some_game @ Y ) ) )
% 3.05/1.60 = ( X2 = none_game ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_43_not__None__eq,axiom,
% 3.05/1.60 ! [X2: option_fml] :
% 3.05/1.60 ( ( X2 != none_fml )
% 3.05/1.60 = ( ? [Y: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 = ( some_fml @ Y ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_44_not__None__eq,axiom,
% 3.05/1.60 ! [X2: option_trm] :
% 3.05/1.60 ( ( X2 != none_trm )
% 3.05/1.60 = ( ? [Y: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 = ( some_trm @ Y ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_45_not__None__eq,axiom,
% 3.05/1.60 ! [X2: option_game] :
% 3.05/1.60 ( ( X2 != none_game )
% 3.05/1.60 = ( ? [Y: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 = ( some_game @ Y ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_46_usubstappf_Osimps_I1_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,P3: char,Theta: trm] :
% 3.05/1.60 ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.05/1.60 = ( case_o325794063ml_trm @ none_fml
% 3.05/1.60 @ ^ [Sigma_theta: trm] :
% 3.05/1.60 ( case_o209804997ml_fml @ ( some_fml @ ( pred @ P3 @ Sigma_theta ) )
% 3.05/1.60 @ ^ [R: fml] :
% 3.05/1.60 ( if_option_fml
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVF @ R ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.05/1.60 @ none_fml )
% 3.05/1.60 @ ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ P3 ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_47_inf__bot__left,axiom,
% 3.05/1.60 ! [X2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ bot_bot_set_variable @ X2 )
% 3.05/1.60 = bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_48_inf__bot__right,axiom,
% 3.05/1.60 ! [X2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ bot_bot_set_variable )
% 3.05/1.60 = bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_49_option_Osplit__sel__asm,axiom,
% 3.05/1.60 ! [P2: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.05/1.60 ( ( P2 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ~ ( ( ( Option = none_fml )
% 3.05/1.60 & ~ ( P2 @ F1 ) )
% 3.05/1.60 | ( ( Option
% 3.05/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.05/1.60 & ~ ( P2 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_50_option_Osplit__sel__asm,axiom,
% 3.05/1.60 ! [P2: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.05/1.60 ( ( P2 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ~ ( ( ( Option = none_trm )
% 3.05/1.60 & ~ ( P2 @ F1 ) )
% 3.05/1.60 | ( ( Option
% 3.05/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.60 & ~ ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_51_option_Osplit__sel__asm,axiom,
% 3.05/1.60 ! [P2: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.60 ( ( P2 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ~ ( ( ( Option = none_trm )
% 3.05/1.60 & ~ ( P2 @ F1 ) )
% 3.05/1.60 | ( ( Option
% 3.05/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.60 & ~ ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_52_f2,axiom,
% 3.05/1.60 ! [Z: option_fml,F: trm > option_fml,Za: option_trm] :
% 3.05/1.60 ( ( ( Za = none_trm )
% 3.05/1.60 => ( ( case_o325794063ml_trm @ Z @ F @ Za )
% 3.05/1.60 = Z ) )
% 3.05/1.60 & ( ( Za != none_trm )
% 3.05/1.60 => ( ( case_o325794063ml_trm @ Z @ F @ Za )
% 3.05/1.60 = ( F @ ( the_trm @ Za ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_53_inf__right__idem,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Y2 )
% 3.05/1.60 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_54_inf_Oright__idem,axiom,
% 3.05/1.60 ! [A: set_variable,B: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ B )
% 3.05/1.60 = ( inf_inf_set_variable @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_55_inf__left__idem,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ X2 @ Y2 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_56_inf_Oleft__idem,axiom,
% 3.05/1.60 ! [A: set_variable,B: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ A @ B ) )
% 3.05/1.60 = ( inf_inf_set_variable @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_57_inf__idem,axiom,
% 3.05/1.60 ! [X2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ X2 )
% 3.05/1.60 = X2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_58_inf_Oidem,axiom,
% 3.05/1.60 ! [A: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A @ A )
% 3.05/1.60 = A ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_59_option_Oinject,axiom,
% 3.05/1.60 ! [X23: fml,Y22: fml] :
% 3.05/1.60 ( ( ( some_fml @ X23 )
% 3.05/1.60 = ( some_fml @ Y22 ) )
% 3.05/1.60 = ( X23 = Y22 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_60_option_Oinject,axiom,
% 3.05/1.60 ! [X23: trm,Y22: trm] :
% 3.05/1.60 ( ( ( some_trm @ X23 )
% 3.05/1.60 = ( some_trm @ Y22 ) )
% 3.05/1.60 = ( X23 = Y22 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_61_option_Oinject,axiom,
% 3.05/1.60 ! [X23: game,Y22: game] :
% 3.05/1.60 ( ( ( some_game @ X23 )
% 3.05/1.60 = ( some_game @ Y22 ) )
% 3.05/1.60 = ( X23 = Y22 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_62_usubstappf__pred,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,P3: char,R2: fml,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 3.05/1.60 ( ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ P3 )
% 3.05/1.60 = ( some_fml @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVF @ R2 ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 = ( some_trm @ Sigma_theta2 ) )
% 3.05/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.05/1.60 = ( uSubst516392804stappf @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_63_Diamondo_Oinduct,axiom,
% 3.05/1.60 ! [P2: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 3.05/1.60 ( ! [Alpha: game,Phi: fml] : ( P2 @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) )
% 3.05/1.60 => ( ! [X_1: option_fml] : ( P2 @ none_game @ X_1 )
% 3.05/1.60 => ( ! [V: game] : ( P2 @ ( some_game @ V ) @ none_fml )
% 3.05/1.60 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_64_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.60 ! [Option: option_fml] :
% 3.05/1.60 ( ( Option != none_fml )
% 3.05/1.60 = ( case_option_o_fml @ $false
% 3.05/1.60 @ ^ [Uu: fml] : $true
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_65_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.60 ! [Option: option_trm] :
% 3.05/1.60 ( ( Option != none_trm )
% 3.05/1.60 = ( case_option_o_trm @ $false
% 3.05/1.60 @ ^ [Uu: trm] : $true
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_66_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.60 ! [Option: option_game] :
% 3.05/1.60 ( ( Option != none_game )
% 3.05/1.60 = ( case_option_o_game @ $false
% 3.05/1.60 @ ^ [Uu: game] : $true
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_67_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.60 ! [Option: option_fml] :
% 3.05/1.60 ( ( Option = none_fml )
% 3.05/1.60 = ( case_option_o_fml @ $true
% 3.05/1.60 @ ^ [Uu: fml] : $false
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_68_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.60 ! [Option: option_trm] :
% 3.05/1.60 ( ( Option = none_trm )
% 3.05/1.60 = ( case_option_o_trm @ $true
% 3.05/1.60 @ ^ [Uu: trm] : $false
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_69_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.60 ! [Option: option_game] :
% 3.05/1.60 ( ( Option = none_game )
% 3.05/1.60 = ( case_option_o_game @ $true
% 3.05/1.60 @ ^ [Uu: game] : $false
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_70_usubstappt__det,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V2: set_variable] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ V2 @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 = ( uSubst516392818stappt @ Sigma @ V2 @ Theta ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_71_mem__Collect__eq,axiom,
% 3.05/1.60 ! [A: variable,P2: variable > $o] :
% 3.05/1.60 ( ( member_variable @ A @ ( collect_variable @ P2 ) )
% 3.05/1.60 = ( P2 @ A ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_72_Collect__mem__eq,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : ( member_variable @ X @ A2 ) )
% 3.05/1.60 = A2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_73_Collect__cong,axiom,
% 3.05/1.60 ! [P2: variable > $o,Q: variable > $o] :
% 3.05/1.60 ( ! [X3: variable] :
% 3.05/1.60 ( ( P2 @ X3 )
% 3.05/1.60 = ( Q @ X3 ) )
% 3.05/1.60 => ( ( collect_variable @ P2 )
% 3.05/1.60 = ( collect_variable @ Q ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_74_case__optionE,axiom,
% 3.05/1.60 ! [P2: $o,Q: fml > $o,X2: option_fml] :
% 3.05/1.60 ( ( case_option_o_fml @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( ( X2 = none_fml )
% 3.05/1.60 => ~ P2 )
% 3.05/1.60 => ~ ! [Y3: fml] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_fml @ Y3 ) )
% 3.05/1.60 => ~ ( Q @ Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_75_case__optionE,axiom,
% 3.05/1.60 ! [P2: $o,Q: trm > $o,X2: option_trm] :
% 3.05/1.60 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( ( X2 = none_trm )
% 3.05/1.60 => ~ P2 )
% 3.05/1.60 => ~ ! [Y3: trm] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_trm @ Y3 ) )
% 3.05/1.60 => ~ ( Q @ Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_76_case__optionE,axiom,
% 3.05/1.60 ! [P2: $o,Q: game > $o,X2: option_game] :
% 3.05/1.60 ( ( case_option_o_game @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( ( X2 = none_game )
% 3.05/1.60 => ~ P2 )
% 3.05/1.60 => ~ ! [Y3: game] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_game @ Y3 ) )
% 3.05/1.60 => ~ ( Q @ Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_77_inf__left__commute,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X2 @ Z2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_78_inf_Oleft__commute,axiom,
% 3.05/1.60 ! [B: set_variable,A: set_variable,C: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ B @ ( inf_inf_set_variable @ A @ C ) )
% 3.05/1.60 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_79_inf__commute,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_80_inf_Ocommute,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [A3: set_variable,B2: set_variable] : ( inf_inf_set_variable @ B2 @ A3 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_81_inf__assoc,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Z2 )
% 3.05/1.60 = ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_82_inf_Oassoc,axiom,
% 3.05/1.60 ! [A: set_variable,B: set_variable,C: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A @ B ) @ C )
% 3.05/1.60 = ( inf_inf_set_variable @ A @ ( inf_inf_set_variable @ B @ C ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_83_boolean__algebra__cancel_Oinf2,axiom,
% 3.05/1.60 ! [B3: set_variable,K: set_variable,B: set_variable,A: set_variable] :
% 3.05/1.60 ( ( B3
% 3.05/1.60 = ( inf_inf_set_variable @ K @ B ) )
% 3.05/1.60 => ( ( inf_inf_set_variable @ A @ B3 )
% 3.05/1.60 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_84_boolean__algebra__cancel_Oinf1,axiom,
% 3.05/1.60 ! [A2: set_variable,K: set_variable,A: set_variable,B: set_variable] :
% 3.05/1.60 ( ( A2
% 3.05/1.60 = ( inf_inf_set_variable @ K @ A ) )
% 3.05/1.60 => ( ( inf_inf_set_variable @ A2 @ B )
% 3.05/1.60 = ( inf_inf_set_variable @ K @ ( inf_inf_set_variable @ A @ B ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_85_inf__sup__aci_I1_J,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [X: set_variable,Y: set_variable] : ( inf_inf_set_variable @ Y @ X ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_86_inf__sup__aci_I2_J,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ X2 @ Y2 ) @ Z2 )
% 3.05/1.60 = ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_87_inf__sup__aci_I3_J,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ Y2 @ Z2 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ Y2 @ ( inf_inf_set_variable @ X2 @ Z2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_88_inf__sup__aci_I4_J,axiom,
% 3.05/1.60 ! [X2: set_variable,Y2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ X2 @ ( inf_inf_set_variable @ X2 @ Y2 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ X2 @ Y2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_89_option_Ocase__distrib,axiom,
% 3.05/1.60 ! [H: option_fml > option_fml,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.05/1.60 ( ( H @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( case_o209804997ml_fml @ ( H @ F1 )
% 3.05/1.60 @ ^ [X: fml] : ( H @ ( F22 @ X ) )
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_90_option_Ocase__distrib,axiom,
% 3.05/1.60 ! [H: option_fml > option_fml,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.05/1.60 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( case_o325794063ml_trm @ ( H @ F1 )
% 3.05/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_91_option_Ocase__distrib,axiom,
% 3.05/1.60 ! [H: option_fml > option_trm,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.05/1.60 ( ( H @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( case_o487727941rm_trm @ ( H @ F1 )
% 3.05/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_92_option_Ocase__distrib,axiom,
% 3.05/1.60 ! [H: option_trm > option_fml,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.60 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( case_o325794063ml_trm @ ( H @ F1 )
% 3.05/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_93_option_Ocase__distrib,axiom,
% 3.05/1.60 ! [H: option_trm > option_trm,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.60 ( ( H @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( case_o487727941rm_trm @ ( H @ F1 )
% 3.05/1.60 @ ^ [X: trm] : ( H @ ( F22 @ X ) )
% 3.05/1.60 @ Option ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_94_option_Odistinct_I1_J,axiom,
% 3.05/1.60 ! [X23: fml] :
% 3.05/1.60 ( none_fml
% 3.05/1.60 != ( some_fml @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_95_option_Odistinct_I1_J,axiom,
% 3.05/1.60 ! [X23: trm] :
% 3.05/1.60 ( none_trm
% 3.05/1.60 != ( some_trm @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_96_option_Odistinct_I1_J,axiom,
% 3.05/1.60 ! [X23: game] :
% 3.05/1.60 ( none_game
% 3.05/1.60 != ( some_game @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_97_option_OdiscI,axiom,
% 3.05/1.60 ! [Option: option_fml,X23: fml] :
% 3.05/1.60 ( ( Option
% 3.05/1.60 = ( some_fml @ X23 ) )
% 3.05/1.60 => ( Option != none_fml ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_98_option_OdiscI,axiom,
% 3.05/1.60 ! [Option: option_trm,X23: trm] :
% 3.05/1.60 ( ( Option
% 3.05/1.60 = ( some_trm @ X23 ) )
% 3.05/1.60 => ( Option != none_trm ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_99_option_OdiscI,axiom,
% 3.05/1.60 ! [Option: option_game,X23: game] :
% 3.05/1.60 ( ( Option
% 3.05/1.60 = ( some_game @ X23 ) )
% 3.05/1.60 => ( Option != none_game ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_100_option_Oexhaust,axiom,
% 3.05/1.60 ! [Y2: option_fml] :
% 3.05/1.60 ( ( Y2 != none_fml )
% 3.05/1.60 => ~ ! [X24: fml] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( some_fml @ X24 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_101_option_Oexhaust,axiom,
% 3.05/1.60 ! [Y2: option_trm] :
% 3.05/1.60 ( ( Y2 != none_trm )
% 3.05/1.60 => ~ ! [X24: trm] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( some_trm @ X24 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_102_option_Oexhaust,axiom,
% 3.05/1.60 ! [Y2: option_game] :
% 3.05/1.60 ( ( Y2 != none_game )
% 3.05/1.60 => ~ ! [X24: game] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( some_game @ X24 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_103_option_Oinducts,axiom,
% 3.05/1.60 ! [P2: option_fml > $o,Option: option_fml] :
% 3.05/1.60 ( ( P2 @ none_fml )
% 3.05/1.60 => ( ! [X3: fml] : ( P2 @ ( some_fml @ X3 ) )
% 3.05/1.60 => ( P2 @ Option ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_104_option_Oinducts,axiom,
% 3.05/1.60 ! [P2: option_trm > $o,Option: option_trm] :
% 3.05/1.60 ( ( P2 @ none_trm )
% 3.05/1.60 => ( ! [X3: trm] : ( P2 @ ( some_trm @ X3 ) )
% 3.05/1.60 => ( P2 @ Option ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_105_option_Oinducts,axiom,
% 3.05/1.60 ! [P2: option_game > $o,Option: option_game] :
% 3.05/1.60 ( ( P2 @ none_game )
% 3.05/1.60 => ( ! [X3: game] : ( P2 @ ( some_game @ X3 ) )
% 3.05/1.60 => ( P2 @ Option ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_106_split__option__ex,axiom,
% 3.05/1.60 ( ( ^ [P4: option_fml > $o] :
% 3.05/1.60 ? [X4: option_fml] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_fml > $o] :
% 3.05/1.60 ( ( P @ none_fml )
% 3.05/1.60 | ? [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_107_split__option__ex,axiom,
% 3.05/1.60 ( ( ^ [P4: option_trm > $o] :
% 3.05/1.60 ? [X4: option_trm] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_trm > $o] :
% 3.05/1.60 ( ( P @ none_trm )
% 3.05/1.60 | ? [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_108_split__option__ex,axiom,
% 3.05/1.60 ( ( ^ [P4: option_game > $o] :
% 3.05/1.60 ? [X4: option_game] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_game > $o] :
% 3.05/1.60 ( ( P @ none_game )
% 3.05/1.60 | ? [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_109_split__option__all,axiom,
% 3.05/1.60 ( ( ^ [P4: option_fml > $o] :
% 3.05/1.60 ! [X4: option_fml] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_fml > $o] :
% 3.05/1.60 ( ( P @ none_fml )
% 3.05/1.60 & ! [X: fml] : ( P @ ( some_fml @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_110_split__option__all,axiom,
% 3.05/1.60 ( ( ^ [P4: option_trm > $o] :
% 3.05/1.60 ! [X4: option_trm] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_trm > $o] :
% 3.05/1.60 ( ( P @ none_trm )
% 3.05/1.60 & ! [X: trm] : ( P @ ( some_trm @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_111_split__option__all,axiom,
% 3.05/1.60 ( ( ^ [P4: option_game > $o] :
% 3.05/1.60 ! [X4: option_game] : ( P4 @ X4 ) )
% 3.05/1.60 = ( ^ [P: option_game > $o] :
% 3.05/1.60 ( ( P @ none_game )
% 3.05/1.60 & ! [X: game] : ( P @ ( some_game @ X ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_112_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_fml,P2: option_fml > option_fml > $o,Y2: option_fml] :
% 3.05/1.60 ( ( ( X2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: fml,B4: fml] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_fml @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_fml @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_113_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_fml,P2: option_fml > option_trm > $o,Y2: option_trm] :
% 3.05/1.60 ( ( ( X2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: fml,B4: trm] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_fml @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_trm @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_114_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_fml,P2: option_fml > option_game > $o,Y2: option_game] :
% 3.05/1.60 ( ( ( X2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: fml,B4: game] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_fml @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_game @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_115_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_trm,P2: option_trm > option_fml > $o,Y2: option_fml] :
% 3.05/1.60 ( ( ( X2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: trm,B4: fml] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_trm @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_fml @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_116_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_trm,P2: option_trm > option_trm > $o,Y2: option_trm] :
% 3.05/1.60 ( ( ( X2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: trm,B4: trm] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_trm @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_trm @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_117_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_trm,P2: option_trm > option_game > $o,Y2: option_game] :
% 3.05/1.60 ( ( ( X2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: trm,B4: game] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_trm @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_game @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_118_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_game,P2: option_game > option_fml > $o,Y2: option_fml] :
% 3.05/1.60 ( ( ( X2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_fml )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: game,B4: fml] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_game @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_fml @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_119_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_game,P2: option_game > option_trm > $o,Y2: option_trm] :
% 3.05/1.60 ( ( ( X2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_trm )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: game,B4: trm] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_game @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_trm @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_120_combine__options__cases,axiom,
% 3.05/1.60 ! [X2: option_game,P2: option_game > option_game > $o,Y2: option_game] :
% 3.05/1.60 ( ( ( X2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ( ( Y2 = none_game )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) )
% 3.05/1.60 => ( ! [A4: game,B4: game] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_game @ A4 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_game @ B4 ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) )
% 3.05/1.60 => ( P2 @ X2 @ Y2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_121_option_Osimps_I4_J,axiom,
% 3.05/1.60 ! [F1: option_fml,F22: fml > option_fml] :
% 3.05/1.60 ( ( case_o209804997ml_fml @ F1 @ F22 @ none_fml )
% 3.05/1.60 = F1 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_122_option_Osimps_I4_J,axiom,
% 3.05/1.60 ! [F1: option_fml,F22: trm > option_fml] :
% 3.05/1.60 ( ( case_o325794063ml_trm @ F1 @ F22 @ none_trm )
% 3.05/1.60 = F1 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_123_option_Osimps_I4_J,axiom,
% 3.05/1.60 ! [F1: option_trm,F22: trm > option_trm] :
% 3.05/1.60 ( ( case_o487727941rm_trm @ F1 @ F22 @ none_trm )
% 3.05/1.60 = F1 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_124_option_Oexpand,axiom,
% 3.05/1.60 ! [Option: option_fml,Option2: option_fml] :
% 3.05/1.60 ( ( ( Option = none_fml )
% 3.05/1.60 = ( Option2 = none_fml ) )
% 3.05/1.60 => ( ( ( Option != none_fml )
% 3.05/1.60 => ( ( Option2 != none_fml )
% 3.05/1.60 => ( ( the_fml @ Option )
% 3.05/1.60 = ( the_fml @ Option2 ) ) ) )
% 3.05/1.60 => ( Option = Option2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_125_option_Oexpand,axiom,
% 3.05/1.60 ! [Option: option_trm,Option2: option_trm] :
% 3.05/1.60 ( ( ( Option = none_trm )
% 3.05/1.60 = ( Option2 = none_trm ) )
% 3.05/1.60 => ( ( ( Option != none_trm )
% 3.05/1.60 => ( ( Option2 != none_trm )
% 3.05/1.60 => ( ( the_trm @ Option )
% 3.05/1.60 = ( the_trm @ Option2 ) ) ) )
% 3.05/1.60 => ( Option = Option2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_126_option_Oexpand,axiom,
% 3.05/1.60 ! [Option: option_game,Option2: option_game] :
% 3.05/1.60 ( ( ( Option = none_game )
% 3.05/1.60 = ( Option2 = none_game ) )
% 3.05/1.60 => ( ( ( Option != none_game )
% 3.05/1.60 => ( ( Option2 != none_game )
% 3.05/1.60 => ( ( the_game @ Option )
% 3.05/1.60 = ( the_game @ Option2 ) ) ) )
% 3.05/1.60 => ( Option = Option2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_127_option_Osimps_I5_J,axiom,
% 3.05/1.60 ! [F1: option_fml,F22: fml > option_fml,X23: fml] :
% 3.05/1.60 ( ( case_o209804997ml_fml @ F1 @ F22 @ ( some_fml @ X23 ) )
% 3.05/1.60 = ( F22 @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_128_option_Osimps_I5_J,axiom,
% 3.05/1.60 ! [F1: option_fml,F22: trm > option_fml,X23: trm] :
% 3.05/1.60 ( ( case_o325794063ml_trm @ F1 @ F22 @ ( some_trm @ X23 ) )
% 3.05/1.60 = ( F22 @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_129_option_Osimps_I5_J,axiom,
% 3.05/1.60 ! [F1: option_trm,F22: trm > option_trm,X23: trm] :
% 3.05/1.60 ( ( case_o487727941rm_trm @ F1 @ F22 @ ( some_trm @ X23 ) )
% 3.05/1.60 = ( F22 @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_130_option_Osel,axiom,
% 3.05/1.60 ! [X23: fml] :
% 3.05/1.60 ( ( the_fml @ ( some_fml @ X23 ) )
% 3.05/1.60 = X23 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_131_option_Osel,axiom,
% 3.05/1.60 ! [X23: trm] :
% 3.05/1.60 ( ( the_trm @ ( some_trm @ X23 ) )
% 3.05/1.60 = X23 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_132_option_Osel,axiom,
% 3.05/1.60 ! [X23: game] :
% 3.05/1.60 ( ( the_game @ ( some_game @ X23 ) )
% 3.05/1.60 = X23 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_133_option_Oexhaust__sel,axiom,
% 3.05/1.60 ! [Option: option_fml] :
% 3.05/1.60 ( ( Option != none_fml )
% 3.05/1.60 => ( Option
% 3.05/1.60 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_134_option_Oexhaust__sel,axiom,
% 3.05/1.60 ! [Option: option_trm] :
% 3.05/1.60 ( ( Option != none_trm )
% 3.05/1.60 => ( Option
% 3.05/1.60 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_135_option_Oexhaust__sel,axiom,
% 3.05/1.60 ! [Option: option_game] :
% 3.05/1.60 ( ( Option != none_game )
% 3.05/1.60 => ( Option
% 3.05/1.60 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_136_option_Ocase__eq__if,axiom,
% 3.05/1.60 ( case_o209804997ml_fml
% 3.05/1.60 = ( ^ [F12: option_fml,F23: fml > option_fml,Option3: option_fml] : ( if_option_fml @ ( Option3 = none_fml ) @ F12 @ ( F23 @ ( the_fml @ Option3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_137_option_Ocase__eq__if,axiom,
% 3.05/1.60 ( case_o325794063ml_trm
% 3.05/1.60 = ( ^ [F12: option_fml,F23: trm > option_fml,Option3: option_trm] : ( if_option_fml @ ( Option3 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_138_option_Ocase__eq__if,axiom,
% 3.05/1.60 ( case_o487727941rm_trm
% 3.05/1.60 = ( ^ [F12: option_trm,F23: trm > option_trm,Option3: option_trm] : ( if_option_trm @ ( Option3 = none_trm ) @ F12 @ ( F23 @ ( the_trm @ Option3 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_139_usubstappf__pred__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,P3: char,Theta: trm] :
% 3.05/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( pred @ P3 @ Theta ) )
% 3.05/1.60 != none_fml )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 & ( ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ P3 )
% 3.05/1.60 = none_fml )
% 3.05/1.60 | ? [R3: fml] :
% 3.05/1.60 ( ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ P3 )
% 3.05/1.60 = ( some_fml @ R3 ) )
% 3.05/1.60 & ( ( inf_inf_set_variable @ ( static_FVF @ R3 ) @ U )
% 3.05/1.60 = bot_bot_set_variable ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_140_option_Osplit__sel,axiom,
% 3.05/1.60 ! [P2: option_fml > $o,F1: option_fml,F22: fml > option_fml,Option: option_fml] :
% 3.05/1.60 ( ( P2 @ ( case_o209804997ml_fml @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ( ( Option = none_fml )
% 3.05/1.60 => ( P2 @ F1 ) )
% 3.05/1.60 & ( ( Option
% 3.05/1.60 = ( some_fml @ ( the_fml @ Option ) ) )
% 3.05/1.60 => ( P2 @ ( F22 @ ( the_fml @ Option ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_141_option_Osplit__sel,axiom,
% 3.05/1.60 ! [P2: option_fml > $o,F1: option_fml,F22: trm > option_fml,Option: option_trm] :
% 3.05/1.60 ( ( P2 @ ( case_o325794063ml_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ( ( Option = none_trm )
% 3.05/1.60 => ( P2 @ F1 ) )
% 3.05/1.60 & ( ( Option
% 3.05/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.60 => ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_142_option_Osplit__sel,axiom,
% 3.05/1.60 ! [P2: option_trm > $o,F1: option_trm,F22: trm > option_trm,Option: option_trm] :
% 3.05/1.60 ( ( P2 @ ( case_o487727941rm_trm @ F1 @ F22 @ Option ) )
% 3.05/1.60 = ( ( ( Option = none_trm )
% 3.05/1.60 => ( P2 @ F1 ) )
% 3.05/1.60 & ( ( Option
% 3.05/1.60 = ( some_trm @ ( the_trm @ Option ) ) )
% 3.05/1.60 => ( P2 @ ( F22 @ ( the_trm @ Option ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_143_fml_Oinject_I1_J,axiom,
% 3.05/1.60 ! [X11: char,X12: trm,Y11: char,Y12: trm] :
% 3.05/1.60 ( ( ( pred @ X11 @ X12 )
% 3.05/1.60 = ( pred @ Y11 @ Y12 ) )
% 3.05/1.60 = ( ( X11 = Y11 )
% 3.05/1.60 & ( X12 = Y12 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_144_Int__iff,axiom,
% 3.05/1.60 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.60 = ( ( member_variable @ C @ A2 )
% 3.05/1.60 & ( member_variable @ C @ B3 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_145_IntI,axiom,
% 3.05/1.60 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( member_variable @ C @ A2 )
% 3.05/1.60 => ( ( member_variable @ C @ B3 )
% 3.05/1.60 => ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_146_empty__Collect__eq,axiom,
% 3.05/1.60 ! [P2: variable > $o] :
% 3.05/1.60 ( ( bot_bot_set_variable
% 3.05/1.60 = ( collect_variable @ P2 ) )
% 3.05/1.60 = ( ! [X: variable] :
% 3.05/1.60 ~ ( P2 @ X ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_147_Collect__empty__eq,axiom,
% 3.05/1.60 ! [P2: variable > $o] :
% 3.05/1.60 ( ( ( collect_variable @ P2 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 = ( ! [X: variable] :
% 3.05/1.60 ~ ( P2 @ X ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_148_all__not__in__conv,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ( ! [X: variable] :
% 3.05/1.60 ~ ( member_variable @ X @ A2 ) )
% 3.05/1.60 = ( A2 = bot_bot_set_variable ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_149_empty__iff,axiom,
% 3.05/1.60 ! [C: variable] :
% 3.05/1.60 ~ ( member_variable @ C @ bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_150_disjoint__iff__not__equal,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 = ( ! [X: variable] :
% 3.05/1.60 ( ( member_variable @ X @ A2 )
% 3.05/1.60 => ! [Y: variable] :
% 3.05/1.60 ( ( member_variable @ Y @ B3 )
% 3.05/1.60 => ( X != Y ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_151_Aterm__Some,axiom,
% 3.05/1.60 some_trm = some_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_152_Loopo_Ocases,axiom,
% 3.05/1.60 ! [X2: option_game] :
% 3.05/1.60 ( ! [Alpha: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( some_game @ Alpha ) )
% 3.05/1.60 => ( X2 = none_game ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_153_ODEo_Oinduct,axiom,
% 3.05/1.60 ! [P2: char > option_trm > $o,A0: char,A1: option_trm] :
% 3.05/1.60 ( ! [X3: char,Theta2: trm] : ( P2 @ X3 @ ( some_trm @ Theta2 ) )
% 3.05/1.60 => ( ! [X3: char] : ( P2 @ X3 @ none_trm )
% 3.05/1.60 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_154_Loopo_Oinduct,axiom,
% 3.05/1.60 ! [P2: option_game > $o,A0: option_game] :
% 3.05/1.60 ( ! [Alpha: game] : ( P2 @ ( some_game @ Alpha ) )
% 3.05/1.60 => ( ( P2 @ none_game )
% 3.05/1.60 => ( P2 @ A0 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_155_undefg__equiv,axiom,
% 3.05/1.60 ! [Alpha2: option_game] :
% 3.05/1.60 ( ( Alpha2 != none_game )
% 3.05/1.60 = ( ? [G: game] :
% 3.05/1.60 ( Alpha2
% 3.05/1.60 = ( some_game @ G ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_156_undeft__equiv,axiom,
% 3.05/1.60 ! [Theta: option_trm] :
% 3.05/1.60 ( ( Theta != none_trm )
% 3.05/1.60 = ( ? [T: trm] :
% 3.05/1.60 ( Theta
% 3.05/1.60 = ( some_trm @ T ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_157_Timeso_Oinduct,axiom,
% 3.05/1.60 ! [P2: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 3.05/1.60 ( ! [Theta2: trm,Eta: trm] : ( P2 @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) )
% 3.05/1.60 => ( ! [X_1: option_trm] : ( P2 @ none_trm @ X_1 )
% 3.05/1.60 => ( ! [V: trm] : ( P2 @ ( some_trm @ V ) @ none_trm )
% 3.05/1.60 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_158_Assigno_Oinduct,axiom,
% 3.05/1.60 ! [P2: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 3.05/1.60 ( ! [X3: variable,Theta2: trm] : ( P2 @ X3 @ ( some_trm @ Theta2 ) )
% 3.05/1.60 => ( ! [X3: variable] : ( P2 @ X3 @ none_trm )
% 3.05/1.60 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_159_Composeo_Oinduct,axiom,
% 3.05/1.60 ! [P2: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 3.05/1.60 ( ! [Alpha: game,Beta: game] : ( P2 @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 3.05/1.60 => ( ! [Alpha: option_game] : ( P2 @ Alpha @ none_game )
% 3.05/1.60 => ( ! [V: game] : ( P2 @ none_game @ ( some_game @ V ) )
% 3.05/1.60 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_160_Differentialo_Ocases,axiom,
% 3.05/1.60 ! [X2: option_trm] :
% 3.05/1.60 ( ! [Theta2: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( some_trm @ Theta2 ) )
% 3.05/1.60 => ( X2 = none_trm ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_161_Differentialo_Oinduct,axiom,
% 3.05/1.60 ! [P2: option_trm > $o,A0: option_trm] :
% 3.05/1.60 ( ! [Theta2: trm] : ( P2 @ ( some_trm @ Theta2 ) )
% 3.05/1.60 => ( ( P2 @ none_trm )
% 3.05/1.60 => ( P2 @ A0 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_162_undeft__None,axiom,
% 3.05/1.60 none_trm = none_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_163_emptyE,axiom,
% 3.05/1.60 ! [A: variable] :
% 3.05/1.60 ~ ( member_variable @ A @ bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_164_equals0D,axiom,
% 3.05/1.60 ! [A2: set_variable,A: variable] :
% 3.05/1.60 ( ( A2 = bot_bot_set_variable )
% 3.05/1.60 => ~ ( member_variable @ A @ A2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_165_equals0I,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ! [Y3: variable] :
% 3.05/1.60 ~ ( member_variable @ Y3 @ A2 )
% 3.05/1.60 => ( A2 = bot_bot_set_variable ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_166_ex__in__conv,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ( ? [X: variable] : ( member_variable @ X @ A2 ) )
% 3.05/1.60 = ( A2 != bot_bot_set_variable ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_167_bot__set__def,axiom,
% 3.05/1.60 ( bot_bot_set_variable
% 3.05/1.60 = ( collect_variable @ bot_bot_variable_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_168_IntE,axiom,
% 3.05/1.60 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.60 => ~ ( ( member_variable @ C @ A2 )
% 3.05/1.60 => ~ ( member_variable @ C @ B3 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_169_IntD1,axiom,
% 3.05/1.60 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.60 => ( member_variable @ C @ A2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_170_IntD2,axiom,
% 3.05/1.60 ! [C: variable,A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( member_variable @ C @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.60 => ( member_variable @ C @ B3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_171_Int__assoc,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ ( inf_inf_set_variable @ A2 @ B3 ) @ C2 )
% 3.05/1.60 = ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_172_Int__absorb,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A2 @ A2 )
% 3.05/1.60 = A2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_173_Int__commute,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [A5: set_variable,B5: set_variable] : ( inf_inf_set_variable @ B5 @ A5 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_174_Int__left__absorb,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ A2 @ B3 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ A2 @ B3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_175_Int__left__commute,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable,C2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A2 @ ( inf_inf_set_variable @ B3 @ C2 ) )
% 3.05/1.60 = ( inf_inf_set_variable @ B3 @ ( inf_inf_set_variable @ A2 @ C2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_176_empty__def,axiom,
% 3.05/1.60 ( bot_bot_set_variable
% 3.05/1.60 = ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : $false ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_177_Collect__conj__eq,axiom,
% 3.05/1.60 ! [P2: variable > $o,Q: variable > $o] :
% 3.05/1.60 ( ( collect_variable
% 3.05/1.60 @ ^ [X: variable] :
% 3.05/1.60 ( ( P2 @ X )
% 3.05/1.60 & ( Q @ X ) ) )
% 3.05/1.60 = ( inf_inf_set_variable @ ( collect_variable @ P2 ) @ ( collect_variable @ Q ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_178_Int__Collect,axiom,
% 3.05/1.60 ! [X2: variable,A2: set_variable,P2: variable > $o] :
% 3.05/1.60 ( ( member_variable @ X2 @ ( inf_inf_set_variable @ A2 @ ( collect_variable @ P2 ) ) )
% 3.05/1.60 = ( ( member_variable @ X2 @ A2 )
% 3.05/1.60 & ( P2 @ X2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_179_Int__def,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.05/1.60 ( collect_variable
% 3.05/1.60 @ ^ [X: variable] :
% 3.05/1.60 ( ( member_variable @ X @ A5 )
% 3.05/1.60 & ( member_variable @ X @ B5 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_180_inf__set__def,axiom,
% 3.05/1.60 ( inf_inf_set_variable
% 3.05/1.60 = ( ^ [A5: set_variable,B5: set_variable] :
% 3.05/1.60 ( collect_variable
% 3.05/1.60 @ ( inf_inf_variable_o
% 3.05/1.60 @ ^ [X: variable] : ( member_variable @ X @ A5 )
% 3.05/1.60 @ ^ [X: variable] : ( member_variable @ X @ B5 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_181_Int__emptyI,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ! [X3: variable] :
% 3.05/1.60 ( ( member_variable @ X3 @ A2 )
% 3.05/1.60 => ~ ( member_variable @ X3 @ B3 ) )
% 3.05/1.60 => ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.60 = bot_bot_set_variable ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_182_disjoint__iff,axiom,
% 3.05/1.60 ! [A2: set_variable,B3: set_variable] :
% 3.05/1.60 ( ( ( inf_inf_set_variable @ A2 @ B3 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 = ( ! [X: variable] :
% 3.05/1.60 ( ( member_variable @ X @ A2 )
% 3.05/1.60 => ~ ( member_variable @ X @ B3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_183_Int__empty__left,axiom,
% 3.05/1.60 ! [B3: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ bot_bot_set_variable @ B3 )
% 3.05/1.60 = bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_184_Int__empty__right,axiom,
% 3.05/1.60 ! [A2: set_variable] :
% 3.05/1.60 ( ( inf_inf_set_variable @ A2 @ bot_bot_set_variable )
% 3.05/1.60 = bot_bot_set_variable ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_185_disjE__realizer2,axiom,
% 3.05/1.60 ! [P2: $o,Q: fml > $o,X2: option_fml,R4: option_fml > $o,F3: option_fml,G2: fml > option_fml] :
% 3.05/1.60 ( ( case_option_o_fml @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( P2
% 3.05/1.60 => ( R4 @ F3 ) )
% 3.05/1.60 => ( ! [Q2: fml] :
% 3.05/1.60 ( ( Q @ Q2 )
% 3.05/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.05/1.60 => ( R4 @ ( case_o209804997ml_fml @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_186_disjE__realizer2,axiom,
% 3.05/1.60 ! [P2: $o,Q: trm > $o,X2: option_trm,R4: option_fml > $o,F3: option_fml,G2: trm > option_fml] :
% 3.05/1.60 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( P2
% 3.05/1.60 => ( R4 @ F3 ) )
% 3.05/1.60 => ( ! [Q2: trm] :
% 3.05/1.60 ( ( Q @ Q2 )
% 3.05/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.05/1.60 => ( R4 @ ( case_o325794063ml_trm @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_187_disjE__realizer2,axiom,
% 3.05/1.60 ! [P2: $o,Q: trm > $o,X2: option_trm,R4: option_trm > $o,F3: option_trm,G2: trm > option_trm] :
% 3.05/1.60 ( ( case_option_o_trm @ P2 @ Q @ X2 )
% 3.05/1.60 => ( ( P2
% 3.05/1.60 => ( R4 @ F3 ) )
% 3.05/1.60 => ( ! [Q2: trm] :
% 3.05/1.60 ( ( Q @ Q2 )
% 3.05/1.60 => ( R4 @ ( G2 @ Q2 ) ) )
% 3.05/1.60 => ( R4 @ ( case_o487727941rm_trm @ F3 @ G2 @ X2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_188_usubstappf__geqr,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.05/1.60 != none_fml )
% 3.05/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.05/1.60 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_189_usubstappf__geq,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.05/1.60 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_190_Geqo_Osimps_I3_J,axiom,
% 3.05/1.60 ! [V3: trm] :
% 3.05/1.60 ( ( uSubst152838031e_Geqo @ ( some_trm @ V3 ) @ none_trm )
% 3.05/1.60 = none_fml ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_191_Set_Ois__empty__def,axiom,
% 3.05/1.60 ( is_empty_variable
% 3.05/1.60 = ( ^ [A5: set_variable] : ( A5 = bot_bot_set_variable ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_192_usubstappf__geq__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.05/1.60 != none_fml )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.05/1.60 != none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_193_fml_Oinject_I2_J,axiom,
% 3.05/1.60 ! [X21: trm,X222: trm,Y21: trm,Y222: trm] :
% 3.05/1.60 ( ( ( geq @ X21 @ X222 )
% 3.05/1.60 = ( geq @ Y21 @ Y222 ) )
% 3.05/1.60 = ( ( X21 = Y21 )
% 3.05/1.60 & ( X222 = Y222 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_194_fml_Odistinct_I1_J,axiom,
% 3.05/1.60 ! [X11: char,X12: trm,X21: trm,X222: trm] :
% 3.05/1.60 ( ( pred @ X11 @ X12 )
% 3.05/1.60 != ( geq @ X21 @ X222 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_195_usubstappf_Osimps_I2_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta2 ) )
% 3.05/1.60 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_196_Geqo_Osimps_I1_J,axiom,
% 3.05/1.60 ! [Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta2 ) )
% 3.05/1.60 = ( some_fml @ ( geq @ Theta @ Eta2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_197_Geqo_Oelims,axiom,
% 3.05/1.60 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 3.05/1.60 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 3.05/1.60 = Y2 )
% 3.05/1.60 => ( ! [Theta2: trm] :
% 3.05/1.60 ( ( X2
% 3.05/1.60 = ( some_trm @ Theta2 ) )
% 3.05/1.60 => ! [Eta: trm] :
% 3.05/1.60 ( ( Xa
% 3.05/1.60 = ( some_trm @ Eta ) )
% 3.05/1.60 => ( Y2
% 3.05/1.60 != ( some_fml @ ( geq @ Theta2 @ Eta ) ) ) ) )
% 3.05/1.60 => ( ( ( X2 = none_trm )
% 3.05/1.60 => ( Y2 != none_fml ) )
% 3.05/1.60 => ~ ( ? [V: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 = ( some_trm @ V ) )
% 3.05/1.60 => ( ( Xa = none_trm )
% 3.05/1.60 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_198_Geqo_Osimps_I2_J,axiom,
% 3.05/1.60 ! [Eta2: option_trm] :
% 3.05/1.60 ( ( uSubst152838031e_Geqo @ none_trm @ Eta2 )
% 3.05/1.60 = none_fml ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_199_Geqo__undef,axiom,
% 3.05/1.60 ! [Theta: option_trm,Eta2: option_trm] :
% 3.05/1.60 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta2 )
% 3.05/1.60 = none_fml )
% 3.05/1.60 = ( ( Theta = none_trm )
% 3.05/1.60 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_200_inf__Int__eq,axiom,
% 3.05/1.60 ! [R4: set_variable,S: set_variable] :
% 3.05/1.60 ( ( inf_inf_variable_o
% 3.05/1.60 @ ^ [X: variable] : ( member_variable @ X @ R4 )
% 3.05/1.60 @ ^ [X: variable] : ( member_variable @ X @ S ) )
% 3.05/1.60 = ( ^ [X: variable] : ( member_variable @ X @ ( inf_inf_set_variable @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_201_Collect__empty__eq__bot,axiom,
% 3.05/1.60 ! [P2: variable > $o] :
% 3.05/1.60 ( ( ( collect_variable @ P2 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 = ( P2 = bot_bot_variable_o ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_202_bot__empty__eq,axiom,
% 3.05/1.60 ( bot_bot_variable_o
% 3.05/1.60 = ( ^ [X: variable] : ( member_variable @ X @ bot_bot_set_variable ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_203_internal__case__prod__def,axiom,
% 3.05/1.60 produc1278328899on_fml = produc1250175341on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_204_internal__case__prod__def,axiom,
% 3.05/1.60 produc2141841102on_trm = produc1231571704on_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_205_internal__case__prod__def,axiom,
% 3.05/1.60 produc377919108on_fml = produc1615133358on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_206_internal__case__prod__def,axiom,
% 3.05/1.60 produc1214549391on_trm = produc1036610745on_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_207_internal__case__prod__def,axiom,
% 3.05/1.60 produc1598111045on_fml = produc1420172399on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_208_internal__case__prod__def,axiom,
% 3.05/1.60 produc1591622303on_fml = produc347802313on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_209_internal__case__prod__def,axiom,
% 3.05/1.60 produc2129367017on_trm = produc885547027on_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_210_internal__case__prod__def,axiom,
% 3.05/1.60 produc1903410526on_fml = produc154833544on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_211_internal__case__prod__def,axiom,
% 3.05/1.60 produc293671592on_trm = produc692578258on_trm ).
% 3.05/1.60
% 3.05/1.60 thf(fact_212_internal__case__prod__def,axiom,
% 3.05/1.60 produc724717725on_fml = produc1499310791on_fml ).
% 3.05/1.60
% 3.05/1.60 thf(fact_213_usubstappt_Osimps_I4_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 3.05/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.05/1.60 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.60 @ ^ [Sigma_theta: trm] :
% 3.05/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta ) )
% 3.05/1.60 @ ^ [R: trm] :
% 3.05/1.60 ( if_option_trm
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.05/1.60 @ none_trm )
% 3.05/1.60 @ ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_214_Diamondo_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1739631244on_fml] :
% 3.05/1.60 ( ! [Alpha: game,Phi: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi ) ) )
% 3.05/1.60 => ( ! [Phi: option_fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2124676926on_fml @ none_game @ Phi ) )
% 3.05/1.60 => ~ ! [V: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2124676926on_fml @ ( some_game @ V ) @ none_fml ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_215_Testo__undef,axiom,
% 3.05/1.60 ! [Phi2: option_fml] :
% 3.05/1.60 ( ( ( uSubst1367128042_Testo @ Phi2 )
% 3.05/1.60 = none_game )
% 3.05/1.60 = ( Phi2 = none_fml ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_216_prod_Oinject,axiom,
% 3.05/1.60 ! [X13: char,X23: option_trm,Y1: char,Y22: option_trm] :
% 3.05/1.60 ( ( ( produc1500300866on_trm @ X13 @ X23 )
% 3.05/1.60 = ( produc1500300866on_trm @ Y1 @ Y22 ) )
% 3.05/1.60 = ( ( X13 = Y1 )
% 3.05/1.60 & ( X23 = Y22 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_217_prod_Oinject,axiom,
% 3.05/1.60 ! [X13: set_variable,X23: trm,Y1: set_variable,Y22: trm] :
% 3.05/1.60 ( ( ( produc1482344242le_trm @ X13 @ X23 )
% 3.05/1.60 = ( produc1482344242le_trm @ Y1 @ Y22 ) )
% 3.05/1.60 = ( ( X13 = Y1 )
% 3.05/1.60 & ( X23 = Y22 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_218_prod_Oinject,axiom,
% 3.05/1.60 ! [X13: char > option_trm,X23: produc62062515n_game,Y1: char > option_trm,Y22: produc62062515n_game] :
% 3.05/1.60 ( ( ( produc1618635950n_game @ X13 @ X23 )
% 3.05/1.60 = ( produc1618635950n_game @ Y1 @ Y22 ) )
% 3.05/1.60 = ( ( X13 = Y1 )
% 3.05/1.60 & ( X23 = Y22 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_219_prod_Oinject,axiom,
% 3.05/1.60 ! [X13: char > option_trm,X23: produc799602994n_game,Y1: char > option_trm,Y22: produc799602994n_game] :
% 3.05/1.60 ( ( ( produc1048060077n_game @ X13 @ X23 )
% 3.05/1.60 = ( produc1048060077n_game @ Y1 @ Y22 ) )
% 3.05/1.60 = ( ( X13 = Y1 )
% 3.05/1.60 & ( X23 = Y22 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_220_prod_Oinject,axiom,
% 3.05/1.60 ! [X13: char > option_fml,X23: char > option_game,Y1: char > option_fml,Y22: char > option_game] :
% 3.05/1.60 ( ( ( produc123610156n_game @ X13 @ X23 )
% 3.05/1.60 = ( produc123610156n_game @ Y1 @ Y22 ) )
% 3.05/1.60 = ( ( X13 = Y1 )
% 3.05/1.60 & ( X23 = Y22 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_221_old_Oprod_Oinject,axiom,
% 3.05/1.60 ! [A: char,B: option_trm,A6: char,B6: option_trm] :
% 3.05/1.60 ( ( ( produc1500300866on_trm @ A @ B )
% 3.05/1.60 = ( produc1500300866on_trm @ A6 @ B6 ) )
% 3.05/1.60 = ( ( A = A6 )
% 3.05/1.60 & ( B = B6 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_222_old_Oprod_Oinject,axiom,
% 3.05/1.60 ! [A: set_variable,B: trm,A6: set_variable,B6: trm] :
% 3.05/1.60 ( ( ( produc1482344242le_trm @ A @ B )
% 3.05/1.60 = ( produc1482344242le_trm @ A6 @ B6 ) )
% 3.05/1.60 = ( ( A = A6 )
% 3.05/1.60 & ( B = B6 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_223_old_Oprod_Oinject,axiom,
% 3.05/1.60 ! [A: char > option_trm,B: produc62062515n_game,A6: char > option_trm,B6: produc62062515n_game] :
% 3.05/1.60 ( ( ( produc1618635950n_game @ A @ B )
% 3.05/1.60 = ( produc1618635950n_game @ A6 @ B6 ) )
% 3.05/1.60 = ( ( A = A6 )
% 3.05/1.60 & ( B = B6 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_224_old_Oprod_Oinject,axiom,
% 3.05/1.60 ! [A: char > option_trm,B: produc799602994n_game,A6: char > option_trm,B6: produc799602994n_game] :
% 3.05/1.60 ( ( ( produc1048060077n_game @ A @ B )
% 3.05/1.60 = ( produc1048060077n_game @ A6 @ B6 ) )
% 3.05/1.60 = ( ( A = A6 )
% 3.05/1.60 & ( B = B6 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_225_old_Oprod_Oinject,axiom,
% 3.05/1.60 ! [A: char > option_fml,B: char > option_game,A6: char > option_fml,B6: char > option_game] :
% 3.05/1.60 ( ( ( produc123610156n_game @ A @ B )
% 3.05/1.60 = ( produc123610156n_game @ A6 @ B6 ) )
% 3.05/1.60 = ( ( A = A6 )
% 3.05/1.60 & ( B = B6 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_226_trm_Oinject_I4_J,axiom,
% 3.05/1.60 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 3.05/1.60 ( ( ( func @ X41 @ X42 )
% 3.05/1.60 = ( func @ Y41 @ Y42 ) )
% 3.05/1.60 = ( ( X41 = Y41 )
% 3.05/1.60 & ( X42 = Y42 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_227_case__prodI,axiom,
% 3.05/1.60 ! [F3: char > option_trm > $o,A: char,B: option_trm] :
% 3.05/1.60 ( ( F3 @ A @ B )
% 3.05/1.60 => ( produc584666985_trm_o @ F3 @ ( produc1500300866on_trm @ A @ B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_228_case__prodI,axiom,
% 3.05/1.60 ! [F3: set_variable > trm > $o,A: set_variable,B: trm] :
% 3.05/1.60 ( ( F3 @ A @ B )
% 3.05/1.60 => ( produc82209913_trm_o @ F3 @ ( produc1482344242le_trm @ A @ B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_229_case__prodI,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc62062515n_game > $o,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.60 ( ( F3 @ A @ B )
% 3.05/1.60 => ( produc1707653117game_o @ F3 @ ( produc1618635950n_game @ A @ B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_230_case__prodI,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > $o,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.60 ( ( F3 @ A @ B )
% 3.05/1.60 => ( produc1868740670game_o @ F3 @ ( produc1048060077n_game @ A @ B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_231_case__prodI,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > $o,A: char > option_fml,B: char > option_game] :
% 3.05/1.60 ( ( F3 @ A @ B )
% 3.05/1.60 => ( produc159680767game_o @ F3 @ ( produc123610156n_game @ A @ B ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_232_case__prodI2,axiom,
% 3.05/1.60 ! [P3: produc464795408on_trm,C: char > option_trm > $o] :
% 3.05/1.60 ( ! [A4: char,B4: option_trm] :
% 3.05/1.60 ( ( P3
% 3.05/1.60 = ( produc1500300866on_trm @ A4 @ B4 ) )
% 3.05/1.60 => ( C @ A4 @ B4 ) )
% 3.05/1.60 => ( produc584666985_trm_o @ C @ P3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_233_case__prodI2,axiom,
% 3.05/1.60 ! [P3: produc1367888000le_trm,C: set_variable > trm > $o] :
% 3.05/1.60 ( ! [A4: set_variable,B4: trm] :
% 3.05/1.60 ( ( P3
% 3.05/1.60 = ( produc1482344242le_trm @ A4 @ B4 ) )
% 3.05/1.60 => ( C @ A4 @ B4 ) )
% 3.05/1.60 => ( produc82209913_trm_o @ C @ P3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_234_case__prodI2,axiom,
% 3.05/1.60 ! [P3: produc1418842292n_game,C: ( char > option_trm ) > produc62062515n_game > $o] :
% 3.05/1.60 ( ! [A4: char > option_trm,B4: produc62062515n_game] :
% 3.05/1.60 ( ( P3
% 3.05/1.60 = ( produc1618635950n_game @ A4 @ B4 ) )
% 3.05/1.60 => ( C @ A4 @ B4 ) )
% 3.05/1.60 => ( produc1707653117game_o @ C @ P3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_235_case__prodI2,axiom,
% 3.05/1.60 ! [P3: produc62062515n_game,C: ( char > option_trm ) > produc799602994n_game > $o] :
% 3.05/1.60 ( ! [A4: char > option_trm,B4: produc799602994n_game] :
% 3.05/1.60 ( ( P3
% 3.05/1.60 = ( produc1048060077n_game @ A4 @ B4 ) )
% 3.05/1.60 => ( C @ A4 @ B4 ) )
% 3.05/1.60 => ( produc1868740670game_o @ C @ P3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_236_case__prodI2,axiom,
% 3.05/1.60 ! [P3: produc799602994n_game,C: ( char > option_fml ) > ( char > option_game ) > $o] :
% 3.05/1.60 ( ! [A4: char > option_fml,B4: char > option_game] :
% 3.05/1.60 ( ( P3
% 3.05/1.60 = ( produc123610156n_game @ A4 @ B4 ) )
% 3.05/1.60 => ( C @ A4 @ B4 ) )
% 3.05/1.60 => ( produc159680767game_o @ C @ P3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_237_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.60 ( ( produc1250175341on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_238_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.60 ( ( produc1231571704on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_239_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.60 ( ( produc1615133358on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_240_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,A: char > option_fml,B: char > option_game] :
% 3.05/1.60 ( ( produc1036610745on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_241_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,A: char > option_fml,B: char > option_game] :
% 3.05/1.60 ( ( produc1420172399on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_242_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_fml,A: char > option_fml,B: char > option_game] :
% 3.05/1.60 ( ( produc347802313on_fml @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_243_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_trm,A: char > option_fml,B: char > option_game] :
% 3.05/1.60 ( ( produc885547027on_trm @ F3 @ ( produc123610156n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_244_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > option_fml,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.60 ( ( produc154833544on_fml @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_245_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > option_trm,A: char > option_trm,B: produc799602994n_game] :
% 3.05/1.60 ( ( produc692578258on_trm @ F3 @ ( produc1048060077n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_246_case__prod__conv,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc62062515n_game > option_fml,A: char > option_trm,B: produc62062515n_game] :
% 3.05/1.60 ( ( produc1499310791on_fml @ F3 @ ( produc1618635950n_game @ A @ B ) )
% 3.05/1.60 = ( F3 @ A @ B ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_247_usubstappt__func2,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable,Theta: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.05/1.60 != bot_bot_set_variable )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.05/1.60 = none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_248_usubstappt__func,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable,Theta: trm,Sigma_theta2: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 = ( some_trm @ Sigma_theta2 ) )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.05/1.60 = ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta2 ) @ bot_bot_set_variable @ R2 ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_249_inf__Int__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 3.05/1.60 ( ( inf_in605351507_trm_o
% 3.05/1.60 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 )
% 3.05/1.60 @ ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) )
% 3.05/1.60 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ ( inf_in1243659096on_trm @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_250_inf__Int__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 3.05/1.60 ( ( inf_in185389155_trm_o
% 3.05/1.60 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 )
% 3.05/1.60 @ ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) )
% 3.05/1.60 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ ( inf_in906025800le_trm @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_251_inf__Int__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 3.05/1.60 ( ( inf_in1920662529game_o
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 )
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) )
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ ( inf_in360367996n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_252_inf__Int__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 3.05/1.60 ( ( inf_in1072207554game_o
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 )
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) )
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ ( inf_in69689467n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_253_inf__Int__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 3.05/1.60 ( ( inf_in243546115game_o
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 )
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) )
% 3.05/1.60 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ ( inf_in1391117306n_game @ R4 @ S ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_254_bot__empty__eq2,axiom,
% 3.05/1.60 ( bot_bo102862421_trm_o
% 3.05/1.60 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ bot_bo18861914on_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_255_bot__empty__eq2,axiom,
% 3.05/1.60 ( bot_bo512610661_trm_o
% 3.05/1.60 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ bot_bo896421962le_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_256_bot__empty__eq2,axiom,
% 3.05/1.60 ( bot_bo849148163game_o
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ bot_bo1453406334n_game ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_257_bot__empty__eq2,axiom,
% 3.05/1.60 ( bot_bo1417568964game_o
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ bot_bo1302831229n_game ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_258_bot__empty__eq2,axiom,
% 3.05/1.60 ( bot_bo1895715589game_o
% 3.05/1.60 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ bot_bo456479484n_game ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_259_pred__equals__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 3.05/1.60 ( ( ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ R4 ) )
% 3.05/1.60 = ( ^ [X: char,Y: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y ) @ S ) ) )
% 3.05/1.60 = ( R4 = S ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_260_pred__equals__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 3.05/1.60 ( ( ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ R4 ) )
% 3.05/1.60 = ( ^ [X: set_variable,Y: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y ) @ S ) ) )
% 3.05/1.60 = ( R4 = S ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_261_pred__equals__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr720454634n_game,S: set_Pr720454634n_game] :
% 3.05/1.60 ( ( ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ R4 ) )
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc62062515n_game] : ( member1940201675n_game @ ( produc1618635950n_game @ X @ Y ) @ S ) ) )
% 3.05/1.60 = ( R4 = S ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_262_pred__equals__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr739694057n_game,S: set_Pr739694057n_game] :
% 3.05/1.60 ( ( ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ R4 ) )
% 3.05/1.60 = ( ^ [X: char > option_trm,Y: produc799602994n_game] : ( member774167626n_game @ ( produc1048060077n_game @ X @ Y ) @ S ) ) )
% 3.05/1.60 = ( R4 = S ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_263_pred__equals__eq2,axiom,
% 3.05/1.60 ! [R4: set_Pr79606376n_game,S: set_Pr79606376n_game] :
% 3.05/1.60 ( ( ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ R4 ) )
% 3.05/1.60 = ( ^ [X: char > option_fml,Y: char > option_game] : ( member849814089n_game @ ( produc123610156n_game @ X @ Y ) @ S ) ) )
% 3.05/1.60 = ( R4 = S ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_264_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc62062515n_game > char > option_fml,G2: produc1418842292n_game > char > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1618635950n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1250175341on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_265_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_trm,G2: produc62062515n_game > char > option_trm] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1231571704on_trm @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_266_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > char > option_fml,G2: produc62062515n_game > char > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1615133358on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_267_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_trm,G2: produc799602994n_game > char > option_trm] :
% 3.05/1.60 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1036610745on_trm @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_268_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > char > option_fml,G2: produc799602994n_game > char > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1420172399on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_269_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_fml,G2: produc799602994n_game > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc347802313on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_270_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_fml ) > ( char > option_game ) > option_trm,G2: produc799602994n_game > option_trm] :
% 3.05/1.60 ( ! [X3: char > option_fml,Y3: char > option_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc123610156n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc885547027on_trm @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_271_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > option_fml,G2: produc62062515n_game > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc154833544on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_272_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc799602994n_game > option_trm,G2: produc62062515n_game > option_trm] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc799602994n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1048060077n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc692578258on_trm @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_273_cond__case__prod__eta,axiom,
% 3.05/1.60 ! [F3: ( char > option_trm ) > produc62062515n_game > option_fml,G2: produc1418842292n_game > option_fml] :
% 3.05/1.60 ( ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 3.05/1.60 ( ( F3 @ X3 @ Y3 )
% 3.05/1.60 = ( G2 @ ( produc1618635950n_game @ X3 @ Y3 ) ) )
% 3.05/1.60 => ( ( produc1499310791on_fml @ F3 )
% 3.05/1.60 = G2 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_274_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc1418842292n_game > char > option_fml] :
% 3.05/1.60 ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_275_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc62062515n_game > char > option_trm] :
% 3.05/1.60 ( ( produc1231571704on_trm
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_276_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc62062515n_game > char > option_fml] :
% 3.05/1.60 ( ( produc1615133358on_fml
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_277_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc799602994n_game > char > option_trm] :
% 3.05/1.60 ( ( produc1036610745on_trm
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_278_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc799602994n_game > char > option_fml] :
% 3.05/1.60 ( ( produc1420172399on_fml
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_279_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc799602994n_game > option_fml] :
% 3.05/1.60 ( ( produc347802313on_fml
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_280_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc799602994n_game > option_trm] :
% 3.05/1.60 ( ( produc885547027on_trm
% 3.05/1.60 @ ^ [X: char > option_fml,Y: char > option_game] : ( F3 @ ( produc123610156n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_281_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc62062515n_game > option_fml] :
% 3.05/1.60 ( ( produc154833544on_fml
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_282_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc62062515n_game > option_trm] :
% 3.05/1.60 ( ( produc692578258on_trm
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc799602994n_game] : ( F3 @ ( produc1048060077n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_283_case__prod__eta,axiom,
% 3.05/1.60 ! [F3: produc1418842292n_game > option_fml] :
% 3.05/1.60 ( ( produc1499310791on_fml
% 3.05/1.60 @ ^ [X: char > option_trm,Y: produc62062515n_game] : ( F3 @ ( produc1618635950n_game @ X @ Y ) ) )
% 3.05/1.60 = F3 ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_284_case__prodE2,axiom,
% 3.05/1.60 ! [Q: option_fml > $o,P2: ( char > option_trm ) > produc62062515n_game > option_fml,Z2: produc1418842292n_game] :
% 3.05/1.60 ( ( Q @ ( produc1499310791on_fml @ P2 @ Z2 ) )
% 3.05/1.60 => ~ ! [X3: char > option_trm,Y3: produc62062515n_game] :
% 3.05/1.60 ( ( Z2
% 3.05/1.60 = ( produc1618635950n_game @ X3 @ Y3 ) )
% 3.05/1.60 => ~ ( Q @ ( P2 @ X3 @ Y3 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_285_usubstappt__func__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 & ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = none_trm )
% 3.05/1.60 | ? [R3: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R3 ) )
% 3.05/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.05/1.60 = bot_bot_set_variable ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_286_Testo_Osimps_I2_J,axiom,
% 3.05/1.60 ( ( uSubst1367128042_Testo @ none_fml )
% 3.05/1.60 = none_game ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_287_usappconst__simp,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( ( uSubst1559070963pconst @ Sigma @ U @ F3 )
% 3.05/1.60 = ( some_trm @ R2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_288_usappconst__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 3.05/1.60 ( ( ( uSubst1559070963pconst @ Sigma @ U @ F3 )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = none_trm )
% 3.05/1.60 | ? [R3: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R3 ) )
% 3.05/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.05/1.60 = bot_bot_set_variable ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_289_usubstappt__const,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,F3: char,R2: trm,U: set_variable] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R2 ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ R2 ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.05/1.60 = ( some_trm @ R2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_290_trm_Oinject_I3_J,axiom,
% 3.05/1.60 ! [X32: char,Y32: char] :
% 3.05/1.60 ( ( ( const @ X32 )
% 3.05/1.60 = ( const @ Y32 ) )
% 3.05/1.60 = ( X32 = Y32 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_291_trm_Odistinct_I23_J,axiom,
% 3.05/1.60 ! [X32: char,X41: char,X42: trm] :
% 3.05/1.60 ( ( const @ X32 )
% 3.05/1.60 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_292_usubstappt_Osimps_I3_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 3.05/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.05/1.60 = ( uSubst1559070963pconst @ Sigma @ U @ F3 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_293_ODEo_Ocases,axiom,
% 3.05/1.60 ! [X2: produc464795408on_trm] :
% 3.05/1.60 ( ! [X3: char,Theta2: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1500300866on_trm @ X3 @ ( some_trm @ Theta2 ) ) )
% 3.05/1.60 => ~ ! [X3: char] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1500300866on_trm @ X3 @ none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_294_Assigno_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1024976764on_trm] :
% 3.05/1.60 ( ! [X3: variable,Theta2: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1743721902on_trm @ X3 @ ( some_trm @ Theta2 ) ) )
% 3.05/1.60 => ~ ! [X3: variable] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1743721902on_trm @ X3 @ none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_295_Timeso_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1072747943on_trm] :
% 3.05/1.60 ( ! [Theta2: trm,Eta: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta ) ) )
% 3.05/1.60 => ( ! [Eta: option_trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc709594775on_trm @ none_trm @ Eta ) )
% 3.05/1.60 => ~ ! [V: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc709594775on_trm @ ( some_trm @ V ) @ none_trm ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_296_Existso_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1408538418on_fml] :
% 3.05/1.60 ( ! [X3: variable,Phi: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1205977188on_fml @ X3 @ ( some_fml @ Phi ) ) )
% 3.05/1.60 => ~ ! [X3: variable] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1205977188on_fml @ X3 @ none_fml ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_297_Ando_Ocases,axiom,
% 3.05/1.60 ! [X2: produc46605351on_fml] :
% 3.05/1.60 ( ! [Phi: fml,Psi: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc909629463on_fml @ ( some_fml @ Phi ) @ ( some_fml @ Psi ) ) )
% 3.05/1.60 => ( ! [Psi: option_fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 3.05/1.60 => ~ ! [V: fml] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc909629463on_fml @ ( some_fml @ V ) @ none_fml ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_298_Composeo_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1016592119n_game] :
% 3.05/1.60 ( ! [Alpha: game,Beta: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 3.05/1.60 => ( ! [Alpha: option_game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 3.05/1.60 => ~ ! [V: game] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc1111617711n_game @ none_game @ ( some_game @ V ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_299_usappconst__def,axiom,
% 3.05/1.60 ( uSubst1559070963pconst
% 3.05/1.60 = ( ^ [Sigma2: produc1418842292n_game,U2: set_variable,F2: char] :
% 3.05/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( const @ F2 ) )
% 3.05/1.60 @ ^ [R: trm] :
% 3.05/1.60 ( if_option_trm
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U2 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( some_trm @ R )
% 3.05/1.60 @ none_trm )
% 3.05/1.60 @ ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma2
% 3.05/1.60 @ F2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_300_usubstappt__const__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = none_trm )
% 3.05/1.60 | ? [R3: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [F0: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F0 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 )
% 3.05/1.60 = ( some_trm @ R3 ) )
% 3.05/1.60 & ( ( inf_inf_set_variable @ ( static_FVT @ R3 ) @ U )
% 3.05/1.60 = bot_bot_set_variable ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_301_usubstappt_Opsimps_I4_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char,Theta: trm] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( func @ F3 @ Theta ) ) ) )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( func @ F3 @ Theta ) )
% 3.05/1.60 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.60 @ ^ [Sigma_theta: trm] :
% 3.05/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F3 @ Sigma_theta ) )
% 3.05/1.60 @ ^ [R: trm] :
% 3.05/1.60 ( if_option_trm
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ U )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.05/1.60 @ none_trm )
% 3.05/1.60 @ ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma
% 3.05/1.60 @ F3 ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_302_usubstappt_Opsimps_I3_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,F3: char] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( const @ F3 ) ) ) )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F3 ) )
% 3.05/1.60 = ( uSubst1559070963pconst @ Sigma @ U @ F3 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_303_usubstappt_Opsimps_I1_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( var @ X2 ) ) ) )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 3.05/1.60 = ( some_trm @ ( var @ X2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_304_usubstappt_Opsimps_I2_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,R2: real] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( number @ R2 ) ) ) )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R2 ) )
% 3.05/1.60 = ( some_trm @ ( number @ R2 ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_305_trm_Oinject_I2_J,axiom,
% 3.05/1.60 ! [X23: real,Y22: real] :
% 3.05/1.60 ( ( ( number @ X23 )
% 3.05/1.60 = ( number @ Y22 ) )
% 3.05/1.60 = ( X23 = Y22 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_306_trm_Oinject_I1_J,axiom,
% 3.05/1.60 ! [X13: variable,Y1: variable] :
% 3.05/1.60 ( ( ( var @ X13 )
% 3.05/1.60 = ( var @ Y1 ) )
% 3.05/1.60 = ( X13 = Y1 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_307_trm_Odistinct_I15_J,axiom,
% 3.05/1.60 ! [X23: real,X41: char,X42: trm] :
% 3.05/1.60 ( ( number @ X23 )
% 3.05/1.60 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_308_trm_Odistinct_I5_J,axiom,
% 3.05/1.60 ! [X13: variable,X41: char,X42: trm] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( func @ X41 @ X42 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_309_trm_Odistinct_I1_J,axiom,
% 3.05/1.60 ! [X13: variable,X23: real] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( number @ X23 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_310_trm_Odistinct_I13_J,axiom,
% 3.05/1.60 ! [X23: real,X32: char] :
% 3.05/1.60 ( ( number @ X23 )
% 3.05/1.60 != ( const @ X32 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_311_trm_Odistinct_I3_J,axiom,
% 3.05/1.60 ! [X13: variable,X32: char] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( const @ X32 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_312_usubstappt_Osimps_I2_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,R2: real] :
% 3.05/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R2 ) )
% 3.05/1.60 = ( some_trm @ ( number @ R2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_313_usubstappt_Osimps_I1_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 3.05/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 3.05/1.60 = ( some_trm @ ( var @ X2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_314_usubstappt_Opinduct,axiom,
% 3.05/1.60 ! [A0: produc1418842292n_game,A1: set_variable,A22: trm,P2: produc1418842292n_game > set_variable > trm > $o] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ A0 @ ( produc1482344242le_trm @ A1 @ A22 ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X3 ) ) ) )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( const @ F5 ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 3.05/1.60 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ( ! [X25: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 = ( some_trm @ X25 ) )
% 3.05/1.60 => ! [X2a: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma3
% 3.05/1.60 @ F5 )
% 3.05/1.60 = ( some_trm @ X2a ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( P2 @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( func @ F5 @ Theta2 ) ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 3.05/1.60 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) )
% 3.05/1.60 => ( ( P2 @ Sigma3
% 3.05/1.60 @ ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : $true )
% 3.05/1.60 @ Theta2 )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) ) )
% 3.05/1.60 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_315_dotsubstt__def,axiom,
% 3.05/1.60 ( uSubst1408967625substt
% 3.05/1.60 = ( ^ [Theta3: trm] :
% 3.05/1.60 ( produc1618635950n_game
% 3.05/1.60 @ ^ [F2: char] :
% 3.05/1.60 ( if_option_trm
% 3.05/1.60 @ ( F2
% 3.05/1.60 = ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) )
% 3.05/1.60 @ ( some_trm @ Theta3 )
% 3.05/1.60 @ none_trm )
% 3.05/1.60 @ ( produc1048060077n_game
% 3.05/1.60 @ ^ [Uu: char] : none_trm
% 3.05/1.60 @ ( produc123610156n_game
% 3.05/1.60 @ ^ [Uu: char] : none_fml
% 3.05/1.60 @ ^ [Uu: char] : none_game ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_316_trm_Oinject_I6_J,axiom,
% 3.05/1.60 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 3.05/1.60 ( ( ( times @ X61 @ X62 )
% 3.05/1.60 = ( times @ Y61 @ Y62 ) )
% 3.05/1.60 = ( ( X61 = Y61 )
% 3.05/1.60 & ( X62 = Y62 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_317_trm_Oinject_I5_J,axiom,
% 3.05/1.60 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 3.05/1.60 ( ( ( plus @ X51 @ X52 )
% 3.05/1.60 = ( plus @ Y51 @ Y52 ) )
% 3.05/1.60 = ( ( X51 = Y51 )
% 3.05/1.60 & ( X52 = Y52 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_318_trm_Oinject_I7_J,axiom,
% 3.05/1.60 ! [X7: trm,Y7: trm] :
% 3.05/1.60 ( ( ( differential @ X7 )
% 3.05/1.60 = ( differential @ Y7 ) )
% 3.05/1.60 = ( X7 = Y7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_319_trm_Odistinct_I7_J,axiom,
% 3.05/1.60 ! [X13: variable,X51: trm,X52: trm] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_320_trm_Odistinct_I9_J,axiom,
% 3.05/1.60 ! [X13: variable,X61: trm,X62: trm] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_321_trm_Odistinct_I11_J,axiom,
% 3.05/1.60 ! [X13: variable,X7: trm] :
% 3.05/1.60 ( ( var @ X13 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_322_trm_Odistinct_I17_J,axiom,
% 3.05/1.60 ! [X23: real,X51: trm,X52: trm] :
% 3.05/1.60 ( ( number @ X23 )
% 3.05/1.60 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_323_trm_Odistinct_I19_J,axiom,
% 3.05/1.60 ! [X23: real,X61: trm,X62: trm] :
% 3.05/1.60 ( ( number @ X23 )
% 3.05/1.60 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_324_trm_Odistinct_I21_J,axiom,
% 3.05/1.60 ! [X23: real,X7: trm] :
% 3.05/1.60 ( ( number @ X23 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_325_trm_Oexhaust,axiom,
% 3.05/1.60 ! [Y2: trm] :
% 3.05/1.60 ( ! [X14: variable] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( var @ X14 ) )
% 3.05/1.60 => ( ! [X24: real] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( number @ X24 ) )
% 3.05/1.60 => ( ! [X33: char] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( const @ X33 ) )
% 3.05/1.60 => ( ! [X412: char,X422: trm] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( func @ X412 @ X422 ) )
% 3.05/1.60 => ( ! [X512: trm,X522: trm] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( plus @ X512 @ X522 ) )
% 3.05/1.60 => ( ! [X612: trm,X622: trm] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( times @ X612 @ X622 ) )
% 3.05/1.60 => ~ ! [X72: trm] :
% 3.05/1.60 ( Y2
% 3.05/1.60 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_326_trm_Oinduct,axiom,
% 3.05/1.60 ! [P2: trm > $o,Trm: trm] :
% 3.05/1.60 ( ! [X3: variable] : ( P2 @ ( var @ X3 ) )
% 3.05/1.60 => ( ! [X3: real] : ( P2 @ ( number @ X3 ) )
% 3.05/1.60 => ( ! [X3: char] : ( P2 @ ( const @ X3 ) )
% 3.05/1.60 => ( ! [X1a: char,X2a2: trm] :
% 3.05/1.60 ( ( P2 @ X2a2 )
% 3.05/1.60 => ( P2 @ ( func @ X1a @ X2a2 ) ) )
% 3.05/1.60 => ( ! [X1a: trm,X2a2: trm] :
% 3.05/1.60 ( ( P2 @ X1a )
% 3.05/1.60 => ( ( P2 @ X2a2 )
% 3.05/1.60 => ( P2 @ ( plus @ X1a @ X2a2 ) ) ) )
% 3.05/1.60 => ( ! [X1a: trm,X2a2: trm] :
% 3.05/1.60 ( ( P2 @ X1a )
% 3.05/1.60 => ( ( P2 @ X2a2 )
% 3.05/1.60 => ( P2 @ ( times @ X1a @ X2a2 ) ) ) )
% 3.05/1.60 => ( ! [X3: trm] :
% 3.05/1.60 ( ( P2 @ X3 )
% 3.05/1.60 => ( P2 @ ( differential @ X3 ) ) )
% 3.05/1.60 => ( P2 @ Trm ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_327_trm_Odistinct_I25_J,axiom,
% 3.05/1.60 ! [X32: char,X51: trm,X52: trm] :
% 3.05/1.60 ( ( const @ X32 )
% 3.05/1.60 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_328_trm_Odistinct_I27_J,axiom,
% 3.05/1.60 ! [X32: char,X61: trm,X62: trm] :
% 3.05/1.60 ( ( const @ X32 )
% 3.05/1.60 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_329_trm_Odistinct_I29_J,axiom,
% 3.05/1.60 ! [X32: char,X7: trm] :
% 3.05/1.60 ( ( const @ X32 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_330_trm_Odistinct_I41_J,axiom,
% 3.05/1.60 ! [X61: trm,X62: trm,X7: trm] :
% 3.05/1.60 ( ( times @ X61 @ X62 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_331_trm_Odistinct_I39_J,axiom,
% 3.05/1.60 ! [X51: trm,X52: trm,X7: trm] :
% 3.05/1.60 ( ( plus @ X51 @ X52 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_332_trm_Odistinct_I37_J,axiom,
% 3.05/1.60 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 3.05/1.60 ( ( plus @ X51 @ X52 )
% 3.05/1.60 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_333_trm_Odistinct_I31_J,axiom,
% 3.05/1.60 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 3.05/1.60 ( ( func @ X41 @ X42 )
% 3.05/1.60 != ( plus @ X51 @ X52 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_334_trm_Odistinct_I33_J,axiom,
% 3.05/1.60 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 3.05/1.60 ( ( func @ X41 @ X42 )
% 3.05/1.60 != ( times @ X61 @ X62 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_335_trm_Odistinct_I35_J,axiom,
% 3.05/1.60 ! [X41: char,X42: trm,X7: trm] :
% 3.05/1.60 ( ( func @ X41 @ X42 )
% 3.05/1.60 != ( differential @ X7 ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_336_usubstappt_Ocases,axiom,
% 3.05/1.60 ! [X2: produc1699626005le_trm] :
% 3.05/1.60 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( var @ X3 ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( number @ R3 ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( const @ F5 ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ~ ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 3.05/1.60 ( X2
% 3.05/1.60 != ( produc2015636557le_trm @ Sigma3 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_337_usubstappt__times__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta2 ) )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.05/1.60 != none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_338_usubstappt__plus__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 3.05/1.60 != none_trm )
% 3.05/1.60 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta2 )
% 3.05/1.60 != none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_339_usubstappt__differential__conv,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 3.05/1.60 != none_trm )
% 3.05/1.60 => ( ( uSubst516392818stappt @ Sigma
% 3.05/1.60 @ ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : $true )
% 3.05/1.60 @ Theta )
% 3.05/1.60 != none_trm ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_340_usubstappt__induct,axiom,
% 3.05/1.60 ! [P2: produc1418842292n_game > set_variable > trm > $o,A0: produc1418842292n_game,A1: set_variable,A22: trm] :
% 3.05/1.60 ( ! [Sigma3: produc1418842292n_game,U3: set_variable,X3: variable] : ( P2 @ Sigma3 @ U3 @ ( var @ X3 ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,R3: real] : ( P2 @ Sigma3 @ U3 @ ( number @ R3 ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char] : ( P2 @ Sigma3 @ U3 @ ( const @ F5 ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,F5: char,Theta2: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ( ! [X25: trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 = ( some_trm @ X25 ) )
% 3.05/1.60 => ! [X2a: trm] :
% 3.05/1.60 ( ( ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ Sigma3
% 3.05/1.60 @ F5 )
% 3.05/1.60 = ( some_trm @ X2a ) )
% 3.05/1.60 => ( ( ( inf_inf_set_variable @ ( static_FVT @ X2a ) @ U3 )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 => ( P2 @ ( uSubst1408967625substt @ X25 ) @ bot_bot_set_variable @ X2a ) ) ) )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( func @ F5 @ Theta2 ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ! [Eta: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( plus @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3 @ U3 @ Theta2 )
% 3.05/1.60 => ! [Eta: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3 @ U3 @ Eta )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( times @ Theta2 @ Eta ) ) ) )
% 3.05/1.60 => ( ! [Sigma3: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 3.05/1.60 ( ( P2 @ Sigma3
% 3.05/1.60 @ ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : $true )
% 3.05/1.60 @ Theta2 )
% 3.05/1.60 => ( P2 @ Sigma3 @ U3 @ ( differential @ Theta2 ) ) )
% 3.05/1.60 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_341_dot__def,axiom,
% 3.05/1.60 ( uSubst_Mirabelle_dot
% 3.05/1.60 = ( const @ ( char2 @ $false @ $true @ $true @ $true @ $false @ $true @ $false @ $false ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_342_usubstappt_Opelims,axiom,
% 3.05/1.60 ! [X2: produc1418842292n_game,Xa: set_variable,Xb: trm,Y2: option_trm] :
% 3.05/1.60 ( ( ( uSubst516392818stappt @ X2 @ Xa @ Xb )
% 3.05/1.60 = Y2 )
% 3.05/1.60 => ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ Xb ) ) )
% 3.05/1.60 => ( ! [X3: variable] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( var @ X3 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_trm @ ( var @ X3 ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( var @ X3 ) ) ) ) ) )
% 3.05/1.60 => ( ! [R3: real] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( number @ R3 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( some_trm @ ( number @ R3 ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( number @ R3 ) ) ) ) ) )
% 3.05/1.60 => ( ! [F5: char] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( const @ F5 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( uSubst1559070963pconst @ X2 @ Xa @ F5 ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( const @ F5 ) ) ) ) ) )
% 3.05/1.60 => ( ! [F5: char,Theta2: trm] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( func @ F5 @ Theta2 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( case_o487727941rm_trm @ none_trm
% 3.05/1.60 @ ^ [Sigma_theta: trm] :
% 3.05/1.60 ( case_o487727941rm_trm @ ( some_trm @ ( func @ F5 @ Sigma_theta ) )
% 3.05/1.60 @ ^ [R: trm] :
% 3.05/1.60 ( if_option_trm
% 3.05/1.60 @ ( ( inf_inf_set_variable @ ( static_FVT @ R ) @ Xa )
% 3.05/1.60 = bot_bot_set_variable )
% 3.05/1.60 @ ( uSubst516392818stappt @ ( uSubst1408967625substt @ Sigma_theta ) @ bot_bot_set_variable @ R )
% 3.05/1.60 @ none_trm )
% 3.05/1.60 @ ( produc866613687on_trm
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1231571704on_trm
% 3.05/1.60 @ ^ [F4: char > option_trm] :
% 3.05/1.60 ( produc1036610745on_trm
% 3.05/1.60 @ ^ [Uv: char > option_fml,Uw: char > option_game] : F4 ) )
% 3.05/1.60 @ X2
% 3.05/1.60 @ F5 ) )
% 3.05/1.60 @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( func @ F5 @ Theta2 ) ) ) ) ) )
% 3.05/1.60 => ( ! [Theta2: trm,Eta: trm] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( plus @ Theta2 @ Eta ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst516392818stappt @ X2 @ Xa @ Eta ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( plus @ Theta2 @ Eta ) ) ) ) ) )
% 3.05/1.60 => ( ! [Theta2: trm,Eta: trm] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( times @ Theta2 @ Eta ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ X2 @ Xa @ Theta2 ) @ ( uSubst516392818stappt @ X2 @ Xa @ Eta ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( times @ Theta2 @ Eta ) ) ) ) ) )
% 3.05/1.60 => ~ ! [Theta2: trm] :
% 3.05/1.60 ( ( Xb
% 3.05/1.60 = ( differential @ Theta2 ) )
% 3.05/1.60 => ( ( Y2
% 3.05/1.60 = ( uSubst716837505ntialo
% 3.05/1.60 @ ( uSubst516392818stappt @ X2
% 3.05/1.60 @ ( collect_variable
% 3.05/1.60 @ ^ [X: variable] : $true )
% 3.05/1.60 @ Theta2 ) ) )
% 3.05/1.60 => ~ ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ X2 @ ( produc1482344242le_trm @ Xa @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_343_Differentialo_Osimps_I2_J,axiom,
% 3.05/1.60 ( ( uSubst716837505ntialo @ none_trm )
% 3.05/1.60 = none_trm ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_344_Differentialo__undef,axiom,
% 3.05/1.60 ! [Theta: option_trm] :
% 3.05/1.60 ( ( ( uSubst716837505ntialo @ Theta )
% 3.05/1.60 = none_trm )
% 3.05/1.60 = ( Theta = none_trm ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_345_Pluso_Osimps_I2_J,axiom,
% 3.05/1.60 ! [Eta2: option_trm] :
% 3.05/1.60 ( ( uSubst141955042_Pluso @ none_trm @ Eta2 )
% 3.05/1.60 = none_trm ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_346_Timeso_Osimps_I2_J,axiom,
% 3.05/1.60 ! [Eta2: option_trm] :
% 3.05/1.60 ( ( uSubst918876924Timeso @ none_trm @ Eta2 )
% 3.05/1.60 = none_trm ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_347_Pluso__undef,axiom,
% 3.05/1.60 ! [Theta: option_trm,Eta2: option_trm] :
% 3.05/1.60 ( ( ( uSubst141955042_Pluso @ Theta @ Eta2 )
% 3.05/1.60 = none_trm )
% 3.05/1.60 = ( ( Theta = none_trm )
% 3.05/1.60 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_348_Timeso__undef,axiom,
% 3.05/1.60 ! [Theta: option_trm,Eta2: option_trm] :
% 3.05/1.60 ( ( ( uSubst918876924Timeso @ Theta @ Eta2 )
% 3.05/1.60 = none_trm )
% 3.05/1.60 = ( ( Theta = none_trm )
% 3.05/1.60 | ( Eta2 = none_trm ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_349_Pluso_Osimps_I3_J,axiom,
% 3.05/1.60 ! [V3: trm] :
% 3.05/1.60 ( ( uSubst141955042_Pluso @ ( some_trm @ V3 ) @ none_trm )
% 3.05/1.60 = none_trm ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_350_Timeso_Osimps_I3_J,axiom,
% 3.05/1.60 ! [V3: trm] :
% 3.05/1.60 ( ( uSubst918876924Timeso @ ( some_trm @ V3 ) @ none_trm )
% 3.05/1.60 = none_trm ) ).
% 3.05/1.60
% 3.05/1.60 thf(fact_351_usubstappt_Osimps_I5_J,axiom,
% 3.05/1.60 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta2: trm] :
% 3.05/1.60 ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta2 ) )
% 3.05/1.60 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta2 ) ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 3.05/1.60 ! [X2: option_fml,Y2: option_fml] :
% 3.05/1.60 ( ( if_option_fml @ $false @ X2 @ Y2 )
% 3.05/1.60 = Y2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Ofml_J_T,axiom,
% 3.05/1.60 ! [X2: option_fml,Y2: option_fml] :
% 3.05/1.60 ( ( if_option_fml @ $true @ X2 @ Y2 )
% 3.05/1.60 = X2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(help_If_3_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.60 ! [P2: $o] :
% 3.05/1.60 ( ( P2 = $true )
% 3.05/1.60 | ( P2 = $false ) ) ).
% 3.05/1.60
% 3.05/1.60 thf(help_If_2_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.60 ! [X2: option_trm,Y2: option_trm] :
% 3.05/1.60 ( ( if_option_trm @ $false @ X2 @ Y2 )
% 3.05/1.60 = Y2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(help_If_1_1_If_001t__Option__Ooption_It__Syntax__Otrm_J_T,axiom,
% 3.05/1.60 ! [X2: option_trm,Y2: option_trm] :
% 3.05/1.60 ( ( if_option_trm @ $true @ X2 @ Y2 )
% 3.05/1.60 = X2 ) ).
% 3.05/1.60
% 3.05/1.60 thf(conj_0,conjecture,
% 3.05/1.60 ( ( produc1250175341on_fml
% 3.05/1.60 @ ^ [Uu: char > option_trm] :
% 3.05/1.60 ( produc1615133358on_fml
% 3.05/1.60 @ ^ [Uv: char > option_trm] :
% 3.05/1.60 ( produc1420172399on_fml
% 3.05/1.60 @ ^ [P: char > option_fml,Uw: char > option_game] : P ) )
% 3.05/1.60 @ sigma
% 3.05/1.60 @ p )
% 3.05/1.60 = none_fml ) ).
% 3.05/1.60 ------------------------
% 3.05/1.64 % (17209)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/183Mi)
% 3.05/1.65 % (17210)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_16880 for (2999ds/4Mi)
% 3.05/1.65 % (17211)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_16880 for (2999ds/27Mi)
% 3.05/1.65 % (17212)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/2Mi)
% 3.05/1.65 % (17213)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_16880 for (2999ds/2Mi)
% 3.05/1.65 % (17214)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_16880 for (2999ds/275Mi)
% 3.05/1.65 % (17215)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/18Mi)
% 3.05/1.65 % (17212)Instruction limit reached!
% 3.05/1.65 % (17212)------------------------------
% 3.05/1.65 % (17212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (17212)Termination reason: Unknown
% 3.05/1.65 % (17212)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (17212)Memory used [KB]: 1535
% 3.05/1.65 % (17212)Time elapsed: 0.004 s
% 3.05/1.65 % (17212)Instructions burned: 2 (million)
% 3.05/1.65 % (17212)------------------------------
% 3.05/1.65 % (17212)------------------------------
% 3.05/1.65 % (17213)Instruction limit reached!
% 3.05/1.65 % (17213)------------------------------
% 3.05/1.65 % (17213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (17213)Termination reason: Unknown
% 3.05/1.65 % (17213)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (17213)Memory used [KB]: 1535
% 3.05/1.65 % (17213)Time elapsed: 0.004 s
% 3.05/1.65 % (17213)Instructions burned: 2 (million)
% 3.05/1.65 % (17213)------------------------------
% 3.05/1.65 % (17213)------------------------------
% 3.05/1.65 % (17210)Instruction limit reached!
% 3.05/1.65 % (17210)------------------------------
% 3.05/1.65 % (17210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (17210)Termination reason: Unknown
% 3.05/1.66 % (17210)Termination phase: shuffling
% 3.05/1.66
% 3.05/1.66 % (17210)Memory used [KB]: 1663
% 3.05/1.66 % (17210)Time elapsed: 0.005 s
% 3.05/1.66 % (17210)Instructions burned: 4 (million)
% 3.05/1.66 % (17210)------------------------------
% 3.05/1.66 % (17210)------------------------------
% 3.05/1.66 % (17215)Instruction limit reached!
% 3.05/1.66 % (17215)------------------------------
% 3.05/1.66 % (17215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (17215)Termination reason: Unknown
% 3.05/1.66 % (17215)Termination phase: shuffling
% 3.05/1.66
% 3.05/1.66 % (17215)Memory used [KB]: 2046
% 3.05/1.66 % (17215)Time elapsed: 0.014 s
% 3.05/1.66 % (17215)Instructions burned: 19 (million)
% 3.05/1.66 % (17215)------------------------------
% 3.05/1.66 % (17215)------------------------------
% 3.05/1.67 % (17211)Instruction limit reached!
% 3.05/1.67 % (17211)------------------------------
% 3.05/1.67 % (17211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (17211)Termination reason: Unknown
% 3.05/1.67 % (17211)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (17211)Memory used [KB]: 2046
% 3.05/1.67 % (17211)Time elapsed: 0.018 s
% 3.05/1.67 % (17211)Instructions burned: 27 (million)
% 3.05/1.67 % (17211)------------------------------
% 3.05/1.67 % (17211)------------------------------
% 3.05/1.67 % (17216)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/3Mi)
% 3.05/1.67 % (17217)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_16880 for (2999ds/37Mi)
% 3.05/1.67 % (17218)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_16880 for (2999ds/15Mi)
% 3.05/1.67 % (17216)Instruction limit reached!
% 3.05/1.67 % (17216)------------------------------
% 3.05/1.67 % (17216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (17216)Termination reason: Unknown
% 3.05/1.67 % (17216)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (17216)Memory used [KB]: 1535
% 3.05/1.67 % (17216)Time elapsed: 0.004 s
% 3.05/1.67 % (17216)Instructions burned: 3 (million)
% 3.05/1.67 % (17216)------------------------------
% 3.05/1.67 % (17216)------------------------------
% 3.05/1.68 % (17219)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_16880 for (2999ds/3Mi)
% 3.05/1.68 % (17218)Instruction limit reached!
% 3.05/1.68 % (17218)------------------------------
% 3.05/1.68 % (17218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (17218)Termination reason: Unknown
% 3.05/1.68 % (17218)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (17218)Memory used [KB]: 1918
% 3.05/1.68 % (17218)Time elapsed: 0.011 s
% 3.05/1.68 % (17218)Instructions burned: 16 (million)
% 3.05/1.68 % (17218)------------------------------
% 3.05/1.68 % (17218)------------------------------
% 3.05/1.68 % (17220)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_16880 for (2999ds/1041Mi)
% 3.05/1.68 % (17219)Instruction limit reached!
% 3.05/1.68 % (17219)------------------------------
% 3.05/1.68 % (17219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (17219)Termination reason: Unknown
% 3.05/1.68 % (17219)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (17219)Memory used [KB]: 1663
% 3.05/1.68 % (17219)Time elapsed: 0.004 s
% 3.05/1.68 % (17219)Instructions burned: 4 (million)
% 3.05/1.68 % (17219)------------------------------
% 3.05/1.68 % (17219)------------------------------
% 3.05/1.69 % (17214)Refutation not found, incomplete strategy
% 3.05/1.69 % (17214)------------------------------
% 3.05/1.69 % (17214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (17214)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.69
% 3.05/1.69
% 3.05/1.69 % (17214)Memory used [KB]: 6652
% 3.05/1.69 % (17214)Time elapsed: 0.035 s
% 3.05/1.69 % (17214)Instructions burned: 58 (million)
% 3.05/1.69 % (17214)------------------------------
% 3.05/1.69 % (17214)------------------------------
% 3.05/1.69 % (17221)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/7Mi)
% 3.05/1.69 % (17217)Instruction limit reached!
% 3.05/1.69 % (17217)------------------------------
% 3.05/1.69 % (17217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (17217)Termination reason: Unknown
% 3.05/1.69 % (17217)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (17217)Memory used [KB]: 2430
% 3.05/1.69 % (17217)Time elapsed: 0.022 s
% 3.05/1.69 % (17217)Instructions burned: 38 (million)
% 3.05/1.69 % (17217)------------------------------
% 3.05/1.69 % (17217)------------------------------
% 3.05/1.69 % (17209)Instruction limit reached!
% 3.05/1.69 % (17209)------------------------------
% 3.05/1.69 % (17209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (17209)Termination reason: Unknown
% 3.05/1.69 % (17209)Termination phase: Saturation
% 3.05/1.69
% 3.05/1.69 % (17209)Memory used [KB]: 7675
% 3.05/1.69 % (17209)Time elapsed: 0.052 s
% 3.05/1.69 % (17209)Instructions burned: 185 (million)
% 3.05/1.69 % (17209)------------------------------
% 3.05/1.69 % (17209)------------------------------
% 3.05/1.70 % (17223)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_16880 for (2999ds/3Mi)
% 3.05/1.70 % (17221)Instruction limit reached!
% 3.05/1.70 % (17221)------------------------------
% 3.05/1.70 % (17221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (17221)Termination reason: Unknown
% 3.05/1.70 % (17221)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (17221)Memory used [KB]: 1663
% 3.05/1.70 % (17221)Time elapsed: 0.006 s
% 3.05/1.70 % (17221)Instructions burned: 7 (million)
% 3.05/1.70 % (17221)------------------------------
% 3.05/1.70 % (17221)------------------------------
% 3.05/1.70 % (17222)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/16Mi)
% 3.05/1.70 % (17223)Instruction limit reached!
% 3.05/1.70 % (17223)------------------------------
% 3.05/1.70 % (17223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (17223)Termination reason: Unknown
% 3.05/1.70 % (17223)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (17223)Memory used [KB]: 1663
% 3.05/1.70 % (17223)Time elapsed: 0.004 s
% 3.05/1.70 % (17223)Instructions burned: 5 (million)
% 3.05/1.70 % (17223)------------------------------
% 3.05/1.70 % (17223)------------------------------
% 3.05/1.70 % (17222)Instruction limit reached!
% 3.05/1.70 % (17222)------------------------------
% 3.05/1.70 % (17222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (17222)Termination reason: Unknown
% 3.05/1.70 % (17222)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (17222)Memory used [KB]: 1918
% 3.05/1.70 % (17222)Time elapsed: 0.008 s
% 3.05/1.70 % (17222)Instructions burned: 18 (million)
% 3.05/1.70 % (17222)------------------------------
% 3.05/1.70 % (17222)------------------------------
% 3.05/1.70 % (17224)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_16880 for (2999ds/3Mi)
% 3.05/1.70 % (17226)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/3Mi)
% 3.05/1.71 % (17226)Instruction limit reached!
% 3.05/1.71 % (17226)------------------------------
% 3.05/1.71 % (17226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (17226)Termination reason: Unknown
% 3.05/1.71 % (17226)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (17226)Memory used [KB]: 1535
% 3.05/1.71 % (17226)Time elapsed: 0.002 s
% 3.05/1.71 % (17226)Instructions burned: 3 (million)
% 3.05/1.71 % (17226)------------------------------
% 3.05/1.71 % (17226)------------------------------
% 3.05/1.71 % (17224)Instruction limit reached!
% 3.05/1.71 % (17224)------------------------------
% 3.05/1.71 % (17224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (17224)Termination reason: Unknown
% 3.05/1.71 % (17224)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (17224)Memory used [KB]: 1663
% 3.05/1.71 % (17224)Time elapsed: 0.004 s
% 3.05/1.71 % (17224)Instructions burned: 3 (million)
% 3.05/1.71 % (17224)------------------------------
% 3.05/1.71 % (17224)------------------------------
% 3.05/1.71 % (17228)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/18Mi)
% 3.05/1.71 % (17227)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/4Mi)
% 3.05/1.71 % (17225)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/7Mi)
% 3.05/1.71 % (17227)Instruction limit reached!
% 3.05/1.71 % (17227)------------------------------
% 3.05/1.71 % (17227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (17227)Termination reason: Unknown
% 3.05/1.71 % (17227)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (17227)Memory used [KB]: 1663
% 3.05/1.71 % (17227)Time elapsed: 0.003 s
% 3.05/1.71 % (17227)Instructions burned: 4 (million)
% 3.05/1.71 % (17227)------------------------------
% 3.05/1.71 % (17227)------------------------------
% 3.05/1.71 % (17229)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/710Mi)
% 3.05/1.71 % (17225)Instruction limit reached!
% 3.05/1.71 % (17225)------------------------------
% 3.05/1.71 % (17225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (17225)Termination reason: Unknown
% 3.05/1.71 % (17225)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (17225)Memory used [KB]: 1663
% 3.05/1.71 % (17225)Time elapsed: 0.006 s
% 3.05/1.71 % (17225)Instructions burned: 7 (million)
% 3.05/1.71 % (17225)------------------------------
% 3.05/1.71 % (17225)------------------------------
% 3.05/1.71 % (17228)Instruction limit reached!
% 3.05/1.71 % (17228)------------------------------
% 3.05/1.71 % (17228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (17228)Termination reason: Unknown
% 3.05/1.71 % (17228)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (17228)Memory used [KB]: 1918
% 3.05/1.71 % (17228)Time elapsed: 0.008 s
% 3.05/1.71 % (17228)Instructions burned: 18 (million)
% 3.05/1.71 % (17228)------------------------------
% 3.05/1.71 % (17228)------------------------------
% 3.05/1.71 % (17230)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/6Mi)
% 3.05/1.72 % (17230)Instruction limit reached!
% 3.05/1.72 % (17230)------------------------------
% 3.05/1.72 % (17230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.72 % (17230)Termination reason: Unknown
% 3.05/1.72 % (17230)Termination phase: shuffling
% 3.05/1.72
% 3.05/1.72 % (17230)Memory used [KB]: 1663
% 3.05/1.72 % (17230)Time elapsed: 0.003 s
% 3.05/1.72 % (17230)Instructions burned: 6 (million)
% 3.05/1.72 % (17230)------------------------------
% 3.05/1.72 % (17230)------------------------------
% 3.05/1.72 % (17232)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_16880 for (2999ds/21Mi)
% 3.05/1.72 % (17231)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_16880 for (2999ds/902Mi)
% 3.05/1.72 % (17233)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16880 for (2999ds/5Mi)
% 3.05/1.73 % (17235)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/377Mi)
% 3.05/1.73 % (17233)Instruction limit reached!
% 3.05/1.73 % (17233)------------------------------
% 3.05/1.73 % (17233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.73 % (17233)Termination reason: Unknown
% 3.05/1.73 % (17233)Termination phase: shuffling
% 3.05/1.73
% 3.05/1.73 % (17233)Memory used [KB]: 1791
% 3.05/1.73 % (17233)Time elapsed: 0.004 s
% 3.05/1.73 % (17233)Instructions burned: 7 (million)
% 3.05/1.73 % (17233)------------------------------
% 3.05/1.73 % (17233)------------------------------
% 3.05/1.73 % (17232)Instruction limit reached!
% 3.05/1.73 % (17232)------------------------------
% 3.05/1.73 % (17232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.73 % (17232)Termination reason: Unknown
% 3.05/1.73 % (17232)Termination phase: shuffling
% 3.05/1.73
% 3.05/1.73 % (17232)Memory used [KB]: 2046
% 3.05/1.73 % (17232)Time elapsed: 0.008 s
% 3.05/1.73 % (17232)Instructions burned: 22 (million)
% 3.05/1.73 % (17232)------------------------------
% 3.05/1.73 % (17232)------------------------------
% 3.05/1.73 % (17234)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_16880 for (2999ds/6Mi)
% 3.05/1.73 % (17229)Refutation not found, incomplete strategy
% 3.05/1.73 % (17229)------------------------------
% 3.05/1.73 % (17229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.73 % (17229)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.73
% 3.05/1.73
% 3.05/1.73 % (17229)Memory used [KB]: 6652
% 3.05/1.73 % (17229)Time elapsed: 0.020 s
% 3.05/1.73 % (17229)Instructions burned: 57 (million)
% 3.05/1.73 % (17229)------------------------------
% 3.05/1.73 % (17229)------------------------------
% 3.05/1.74 % (17234)Instruction limit reached!
% 3.05/1.74 % (17234)------------------------------
% 3.05/1.74 % (17234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.74 % (17234)Termination reason: Unknown
% 3.05/1.74 % (17234)Termination phase: shuffling
% 3.05/1.74
% 3.05/1.74 % (17234)Memory used [KB]: 1791
% 3.05/1.74 % (17234)Time elapsed: 0.006 s
% 3.05/1.74 % (17234)Instructions burned: 7 (million)
% 3.05/1.74 % (17234)------------------------------
% 3.05/1.74 % (17234)------------------------------
% 3.05/1.74 % (17236)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_16880 for (2998ds/779Mi)
% 3.05/1.74 % (17237)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_16880 for (2998ds/19Mi)
% 3.05/1.74 % (17238)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/879Mi)
% 3.05/1.74 % (17237)Instruction limit reached!
% 3.05/1.74 % (17237)------------------------------
% 3.05/1.74 % (17237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.74 % (17237)Termination reason: Unknown
% 3.05/1.74 % (17237)Termination phase: shuffling
% 3.05/1.74
% 3.05/1.74 % (17237)Memory used [KB]: 2046
% 3.05/1.74 % (17237)Time elapsed: 0.007 s
% 3.05/1.74 % (17237)Instructions burned: 21 (million)
% 3.05/1.74 % (17237)------------------------------
% 3.05/1.74 % (17237)------------------------------
% 3.05/1.75 % (17239)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/17Mi)
% 3.05/1.75 % (17240)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/3Mi)
% 3.05/1.76 % (17240)Instruction limit reached!
% 3.05/1.76 % (17240)------------------------------
% 3.05/1.76 % (17240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.76 % (17240)Termination reason: Unknown
% 3.05/1.76 % (17240)Termination phase: shuffling
% 3.05/1.76
% 3.05/1.76 % (17240)Memory used [KB]: 1663
% 3.05/1.76 % (17240)Time elapsed: 0.003 s
% 3.05/1.76 % (17240)Instructions burned: 6 (million)
% 3.05/1.76 % (17240)------------------------------
% 3.05/1.76 % (17240)------------------------------
% 3.05/1.76 % (17239)Instruction limit reached!
% 3.05/1.76 % (17239)------------------------------
% 3.05/1.76 % (17239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.76 % (17239)Termination reason: Unknown
% 3.05/1.76 % (17239)Termination phase: shuffling
% 3.05/1.76
% 3.05/1.76 % (17239)Memory used [KB]: 1918
% 3.05/1.76 % (17239)Time elapsed: 0.012 s
% 3.05/1.76 % (17239)Instructions burned: 18 (million)
% 3.05/1.76 % (17239)------------------------------
% 3.05/1.76 % (17239)------------------------------
% 3.05/1.77 % (17241)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/30Mi)
% 3.05/1.77 % (17241)Instruction limit reached!
% 3.05/1.77 % (17241)------------------------------
% 3.05/1.77 % (17241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.77 % (17241)Termination reason: Unknown
% 3.05/1.77 % (17241)Termination phase: shuffling
% 3.05/1.77
% 3.05/1.77 % (17241)Memory used [KB]: 2174
% 3.05/1.77 % (17241)Time elapsed: 0.011 s
% 3.05/1.77 % (17241)Instructions burned: 32 (million)
% 3.05/1.77 % (17241)------------------------------
% 3.05/1.77 % (17241)------------------------------
% 3.05/1.78 % (17242)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/127Mi)
% 3.05/1.78 % (17243)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16880 for (2998ds/100Mi)
% 3.05/1.81 % (17243)Instruction limit reached!
% 3.05/1.81 % (17243)------------------------------
% 3.05/1.81 % (17243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.81 % (17243)Termination reason: Unknown
% 3.05/1.81 % (17243)Termination phase: Property scanning
% 3.05/1.81
% 3.05/1.81 % (17243)Memory used [KB]: 2942
% 3.05/1.81 % (17243)Time elapsed: 0.029 s
% 3.05/1.81 % (17243)Instructions burned: 100 (million)
% 3.05/1.81 % (17243)------------------------------
% 3.05/1.81 % (17243)------------------------------
% 3.05/1.82 % (17242)Instruction limit reached!
% 3.05/1.82 % (17242)------------------------------
% 3.05/1.82 % (17242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.82 % (17242)Termination reason: Unknown
% 3.05/1.82 % (17242)Termination phase: Property scanning
% 3.05/1.82
% 3.05/1.82 % (17242)Memory used [KB]: 3070
% 3.05/1.82 % (17242)Time elapsed: 0.042 s
% 3.05/1.82 % (17242)Instructions burned: 128 (million)
% 3.05/1.82 % (17242)------------------------------
% 3.05/1.82 % (17242)------------------------------
% 3.05/1.82 % (17244)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_16880 for (2998ds/3Mi)
% 3.05/1.82 % (17244)Instruction limit reached!
% 3.05/1.82 % (17244)------------------------------
% 3.05/1.82 % (17244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.82 % (17244)Termination reason: Unknown
% 3.05/1.82 % (17244)Termination phase: shuffling
% 3.05/1.82
% 3.05/1.82 % (17244)Memory used [KB]: 1535
% 3.05/1.82 % (17244)Time elapsed: 0.002 s
% 3.05/1.82 % (17244)Instructions burned: 3 (million)
% 3.05/1.82 % (17244)------------------------------
% 3.05/1.82 % (17244)------------------------------
% 3.05/1.83 % (17245)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_16880 for (2998ds/20Mi)
% 3.05/1.83 % (17246)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_16880 for (2997ds/86Mi)
% 3.05/1.84 % (17235)Instruction limit reached!
% 3.05/1.84 % (17235)------------------------------
% 3.05/1.84 % (17235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.84 % (17235)Termination reason: Unknown
% 3.05/1.84 % (17235)Termination phase: Saturation
% 3.05/1.84
% 3.05/1.84 % (17235)Memory used [KB]: 9210
% 3.05/1.84 % (17235)Time elapsed: 0.111 s
% 3.05/1.84 % (17235)Instructions burned: 379 (million)
% 3.05/1.84 % (17235)------------------------------
% 3.05/1.84 % (17235)------------------------------
% 3.05/1.84 % (17245)Instruction limit reached!
% 3.05/1.84 % (17245)------------------------------
% 3.05/1.84 % (17245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.84 % (17245)Termination reason: Unknown
% 3.05/1.84 % (17245)Termination phase: shuffling
% 3.05/1.84
% 3.05/1.84 % (17245)Memory used [KB]: 2046
% 3.05/1.84 % (17245)Time elapsed: 0.009 s
% 3.05/1.84 % (17245)Instructions burned: 21 (million)
% 3.05/1.84 % (17245)------------------------------
% 3.05/1.84 % (17245)------------------------------
% 3.05/1.85 % (17247)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_16880 for (2997ds/107Mi)
% 3.05/1.85 % (17248)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_16880 for (2997ds/39Mi)
% 3.05/1.86 % (17246)Instruction limit reached!
% 3.05/1.86 % (17246)------------------------------
% 3.05/1.86 % (17246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.86 % (17246)Termination reason: Unknown
% 3.05/1.86 % (17246)Termination phase: Property scanning
% 3.05/1.86
% 3.05/1.86 % (17246)Memory used [KB]: 2942
% 3.05/1.86 % (17246)Time elapsed: 0.027 s
% 3.05/1.86 % (17246)Instructions burned: 88 (million)
% 3.05/1.86 % (17246)------------------------------
% 3.05/1.86 % (17246)------------------------------
% 3.05/1.86 % (17248)Instruction limit reached!
% 3.05/1.86 % (17248)------------------------------
% 3.05/1.86 % (17248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.86 % (17248)Termination reason: Unknown
% 3.05/1.86 % (17248)Termination phase: shuffling
% 3.05/1.86
% 3.05/1.86 % (17248)Memory used [KB]: 2430
% 3.05/1.86 % (17248)Time elapsed: 0.013 s
% 3.05/1.86 % (17248)Instructions burned: 41 (million)
% 3.05/1.86 % (17248)------------------------------
% 3.05/1.86 % (17248)------------------------------
% 3.05/1.87 % (17249)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_16880 for (2997ds/448Mi)
% 3.05/1.87 % (17250)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_16880 for (2997ds/46Mi)
% 3.05/1.88 % (17247)Instruction limit reached!
% 3.05/1.88 % (17247)------------------------------
% 3.05/1.88 % (17247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.88 % (17247)Termination reason: Unknown
% 3.05/1.88 % (17247)Termination phase: Property scanning
% 3.05/1.88
% 3.05/1.88 % (17247)Memory used [KB]: 2814
% 3.05/1.88 % (17247)Time elapsed: 0.033 s
% 3.05/1.88 % (17247)Instructions burned: 110 (million)
% 3.05/1.88 % (17247)------------------------------
% 3.05/1.88 % (17247)------------------------------
% 3.05/1.88 % (17250)Instruction limit reached!
% 3.05/1.88 % (17250)------------------------------
% 3.05/1.88 % (17250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.88 % (17250)Termination reason: Unknown
% 3.05/1.88 % (17250)Termination phase: Property scanning
% 3.05/1.88
% 3.05/1.88 % (17250)Memory used [KB]: 2174
% 3.05/1.88 % (17250)Time elapsed: 0.017 s
% 3.05/1.88 % (17250)Instructions burned: 48 (million)
% 3.05/1.88 % (17250)------------------------------
% 3.05/1.88 % (17250)------------------------------
% 3.05/1.89 % (17251)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_16880 for (2997ds/98Mi)
% 3.05/1.90 % (17252)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_16880 for (2997ds/507Mi)
% 3.05/1.91 % (17251)Instruction limit reached!
% 3.05/1.91 % (17251)------------------------------
% 3.05/1.91 % (17251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.91 % (17251)Termination reason: Unknown
% 3.05/1.91 % (17251)Termination phase: Property scanning
% 3.05/1.91
% 3.05/1.91 % (17251)Memory used [KB]: 2942
% 3.05/1.91 % (17251)Time elapsed: 0.028 s
% 3.05/1.91 % (17251)Instructions burned: 98 (million)
% 3.05/1.91 % (17251)------------------------------
% 3.05/1.91 % (17251)------------------------------
% 3.05/1.92 % (17253)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_16880 for (2997ds/149Mi)
% 3.05/1.96 % (17253)Instruction limit reached!
% 3.05/1.96 % (17253)------------------------------
% 3.05/1.96 % (17253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.96 % (17253)Termination reason: Unknown
% 3.05/1.96 % (17253)Termination phase: Property scanning
% 3.05/1.96
% 3.05/1.96 % (17253)Memory used [KB]: 3709
% 3.05/1.96 % (17253)Time elapsed: 0.040 s
% 3.05/1.96 % (17253)Instructions burned: 150 (million)
% 3.05/1.96 % (17253)------------------------------
% 3.05/1.96 % (17253)------------------------------
% 3.05/1.97 % (17254)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_16880 for (2996ds/39Mi)
% 3.05/1.98 % (17252)Refutation not found, incomplete strategy
% 3.05/1.98 % (17252)------------------------------
% 3.05/1.98 % (17252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.98 % (17252)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.98
% 3.05/1.98
% 3.05/1.98 % (17252)Memory used [KB]: 8955
% 3.05/1.98 % (17252)Time elapsed: 0.111 s
% 3.05/1.98 % (17252)Instructions burned: 275 (million)
% 3.05/1.98 % (17252)------------------------------
% 3.05/1.98 % (17252)------------------------------
% 3.05/1.99 % (17254)Instruction limit reached!
% 3.05/1.99 % (17254)------------------------------
% 3.05/1.99 % (17254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (17254)Termination reason: Unknown
% 3.05/1.99 % (17254)Termination phase: Property scanning
% 3.05/1.99
% 3.05/1.99 % (17254)Memory used [KB]: 2174
% 3.05/1.99 % (17254)Time elapsed: 0.014 s
% 3.05/1.99 % (17254)Instructions burned: 41 (million)
% 3.05/1.99 % (17254)------------------------------
% 3.05/1.99 % (17254)------------------------------
% 3.05/1.99 % (17236)Instruction limit reached!
% 3.05/1.99 % (17236)------------------------------
% 3.05/1.99 % (17236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (17236)Termination reason: Unknown
% 3.05/1.99 % (17236)Termination phase: Saturation
% 3.05/1.99
% 3.05/1.99 % (17236)Memory used [KB]: 9722
% 3.05/1.99 % (17236)Time elapsed: 0.251 s
% 3.05/1.99 % (17236)Instructions burned: 780 (million)
% 3.05/1.99 % (17236)------------------------------
% 3.05/1.99 % (17236)------------------------------
% 3.05/1.99 % (17255)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_16880 for (2996ds/6Mi)
% 3.05/1.99 % (17249)Instruction limit reached!
% 3.05/1.99 % (17249)------------------------------
% 3.05/1.99 % (17249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (17249)Termination reason: Unknown
% 3.05/1.99 % (17249)Termination phase: Saturation
% 3.05/1.99
% 3.05/1.99 % (17249)Memory used [KB]: 9466
% 3.05/1.99 % (17249)Time elapsed: 0.149 s
% 3.05/1.99 % (17249)Instructions burned: 450 (million)
% 3.05/1.99 % (17249)------------------------------
% 3.05/1.99 % (17249)------------------------------
% 3.05/1.99 % (17255)Instruction limit reached!
% 3.05/1.99 % (17255)------------------------------
% 3.05/1.99 % (17255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (17255)Termination reason: Unknown
% 3.05/1.99 % (17255)Termination phase: shuffling
% 3.05/1.99
% 3.05/1.99 % (17255)Memory used [KB]: 1663
% 3.05/1.99 % (17255)Time elapsed: 0.003 s
% 3.05/1.99 % (17255)Instructions burned: 6 (million)
% 3.05/1.99 % (17255)------------------------------
% 3.05/1.99 % (17255)------------------------------
% 3.05/2.00 % (17256)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_16880 for (2996ds/1087Mi)
% 3.05/2.00 % (17257)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_16880 for (2996ds/47Mi)
% 3.05/2.00 % (17258)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_16880 for (2996ds/44Mi)
% 3.05/2.01 % (17238)Instruction limit reached!
% 3.05/2.01 % (17238)------------------------------
% 3.05/2.01 % (17238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.01 % (17220)Instruction limit reached!
% 3.05/2.01 % (17220)------------------------------
% 3.05/2.01 % (17220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.01 % (17220)Termination reason: Unknown
% 3.05/2.01 % (17220)Termination phase: Saturation
% 3.05/2.01
% 3.05/2.01 % (17220)Memory used [KB]: 10618
% 3.05/2.01 % (17220)Time elapsed: 0.326 s
% 3.05/2.01 % (17220)Instructions burned: 1042 (million)
% 3.05/2.01 % (17220)------------------------------
% 3.05/2.01 % (17220)------------------------------
% 3.05/2.01 % (17238)Termination reason: Unknown
% 3.05/2.01 % (17238)Termination phase: Saturation
% 3.05/2.01
% 3.05/2.01 % (17238)Memory used [KB]: 8187
% 3.05/2.01 % (17238)Time elapsed: 0.266 s
% 3.05/2.01 % (17238)Instructions burned: 881 (million)
% 3.05/2.01 % (17238)------------------------------
% 3.05/2.01 % (17238)------------------------------
% 5.67/2.01 % (17257)Instruction limit reached!
% 5.67/2.01 % (17257)------------------------------
% 5.67/2.01 % (17257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.01 % (17257)Termination reason: Unknown
% 5.67/2.01 % (17257)Termination phase: Property scanning
% 5.67/2.01
% 5.67/2.01 % (17257)Memory used [KB]: 2174
% 5.67/2.01 % (17257)Time elapsed: 0.016 s
% 5.67/2.01 % (17257)Instructions burned: 47 (million)
% 5.67/2.01 % (17257)------------------------------
% 5.67/2.01 % (17257)------------------------------
% 5.67/2.01 % (17259)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_16880 for (2996ds/432Mi)
% 5.67/2.01 % (17231)Instruction limit reached!
% 5.67/2.01 % (17231)------------------------------
% 5.67/2.01 % (17231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.01 % (17231)Termination reason: Unknown
% 5.67/2.01 % (17231)Termination phase: Saturation
% 5.67/2.01
% 5.67/2.01 % (17231)Memory used [KB]: 8827
% 5.67/2.01 % (17231)Time elapsed: 0.291 s
% 5.67/2.01 % (17231)Instructions burned: 905 (million)
% 5.67/2.01 % (17231)------------------------------
% 5.67/2.01 % (17231)------------------------------
% 5.67/2.02 % (17260)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_16880 for (2996ds/62Mi)
% 5.67/2.02 % (17261)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_16880 for (2996ds/31Mi)
% 5.67/2.02 % (17258)Instruction limit reached!
% 5.67/2.02 % (17258)------------------------------
% 5.67/2.02 % (17258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.02 % (17258)Termination reason: Unknown
% 5.67/2.02 % (17258)Termination phase: shuffling
% 5.67/2.02
% 5.67/2.02 % (17258)Memory used [KB]: 2430
% 5.67/2.02 % (17258)Time elapsed: 0.015 s
% 5.67/2.02 % (17258)Instructions burned: 44 (million)
% 5.67/2.02 % (17258)------------------------------
% 5.67/2.02 % (17258)------------------------------
% 5.67/2.02 % (17262)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_16880 for (2996ds/96Mi)
% 5.67/2.02 % (17263)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_16880 for (2996ds/453Mi)
% 5.67/2.03 % (17261)Instruction limit reached!
% 5.67/2.03 % (17261)------------------------------
% 5.67/2.03 % (17261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.03 % (17261)Termination reason: Unknown
% 5.67/2.03 % (17261)Termination phase: shuffling
% 5.67/2.03
% 5.67/2.03 % (17261)Memory used [KB]: 2174
% 5.67/2.03 % (17261)Time elapsed: 0.011 s
% 5.67/2.03 % (17261)Instructions burned: 32 (million)
% 5.67/2.03 % (17261)------------------------------
% 5.67/2.03 % (17261)------------------------------
% 5.67/2.03 % (17264)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_16880 for (2996ds/71Mi)
% 5.67/2.03 % (17260)Instruction limit reached!
% 5.67/2.03 % (17260)------------------------------
% 5.67/2.03 % (17260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.03 % (17260)Termination reason: Unknown
% 5.67/2.03 % (17260)Termination phase: shuffling
% 5.67/2.03
% 5.67/2.03 % (17260)Memory used [KB]: 2942
% 5.67/2.03 % (17260)Time elapsed: 0.018 s
% 5.67/2.03 % (17260)Instructions burned: 63 (million)
% 5.67/2.03 % (17260)------------------------------
% 5.67/2.03 % (17260)------------------------------
% 5.67/2.04 % (17265)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/83Mi)
% 5.67/2.04 % (17266)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/11Mi)
% 5.67/2.05 % (17266)Instruction limit reached!
% 5.67/2.05 % (17266)------------------------------
% 5.67/2.05 % (17266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.05 % (17266)Termination reason: Unknown
% 5.67/2.05 % (17266)Termination phase: shuffling
% 5.67/2.05
% 5.67/2.05 % (17266)Memory used [KB]: 1791
% 5.67/2.05 % (17266)Time elapsed: 0.004 s
% 5.67/2.05 % (17266)Instructions burned: 11 (million)
% 5.67/2.05 % (17266)------------------------------
% 5.67/2.05 % (17266)------------------------------
% 5.67/2.05 % (17264)Instruction limit reached!
% 5.67/2.05 % (17264)------------------------------
% 5.67/2.05 % (17264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.05 % (17264)Termination reason: Unknown
% 5.67/2.05 % (17264)Termination phase: Preprocessing 3
% 5.67/2.05
% 5.67/2.05 % (17264)Memory used [KB]: 2686
% 5.67/2.05 % (17264)Time elapsed: 0.024 s
% 5.67/2.05 % (17264)Instructions burned: 71 (million)
% 5.67/2.05 % (17264)------------------------------
% 5.67/2.05 % (17264)------------------------------
% 5.67/2.05 % (17262)Instruction limit reached!
% 5.67/2.05 % (17262)------------------------------
% 5.67/2.05 % (17262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.05 % (17262)Termination reason: Unknown
% 5.67/2.05 % (17262)Termination phase: Property scanning
% 5.67/2.05
% 5.67/2.05 % (17262)Memory used [KB]: 2942
% 5.67/2.05 % (17262)Time elapsed: 0.032 s
% 5.67/2.05 % (17262)Instructions burned: 98 (million)
% 5.67/2.05 % (17262)------------------------------
% 5.67/2.05 % (17262)------------------------------
% 5.67/2.06 % (17267)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_16880 for (2995ds/41Mi)
% 5.67/2.06 % (17265)Refutation not found, incomplete strategy
% 5.67/2.06 % (17265)------------------------------
% 5.67/2.06 % (17265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.06 % (17265)Termination reason: Refutation not found, incomplete strategy
% 5.67/2.06
% 5.67/2.06
% 5.67/2.06 % (17265)Memory used [KB]: 6652
% 5.67/2.06 % (17265)Time elapsed: 0.021 s
% 5.67/2.06 % (17265)Instructions burned: 69 (million)
% 5.67/2.06 % (17265)------------------------------
% 5.67/2.06 % (17265)------------------------------
% 5.67/2.06 % (17268)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/6Mi)
% 5.67/2.06 % (17269)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/150Mi)
% 5.67/2.06 % (17268)Instruction limit reached!
% 5.67/2.06 % (17268)------------------------------
% 5.67/2.06 % (17268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.06 % (17268)Termination reason: Unknown
% 5.67/2.06 % (17268)Termination phase: shuffling
% 5.67/2.06
% 5.67/2.06 % (17268)Memory used [KB]: 1663
% 5.67/2.06 % (17268)Time elapsed: 0.004 s
% 5.67/2.06 % (17268)Instructions burned: 6 (million)
% 5.67/2.06 % (17268)------------------------------
% 5.67/2.06 % (17268)------------------------------
% 5.67/2.07 % (17270)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/343Mi)
% 5.67/2.07 % (17267)Instruction limit reached!
% 5.67/2.07 % (17267)------------------------------
% 5.67/2.07 % (17267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.07 % (17267)Termination reason: Unknown
% 5.67/2.07 % (17267)Termination phase: shuffling
% 5.67/2.07
% 5.67/2.07 % (17267)Memory used [KB]: 2430
% 5.67/2.07 % (17267)Time elapsed: 0.013 s
% 5.67/2.07 % (17267)Instructions burned: 43 (million)
% 5.67/2.07 % (17267)------------------------------
% 5.67/2.07 % (17267)------------------------------
% 5.67/2.07 % (17271)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_16880 for (2995ds/109Mi)
% 5.67/2.08 % (17272)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_16880 for (2995ds/253Mi)
% 5.67/2.09 % (17272)Refutation not found, incomplete strategy
% 5.67/2.09 % (17272)------------------------------
% 5.67/2.09 % (17272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.09 % (17272)Termination reason: Refutation not found, incomplete strategy
% 5.67/2.09
% 5.67/2.09
% 5.67/2.09 % (17272)Memory used [KB]: 6652
% 5.67/2.09 % (17272)Time elapsed: 0.018 s
% 5.67/2.09 % (17272)Instructions burned: 58 (million)
% 5.67/2.09 % (17272)------------------------------
% 5.67/2.09 % (17272)------------------------------
% 5.67/2.10 % (17269)Instruction limit reached!
% 5.67/2.10 % (17269)------------------------------
% 5.67/2.10 % (17269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.10 % (17269)Termination reason: Unknown
% 5.67/2.10 % (17269)Termination phase: Property scanning
% 5.67/2.10
% 5.67/2.10 % (17269)Memory used [KB]: 3198
% 5.67/2.10 % (17269)Time elapsed: 0.043 s
% 5.67/2.10 % (17269)Instructions burned: 150 (million)
% 5.67/2.10 % (17269)------------------------------
% 5.67/2.10 % (17269)------------------------------
% 5.67/2.10 % (17273)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_16880 for (2995ds/140Mi)
% 5.67/2.11 % (17271)Instruction limit reached!
% 5.67/2.11 % (17271)------------------------------
% 5.67/2.11 % (17271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.11 % (17271)Termination reason: Unknown
% 5.67/2.11 % (17271)Termination phase: Property scanning
% 5.67/2.11
% 5.67/2.11 % (17271)Memory used [KB]: 2814
% 5.67/2.11 % (17271)Time elapsed: 0.035 s
% 5.67/2.11 % (17271)Instructions burned: 109 (million)
% 5.67/2.11 % (17271)------------------------------
% 5.67/2.11 % (17271)------------------------------
% 6.20/2.11 % (17274)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_16880 for (2995ds/614Mi)
% 6.20/2.12 % (17275)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_16880 for (2994ds/202Mi)
% 6.20/2.13 % (17273)Refutation not found, incomplete strategy
% 6.20/2.13 % (17273)------------------------------
% 6.20/2.13 % (17273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.13 % (17273)Termination reason: Refutation not found, incomplete strategy
% 6.20/2.13
% 6.20/2.13
% 6.20/2.13 % (17273)Memory used [KB]: 7036
% 6.20/2.13 % (17273)Time elapsed: 0.053 s
% 6.20/2.13 % (17273)Instructions burned: 87 (million)
% 6.20/2.13 % (17273)------------------------------
% 6.20/2.13 % (17273)------------------------------
% 6.20/2.14 % (17276)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_16880 for (2994ds/339Mi)
% 6.20/2.15 % (17275)Refutation not found, incomplete strategy
% 6.20/2.15 % (17275)------------------------------
% 6.20/2.15 % (17275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.15 % (17275)Termination reason: Refutation not found, incomplete strategy
% 6.20/2.15
% 6.20/2.15
% 6.20/2.15 % (17275)Memory used [KB]: 7164
% 6.20/2.15 % (17275)Time elapsed: 0.030 s
% 6.20/2.15 % (17275)Instructions burned: 89 (million)
% 6.20/2.15 % (17275)------------------------------
% 6.20/2.15 % (17275)------------------------------
% 6.20/2.15 % (17263)Instruction limit reached!
% 6.20/2.15 % (17263)------------------------------
% 6.20/2.15 % (17263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.15 % (17263)Termination reason: Unknown
% 6.20/2.15 % (17263)Termination phase: Saturation
% 6.20/2.15
% 6.20/2.15 % (17263)Memory used [KB]: 8955
% 6.20/2.15 % (17263)Time elapsed: 0.130 s
% 6.20/2.15 % (17263)Instructions burned: 455 (million)
% 6.20/2.15 % (17263)------------------------------
% 6.20/2.15 % (17263)------------------------------
% 6.20/2.16 % (17277)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_16880 for (2994ds/283Mi)
% 6.20/2.16 % (17278)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_16880 for (2994ds/134Mi)
% 6.20/2.17 % (17270)Instruction limit reached!
% 6.20/2.17 % (17270)------------------------------
% 6.20/2.17 % (17270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.17 % (17270)Termination reason: Unknown
% 6.20/2.17 % (17270)Termination phase: Saturation
% 6.20/2.17
% 6.20/2.17 % (17270)Memory used [KB]: 8315
% 6.20/2.17 % (17270)Time elapsed: 0.128 s
% 6.20/2.17 % (17270)Instructions burned: 345 (million)
% 6.20/2.17 % (17270)------------------------------
% 6.20/2.17 % (17270)------------------------------
% 6.20/2.18 % (17279)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_16880 for (2994ds/298Mi)
% 6.20/2.18 % (17259)Instruction limit reached!
% 6.20/2.18 % (17259)------------------------------
% 6.20/2.18 % (17259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.20/2.18 % (17259)Termination reason: Unknown
% 6.20/2.18 % (17259)Termination phase: Saturation
% 6.20/2.18
% 6.20/2.18 % (17259)Memory used [KB]: 4861
% 6.20/2.18 % (17259)Time elapsed: 0.172 s
% 6.20/2.18 % (17259)Instructions burned: 434 (million)
% 6.20/2.18 % (17259)------------------------------
% 6.20/2.18 % (17259)------------------------------
% 6.20/2.19 % (17280)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_16880 for (2994ds/192Mi)
% 6.70/2.20 % (17278)Instruction limit reached!
% 6.70/2.20 % (17278)------------------------------
% 6.70/2.20 % (17278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.20 % (17278)Termination reason: Unknown
% 6.70/2.20 % (17278)Termination phase: Property scanning
% 6.70/2.20
% 6.70/2.20 % (17278)Memory used [KB]: 3070
% 6.70/2.20 % (17278)Time elapsed: 0.039 s
% 6.70/2.20 % (17278)Instructions burned: 137 (million)
% 6.70/2.20 % (17278)------------------------------
% 6.70/2.20 % (17278)------------------------------
% 6.70/2.21 % (17281)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_16880 for (2994ds/258Mi)
% 6.70/2.23 % (17277)Instruction limit reached!
% 6.70/2.23 % (17277)------------------------------
% 6.70/2.23 % (17277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.23 % (17277)Termination reason: Unknown
% 6.70/2.23 % (17277)Termination phase: Saturation
% 6.70/2.23
% 6.70/2.23 % (17277)Memory used [KB]: 7931
% 6.70/2.23 % (17277)Time elapsed: 0.075 s
% 6.70/2.23 % (17277)Instructions burned: 285 (million)
% 6.70/2.23 % (17277)------------------------------
% 6.70/2.23 % (17277)------------------------------
% 6.70/2.24 % (17276)Instruction limit reached!
% 6.70/2.24 % (17276)------------------------------
% 6.70/2.24 % (17276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.24 % (17276)Termination reason: Unknown
% 6.70/2.24 % (17276)Termination phase: Saturation
% 6.70/2.24
% 6.70/2.24 % (17276)Memory used [KB]: 7803
% 6.70/2.24 % (17276)Time elapsed: 0.097 s
% 6.70/2.24 % (17276)Instructions burned: 340 (million)
% 6.70/2.24 % (17276)------------------------------
% 6.70/2.24 % (17276)------------------------------
% 6.70/2.24 % (17282)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_16880 for (2993ds/90Mi)
% 6.70/2.25 % (17283)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_16880 for (2993ds/231Mi)
% 6.70/2.25 % (17280)Instruction limit reached!
% 6.70/2.25 % (17280)------------------------------
% 6.70/2.25 % (17280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.25 % (17280)Termination reason: Unknown
% 6.70/2.25 % (17280)Termination phase: Saturation
% 6.70/2.25
% 6.70/2.25 % (17280)Memory used [KB]: 3709
% 6.70/2.25 % (17280)Time elapsed: 0.059 s
% 6.70/2.25 % (17280)Instructions burned: 194 (million)
% 6.70/2.25 % (17280)------------------------------
% 6.70/2.25 % (17280)------------------------------
% 6.70/2.26 % (17279)Instruction limit reached!
% 6.70/2.26 % (17279)------------------------------
% 6.70/2.26 % (17279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.26 % (17279)Termination reason: Unknown
% 6.70/2.26 % (17279)Termination phase: Saturation
% 6.70/2.26
% 6.70/2.26 % (17279)Memory used [KB]: 8443
% 6.70/2.26 % (17279)Time elapsed: 0.079 s
% 6.70/2.26 % (17279)Instructions burned: 300 (million)
% 6.70/2.26 % (17279)------------------------------
% 6.70/2.26 % (17279)------------------------------
% 6.70/2.26 % (17284)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_16880 for (2993ds/458Mi)
% 6.70/2.26 % (17282)Instruction limit reached!
% 6.70/2.26 % (17282)------------------------------
% 6.70/2.26 % (17282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.26 % (17282)Termination reason: Unknown
% 6.70/2.26 % (17282)Termination phase: Property scanning
% 6.70/2.26
% 6.70/2.26 % (17282)Memory used [KB]: 2942
% 6.70/2.26 % (17282)Time elapsed: 0.027 s
% 6.70/2.26 % (17282)Instructions burned: 91 (million)
% 6.70/2.26 % (17282)------------------------------
% 6.70/2.26 % (17282)------------------------------
% 6.70/2.27 % (17285)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_16880 for (2993ds/31Mi)
% 6.70/2.27 % (17281)Instruction limit reached!
% 6.70/2.27 % (17281)------------------------------
% 6.70/2.27 % (17281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.27 % (17281)Termination reason: Unknown
% 6.70/2.27 % (17281)Termination phase: Property scanning
% 6.70/2.27
% 6.70/2.27 % (17281)Memory used [KB]: 3454
% 6.70/2.27 % (17281)Time elapsed: 0.065 s
% 6.70/2.27 % (17281)Instructions burned: 258 (million)
% 6.70/2.27 % (17281)------------------------------
% 6.70/2.27 % (17281)------------------------------
% 6.70/2.27 % (17286)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_16880 for (2993ds/297Mi)
% 6.70/2.28 % (17285)Instruction limit reached!
% 6.70/2.28 % (17285)------------------------------
% 6.70/2.28 % (17285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.28 % (17285)Termination reason: Unknown
% 6.70/2.28 % (17285)Termination phase: shuffling
% 6.70/2.28
% 6.70/2.28 % (17285)Memory used [KB]: 2174
% 6.70/2.28 % (17285)Time elapsed: 0.011 s
% 6.70/2.28 % (17285)Instructions burned: 32 (million)
% 6.70/2.28 % (17285)------------------------------
% 6.70/2.28 % (17285)------------------------------
% 6.70/2.28 % (17287)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_16880 for (2993ds/987Mi)
% 6.70/2.29 % (17288)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_16880 for (2993ds/182Mi)
% 6.70/2.29 % (17274)Instruction limit reached!
% 6.70/2.29 % (17274)------------------------------
% 6.70/2.29 % (17274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.29 % (17274)Termination reason: Unknown
% 6.70/2.29 % (17274)Termination phase: Saturation
% 6.70/2.29
% 6.70/2.29 % (17274)Memory used [KB]: 9850
% 6.70/2.29 % (17274)Time elapsed: 0.178 s
% 6.70/2.29 % (17274)Instructions burned: 615 (million)
% 6.70/2.29 % (17274)------------------------------
% 6.70/2.29 % (17274)------------------------------
% 7.50/2.30 % (17289)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_16880 for (2993ds/182Mi)
% 7.50/2.30 % (17283)Instruction limit reached!
% 7.50/2.30 % (17283)------------------------------
% 7.50/2.30 % (17283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.30 % (17283)Termination reason: Unknown
% 7.50/2.30 % (17283)Termination phase: Saturation
% 7.50/2.30
% 7.50/2.30 % (17283)Memory used [KB]: 7675
% 7.50/2.31 % (17283)Time elapsed: 0.060 s
% 7.50/2.31 % (17283)Instructions burned: 231 (million)
% 7.50/2.31 % (17283)------------------------------
% 7.50/2.31 % (17283)------------------------------
% 7.50/2.31 % (17286)Refutation not found, incomplete strategy
% 7.50/2.31 % (17286)------------------------------
% 7.50/2.31 % (17286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.31 % (17286)Termination reason: Refutation not found, incomplete strategy
% 7.50/2.31
% 7.50/2.31
% 7.50/2.31 % (17286)Memory used [KB]: 7419
% 7.50/2.31 % (17286)Time elapsed: 0.037 s
% 7.50/2.31 % (17286)Instructions burned: 134 (million)
% 7.50/2.31 % (17286)------------------------------
% 7.50/2.31 % (17286)------------------------------
% 7.50/2.31 % (17290)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_16880 for (2993ds/154Mi)
% 7.50/2.32 % (17291)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_16880 for (2993ds/79Mi)
% 7.50/2.33 % (17256)Instruction limit reached!
% 7.50/2.33 % (17256)------------------------------
% 7.50/2.33 % (17256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.33 % (17256)Termination reason: Unknown
% 7.50/2.33 % (17256)Termination phase: Saturation
% 7.50/2.33
% 7.50/2.33 % (17256)Memory used [KB]: 8187
% 7.50/2.33 % (17256)Time elapsed: 0.335 s
% 7.50/2.33 % (17256)Instructions burned: 1087 (million)
% 7.50/2.33 % (17256)------------------------------
% 7.50/2.33 % (17256)------------------------------
% 7.50/2.33 % (17288)Instruction limit reached!
% 7.50/2.33 % (17288)------------------------------
% 7.50/2.33 % (17288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.33 % (17288)Termination reason: Unknown
% 7.50/2.33 % (17288)Termination phase: Property scanning
% 7.50/2.33
% 7.50/2.33 % (17288)Memory used [KB]: 3709
% 7.50/2.33 % (17288)Time elapsed: 0.049 s
% 7.50/2.33 % (17288)Instructions burned: 183 (million)
% 7.50/2.33 % (17288)------------------------------
% 7.50/2.33 % (17288)------------------------------
% 7.50/2.34 % (17292)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_16880 for (2992ds/216Mi)
% 7.50/2.34 % (17291)Instruction limit reached!
% 7.50/2.34 % (17291)------------------------------
% 7.50/2.34 % (17291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.34 % (17291)Termination reason: Unknown
% 7.50/2.34 % (17291)Termination phase: Property scanning
% 7.50/2.34
% 7.50/2.34 % (17291)Memory used [KB]: 2942
% 7.50/2.34 % (17291)Time elapsed: 0.025 s
% 7.50/2.34 % (17291)Instructions burned: 79 (million)
% 7.50/2.34 % (17291)------------------------------
% 7.50/2.34 % (17291)------------------------------
% 7.50/2.34 % (17293)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_16880 for (2992ds/114Mi)
% 7.50/2.35 % (17289)Instruction limit reached!
% 7.50/2.35 % (17289)------------------------------
% 7.50/2.35 % (17289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.35 % (17289)Termination reason: Unknown
% 7.50/2.35 % (17289)Termination phase: Saturation
% 7.50/2.35
% 7.50/2.35 % (17289)Memory used [KB]: 7803
% 7.50/2.35 % (17289)Time elapsed: 0.054 s
% 7.50/2.35 % (17289)Instructions burned: 184 (million)
% 7.50/2.35 % (17289)------------------------------
% 7.50/2.35 % (17289)------------------------------
% 7.50/2.35 % (17294)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_16880 for (2992ds/922Mi)
% 7.50/2.36 % (17290)Instruction limit reached!
% 7.50/2.36 % (17290)------------------------------
% 7.50/2.36 % (17290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.36 % (17290)Termination reason: Unknown
% 7.50/2.36 % (17290)Termination phase: Function definition elimination
% 7.50/2.36
% 7.50/2.36 % (17290)Memory used [KB]: 3070
% 7.50/2.36 % (17290)Time elapsed: 0.042 s
% 7.50/2.36 % (17290)Instructions burned: 154 (million)
% 7.50/2.36 % (17290)------------------------------
% 7.50/2.36 % (17290)------------------------------
% 7.50/2.36 % (17295)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_16880 for (2992ds/182Mi)
% 7.50/2.37 % (17296)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_16880 for (2992ds/164Mi)
% 7.50/2.37 % (17294)Refutation not found, incomplete strategy
% 7.50/2.37 % (17294)------------------------------
% 7.50/2.37 % (17294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.37 % (17294)Termination reason: Refutation not found, incomplete strategy
% 7.50/2.37
% 7.50/2.37
% 7.50/2.37 % (17294)Memory used [KB]: 6652
% 7.50/2.37 % (17294)Time elapsed: 0.018 s
% 7.50/2.37 % (17294)Instructions burned: 58 (million)
% 7.50/2.37 % (17294)------------------------------
% 7.50/2.37 % (17294)------------------------------
% 7.50/2.38 % (17293)Instruction limit reached!
% 7.50/2.38 % (17293)------------------------------
% 7.50/2.38 % (17293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.38 % (17293)Termination reason: Unknown
% 7.50/2.38 % (17293)Termination phase: Function definition elimination
% 7.50/2.38
% 7.50/2.38 % (17293)Memory used [KB]: 2942
% 7.50/2.38 % (17293)Time elapsed: 0.033 s
% 7.50/2.38 % (17293)Instructions burned: 114 (million)
% 7.50/2.38 % (17293)------------------------------
% 7.50/2.38 % (17293)------------------------------
% 7.50/2.38 % (17297)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_16880 for (2992ds/50Mi)
% 7.50/2.39 % (17298)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_16880 for (2992ds/368Mi)
% 7.50/2.39 % (17297)Instruction limit reached!
% 7.50/2.39 % (17297)------------------------------
% 7.50/2.39 % (17297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.39 % (17297)Termination reason: Unknown
% 7.50/2.39 % (17297)Termination phase: shuffling
% 7.50/2.39
% 7.50/2.39 % (17297)Memory used [KB]: 2558
% 7.50/2.39 % (17297)Time elapsed: 0.015 s
% 7.50/2.40 % (17297)Instructions burned: 52 (million)
% 7.50/2.40 % (17297)------------------------------
% 7.50/2.40 % (17297)------------------------------
% 7.50/2.40 % (17292)Instruction limit reached!
% 7.50/2.40 % (17292)------------------------------
% 7.50/2.40 % (17292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.40 % (17292)Termination reason: Unknown
% 7.50/2.40 % (17292)Termination phase: Saturation
% 7.50/2.40
% 7.50/2.40 % (17292)Memory used [KB]: 7547
% 7.50/2.40 % (17292)Time elapsed: 0.058 s
% 7.50/2.40 % (17292)Instructions burned: 218 (million)
% 7.50/2.40 % (17292)------------------------------
% 7.50/2.40 % (17292)------------------------------
% 8.04/2.40 % (17296)Refutation not found, incomplete strategy
% 8.04/2.40 % (17296)------------------------------
% 8.04/2.40 % (17296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.40 % (17296)Termination reason: Refutation not found, incomplete strategy
% 8.04/2.40
% 8.04/2.40
% 8.04/2.40 % (17296)Memory used [KB]: 2942
% 8.04/2.40 % (17296)Time elapsed: 0.036 s
% 8.04/2.40 % (17296)Instructions burned: 133 (million)
% 8.04/2.40 % (17296)------------------------------
% 8.04/2.40 % (17296)------------------------------
% 8.04/2.40 % (17299)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_16880 for (2992ds/1021Mi)
% 8.04/2.40 % (17284)Instruction limit reached!
% 8.04/2.40 % (17284)------------------------------
% 8.04/2.40 % (17284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.40 % (17284)Termination reason: Unknown
% 8.04/2.40 % (17284)Termination phase: Saturation
% 8.04/2.40
% 8.04/2.40 % (17284)Memory used [KB]: 9083
% 8.04/2.40 % (17284)Time elapsed: 0.146 s
% 8.04/2.40 % (17284)Instructions burned: 459 (million)
% 8.04/2.40 % (17284)------------------------------
% 8.04/2.40 % (17284)------------------------------
% 8.04/2.41 % (17300)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_16880 for (2992ds/267Mi)
% 8.04/2.41 % (17295)Instruction limit reached!
% 8.04/2.41 % (17295)------------------------------
% 8.04/2.41 % (17295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.41 % (17295)Termination reason: Unknown
% 8.04/2.41 % (17295)Termination phase: Property scanning
% 8.04/2.41
% 8.04/2.41 % (17295)Memory used [KB]: 3198
% 8.04/2.41 % (17295)Time elapsed: 0.048 s
% 8.04/2.41 % (17295)Instructions burned: 183 (million)
% 8.04/2.41 % (17295)------------------------------
% 8.04/2.41 % (17295)------------------------------
% 8.04/2.41 % (17301)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_16880 for (2992ds/204Mi)
% 8.04/2.42 % (17302)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_16880 for (2992ds/26Mi)
% 8.04/2.42 % (17303)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_16880 for (2992ds/53Mi)
% 8.04/2.42 % (17302)Instruction limit reached!
% 8.04/2.42 % (17302)------------------------------
% 8.04/2.42 % (17302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.42 % (17302)Termination reason: Unknown
% 8.04/2.42 % (17302)Termination phase: shuffling
% 8.04/2.42
% 8.04/2.42 % (17302)Memory used [KB]: 2174
% 8.04/2.42 % (17302)Time elapsed: 0.010 s
% 8.04/2.42 % (17302)Instructions burned: 27 (million)
% 8.04/2.42 % (17302)------------------------------
% 8.04/2.42 % (17302)------------------------------
% 8.04/2.43 % (17304)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_16880 for (2991ds/4436Mi)
% 8.04/2.43 % (17303)Instruction limit reached!
% 8.04/2.43 % (17303)------------------------------
% 8.04/2.43 % (17303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.43 % (17303)Termination reason: Unknown
% 8.04/2.43 % (17303)Termination phase: shuffling
% 8.04/2.43
% 8.04/2.43 % (17303)Memory used [KB]: 2814
% 8.04/2.43 % (17303)Time elapsed: 0.016 s
% 8.04/2.43 % (17303)Instructions burned: 55 (million)
% 8.04/2.43 % (17303)------------------------------
% 8.04/2.43 % (17303)------------------------------
% 8.04/2.44 % (17305)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_16880 for (2991ds/1539Mi)
% 8.04/2.47 % (17301)Instruction limit reached!
% 8.04/2.47 % (17301)------------------------------
% 8.04/2.47 % (17301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.47 % (17301)Termination reason: Unknown
% 8.04/2.47 % (17301)Termination phase: Saturation
% 8.04/2.47
% 8.04/2.47 % (17301)Memory used [KB]: 7547
% 8.04/2.47 % (17301)Time elapsed: 0.057 s
% 8.04/2.47 % (17301)Instructions burned: 204 (million)
% 8.04/2.47 % (17301)------------------------------
% 8.04/2.47 % (17301)------------------------------
% 8.04/2.48 % (17300)Instruction limit reached!
% 8.04/2.48 % (17300)------------------------------
% 8.04/2.48 % (17300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.48 % (17300)Termination reason: Unknown
% 8.04/2.48 % (17300)Termination phase: Saturation
% 8.04/2.48
% 8.04/2.48 % (17300)Memory used [KB]: 7931
% 8.04/2.48 % (17300)Time elapsed: 0.071 s
% 8.04/2.48 % (17300)Instructions burned: 269 (million)
% 8.04/2.48 % (17300)------------------------------
% 8.04/2.48 % (17300)------------------------------
% 8.04/2.48 % (17306)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_16880 for (2991ds/408Mi)
% 8.04/2.48 % (17307)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_16880 for (2991ds/5205Mi)
% 8.04/2.50 % (17298)Instruction limit reached!
% 8.04/2.50 % (17298)------------------------------
% 8.04/2.50 % (17298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.50 % (17298)Termination reason: Unknown
% 8.04/2.50 % (17298)Termination phase: Saturation
% 8.04/2.50
% 8.04/2.50 % (17298)Memory used [KB]: 9338
% 8.04/2.50 % (17298)Time elapsed: 0.110 s
% 8.04/2.50 % (17298)Instructions burned: 369 (million)
% 8.04/2.50 % (17298)------------------------------
% 8.04/2.50 % (17298)------------------------------
% 8.60/2.50 % (17308)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_16880 for (2991ds/1913Mi)
% 8.60/2.57 % (17287)Instruction limit reached!
% 8.60/2.57 % (17287)------------------------------
% 8.60/2.57 % (17287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.57 % (17287)Termination reason: Unknown
% 8.60/2.57 % (17287)Termination phase: Saturation
% 8.60/2.57
% 8.60/2.57 % (17287)Memory used [KB]: 9850
% 8.60/2.57 % (17287)Time elapsed: 0.289 s
% 8.60/2.57 % (17287)Instructions burned: 990 (million)
% 8.60/2.57 % (17287)------------------------------
% 8.60/2.57 % (17287)------------------------------
% 8.60/2.58 % (17309)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_16880 for (2990ds/4350Mi)
% 8.60/2.59 % (17306)Instruction limit reached!
% 8.60/2.59 % (17306)------------------------------
% 8.60/2.59 % (17306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.59 % (17306)Termination reason: Unknown
% 8.60/2.59 % (17306)Termination phase: Saturation
% 8.60/2.59
% 8.60/2.59 % (17306)Memory used [KB]: 9083
% 8.60/2.59 % (17306)Time elapsed: 0.141 s
% 8.60/2.59 % (17306)Instructions burned: 409 (million)
% 8.60/2.59 % (17306)------------------------------
% 8.60/2.59 % (17306)------------------------------
% 9.02/2.60 % (17309)Refutation not found, incomplete strategy
% 9.02/2.60 % (17309)------------------------------
% 9.02/2.60 % (17309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.60 % (17309)Termination reason: Refutation not found, incomplete strategy
% 9.02/2.60
% 9.02/2.60
% 9.02/2.60 % (17309)Memory used [KB]: 6780
% 9.02/2.60 % (17309)Time elapsed: 0.023 s
% 9.02/2.60 % (17309)Instructions burned: 72 (million)
% 9.02/2.60 % (17309)------------------------------
% 9.02/2.60 % (17309)------------------------------
% 9.02/2.60 % (17310)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_16880 for (2990ds/68Mi)
% 9.02/2.61 % (17311)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_16880 for (2989ds/358Mi)
% 9.02/2.62 % (17310)Instruction limit reached!
% 9.02/2.62 % (17310)------------------------------
% 9.02/2.62 % (17310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.62 % (17310)Termination reason: Unknown
% 9.02/2.62 % (17310)Termination phase: Preprocessing 1
% 9.02/2.62
% 9.02/2.62 % (17310)Memory used [KB]: 2174
% 9.02/2.62 % (17310)Time elapsed: 0.021 s
% 9.02/2.62 % (17310)Instructions burned: 70 (million)
% 9.02/2.62 % (17310)------------------------------
% 9.02/2.62 % (17310)------------------------------
% 9.02/2.63 % (17312)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_16880 for (2989ds/31Mi)
% 9.02/2.64 % (17312)Instruction limit reached!
% 9.02/2.64 % (17312)------------------------------
% 9.02/2.64 % (17312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.64 % (17312)Termination reason: Unknown
% 9.02/2.64 % (17312)Termination phase: shuffling
% 9.02/2.64
% 9.02/2.64 % (17312)Memory used [KB]: 2174
% 9.02/2.64 % (17312)Time elapsed: 0.011 s
% 9.02/2.64 % (17312)Instructions burned: 33 (million)
% 9.02/2.64 % (17312)------------------------------
% 9.02/2.64 % (17312)------------------------------
% 9.02/2.65 % (17313)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_16880 for (2989ds/279Mi)
% 9.02/2.69 % (17313)Refutation not found, incomplete strategy
% 9.02/2.69 % (17313)------------------------------
% 9.02/2.69 % (17313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.69 % (17313)Termination reason: Refutation not found, incomplete strategy
% 9.02/2.69
% 9.02/2.69
% 9.02/2.69 % (17313)Memory used [KB]: 7419
% 9.02/2.69 % (17313)Time elapsed: 0.034 s
% 9.02/2.69 % (17313)Instructions burned: 120 (million)
% 9.02/2.69 % (17313)------------------------------
% 9.02/2.69 % (17313)------------------------------
% 9.16/2.70 % (17314)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_16880 for (2989ds/258Mi)
% 9.16/2.72 % (17311)Instruction limit reached!
% 9.16/2.72 % (17311)------------------------------
% 9.16/2.72 % (17311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.72 % (17311)Termination reason: Unknown
% 9.16/2.72 % (17311)Termination phase: Saturation
% 9.16/2.72
% 9.16/2.72 % (17311)Memory used [KB]: 8187
% 9.16/2.72 % (17311)Time elapsed: 0.107 s
% 9.16/2.72 % (17311)Instructions burned: 360 (million)
% 9.16/2.72 % (17311)------------------------------
% 9.16/2.72 % (17311)------------------------------
% 9.16/2.72 % (17299)Instruction limit reached!
% 9.16/2.72 % (17299)------------------------------
% 9.16/2.72 % (17299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.72 % (17299)Termination reason: Unknown
% 9.16/2.72 % (17299)Termination phase: Saturation
% 9.16/2.72
% 9.16/2.72 % (17299)Memory used [KB]: 10234
% 9.16/2.72 % (17299)Time elapsed: 0.316 s
% 9.16/2.72 % (17299)Instructions burned: 1021 (million)
% 9.16/2.72 % (17299)------------------------------
% 9.16/2.72 % (17299)------------------------------
% 9.16/2.73 % (17315)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_16880 for (2988ds/26Mi)
% 9.16/2.73 % (17316)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_16880 for (2988ds/995Mi)
% 9.16/2.74 % (17315)Instruction limit reached!
% 9.16/2.74 % (17315)------------------------------
% 9.16/2.74 % (17315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.74 % (17315)Termination reason: Unknown
% 9.16/2.74 % (17315)Termination phase: shuffling
% 9.16/2.74
% 9.16/2.74 % (17315)Memory used [KB]: 2174
% 9.16/2.74 % (17315)Time elapsed: 0.009 s
% 9.16/2.74 % (17315)Instructions burned: 28 (million)
% 9.16/2.74 % (17315)------------------------------
% 9.16/2.74 % (17315)------------------------------
% 9.16/2.75 % (17317)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_16880 for (2988ds/373Mi)
% 9.16/2.77 % (17314)Instruction limit reached!
% 9.16/2.77 % (17314)------------------------------
% 9.16/2.77 % (17314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.77 % (17314)Termination reason: Unknown
% 9.16/2.77 % (17314)Termination phase: Saturation
% 9.16/2.77
% 9.16/2.77 % (17314)Memory used [KB]: 8443
% 9.16/2.77 % (17314)Time elapsed: 0.077 s
% 9.16/2.77 % (17314)Instructions burned: 260 (million)
% 9.16/2.77 % (17314)------------------------------
% 9.16/2.77 % (17314)------------------------------
% 9.16/2.78 % (17318)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_16880 for (2988ds/253Mi)
% 9.70/2.85 % (17318)Instruction limit reached!
% 9.70/2.85 % (17318)------------------------------
% 9.70/2.85 % (17318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.85 % (17318)Termination reason: Unknown
% 9.70/2.85 % (17318)Termination phase: Saturation
% 9.70/2.85
% 9.70/2.85 % (17318)Memory used [KB]: 7803
% 9.70/2.85 % (17318)Time elapsed: 0.066 s
% 9.70/2.85 % (17318)Instructions burned: 255 (million)
% 9.70/2.85 % (17318)------------------------------
% 9.70/2.85 % (17318)------------------------------
% 9.70/2.85 % (17317)Instruction limit reached!
% 9.70/2.85 % (17317)------------------------------
% 9.70/2.85 % (17317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.85 % (17317)Termination reason: Unknown
% 9.70/2.85 % (17317)Termination phase: Saturation
% 9.70/2.85
% 9.70/2.85 % (17317)Memory used [KB]: 8699
% 9.70/2.85 % (17317)Time elapsed: 0.109 s
% 9.70/2.85 % (17317)Instructions burned: 373 (million)
% 9.70/2.85 % (17317)------------------------------
% 9.70/2.85 % (17317)------------------------------
% 9.70/2.86 % (17319)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_16880 for (2987ds/832Mi)
% 9.70/2.86 % (17305)Instruction limit reached!
% 9.70/2.86 % (17305)------------------------------
% 9.70/2.86 % (17305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.86 % (17305)Termination reason: Unknown
% 9.70/2.86 % (17305)Termination phase: Saturation
% 9.70/2.86
% 9.70/2.86 % (17305)Memory used [KB]: 10106
% 9.70/2.86 % (17305)Time elapsed: 0.442 s
% 9.70/2.86 % (17305)Instructions burned: 1539 (million)
% 9.70/2.86 % (17305)------------------------------
% 9.70/2.86 % (17305)------------------------------
% 9.70/2.86 % (17320)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_16880 for (2987ds/668Mi)
% 9.70/2.87 % (17321)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=40:si=on:rtra=on_0 on DTF2THF_16880 for (2987ds/40Mi)
% 9.70/2.89 % (17321)Instruction limit reached!
% 9.70/2.89 % (17321)------------------------------
% 9.70/2.89 % (17321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.89 % (17321)Termination reason: Unknown
% 9.70/2.89 % (17321)Termination phase: shuffling
% 9.70/2.89
% 9.70/2.89 % (17321)Memory used [KB]: 2430
% 9.70/2.89 % (17321)Time elapsed: 0.013 s
% 9.70/2.89 % (17321)Instructions burned: 43 (million)
% 9.70/2.89 % (17321)------------------------------
% 9.70/2.89 % (17321)------------------------------
% 9.70/2.89 % (17322)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_16880 for (2987ds/294Mi)
% 10.35/2.94 % (17322)Refutation not found, incomplete strategy
% 10.35/2.94 % (17322)------------------------------
% 10.35/2.94 % (17322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.94 % (17322)Termination reason: Refutation not found, incomplete strategy
% 10.35/2.94
% 10.35/2.94
% 10.35/2.94 % (17322)Memory used [KB]: 7803
% 10.35/2.94 % (17322)Time elapsed: 0.044 s
% 10.35/2.94 % (17322)Instructions burned: 157 (million)
% 10.35/2.94 % (17322)------------------------------
% 10.35/2.94 % (17322)------------------------------
% 10.35/2.95 % (17323)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_16880 for (2986ds/187Mi)
% 10.35/3.00 % (17323)Instruction limit reached!
% 10.35/3.00 % (17323)------------------------------
% 10.35/3.00 % (17323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/3.00 % (17323)Termination reason: Unknown
% 10.35/3.00 % (17323)Termination phase: Saturation
% 10.35/3.00
% 10.35/3.00 % (17323)Memory used [KB]: 7675
% 10.35/3.00 % (17323)Time elapsed: 0.052 s
% 10.35/3.00 % (17323)Instructions burned: 189 (million)
% 10.35/3.00 % (17323)------------------------------
% 10.35/3.00 % (17323)------------------------------
% 10.35/3.01 % (17324)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_16880 for (2986ds/371Mi)
% 10.35/3.02 % (17316)Instruction limit reached!
% 10.35/3.02 % (17316)------------------------------
% 10.35/3.02 % (17316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/3.02 % (17316)Termination reason: Unknown
% 10.35/3.02 % (17316)Termination phase: Saturation
% 10.35/3.02
% 10.35/3.02 % (17316)Memory used [KB]: 10234
% 10.35/3.02 % (17316)Time elapsed: 0.288 s
% 10.35/3.02 % (17316)Instructions burned: 995 (million)
% 10.35/3.02 % (17316)------------------------------
% 10.35/3.02 % (17316)------------------------------
% 12.71/3.03 % (17325)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_16880 for (2985ds/1827Mi)
% 12.71/3.05 % (17320)Instruction limit reached!
% 12.71/3.05 % (17320)------------------------------
% 12.71/3.05 % (17320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.05 % (17320)Termination reason: Unknown
% 12.71/3.05 % (17320)Termination phase: Saturation
% 12.71/3.05
% 12.71/3.05 % (17320)Memory used [KB]: 13432
% 12.71/3.05 % (17320)Time elapsed: 0.189 s
% 12.71/3.05 % (17320)Instructions burned: 668 (million)
% 12.71/3.05 % (17320)------------------------------
% 12.71/3.05 % (17320)------------------------------
% 12.71/3.06 % (17326)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_16880 for (2985ds/70Mi)
% 12.71/3.08 % (17326)Instruction limit reached!
% 12.71/3.08 % (17326)------------------------------
% 12.71/3.08 % (17326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.08 % (17326)Termination reason: Unknown
% 12.71/3.08 % (17326)Termination phase: Property scanning
% 12.71/3.08
% 12.71/3.08 % (17326)Memory used [KB]: 2942
% 12.71/3.08 % (17326)Time elapsed: 0.021 s
% 12.71/3.08 % (17326)Instructions burned: 73 (million)
% 12.71/3.08 % (17326)------------------------------
% 12.71/3.08 % (17326)------------------------------
% 12.71/3.09 % (17308)Instruction limit reached!
% 12.71/3.09 % (17308)------------------------------
% 12.71/3.09 % (17308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.09 % (17308)Termination reason: Unknown
% 12.71/3.09 % (17308)Termination phase: Saturation
% 12.71/3.09
% 12.71/3.09 % (17308)Memory used [KB]: 4989
% 12.71/3.09 % (17308)Time elapsed: 0.608 s
% 12.71/3.09 % (17308)Instructions burned: 1915 (million)
% 12.71/3.09 % (17308)------------------------------
% 12.71/3.09 % (17308)------------------------------
% 12.71/3.09 % (17327)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_16880 for (2985ds/316Mi)
% 12.71/3.10 % (17328)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_16880 for (2985ds/932Mi)
% 12.71/3.10 % (17319)Instruction limit reached!
% 12.71/3.10 % (17319)------------------------------
% 12.71/3.10 % (17319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.10 % (17319)Termination reason: Unknown
% 12.71/3.10 % (17319)Termination phase: Saturation
% 12.71/3.10
% 12.71/3.10 % (17319)Memory used [KB]: 8955
% 12.71/3.10 % (17319)Time elapsed: 0.245 s
% 12.71/3.10 % (17319)Instructions burned: 834 (million)
% 12.71/3.10 % (17319)------------------------------
% 12.71/3.10 % (17319)------------------------------
% 12.71/3.11 % (17329)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_16880 for (2985ds/4714Mi)
% 12.71/3.12 % (17324)Instruction limit reached!
% 12.71/3.12 % (17324)------------------------------
% 12.71/3.12 % (17324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.71/3.12 % (17324)Termination reason: Unknown
% 12.71/3.12 % (17324)Termination phase: Saturation
% 12.71/3.12
% 12.71/3.12 % (17324)Memory used [KB]: 8571
% 12.71/3.12 % (17324)Time elapsed: 0.114 s
% 12.71/3.12 % (17324)Instructions burned: 373 (million)
% 12.71/3.12 % (17324)------------------------------
% 12.71/3.12 % (17324)------------------------------
% 13.28/3.13 % (17330)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_16880 for (2984ds/8250Mi)
% 13.28/3.17 % (17327)Instruction limit reached!
% 13.28/3.17 % (17327)------------------------------
% 13.28/3.17 % (17327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.28/3.17 % (17327)Termination reason: Unknown
% 13.28/3.17 % (17327)Termination phase: Saturation
% 13.28/3.17
% 13.28/3.17 % (17327)Memory used [KB]: 4349
% 13.28/3.17 % (17327)Time elapsed: 0.085 s
% 13.28/3.17 % (17327)Instructions burned: 317 (million)
% 13.28/3.17 % (17327)------------------------------
% 13.28/3.17 % (17327)------------------------------
% 13.28/3.18 % (17331)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_16880 for (2984ds/770Mi)
% 13.52/3.20 % (17329)Refutation not found, incomplete strategy
% 13.52/3.20 % (17329)------------------------------
% 13.52/3.20 % (17329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.20 % (17329)Termination reason: Refutation not found, incomplete strategy
% 13.52/3.20
% 13.52/3.20
% 13.52/3.20 % (17329)Memory used [KB]: 9083
% 13.52/3.20 % (17329)Time elapsed: 0.091 s
% 13.52/3.20 % (17329)Instructions burned: 336 (million)
% 13.52/3.20 % (17329)------------------------------
% 13.52/3.20 % (17329)------------------------------
% 13.52/3.21 % (17331)Refutation not found, incomplete strategy
% 13.52/3.21 % (17331)------------------------------
% 13.52/3.21 % (17331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.21 % (17331)Termination reason: Refutation not found, incomplete strategy
% 13.52/3.21
% 13.52/3.21
% 13.52/3.21 % (17331)Memory used [KB]: 6908
% 13.52/3.21 % (17331)Time elapsed: 0.022 s
% 13.52/3.21 % (17331)Instructions burned: 68 (million)
% 13.52/3.21 % (17331)------------------------------
% 13.52/3.21 % (17331)------------------------------
% 13.52/3.21 % (17332)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_16880 for (2984ds/794Mi)
% 13.52/3.22 % (17333)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_16880 for (2984ds/464Mi)
% 13.86/3.35 % (17333)Instruction limit reached!
% 13.86/3.35 % (17333)------------------------------
% 13.86/3.35 % (17333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.35 % (17333)Termination reason: Unknown
% 13.86/3.35 % (17333)Termination phase: Saturation
% 13.86/3.35
% 13.86/3.35 % (17333)Memory used [KB]: 8443
% 13.86/3.35 % (17333)Time elapsed: 0.131 s
% 13.86/3.35 % (17333)Instructions burned: 465 (million)
% 13.86/3.35 % (17333)------------------------------
% 13.86/3.35 % (17333)------------------------------
% 13.86/3.36 % (17334)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_16880 for (2982ds/1376Mi)
% 13.86/3.36 % (17328)Instruction limit reached!
% 13.86/3.36 % (17328)------------------------------
% 13.86/3.36 % (17328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.36 % (17328)Termination reason: Unknown
% 13.86/3.36 % (17328)Termination phase: Saturation
% 13.86/3.36
% 13.86/3.36 % (17328)Memory used [KB]: 10746
% 13.86/3.36 % (17328)Time elapsed: 0.261 s
% 13.86/3.36 % (17328)Instructions burned: 934 (million)
% 13.86/3.36 % (17328)------------------------------
% 13.86/3.36 % (17328)------------------------------
% 13.86/3.37 % (17335)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_16880 for (2982ds/906Mi)
% 14.46/3.45 % (17332)Instruction limit reached!
% 14.46/3.45 % (17332)------------------------------
% 14.46/3.45 % (17332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.45 % (17332)Termination reason: Unknown
% 14.46/3.45 % (17332)Termination phase: Saturation
% 14.46/3.45
% 14.46/3.45 % (17332)Memory used [KB]: 7036
% 14.46/3.45 % (17332)Time elapsed: 0.244 s
% 14.46/3.45 % (17332)Instructions burned: 796 (million)
% 14.46/3.45 % (17332)------------------------------
% 14.46/3.45 % (17332)------------------------------
% 14.46/3.47 % (17336)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_16880 for (2981ds/434Mi)
% 14.46/3.48 % (17336)Refutation not found, incomplete strategy
% 14.46/3.48 % (17336)------------------------------
% 14.46/3.48 % (17336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.48 % (17336)Termination reason: Refutation not found, incomplete strategy
% 14.46/3.48
% 14.46/3.48
% 14.46/3.48 % (17336)Memory used [KB]: 6652
% 14.46/3.48 % (17336)Time elapsed: 0.019 s
% 14.46/3.48 % (17336)Instructions burned: 57 (million)
% 14.46/3.48 % (17336)------------------------------
% 14.46/3.48 % (17336)------------------------------
% 14.46/3.49 % (17337)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_16880 for (2981ds/865Mi)
% 14.96/3.52 % (17337)Refutation not found, incomplete strategy
% 14.96/3.52 % (17337)------------------------------
% 14.96/3.52 % (17337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.96/3.52 % (17337)Termination reason: Refutation not found, incomplete strategy
% 14.96/3.52
% 14.96/3.52
% 14.96/3.52 % (17337)Memory used [KB]: 7419
% 14.96/3.52 % (17337)Time elapsed: 0.032 s
% 14.96/3.52 % (17337)Instructions burned: 118 (million)
% 14.96/3.52 % (17337)------------------------------
% 14.96/3.52 % (17337)------------------------------
% 14.96/3.53 % (17338)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_16880 for (2980ds/593Mi)
% 15.19/3.60 % (17325)Instruction limit reached!
% 15.19/3.60 % (17325)------------------------------
% 15.19/3.60 % (17325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.60 % (17325)Termination reason: Unknown
% 15.19/3.60 % (17325)Termination phase: Saturation
% 15.19/3.60
% 15.19/3.60 % (17325)Memory used [KB]: 10234
% 15.19/3.60 % (17325)Time elapsed: 0.576 s
% 15.19/3.60 % (17325)Instructions burned: 1827 (million)
% 15.19/3.60 % (17325)------------------------------
% 15.19/3.60 % (17325)------------------------------
% 15.19/3.61 % (17339)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_16880 for (2980ds/443Mi)
% 15.19/3.69 % (17335)Instruction limit reached!
% 15.19/3.69 % (17335)------------------------------
% 15.19/3.69 % (17335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.69 % (17335)Termination reason: Unknown
% 15.19/3.69 % (17335)Termination phase: Saturation
% 15.19/3.69
% 15.19/3.69 % (17335)Memory used [KB]: 14200
% 15.19/3.69 % (17335)Time elapsed: 0.321 s
% 15.19/3.69 % (17335)Instructions burned: 908 (million)
% 15.19/3.69 % (17335)------------------------------
% 15.19/3.69 % (17335)------------------------------
% 15.19/3.69 % (17338)Instruction limit reached!
% 15.19/3.69 % (17338)------------------------------
% 15.19/3.69 % (17338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.69 % (17338)Termination reason: Unknown
% 15.19/3.69 % (17338)Termination phase: Saturation
% 15.19/3.69
% 15.19/3.69 % (17338)Memory used [KB]: 9338
% 15.19/3.69 % (17338)Time elapsed: 0.161 s
% 15.19/3.69 % (17338)Instructions burned: 596 (million)
% 15.19/3.69 % (17338)------------------------------
% 15.19/3.69 % (17338)------------------------------
% 16.48/3.70 % (17340)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_16880 for (2979ds/594Mi)
% 16.48/3.70 % (17341)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_16880 for (2979ds/327Mi)
% 16.48/3.74 % (17339)Instruction limit reached!
% 16.48/3.74 % (17339)------------------------------
% 16.48/3.74 % (17339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.48/3.74 % (17339)Termination reason: Unknown
% 16.48/3.74 % (17339)Termination phase: Saturation
% 16.48/3.74
% 16.48/3.74 % (17339)Memory used [KB]: 8443
% 16.48/3.74 % (17339)Time elapsed: 0.133 s
% 16.48/3.74 % (17339)Instructions burned: 443 (million)
% 16.48/3.74 % (17339)------------------------------
% 16.48/3.74 % (17339)------------------------------
% 16.48/3.75 % (17342)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_16880 for (2978ds/5411Mi)
% 16.48/3.76 % (17334)Instruction limit reached!
% 16.48/3.76 % (17334)------------------------------
% 16.48/3.76 % (17334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.48/3.76 % (17334)Termination reason: Unknown
% 16.48/3.76 % (17334)Termination phase: Saturation
% 16.48/3.76
% 16.48/3.76 % (17334)Memory used [KB]: 13944
% 16.48/3.76 % (17334)Time elapsed: 0.404 s
% 16.48/3.76 % (17334)Instructions burned: 1377 (million)
% 16.48/3.76 % (17334)------------------------------
% 16.48/3.76 % (17334)------------------------------
% 16.48/3.77 % (17343)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_16880 for (2978ds/1762Mi)
% 16.48/3.77 % (17342)Refutation not found, incomplete strategy
% 16.48/3.77 % (17342)------------------------------
% 16.48/3.77 % (17342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.48/3.77 % (17342)Termination reason: Refutation not found, incomplete strategy
% 16.48/3.77
% 16.48/3.77
% 16.48/3.77 % (17342)Memory used [KB]: 6652
% 16.48/3.77 % (17342)Time elapsed: 0.018 s
% 16.48/3.77 % (17342)Instructions burned: 56 (million)
% 16.48/3.77 % (17342)------------------------------
% 16.48/3.77 % (17342)------------------------------
% 16.48/3.78 % (17344)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_16880 for (2978ds/96Mi)
% 17.25/3.80 % (17341)Instruction limit reached!
% 17.25/3.80 % (17341)------------------------------
% 17.25/3.80 % (17341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.80 % (17341)Termination reason: Unknown
% 17.25/3.80 % (17341)Termination phase: Saturation
% 17.25/3.80
% 17.25/3.80 % (17341)Memory used [KB]: 8699
% 17.25/3.80 % (17341)Time elapsed: 0.099 s
% 17.25/3.80 % (17341)Instructions burned: 330 (million)
% 17.25/3.80 % (17341)------------------------------
% 17.25/3.80 % (17341)------------------------------
% 17.25/3.80 % (17304)Instruction limit reached!
% 17.25/3.80 % (17304)------------------------------
% 17.25/3.80 % (17304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.80 % (17304)Termination reason: Unknown
% 17.25/3.80 % (17304)Termination phase: Saturation
% 17.25/3.80
% 17.25/3.80 % (17304)Memory used [KB]: 10618
% 17.25/3.80 % (17304)Time elapsed: 1.392 s
% 17.25/3.80 % (17304)Instructions burned: 4439 (million)
% 17.25/3.80 % (17304)------------------------------
% 17.25/3.80 % (17304)------------------------------
% 17.25/3.81 % (17344)Instruction limit reached!
% 17.25/3.81 % (17344)------------------------------
% 17.25/3.81 % (17344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.81 % (17344)Termination reason: Unknown
% 17.25/3.81 % (17344)Termination phase: Property scanning
% 17.25/3.81
% 17.25/3.81 % (17344)Memory used [KB]: 2942
% 17.25/3.81 % (17344)Time elapsed: 0.027 s
% 17.25/3.81 % (17344)Instructions burned: 99 (million)
% 17.25/3.81 % (17344)------------------------------
% 17.25/3.81 % (17344)------------------------------
% 17.25/3.81 % (17345)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_16880 for (2978ds/503Mi)
% 17.25/3.81 % (17346)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_16880 for (2978ds/90Mi)
% 17.25/3.82 % (17347)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_16880 for (2978ds/593Mi)
% 17.25/3.83 % (17345)Refutation not found, incomplete strategy
% 17.25/3.83 % (17345)------------------------------
% 17.25/3.83 % (17345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.83 % (17345)Termination reason: Refutation not found, incomplete strategy
% 17.25/3.83
% 17.25/3.83
% 17.25/3.83 % (17345)Memory used [KB]: 6652
% 17.25/3.83 % (17345)Time elapsed: 0.041 s
% 17.25/3.83 % (17345)Instructions burned: 60 (million)
% 17.25/3.83 % (17345)------------------------------
% 17.25/3.83 % (17345)------------------------------
% 17.25/3.84 % (17346)Instruction limit reached!
% 17.25/3.84 % (17346)------------------------------
% 17.25/3.84 % (17346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.84 % (17346)Termination reason: Unknown
% 17.25/3.84 % (17346)Termination phase: Property scanning
% 17.25/3.84
% 17.25/3.84 % (17346)Memory used [KB]: 2942
% 17.25/3.84 % (17346)Time elapsed: 0.028 s
% 17.25/3.84 % (17346)Instructions burned: 93 (million)
% 17.25/3.84 % (17346)------------------------------
% 17.25/3.84 % (17346)------------------------------
% 17.25/3.84 % (17348)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_16880 for (2977ds/1512Mi)
% 17.25/3.85 % (17349)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_16880 for (2977ds/569Mi)
% 17.25/3.88 % (17340)Instruction limit reached!
% 17.25/3.88 % (17340)------------------------------
% 17.25/3.88 % (17340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.25/3.88 % (17340)Termination reason: Unknown
% 17.25/3.88 % (17340)Termination phase: Saturation
% 17.25/3.88
% 17.25/3.88 % (17340)Memory used [KB]: 8571
% 17.25/3.88 % (17340)Time elapsed: 0.183 s
% 17.25/3.88 % (17340)Instructions burned: 595 (million)
% 17.25/3.88 % (17340)------------------------------
% 17.25/3.88 % (17340)------------------------------
% 17.25/3.89 % (17350)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_16880 for (2977ds/501Mi)
% 17.78/3.99 % (17347)Instruction limit reached!
% 17.78/3.99 % (17347)------------------------------
% 17.78/3.99 % (17347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.78/3.99 % (17347)Termination reason: Unknown
% 17.78/3.99 % (17347)Termination phase: Saturation
% 17.78/3.99
% 17.78/3.99 % (17347)Memory used [KB]: 9722
% 17.78/3.99 % (17347)Time elapsed: 0.201 s
% 17.78/3.99 % (17347)Instructions burned: 594 (million)
% 17.78/3.99 % (17347)------------------------------
% 17.78/3.99 % (17347)------------------------------
% 17.78/4.00 % (17351)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_16880 for (2976ds/562Mi)
% 17.78/4.01 % (17349)Instruction limit reached!
% 17.78/4.01 % (17349)------------------------------
% 17.78/4.01 % (17349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.78/4.01 % (17349)Termination reason: Unknown
% 17.78/4.01 % (17349)Termination phase: Saturation
% 17.78/4.01
% 17.78/4.01 % (17349)Memory used [KB]: 9466
% 17.78/4.01 % (17349)Time elapsed: 0.159 s
% 17.78/4.01 % (17349)Instructions burned: 571 (million)
% 17.78/4.01 % (17349)------------------------------
% 17.78/4.01 % (17349)------------------------------
% 17.78/4.02 % (17352)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_16880 for (2976ds/406Mi)
% 19.73/4.03 % (17350)Instruction limit reached!
% 19.73/4.03 % (17350)------------------------------
% 19.73/4.03 % (17350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.73/4.03 % (17350)Termination reason: Unknown
% 19.73/4.03 % (17350)Termination phase: Saturation
% 19.73/4.03
% 19.73/4.03 % (17350)Memory used [KB]: 9978
% 19.73/4.03 % (17350)Time elapsed: 0.144 s
% 19.73/4.03 % (17350)Instructions burned: 504 (million)
% 19.73/4.03 % (17350)------------------------------
% 19.73/4.03 % (17350)------------------------------
% 19.73/4.04 % (17351)Refutation not found, incomplete strategy
% 19.73/4.04 % (17351)------------------------------
% 19.73/4.04 % (17351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.73/4.04 % (17351)Termination reason: Refutation not found, incomplete strategy
% 19.73/4.04
% 19.73/4.04
% 19.73/4.04 % (17351)Memory used [KB]: 7419
% 19.73/4.04 % (17351)Time elapsed: 0.032 s
% 19.73/4.04 % (17351)Instructions burned: 117 (million)
% 19.73/4.04 % (17351)------------------------------
% 19.73/4.04 % (17351)------------------------------
% 19.73/4.04 % (17307)Instruction limit reached!
% 19.73/4.04 % (17307)------------------------------
% 19.73/4.04 % (17307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.73/4.04 % (17307)Termination reason: Unknown
% 19.73/4.04 % (17307)Termination phase: Saturation
% 19.73/4.04
% 19.73/4.04 % (17307)Memory used [KB]: 15479
% 19.73/4.04 % (17307)Time elapsed: 1.578 s
% 19.73/4.04 % (17307)Instructions burned: 5207 (million)
% 19.73/4.04 % (17307)------------------------------
% 19.73/4.04 % (17307)------------------------------
% 19.73/4.04 % (17353)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_16880 for (2975ds/582Mi)
% 19.73/4.05 % (17354)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_16880 for (2975ds/456Mi)
% 19.73/4.05 % (17355)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_16880 for (2975ds/393Mi)
% 20.11/4.14 % (17352)Instruction limit reached!
% 20.11/4.14 % (17352)------------------------------
% 20.11/4.14 % (17352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.14 % (17352)Termination reason: Unknown
% 20.11/4.14 % (17352)Termination phase: Saturation
% 20.11/4.14
% 20.11/4.14 % (17352)Memory used [KB]: 9210
% 20.11/4.14 % (17352)Time elapsed: 0.124 s
% 20.11/4.14 % (17352)Instructions burned: 406 (million)
% 20.11/4.14 % (17352)------------------------------
% 20.11/4.14 % (17352)------------------------------
% 20.11/4.15 % (17356)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_16880 for (2974ds/1335Mi)
% 20.11/4.16 % (17355)Instruction limit reached!
% 20.11/4.16 % (17355)------------------------------
% 20.11/4.16 % (17355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.16 % (17355)Termination reason: Unknown
% 20.11/4.16 % (17355)Termination phase: Saturation
% 20.11/4.16
% 20.11/4.16 % (17355)Memory used [KB]: 8827
% 20.11/4.16 % (17355)Time elapsed: 0.107 s
% 20.11/4.16 % (17355)Instructions burned: 393 (million)
% 20.11/4.16 % (17355)------------------------------
% 20.11/4.16 % (17355)------------------------------
% 20.11/4.17 % (17357)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_16880 for (2974ds/3373Mi)
% 20.11/4.18 % (17354)Instruction limit reached!
% 20.11/4.18 % (17354)------------------------------
% 20.11/4.18 % (17354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.18 % (17354)Termination reason: Unknown
% 20.11/4.18 % (17354)Termination phase: Saturation
% 20.11/4.18
% 20.11/4.18 % (17354)Memory used [KB]: 9210
% 20.11/4.18 % (17354)Time elapsed: 0.134 s
% 20.11/4.18 % (17354)Instructions burned: 458 (million)
% 20.11/4.18 % (17354)------------------------------
% 20.11/4.18 % (17354)------------------------------
% 20.11/4.19 % (17358)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_16880 for (2974ds/474Mi)
% 20.73/4.22 % (17353)Instruction limit reached!
% 20.73/4.22 % (17353)------------------------------
% 20.73/4.22 % (17353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.22 % (17353)Termination reason: Unknown
% 20.73/4.22 % (17353)Termination phase: Saturation
% 20.73/4.22
% 20.73/4.22 % (17353)Memory used [KB]: 8443
% 20.73/4.22 % (17353)Time elapsed: 0.175 s
% 20.73/4.22 % (17353)Instructions burned: 582 (million)
% 20.73/4.22 % (17353)------------------------------
% 20.73/4.22 % (17353)------------------------------
% 20.73/4.23 % (17359)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_16880 for (2974ds/157Mi)
% 20.73/4.27 % (17359)Instruction limit reached!
% 20.73/4.27 % (17359)------------------------------
% 20.73/4.27 % (17359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.27 % (17359)Termination reason: Unknown
% 20.73/4.27 % (17359)Termination phase: Property scanning
% 20.73/4.27
% 20.73/4.27 % (17359)Memory used [KB]: 3070
% 20.73/4.27 % (17359)Time elapsed: 0.044 s
% 20.73/4.27 % (17359)Instructions burned: 158 (million)
% 20.73/4.27 % (17359)------------------------------
% 20.73/4.27 % (17359)------------------------------
% 20.73/4.28 % (17343)Instruction limit reached!
% 20.73/4.28 % (17343)------------------------------
% 20.73/4.28 % (17343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.28 % (17343)Termination reason: Unknown
% 20.73/4.28 % (17343)Termination phase: Saturation
% 20.73/4.28
% 20.73/4.28 % (17343)Memory used [KB]: 10234
% 20.73/4.28 % (17343)Time elapsed: 0.512 s
% 20.73/4.28 % (17343)Instructions burned: 1762 (million)
% 20.73/4.28 % (17343)------------------------------
% 20.73/4.28 % (17343)------------------------------
% 20.73/4.28 % (17360)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_16880 for (2973ds/590Mi)
% 20.73/4.28 % (17348)Instruction limit reached!
% 20.73/4.28 % (17348)------------------------------
% 20.73/4.28 % (17348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.28 % (17348)Termination reason: Unknown
% 20.73/4.28 % (17348)Termination phase: Saturation
% 20.73/4.28
% 20.73/4.28 % (17348)Memory used [KB]: 9338
% 20.73/4.28 % (17348)Time elapsed: 0.441 s
% 20.73/4.28 % (17348)Instructions burned: 1512 (million)
% 20.73/4.28 % (17348)------------------------------
% 20.73/4.28 % (17348)------------------------------
% 20.73/4.29 % (17361)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_16880 for (2973ds/104Mi)
% 20.73/4.29 % (17362)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_16880 for (2973ds/414Mi)
% 21.27/4.32 % (17361)Instruction limit reached!
% 21.27/4.32 % (17361)------------------------------
% 21.27/4.32 % (17361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.27/4.32 % (17361)Termination reason: Unknown
% 21.27/4.32 % (17361)Termination phase: Property scanning
% 21.27/4.32
% 21.27/4.32 % (17361)Memory used [KB]: 2942
% 21.27/4.32 % (17361)Time elapsed: 0.032 s
% 21.27/4.32 % (17361)Instructions burned: 106 (million)
% 21.27/4.32 % (17361)------------------------------
% 21.27/4.32 % (17361)------------------------------
% 21.27/4.32 % (17358)Instruction limit reached!
% 21.27/4.32 % (17358)------------------------------
% 21.27/4.32 % (17358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.27/4.32 % (17358)Termination reason: Unknown
% 21.27/4.32 % (17358)Termination phase: Saturation
% 21.27/4.32
% 21.27/4.32 % (17358)Memory used [KB]: 9083
% 21.27/4.32 % (17358)Time elapsed: 0.138 s
% 21.27/4.32 % (17358)Instructions burned: 477 (million)
% 21.27/4.32 % (17358)------------------------------
% 21.27/4.32 % (17358)------------------------------
% 21.27/4.33 % (17363)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_16880 for (2972ds/715Mi)
% 21.27/4.33 % (17364)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_16880 for (2972ds/961Mi)
% 21.56/4.41 % (17362)Instruction limit reached!
% 21.56/4.41 % (17362)------------------------------
% 21.56/4.41 % (17362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.56/4.41 % (17362)Termination reason: Unknown
% 21.56/4.41 % (17362)Termination phase: Saturation
% 21.56/4.41
% 21.56/4.41 % (17362)Memory used [KB]: 8827
% 21.56/4.41 % (17362)Time elapsed: 0.140 s
% 21.56/4.41 % (17362)Instructions burned: 414 (million)
% 21.56/4.41 % (17362)------------------------------
% 21.56/4.41 % (17362)------------------------------
% 21.56/4.42 % (17365)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_16880 for (2971ds/1213Mi)
% 21.56/4.45 % (17360)Instruction limit reached!
% 21.56/4.45 % (17360)------------------------------
% 21.56/4.45 % (17360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.56/4.45 % (17360)Termination reason: Unknown
% 21.56/4.45 % (17360)Termination phase: Saturation
% 21.56/4.45
% 21.56/4.45 % (17360)Memory used [KB]: 8571
% 21.56/4.45 % (17360)Time elapsed: 0.167 s
% 21.56/4.45 % (17360)Instructions burned: 591 (million)
% 21.56/4.45 % (17360)------------------------------
% 21.56/4.45 % (17360)------------------------------
% 21.56/4.46 % (17366)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_16880 for (2971ds/1979Mi)
% 21.96/4.55 % (17363)Instruction limit reached!
% 21.96/4.55 % (17363)------------------------------
% 21.96/4.55 % (17363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.96/4.55 % (17363)Termination reason: Unknown
% 21.96/4.55 % (17363)Termination phase: Saturation
% 21.96/4.55
% 21.96/4.55 % (17363)Memory used [KB]: 4733
% 21.96/4.55 % (17363)Time elapsed: 0.221 s
% 21.96/4.55 % (17363)Instructions burned: 715 (million)
% 21.96/4.55 % (17363)------------------------------
% 21.96/4.55 % (17363)------------------------------
% 21.96/4.55 % (17356)Instruction limit reached!
% 21.96/4.55 % (17356)------------------------------
% 21.96/4.55 % (17356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.96/4.55 % (17356)Termination reason: Unknown
% 21.96/4.55 % (17356)Termination phase: Saturation
% 21.96/4.55
% 21.96/4.55 % (17356)Memory used [KB]: 10362
% 21.96/4.55 % (17356)Time elapsed: 0.402 s
% 21.96/4.55 % (17356)Instructions burned: 1337 (million)
% 21.96/4.55 % (17356)------------------------------
% 21.96/4.55 % (17356)------------------------------
% 21.96/4.56 % (17367)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_16880 for (2970ds/481Mi)
% 21.96/4.56 % (17368)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_16880 for (2970ds/783Mi)
% 21.96/4.58 % (17368)Refutation not found, incomplete strategy
% 21.96/4.58 % (17368)------------------------------
% 21.96/4.58 % (17368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.96/4.58 % (17368)Termination reason: Refutation not found, incomplete strategy
% 21.96/4.58
% 21.96/4.58
% 21.96/4.58 % (17368)Memory used [KB]: 6780
% 21.96/4.58 % (17368)Time elapsed: 0.021 s
% 21.96/4.58 % (17368)Instructions burned: 66 (million)
% 21.96/4.58 % (17368)------------------------------
% 21.96/4.58 % (17368)------------------------------
% 21.96/4.59 % (17369)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_16880 for (2970ds/432Mi)
% 22.73/4.61 % (17369)Refutation not found, incomplete strategy
% 22.73/4.61 % (17369)------------------------------
% 22.73/4.61 % (17369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.61 % (17369)Termination reason: Refutation not found, incomplete strategy
% 22.73/4.61
% 22.73/4.61
% 22.73/4.61 % (17369)Memory used [KB]: 6652
% 22.73/4.61 % (17369)Time elapsed: 0.020 s
% 22.73/4.61 % (17369)Instructions burned: 62 (million)
% 22.73/4.61 % (17369)------------------------------
% 22.73/4.61 % (17369)------------------------------
% 22.73/4.62 % (17370)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_16880 for (2969ds/1670Mi)
% 22.73/4.63 % (17364)Instruction limit reached!
% 22.73/4.63 % (17364)------------------------------
% 22.73/4.63 % (17364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.63 % (17364)Termination reason: Unknown
% 22.73/4.63 % (17364)Termination phase: Saturation
% 22.73/4.63
% 22.73/4.63 % (17364)Memory used [KB]: 8699
% 22.73/4.63 % (17364)Time elapsed: 0.300 s
% 22.73/4.63 % (17364)Instructions burned: 961 (million)
% 22.73/4.63 % (17364)------------------------------
% 22.73/4.63 % (17364)------------------------------
% 22.73/4.64 % (17371)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_16880 for (2969ds/90Mi)
% 22.73/4.67 % (17371)Instruction limit reached!
% 22.73/4.67 % (17371)------------------------------
% 22.73/4.67 % (17371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.67 % (17371)Termination reason: Unknown
% 22.73/4.67 % (17371)Termination phase: Property scanning
% 22.73/4.67
% 22.73/4.67 % (17371)Memory used [KB]: 2942
% 22.73/4.67 % (17371)Time elapsed: 0.027 s
% 22.73/4.67 % (17371)Instructions burned: 90 (million)
% 22.73/4.67 % (17371)------------------------------
% 22.73/4.67 % (17371)------------------------------
% 22.73/4.68 % (17372)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_16880 for (2969ds/346Mi)
% 23.21/4.70 % (17367)Instruction limit reached!
% 23.21/4.70 % (17367)------------------------------
% 23.21/4.70 % (17367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.21/4.70 % (17367)Termination reason: Unknown
% 23.21/4.70 % (17367)Termination phase: Saturation
% 23.21/4.70
% 23.21/4.70 % (17367)Memory used [KB]: 8827
% 23.21/4.70 % (17367)Time elapsed: 0.138 s
% 23.21/4.70 % (17367)Instructions burned: 482 (million)
% 23.21/4.70 % (17367)------------------------------
% 23.21/4.70 % (17367)------------------------------
% 23.21/4.71 % (17373)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_16880 for (2969ds/401Mi)
% 23.21/4.77 % (17372)Instruction limit reached!
% 23.21/4.77 % (17372)------------------------------
% 23.21/4.77 % (17372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.21/4.77 % (17372)Termination reason: Unknown
% 23.21/4.77 % (17372)Termination phase: Saturation
% 23.21/4.77
% 23.21/4.77 % (17372)Memory used [KB]: 8699
% 23.21/4.77 % (17372)Time elapsed: 0.094 s
% 23.21/4.77 % (17372)Instructions burned: 346 (million)
% 23.21/4.77 % (17372)------------------------------
% 23.21/4.77 % (17372)------------------------------
% 23.21/4.78 % (17374)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_16880 for (2968ds/6454Mi)
% 23.21/4.78 % (17365)Instruction limit reached!
% 23.21/4.78 % (17365)------------------------------
% 23.21/4.78 % (17365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.21/4.78 % (17365)Termination reason: Unknown
% 23.21/4.78 % (17365)Termination phase: Saturation
% 23.21/4.78
% 23.21/4.78 % (17365)Memory used [KB]: 9722
% 23.21/4.78 % (17365)Time elapsed: 0.368 s
% 23.21/4.78 % (17365)Instructions burned: 1213 (million)
% 23.21/4.78 % (17365)------------------------------
% 23.21/4.78 % (17365)------------------------------
% 23.21/4.79 % (17375)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_16880 for (2968ds/283Mi)
% 23.93/4.81 % (17373)Instruction limit reached!
% 23.93/4.81 % (17373)------------------------------
% 23.93/4.81 % (17373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.93/4.81 % (17373)Termination reason: Unknown
% 23.93/4.81 % (17373)Termination phase: Saturation
% 23.93/4.81
% 23.93/4.81 % (17373)Memory used [KB]: 8955
% 23.93/4.81 % (17373)Time elapsed: 0.107 s
% 23.93/4.81 % (17373)Instructions burned: 401 (million)
% 23.93/4.81 % (17373)------------------------------
% 23.93/4.81 % (17373)------------------------------
% 23.93/4.82 % (17376)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_16880 for (2967ds/865Mi)
% 23.93/4.88 % (17375)Instruction limit reached!
% 23.93/4.88 % (17375)------------------------------
% 23.93/4.88 % (17375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.93/4.88 % (17375)Termination reason: Unknown
% 23.93/4.88 % (17375)Termination phase: Saturation
% 23.93/4.88
% 23.93/4.88 % (17375)Memory used [KB]: 8315
% 23.93/4.88 % (17375)Time elapsed: 0.085 s
% 23.93/4.88 % (17375)Instructions burned: 284 (million)
% 23.93/4.88 % (17375)------------------------------
% 23.93/4.88 % (17375)------------------------------
% 23.93/4.89 % (17377)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_16880 for (2967ds/4528Mi)
% 24.24/4.91 % (17377)Refutation not found, incomplete strategy
% 24.24/4.91 % (17377)------------------------------
% 24.24/4.91 % (17377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.24/4.91 % (17377)Termination reason: Refutation not found, incomplete strategy
% 24.24/4.91
% 24.24/4.91
% 24.24/4.91 % (17377)Memory used [KB]: 2430
% 24.24/4.91 % (17377)Time elapsed: 0.022 s
% 24.24/4.91 % (17377)Instructions burned: 69 (million)
% 24.24/4.91 % (17377)------------------------------
% 24.24/4.91 % (17377)------------------------------
% 24.24/4.92 % (17378)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_16880 for (2967ds/1001Mi)
% 26.77/5.06 % (17366)Instruction limit reached!
% 26.77/5.06 % (17366)------------------------------
% 26.77/5.06 % (17366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/5.06 % (17366)Termination reason: Unknown
% 26.77/5.06 % (17366)Termination phase: Saturation
% 26.77/5.06
% 26.77/5.06 % (17366)Memory used [KB]: 9466
% 26.77/5.06 % (17366)Time elapsed: 0.605 s
% 26.77/5.06 % (17366)Instructions burned: 1979 (million)
% 26.77/5.06 % (17366)------------------------------
% 26.77/5.06 % (17366)------------------------------
% 26.77/5.07 % (17379)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_16880 for (2965ds/102Mi)
% 26.77/5.08 % (17376)Instruction limit reached!
% 26.77/5.08 % (17376)------------------------------
% 26.77/5.08 % (17376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/5.08 % (17376)Termination reason: Unknown
% 26.77/5.08 % (17376)Termination phase: Saturation
% 26.77/5.08
% 26.77/5.08 % (17376)Memory used [KB]: 10874
% 26.77/5.08 % (17376)Time elapsed: 0.260 s
% 26.77/5.08 % (17376)Instructions burned: 867 (million)
% 26.77/5.08 % (17376)------------------------------
% 26.77/5.08 % (17376)------------------------------
% 26.77/5.09 % (17380)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_16880 for (2965ds/952Mi)
% 26.77/5.09 % (17370)Instruction limit reached!
% 26.77/5.09 % (17370)------------------------------
% 26.77/5.09 % (17370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/5.09 % (17370)Termination reason: Unknown
% 26.77/5.09 % (17370)Termination phase: Saturation
% 26.77/5.09
% 26.77/5.09 % (17370)Memory used [KB]: 9594
% 26.77/5.09 % (17370)Time elapsed: 0.475 s
% 26.77/5.09 % (17370)Instructions burned: 1671 (million)
% 26.77/5.09 % (17370)------------------------------
% 26.77/5.09 % (17370)------------------------------
% 26.77/5.10 % (17379)Instruction limit reached!
% 26.77/5.10 % (17379)------------------------------
% 26.77/5.10 % (17379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.77/5.10 % (17379)Termination reason: Unknown
% 26.77/5.10 % (17379)Termination phase: Property scanning
% 26.77/5.10
% 26.77/5.10 % (17379)Memory used [KB]: 2942
% 26.77/5.10 % (17379)Time elapsed: 0.030 s
% 26.77/5.10 % (17379)Instructions burned: 102 (million)
% 26.77/5.10 % (17379)------------------------------
% 26.77/5.10 % (17379)------------------------------
% 26.77/5.10 % (17381)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_16880 for (2965ds/578Mi)
% 26.77/5.11 % (17382)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_16880 for (2965ds/643Mi)
% 27.42/5.14 % (17330)First to succeed.
% 27.42/5.14 % (17330)Refutation found. Thanks to Tanya!
% 27.42/5.14 % SZS status Theorem for DTF2THF_16880
% 27.42/5.14 % SZS output start Proof for DTF2THF_16880
% 27.42/5.14 thf(type_def_5, type, option_fml: $tType).
% 27.42/5.14 thf(type_def_7, type, option_trm: $tType).
% 27.42/5.14 thf(type_def_8, type, char: $tType).
% 27.42/5.14 thf(type_def_9, type, option_game: $tType).
% 27.42/5.14 thf(type_def_10, type, produc799602994n_game: $tType).
% 27.42/5.14 thf(type_def_11, type, produc62062515n_game: $tType).
% 27.42/5.14 thf(type_def_12, type, set_variable: $tType).
% 27.42/5.14 thf(type_def_13, type, trm: $tType).
% 27.42/5.14 thf(type_def_14, type, variable: $tType).
% 27.42/5.14 thf(type_def_15, type, set_Pr79606376n_game: $tType).
% 27.42/5.14 thf(type_def_16, type, set_Pr739694057n_game: $tType).
% 27.42/5.14 thf(type_def_17, type, set_Pr720454634n_game: $tType).
% 27.42/5.14 thf(type_def_18, type, set_Pr1235432374le_trm: $tType).
% 27.42/5.14 thf(type_def_19, type, set_Pr943832262on_trm: $tType).
% 27.42/5.14 thf(type_def_20, type, fml: $tType).
% 27.42/5.14 thf(type_def_21, type, game: $tType).
% 27.42/5.14 thf(type_def_22, type, produc1418842292n_game: $tType).
% 27.42/5.14 thf(type_def_23, type, produc46605351on_fml: $tType).
% 27.42/5.14 thf(type_def_24, type, produc1739631244on_fml: $tType).
% 27.42/5.14 thf(type_def_25, type, produc1016592119n_game: $tType).
% 27.42/5.14 thf(type_def_26, type, produc1072747943on_trm: $tType).
% 27.42/5.14 thf(type_def_27, type, produc1367888000le_trm: $tType).
% 27.42/5.14 thf(type_def_28, type, produc1699626005le_trm: $tType).
% 27.42/5.14 thf(type_def_29, type, produc464795408on_trm: $tType).
% 27.42/5.14 thf(type_def_30, type, produc1408538418on_fml: $tType).
% 27.42/5.14 thf(type_def_31, type, produc1024976764on_trm: $tType).
% 27.42/5.14 thf(type_def_32, type, real: $tType).
% 27.42/5.14 thf(func_def_0, type, produc1699626005le_trm: $tType).
% 27.42/5.14 thf(func_def_1, type, set_Pr720454634n_game: $tType).
% 27.42/5.14 thf(func_def_2, type, produc1418842292n_game: $tType).
% 27.42/5.14 thf(func_def_3, type, set_Pr739694057n_game: $tType).
% 27.42/5.14 thf(func_def_4, type, produc62062515n_game: $tType).
% 27.42/5.14 thf(func_def_5, type, set_Pr79606376n_game: $tType).
% 27.42/5.14 thf(func_def_6, type, produc799602994n_game: $tType).
% 27.42/5.14 thf(func_def_7, type, produc1016592119n_game: $tType).
% 27.42/5.14 thf(func_def_8, type, produc1739631244on_fml: $tType).
% 27.42/5.14 thf(func_def_9, type, produc1072747943on_trm: $tType).
% 27.42/5.14 thf(func_def_10, type, produc46605351on_fml: $tType).
% 27.42/5.14 thf(func_def_11, type, set_Pr943832262on_trm: $tType).
% 27.42/5.14 thf(func_def_12, type, set_Pr1235432374le_trm: $tType).
% 27.42/5.14 thf(func_def_13, type, produc1024976764on_trm: $tType).
% 27.42/5.14 thf(func_def_14, type, produc1408538418on_fml: $tType).
% 27.42/5.14 thf(func_def_15, type, produc464795408on_trm: $tType).
% 27.42/5.14 thf(func_def_16, type, produc1367888000le_trm: $tType).
% 27.42/5.14 thf(func_def_17, type, option_game: $tType).
% 27.42/5.14 thf(func_def_18, type, option_trm: $tType).
% 27.42/5.14 thf(func_def_19, type, option_fml: $tType).
% 27.42/5.14 thf(func_def_20, type, set_variable: $tType).
% 27.42/5.14 thf(func_def_21, type, variable: $tType).
% 27.42/5.14 thf(func_def_22, type, game: $tType).
% 27.42/5.14 thf(func_def_23, type, char: $tType).
% 27.42/5.14 thf(func_def_24, type, trm: $tType).
% 27.42/5.14 thf(func_def_25, type, fml: $tType).
% 27.42/5.14 thf(func_def_26, type, real: $tType).
% 27.42/5.14 thf(func_def_27, type, if_option_fml: $o > option_fml > option_fml > option_fml).
% 27.42/5.14 thf(func_def_28, type, if_option_trm: $o > option_trm > option_trm > option_trm).
% 27.42/5.14 thf(func_def_29, type, inf_in243546115game_o: ((char > option_fml) > (char > option_game) > $o) > ((char > option_fml) > (char > option_game) > $o) > (char > option_fml) > (char > option_game) > $o).
% 27.42/5.14 thf(func_def_30, type, inf_in1072207554game_o: ((char > option_trm) > produc799602994n_game > $o) > ((char > option_trm) > produc799602994n_game > $o) > (char > option_trm) > produc799602994n_game > $o).
% 27.42/5.14 thf(func_def_31, type, inf_in1920662529game_o: ((char > option_trm) > produc62062515n_game > $o) > ((char > option_trm) > produc62062515n_game > $o) > (char > option_trm) > produc62062515n_game > $o).
% 27.42/5.14 thf(func_def_32, type, inf_in185389155_trm_o: (set_variable > trm > $o) > (set_variable > trm > $o) > set_variable > trm > $o).
% 27.42/5.14 thf(func_def_33, type, inf_in605351507_trm_o: (char > option_trm > $o) > (char > option_trm > $o) > char > option_trm > $o).
% 27.42/5.14 thf(func_def_34, type, inf_inf_variable_o: (variable > $o) > (variable > $o) > variable > $o).
% 27.42/5.14 thf(func_def_35, type, inf_in1391117306n_game: set_Pr79606376n_game > set_Pr79606376n_game > set_Pr79606376n_game).
% 27.42/5.14 thf(func_def_36, type, inf_in69689467n_game: set_Pr739694057n_game > set_Pr739694057n_game > set_Pr739694057n_game).
% 27.42/5.14 thf(func_def_37, type, inf_in360367996n_game: set_Pr720454634n_game > set_Pr720454634n_game > set_Pr720454634n_game).
% 27.42/5.14 thf(func_def_38, type, inf_in906025800le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > set_Pr1235432374le_trm).
% 27.42/5.14 thf(func_def_39, type, inf_in1243659096on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > set_Pr943832262on_trm).
% 27.42/5.14 thf(func_def_40, type, inf_inf_set_variable: set_variable > set_variable > set_variable).
% 27.42/5.14 thf(func_def_41, type, none_fml: option_fml).
% 27.42/5.14 thf(func_def_42, type, none_game: option_game).
% 27.42/5.14 thf(func_def_43, type, none_trm: option_trm).
% 27.42/5.14 thf(func_def_44, type, some_fml: fml > option_fml).
% 27.42/5.14 thf(func_def_45, type, some_game: game > option_game).
% 27.42/5.14 thf(func_def_46, type, some_trm: trm > option_trm).
% 27.42/5.14 thf(func_def_47, type, case_option_o_fml: $o > (fml > $o) > option_fml > $o).
% 27.42/5.14 thf(func_def_48, type, case_option_o_game: $o > (game > $o) > option_game > $o).
% 27.42/5.14 thf(func_def_49, type, case_option_o_trm: $o > (trm > $o) > option_trm > $o).
% 27.42/5.14 thf(func_def_50, type, case_o209804997ml_fml: option_fml > (fml > option_fml) > option_fml > option_fml).
% 27.42/5.14 thf(func_def_51, type, case_o325794063ml_trm: option_fml > (trm > option_fml) > option_trm > option_fml).
% 27.42/5.14 thf(func_def_52, type, case_o487727941rm_trm: option_trm > (trm > option_trm) > option_trm > option_trm).
% 27.42/5.14 thf(func_def_53, type, the_fml: option_fml > fml).
% 27.42/5.14 thf(func_def_54, type, the_game: option_game > game).
% 27.42/5.14 thf(func_def_55, type, the_trm: option_trm > trm).
% 27.42/5.14 thf(func_def_56, type, bot_bo1895715589game_o: (char > option_fml) > (char > option_game) > $o).
% 27.42/5.14 thf(func_def_57, type, bot_bo1417568964game_o: (char > option_trm) > produc799602994n_game > $o).
% 27.42/5.14 thf(func_def_58, type, bot_bo849148163game_o: (char > option_trm) > produc62062515n_game > $o).
% 27.42/5.14 thf(func_def_59, type, bot_bo512610661_trm_o: set_variable > trm > $o).
% 27.42/5.14 thf(func_def_60, type, bot_bo102862421_trm_o: char > option_trm > $o).
% 27.42/5.14 thf(func_def_61, type, bot_bot_variable_o: variable > $o).
% 27.42/5.14 thf(func_def_62, type, bot_bo456479484n_game: set_Pr79606376n_game).
% 27.42/5.14 thf(func_def_63, type, bot_bo1302831229n_game: set_Pr739694057n_game).
% 27.42/5.14 thf(func_def_64, type, bot_bo1453406334n_game: set_Pr720454634n_game).
% 27.42/5.14 thf(func_def_65, type, bot_bo896421962le_trm: set_Pr1235432374le_trm).
% 27.42/5.14 thf(func_def_66, type, bot_bo18861914on_trm: set_Pr943832262on_trm).
% 27.42/5.14 thf(func_def_67, type, bot_bot_set_variable: set_variable).
% 27.42/5.14 thf(func_def_68, type, produc123610156n_game: (char > option_fml) > (char > option_game) > produc799602994n_game).
% 27.42/5.14 thf(func_def_69, type, produc1048060077n_game: (char > option_trm) > produc799602994n_game > produc62062515n_game).
% 27.42/5.14 thf(func_def_70, type, produc1618635950n_game: (char > option_trm) > produc62062515n_game > produc1418842292n_game).
% 27.42/5.14 thf(func_def_71, type, produc909629463on_fml: option_fml > option_fml > produc46605351on_fml).
% 27.42/5.14 thf(func_def_72, type, produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml).
% 27.42/5.14 thf(func_def_73, type, produc1111617711n_game: option_game > option_game > produc1016592119n_game).
% 27.42/5.14 thf(func_def_74, type, produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm).
% 27.42/5.14 thf(func_def_75, type, produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm).
% 27.42/5.14 thf(func_def_76, type, produc1482344242le_trm: set_variable > trm > produc1367888000le_trm).
% 27.42/5.14 thf(func_def_77, type, produc1500300866on_trm: char > option_trm > produc464795408on_trm).
% 27.42/5.14 thf(func_def_78, type, produc1205977188on_fml: variable > option_fml > produc1408538418on_fml).
% 27.42/5.14 thf(func_def_79, type, produc1743721902on_trm: variable > option_trm > produc1024976764on_trm).
% 27.42/5.14 thf(func_def_80, type, produc1598111045on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 27.42/5.14 thf(func_def_81, type, produc1214549391on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 27.42/5.14 thf(func_def_82, type, produc1591622303on_fml: ((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml).
% 27.42/5.14 thf(func_def_83, type, produc2129367017on_trm: ((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm).
% 27.42/5.14 thf(func_def_84, type, produc377919108on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 27.42/5.14 thf(func_def_85, type, produc2141841102on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 27.42/5.14 thf(func_def_86, type, produc1903410526on_fml: ((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml).
% 27.42/5.14 thf(func_def_87, type, produc293671592on_trm: ((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm).
% 27.42/5.14 thf(func_def_88, type, produc1278328899on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 27.42/5.14 thf(func_def_89, type, produc724717725on_fml: ((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml).
% 27.42/5.14 thf(func_def_90, type, produc1420172399on_fml: ((char > option_fml) > (char > option_game) > char > option_fml) > produc799602994n_game > char > option_fml).
% 27.42/5.14 thf(func_def_91, type, produc1036610745on_trm: ((char > option_fml) > (char > option_game) > char > option_trm) > produc799602994n_game > char > option_trm).
% 27.42/5.14 thf(func_def_92, type, produc159680767game_o: ((char > option_fml) > (char > option_game) > $o) > produc799602994n_game > $o).
% 27.42/5.14 thf(func_def_93, type, produc347802313on_fml: ((char > option_fml) > (char > option_game) > option_fml) > produc799602994n_game > option_fml).
% 27.42/5.14 thf(func_def_94, type, produc885547027on_trm: ((char > option_fml) > (char > option_game) > option_trm) > produc799602994n_game > option_trm).
% 27.42/5.14 thf(func_def_95, type, produc1615133358on_fml: ((char > option_trm) > produc799602994n_game > char > option_fml) > produc62062515n_game > char > option_fml).
% 27.42/5.14 thf(func_def_96, type, produc1231571704on_trm: ((char > option_trm) > produc799602994n_game > char > option_trm) > produc62062515n_game > char > option_trm).
% 27.42/5.14 thf(func_def_97, type, produc1868740670game_o: ((char > option_trm) > produc799602994n_game > $o) > produc62062515n_game > $o).
% 27.42/5.14 thf(func_def_98, type, produc154833544on_fml: ((char > option_trm) > produc799602994n_game > option_fml) > produc62062515n_game > option_fml).
% 27.42/5.14 thf(func_def_99, type, produc692578258on_trm: ((char > option_trm) > produc799602994n_game > option_trm) > produc62062515n_game > option_trm).
% 27.42/5.14 thf(func_def_100, type, produc1250175341on_fml: ((char > option_trm) > produc62062515n_game > char > option_fml) > produc1418842292n_game > char > option_fml).
% 27.42/5.14 thf(func_def_101, type, produc866613687on_trm: ((char > option_trm) > produc62062515n_game > char > option_trm) > produc1418842292n_game > char > option_trm).
% 27.42/5.14 thf(func_def_102, type, produc1707653117game_o: ((char > option_trm) > produc62062515n_game > $o) > produc1418842292n_game > $o).
% 27.42/5.14 thf(func_def_103, type, produc1499310791on_fml: ((char > option_trm) > produc62062515n_game > option_fml) > produc1418842292n_game > option_fml).
% 27.42/5.14 thf(func_def_104, type, produc82209913_trm_o: (set_variable > trm > $o) > produc1367888000le_trm > $o).
% 27.42/5.14 thf(func_def_105, type, produc584666985_trm_o: (char > option_trm > $o) > produc464795408on_trm > $o).
% 27.42/5.14 thf(func_def_106, type, collect_variable: (variable > $o) > set_variable).
% 27.42/5.14 thf(func_def_107, type, is_empty_variable: set_variable > $o).
% 27.42/5.14 thf(func_def_108, type, static_FVF: fml > set_variable).
% 27.42/5.14 thf(func_def_109, type, static_FVT: trm > set_variable).
% 27.42/5.14 thf(func_def_110, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 27.42/5.14 thf(func_def_111, type, geq: trm > trm > fml).
% 27.42/5.14 thf(func_def_112, type, pred: char > trm > fml).
% 27.42/5.14 thf(func_def_113, type, const: char > trm).
% 27.42/5.14 thf(func_def_114, type, differential: trm > trm).
% 27.42/5.14 thf(func_def_115, type, func: char > trm > trm).
% 27.42/5.14 thf(func_def_116, type, number: real > trm).
% 27.42/5.14 thf(func_def_117, type, plus: trm > trm > trm).
% 27.42/5.14 thf(func_def_118, type, times: trm > trm > trm).
% 27.42/5.14 thf(func_def_119, type, var: variable > trm).
% 27.42/5.14 thf(func_def_120, type, uSubst716837505ntialo: option_trm > option_trm).
% 27.42/5.14 thf(func_def_121, type, uSubst152838031e_Geqo: option_trm > option_trm > option_fml).
% 27.42/5.14 thf(func_def_122, type, uSubst141955042_Pluso: option_trm > option_trm > option_trm).
% 27.42/5.14 thf(func_def_123, type, uSubst1367128042_Testo: option_fml > option_game).
% 27.42/5.14 thf(func_def_124, type, uSubst918876924Timeso: option_trm > option_trm > option_trm).
% 27.42/5.14 thf(func_def_125, type, uSubst_Mirabelle_dot: trm).
% 27.42/5.14 thf(func_def_126, type, uSubst1408967625substt: trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_127, type, uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm).
% 27.42/5.14 thf(func_def_128, type, uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml).
% 27.42/5.14 thf(func_def_129, type, uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm).
% 27.42/5.14 thf(func_def_130, type, uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o).
% 27.42/5.14 thf(func_def_131, type, accp_P1877119646le_trm: (produc1699626005le_trm > produc1699626005le_trm > $o) > produc1699626005le_trm > $o).
% 27.42/5.14 thf(func_def_132, type, member849814089n_game: produc799602994n_game > set_Pr79606376n_game > $o).
% 27.42/5.14 thf(func_def_133, type, member774167626n_game: produc62062515n_game > set_Pr739694057n_game > $o).
% 27.42/5.14 thf(func_def_134, type, member1940201675n_game: produc1418842292n_game > set_Pr720454634n_game > $o).
% 27.42/5.14 thf(func_def_135, type, member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o).
% 27.42/5.14 thf(func_def_136, type, member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o).
% 27.42/5.14 thf(func_def_137, type, member_variable: variable > set_variable > $o).
% 27.42/5.14 thf(func_def_138, type, ua: set_variable).
% 27.42/5.14 thf(func_def_139, type, va: set_variable).
% 27.42/5.14 thf(func_def_140, type, sigma: produc1418842292n_game).
% 27.42/5.14 thf(func_def_141, type, theta: trm).
% 27.42/5.14 thf(func_def_142, type, p: char).
% 27.42/5.14 thf(func_def_157, type, sP0: (option_trm > option_fml > $o) > option_trm > option_fml > $o).
% 27.42/5.14 thf(func_def_158, type, sP1: (option_fml > option_fml > $o) > option_fml > option_fml > $o).
% 27.42/5.14 thf(func_def_159, type, sP2: (option_fml > option_game > $o) > option_fml > option_game > $o).
% 27.42/5.14 thf(func_def_160, type, sP3: option_trm > option_trm > option_fml > $o).
% 27.42/5.14 thf(func_def_161, type, sP4: (option_game > option_fml > $o) > option_fml > option_game > $o).
% 27.42/5.14 thf(func_def_162, type, sP5: (option_trm > option_trm > $o) > option_trm > option_trm > $o).
% 27.42/5.14 thf(func_def_163, type, sP6: (option_game > option_trm > $o) > option_game > option_trm > $o).
% 27.42/5.14 thf(func_def_164, type, sP7: (option_fml > option_trm > $o) > option_fml > option_trm > $o).
% 27.42/5.14 thf(func_def_165, type, sP8: (trm > $o) > $o).
% 27.42/5.14 thf(func_def_166, type, sP9: (trm > $o) > $o).
% 27.42/5.14 thf(func_def_167, type, sP10: (option_trm > option_game > $o) > option_trm > option_game > $o).
% 27.42/5.14 thf(func_def_168, type, sP11: (option_game > option_game > $o) > option_game > option_game > $o).
% 27.42/5.14 thf(func_def_169, type, sP12: trm > produc1418842292n_game > set_variable > option_trm > $o).
% 27.42/5.14 thf(func_def_170, type, sP13: trm > produc1418842292n_game > set_variable > option_trm > $o).
% 27.42/5.14 thf(func_def_171, type, sP14: trm > produc1418842292n_game > set_variable > option_trm > $o).
% 27.42/5.14 thf(func_def_172, type, sP15: trm > produc1418842292n_game > set_variable > option_trm > $o).
% 27.42/5.14 thf(func_def_173, type, sP16: trm > option_trm > produc1418842292n_game > set_variable > $o).
% 27.42/5.14 thf(func_def_174, type, sP17: trm > option_trm > produc1418842292n_game > set_variable > $o).
% 27.42/5.14 thf(func_def_175, type, sP18: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_176, type, sP19: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_177, type, sP20: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_178, type, sP21: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_179, type, sP22: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_180, type, sP23: (produc1418842292n_game > set_variable > trm > $o) > $o).
% 27.42/5.14 thf(func_def_181, type, sK24: (trm > $o) > (trm > option_fml) > (option_fml > $o) > trm).
% 27.42/5.14 thf(func_def_182, type, sK25: (option_trm > option_fml > $o) > option_trm > option_fml > trm).
% 27.42/5.14 thf(func_def_183, type, sK26: (option_trm > option_fml > $o) > option_trm > option_fml > fml).
% 27.42/5.14 thf(func_def_184, type, sK27: produc799602994n_game > ((char > option_fml) > (char > option_game) > $o) > char > option_fml).
% 27.42/5.14 thf(func_def_185, type, sK28: produc799602994n_game > ((char > option_fml) > (char > option_game) > $o) > char > option_game).
% 27.42/5.14 thf(func_def_186, type, sK29: (option_fml > option_fml > $o) > option_fml > option_fml > fml).
% 27.42/5.14 thf(func_def_187, type, sK30: (option_fml > option_fml > $o) > option_fml > option_fml > fml).
% 27.42/5.14 thf(func_def_188, type, sK31: (option_fml > option_game > $o) > option_fml > option_game > game).
% 27.42/5.14 thf(func_def_189, type, sK32: (option_fml > option_game > $o) > option_fml > option_game > fml).
% 27.42/5.14 thf(func_def_190, type, sK33: produc1016592119n_game > game).
% 27.42/5.14 thf(func_def_191, type, sK34: produc1016592119n_game > game).
% 27.42/5.14 thf(func_def_192, type, sK35: produc1016592119n_game > game).
% 27.42/5.14 thf(func_def_193, type, sK36: produc1016592119n_game > option_game).
% 27.42/5.14 thf(func_def_194, type, sK37: option_fml > fml).
% 27.42/5.14 thf(func_def_195, type, sK38: set_variable > char > produc1418842292n_game > trm).
% 27.42/5.14 thf(func_def_196, type, sK39: set_variable > set_variable > variable).
% 27.42/5.14 thf(func_def_197, type, sK40: (variable > $o) > variable).
% 27.42/5.14 thf(func_def_198, type, sK41: option_trm > trm).
% 27.42/5.14 thf(func_def_199, type, sK42: option_fml > option_trm > option_trm > trm).
% 27.42/5.14 thf(func_def_200, type, sK43: option_fml > option_trm > option_trm > trm).
% 27.42/5.14 thf(func_def_201, type, sK44: option_trm > trm).
% 27.42/5.14 thf(func_def_202, type, sK45: (set_variable > trm > $o) > produc1367888000le_trm > trm).
% 27.42/5.14 thf(func_def_203, type, sK46: (set_variable > trm > $o) > produc1367888000le_trm > set_variable).
% 27.42/5.14 thf(func_def_204, type, sK47: (char > option_trm > $o) > char).
% 27.42/5.14 thf(func_def_205, type, sK48: (char > option_trm > $o) > char).
% 27.42/5.14 thf(func_def_206, type, sK49: (char > option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_207, type, sK50: (produc799602994n_game > char > option_fml) > ((char > option_fml) > (char > option_game) > char > option_fml) > char > option_fml).
% 27.42/5.14 thf(func_def_208, type, sK51: (produc799602994n_game > char > option_fml) > ((char > option_fml) > (char > option_game) > char > option_fml) > char > option_game).
% 27.42/5.14 thf(func_def_209, type, sK52: (option_game > $o) > game).
% 27.42/5.14 thf(func_def_210, type, sK53: produc1418842292n_game > char > set_variable > trm).
% 27.42/5.14 thf(func_def_211, type, sK54: option_game > (game > $o) > game).
% 27.42/5.14 thf(func_def_212, type, sK55: option_game > game).
% 27.42/5.14 thf(func_def_213, type, sK56: (variable > option_fml > $o) > variable).
% 27.42/5.14 thf(func_def_214, type, sK57: (variable > option_fml > $o) > variable).
% 27.42/5.14 thf(func_def_215, type, sK58: (variable > option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_216, type, sK59: set_variable > set_variable > variable).
% 27.42/5.14 thf(func_def_217, type, sK60: set_variable > set_variable > variable).
% 27.42/5.14 thf(func_def_218, type, sK61: (option_game > option_fml > $o) > game).
% 27.42/5.14 thf(func_def_219, type, sK62: (option_game > option_fml > $o) > option_fml).
% 27.42/5.14 thf(func_def_220, type, sK63: (option_game > option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_221, type, sK64: (option_game > option_fml > $o) > game).
% 27.42/5.14 thf(func_def_222, type, sK65: (option_game > option_fml > $o) > option_fml > option_game > fml).
% 27.42/5.14 thf(func_def_223, type, sK66: (option_game > option_fml > $o) > option_fml > option_game > game).
% 27.42/5.14 thf(func_def_224, type, sK67: ((char > option_trm) > produc62062515n_game > $o) > produc1418842292n_game > char > option_trm).
% 27.42/5.14 thf(func_def_225, type, sK68: ((char > option_trm) > produc62062515n_game > $o) > produc1418842292n_game > produc62062515n_game).
% 27.42/5.14 thf(func_def_226, type, sK69: ((char > option_fml) > (char > option_game) > option_fml) > (produc799602994n_game > option_fml) > char > option_game).
% 27.42/5.14 thf(func_def_227, type, sK70: ((char > option_fml) > (char > option_game) > option_fml) > (produc799602994n_game > option_fml) > char > option_fml).
% 27.42/5.14 thf(func_def_228, type, sK71: option_game > game).
% 27.42/5.14 thf(func_def_229, type, sK72: (option_trm > option_trm > $o) > option_trm > option_trm > trm).
% 27.42/5.14 thf(func_def_230, type, sK73: (option_trm > option_trm > $o) > option_trm > option_trm > trm).
% 27.42/5.14 thf(func_def_231, type, sK74: set_variable > set_variable > variable).
% 27.42/5.14 thf(func_def_232, type, sK75: (variable > $o) > (variable > $o) > variable).
% 27.42/5.14 thf(func_def_233, type, sK76: (produc799602994n_game > char > option_trm) > ((char > option_fml) > (char > option_game) > char > option_trm) > char > option_fml).
% 27.42/5.14 thf(func_def_234, type, sK77: (produc799602994n_game > char > option_trm) > ((char > option_fml) > (char > option_game) > char > option_trm) > char > option_game).
% 27.42/5.14 thf(func_def_235, type, sK78: (option_game > option_trm > $o) > option_game > option_trm > game).
% 27.42/5.14 thf(func_def_236, type, sK79: (option_game > option_trm > $o) > option_game > option_trm > trm).
% 27.42/5.14 thf(func_def_237, type, sK80: option_game > game).
% 27.42/5.14 thf(func_def_238, type, sK81: trm > trm).
% 27.42/5.14 thf(func_def_239, type, sK82: trm > trm).
% 27.42/5.14 thf(func_def_240, type, sK83: trm > char).
% 27.42/5.14 thf(func_def_241, type, sK84: trm > trm).
% 27.42/5.14 thf(func_def_242, type, sK85: trm > trm).
% 27.42/5.14 thf(func_def_243, type, sK86: trm > trm).
% 27.42/5.14 thf(func_def_244, type, sK87: trm > variable).
% 27.42/5.14 thf(func_def_245, type, sK88: trm > real).
% 27.42/5.14 thf(func_def_246, type, sK89: trm > char).
% 27.42/5.14 thf(func_def_247, type, sK90: trm > trm).
% 27.42/5.14 thf(func_def_248, type, sK91: option_fml > fml).
% 27.42/5.14 thf(func_def_249, type, sK92: produc1024976764on_trm > variable).
% 27.42/5.14 thf(func_def_250, type, sK93: produc1024976764on_trm > trm).
% 27.42/5.14 thf(func_def_251, type, sK94: produc1024976764on_trm > variable).
% 27.42/5.14 thf(func_def_252, type, sK95: option_fml > (fml > $o) > fml).
% 27.42/5.14 thf(func_def_253, type, sK96: ((char > option_trm) > produc62062515n_game > char > option_fml) > (produc1418842292n_game > char > option_fml) > produc62062515n_game).
% 27.42/5.14 thf(func_def_254, type, sK97: ((char > option_trm) > produc62062515n_game > char > option_fml) > (produc1418842292n_game > char > option_fml) > char > option_trm).
% 27.42/5.14 thf(func_def_255, type, sK98: ((char > option_trm) > produc62062515n_game > option_fml) > (produc1418842292n_game > option_fml) > char > option_trm).
% 27.42/5.14 thf(func_def_256, type, sK99: ((char > option_trm) > produc62062515n_game > option_fml) > (produc1418842292n_game > option_fml) > produc62062515n_game).
% 27.42/5.14 thf(func_def_257, type, sK100: (option_fml > option_trm > $o) > option_fml > option_trm > trm).
% 27.42/5.14 thf(func_def_258, type, sK101: (option_fml > option_trm > $o) > option_fml > option_trm > fml).
% 27.42/5.14 thf(func_def_259, type, sK102: option_fml > fml).
% 27.42/5.14 thf(func_def_260, type, sK103: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_261, type, sK104: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_262, type, sK105: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_263, type, sK106: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_264, type, sK107: (trm > $o) > char).
% 27.42/5.14 thf(func_def_265, type, sK108: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_266, type, sK109: (trm > $o) > trm).
% 27.42/5.14 thf(func_def_267, type, sK110: (trm > $o) > variable).
% 27.42/5.14 thf(func_def_268, type, sK111: (trm > $o) > char).
% 27.42/5.14 thf(func_def_269, type, sK112: (trm > $o) > real).
% 27.42/5.14 thf(func_def_270, type, sK113: produc46605351on_fml > option_fml).
% 27.42/5.14 thf(func_def_271, type, sK114: produc46605351on_fml > fml).
% 27.42/5.14 thf(func_def_272, type, sK115: produc46605351on_fml > fml).
% 27.42/5.14 thf(func_def_273, type, sK116: produc46605351on_fml > fml).
% 27.42/5.14 thf(func_def_274, type, sK117: produc1408538418on_fml > variable).
% 27.42/5.14 thf(func_def_275, type, sK118: produc1408538418on_fml > fml).
% 27.42/5.14 thf(func_def_276, type, sK119: produc1408538418on_fml > variable).
% 27.42/5.14 thf(func_def_277, type, sK120: (char > option_trm > $o) > produc464795408on_trm > option_trm).
% 27.42/5.14 thf(func_def_278, type, sK121: (char > option_trm > $o) > produc464795408on_trm > char).
% 27.42/5.14 thf(func_def_279, type, sK122: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_280, type, sK123: produc1699626005le_trm > real).
% 27.42/5.14 thf(func_def_281, type, sK124: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_282, type, sK125: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_283, type, sK126: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_284, type, sK127: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_285, type, sK128: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_286, type, sK129: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_287, type, sK130: produc1699626005le_trm > char).
% 27.42/5.14 thf(func_def_288, type, sK131: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_289, type, sK132: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_290, type, sK133: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_291, type, sK134: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_292, type, sK135: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_293, type, sK136: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_294, type, sK137: produc1699626005le_trm > trm).
% 27.42/5.14 thf(func_def_295, type, sK138: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_296, type, sK139: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_297, type, sK140: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_298, type, sK141: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_299, type, sK142: produc1699626005le_trm > char).
% 27.42/5.14 thf(func_def_300, type, sK143: produc1699626005le_trm > set_variable).
% 27.42/5.14 thf(func_def_301, type, sK144: produc1699626005le_trm > variable).
% 27.42/5.14 thf(func_def_302, type, sK145: produc1699626005le_trm > produc1418842292n_game).
% 27.42/5.14 thf(func_def_303, type, sK146: (variable > option_trm > $o) > variable).
% 27.42/5.14 thf(func_def_304, type, sK147: (variable > option_trm > $o) > variable).
% 27.42/5.14 thf(func_def_305, type, sK148: (variable > option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_306, type, sK149: ((char > option_trm) > produc799602994n_game > option_trm) > (produc62062515n_game > option_trm) > char > option_trm).
% 27.42/5.14 thf(func_def_307, type, sK150: ((char > option_trm) > produc799602994n_game > option_trm) > (produc62062515n_game > option_trm) > produc799602994n_game).
% 27.42/5.14 thf(func_def_308, type, sK151: option_trm > trm).
% 27.42/5.14 thf(func_def_309, type, sK152: (option_game > $o) > game).
% 27.42/5.14 thf(func_def_310, type, sK153: ((char > option_fml) > (char > option_game) > option_trm) > (produc799602994n_game > option_trm) > char > option_fml).
% 27.42/5.14 thf(func_def_311, type, sK154: ((char > option_fml) > (char > option_game) > option_trm) > (produc799602994n_game > option_trm) > char > option_game).
% 27.42/5.14 thf(func_def_312, type, sK155: (produc62062515n_game > char > option_trm) > ((char > option_trm) > produc799602994n_game > char > option_trm) > char > option_trm).
% 27.42/5.14 thf(func_def_313, type, sK156: (produc62062515n_game > char > option_trm) > ((char > option_trm) > produc799602994n_game > char > option_trm) > produc799602994n_game).
% 27.42/5.14 thf(func_def_314, type, sK157: set_variable > variable).
% 27.42/5.14 thf(func_def_315, type, sK158: (variable > $o) > variable).
% 27.42/5.14 thf(func_def_316, type, sK159: (fml > $o) > (option_fml > $o) > (fml > option_fml) > fml).
% 27.42/5.14 thf(func_def_317, type, sK160: produc1739631244on_fml > fml).
% 27.42/5.14 thf(func_def_318, type, sK161: produc1739631244on_fml > game).
% 27.42/5.14 thf(func_def_319, type, sK162: produc1739631244on_fml > option_fml).
% 27.42/5.14 thf(func_def_320, type, sK163: produc1739631244on_fml > game).
% 27.42/5.14 thf(func_def_321, type, sK164: (produc62062515n_game > char > option_fml) > ((char > option_trm) > produc799602994n_game > char > option_fml) > char > option_trm).
% 27.42/5.14 thf(func_def_322, type, sK165: (produc62062515n_game > char > option_fml) > ((char > option_trm) > produc799602994n_game > char > option_fml) > produc799602994n_game).
% 27.42/5.14 thf(func_def_323, type, sK166: produc1418842292n_game > char > set_variable > fml).
% 27.42/5.14 thf(func_def_324, type, sK167: option_game > game).
% 27.42/5.14 thf(func_def_325, type, sK168: option_trm > trm).
% 27.42/5.14 thf(func_def_326, type, sK169: (trm > $o) > option_trm > trm).
% 27.42/5.14 thf(func_def_327, type, sK170: (option_trm > option_game > $o) > option_trm > option_game > game).
% 27.42/5.14 thf(func_def_328, type, sK171: (option_trm > option_game > $o) > option_trm > option_game > trm).
% 27.42/5.14 thf(func_def_329, type, sK172: (option_game > option_game > $o) > option_game).
% 27.42/5.14 thf(func_def_330, type, sK173: (option_game > option_game > $o) > game).
% 27.42/5.14 thf(func_def_331, type, sK174: (option_game > option_game > $o) > game).
% 27.42/5.14 thf(func_def_332, type, sK175: (option_game > option_game > $o) > game).
% 27.42/5.14 thf(func_def_333, type, sK176: set_variable > variable).
% 27.42/5.14 thf(func_def_334, type, sK177: produc464795408on_trm > char).
% 27.42/5.14 thf(func_def_335, type, sK178: produc464795408on_trm > trm).
% 27.42/5.14 thf(func_def_336, type, sK179: produc464795408on_trm > char).
% 27.42/5.14 thf(func_def_337, type, sK180: (option_game > option_game > $o) > option_game > option_game > game).
% 27.42/5.14 thf(func_def_338, type, sK181: (option_game > option_game > $o) > option_game > option_game > game).
% 27.42/5.14 thf(func_def_339, type, sK182: option_fml > fml).
% 27.42/5.14 thf(func_def_340, type, sK183: produc1072747943on_trm > trm).
% 27.42/5.14 thf(func_def_341, type, sK184: produc1072747943on_trm > trm).
% 27.42/5.14 thf(func_def_342, type, sK185: produc1072747943on_trm > trm).
% 27.42/5.14 thf(func_def_343, type, sK186: produc1072747943on_trm > option_trm).
% 27.42/5.14 thf(func_def_344, type, sK187: ((char > option_trm) > produc799602994n_game > option_fml) > (produc62062515n_game > option_fml) > char > option_trm).
% 27.42/5.14 thf(func_def_345, type, sK188: ((char > option_trm) > produc799602994n_game > option_fml) > (produc62062515n_game > option_fml) > produc799602994n_game).
% 27.42/5.14 thf(func_def_346, type, sK189: (option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_347, type, sK190: option_trm > trm).
% 27.42/5.14 thf(func_def_348, type, sK191: (option_trm > option_trm > $o) > option_trm).
% 27.42/5.14 thf(func_def_349, type, sK192: (option_trm > option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_350, type, sK193: (option_trm > option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_351, type, sK194: (option_trm > option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_352, type, sK195: set_variable > variable).
% 27.42/5.14 thf(func_def_353, type, sK196: option_fml > fml).
% 27.42/5.14 thf(func_def_354, type, sK197: produc1418842292n_game > set_variable > char > trm).
% 27.42/5.14 thf(func_def_355, type, sK198: option_game > game).
% 27.42/5.14 thf(func_def_356, type, sK199: (option_fml > $o) > produc1418842292n_game > ((char > option_trm) > produc62062515n_game > option_fml) > char > option_trm).
% 27.42/5.14 thf(func_def_357, type, sK200: (option_fml > $o) > produc1418842292n_game > ((char > option_trm) > produc62062515n_game > option_fml) > produc62062515n_game).
% 27.42/5.14 thf(func_def_358, type, sK201: (option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_359, type, sK202: (option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_360, type, sK203: (trm > $o) > (trm > option_trm) > (option_trm > $o) > trm).
% 27.42/5.14 thf(func_def_361, type, sK204: option_trm > trm).
% 27.42/5.14 thf(func_def_362, type, sK205: trm > option_trm > produc1418842292n_game > set_variable > trm).
% 27.42/5.14 thf(func_def_363, type, sK206: trm > option_trm > produc1418842292n_game > set_variable > trm).
% 27.42/5.14 thf(func_def_364, type, sK207: trm > option_trm > produc1418842292n_game > set_variable > trm).
% 27.42/5.14 thf(func_def_365, type, sK208: trm > produc1418842292n_game > set_variable > option_trm > char).
% 27.42/5.14 thf(func_def_366, type, sK209: trm > produc1418842292n_game > set_variable > option_trm > char).
% 27.42/5.14 thf(func_def_367, type, sK210: trm > produc1418842292n_game > set_variable > option_trm > trm).
% 27.42/5.14 thf(func_def_368, type, sK211: trm > produc1418842292n_game > set_variable > option_trm > variable).
% 27.42/5.14 thf(func_def_369, type, sK212: trm > produc1418842292n_game > set_variable > option_trm > real).
% 27.42/5.14 thf(func_def_370, type, sK213: option_trm > set_variable > produc1418842292n_game > trm > trm).
% 27.42/5.14 thf(func_def_371, type, sK214: option_trm > set_variable > produc1418842292n_game > trm > trm).
% 27.42/5.14 thf(func_def_372, type, sK215: (option_fml > option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_373, type, sK216: (option_fml > option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_374, type, sK217: (option_fml > option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_375, type, sK218: (option_fml > option_fml > $o) > option_fml).
% 27.42/5.14 thf(func_def_376, type, sK219: (option_fml > $o) > fml).
% 27.42/5.14 thf(func_def_377, type, sK220: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_378, type, sK221: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_379, type, sK222: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_380, type, sK223: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_381, type, sK224: (produc1418842292n_game > set_variable > trm > $o) > char).
% 27.42/5.14 thf(func_def_382, type, sK225: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_383, type, sK226: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_384, type, sK227: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_385, type, sK228: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_386, type, sK229: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_387, type, sK230: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_388, type, sK231: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_389, type, sK232: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_390, type, sK233: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_391, type, sK234: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_392, type, sK235: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_393, type, sK236: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_394, type, sK237: (produc1418842292n_game > set_variable > trm > $o) > variable).
% 27.42/5.14 thf(func_def_395, type, sK238: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_396, type, sK239: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_397, type, sK240: (produc1418842292n_game > set_variable > trm > $o) > char).
% 27.42/5.14 thf(func_def_398, type, sK241: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_399, type, sK242: (produc1418842292n_game > set_variable > trm > $o) > real).
% 27.42/5.14 thf(func_def_400, type, sK243: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_401, type, sK244: ((char > option_trm) > produc799602994n_game > $o) > produc62062515n_game > produc799602994n_game).
% 27.42/5.14 thf(func_def_402, type, sK245: ((char > option_trm) > produc799602994n_game > $o) > produc62062515n_game > char > option_trm).
% 27.42/5.14 thf(func_def_403, type, sK246: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_404, type, sK247: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_405, type, sK248: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_406, type, sK249: (produc1418842292n_game > set_variable > trm > $o) > char).
% 27.42/5.14 thf(func_def_407, type, sK250: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_408, type, sK251: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_409, type, sK252: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_410, type, sK253: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_411, type, sK254: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_412, type, sK255: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_413, type, sK256: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_414, type, sK257: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_415, type, sK258: (produc1418842292n_game > set_variable > trm > $o) > trm).
% 27.42/5.14 thf(func_def_416, type, sK259: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_417, type, sK260: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_418, type, sK261: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_419, type, sK262: (produc1418842292n_game > set_variable > trm > $o) > char).
% 27.42/5.14 thf(func_def_420, type, sK263: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_421, type, sK264: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_422, type, sK265: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_423, type, sK266: (produc1418842292n_game > set_variable > trm > $o) > real).
% 27.42/5.14 thf(func_def_424, type, sK267: (produc1418842292n_game > set_variable > trm > $o) > produc1418842292n_game).
% 27.42/5.14 thf(func_def_425, type, sK268: (produc1418842292n_game > set_variable > trm > $o) > set_variable).
% 27.42/5.14 thf(func_def_426, type, sK269: (produc1418842292n_game > set_variable > trm > $o) > variable).
% 27.42/5.14 thf(func_def_429, type, ph271: !>[X0: $tType]:(X0)).
% 27.42/5.14 thf(f12225,plain,(
% 27.42/5.14 $false),
% 27.42/5.14 inference(avatar_sat_refutation,[status(thm)],[f2401,f2409,f5857,f12213])).
% 27.42/5.14 thf(f12213,plain,(
% 27.42/5.14 ~spl270_37),
% 27.42/5.14 inference(avatar_contradiction_clause,[status(thm)],[f12212])).
% 27.42/5.14 thf(f12212,plain,(
% 27.42/5.14 $false | ~spl270_37),
% 27.42/5.14 inference(trivial_inequality_removal,[status(thm)],[f12211])).
% 27.42/5.14 thf(f12211,plain,(
% 27.42/5.14 (none_fml != none_fml) | ~spl270_37),
% 27.42/5.14 inference(superposition,[status(thm)],[f1777,f5850])).
% 27.42/5.14 thf(f5850,plain,(
% 27.42/5.14 ( ! [X1 : trm] : ((none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X1)))) ) | ~spl270_37),
% 27.42/5.14 inference(avatar_component_clause,[status(thm)],[f5849])).
% 27.42/5.14 thf(f5849,definition,(
% 27.42/5.14 spl270_37 <=> ! [X1 : trm] : (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X1)))),
% 27.42/5.14 introduced(definition,[new_symbols(naming,[spl270_37])],[avatar_definition])).
% 27.42/5.14 thf(f1777,plain,(
% 27.42/5.14 (none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f2])).
% 27.42/5.14 thf(f2,axiom,(
% 27.42/5.14 (none_fml != (uSubst516392804stappf @ sigma @ va @ (pred @ p @ theta)))),
% 27.42/5.14 file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_1_Pred_Oprems_I2_J)).
% 27.42/5.14 thf(f5857,plain,(
% 27.42/5.14 spl270_37 | spl270_37 | spl270_2 | spl270_4),
% 27.42/5.14 inference(avatar_split_clause,[status(thm)],[f5856,f2385,f2375,f5849,f5849])).
% 27.42/5.14 thf(f2375,definition,(
% 27.42/5.14 spl270_2 <=> (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 27.42/5.14 introduced(definition,[new_symbols(naming,[spl270_2])],[avatar_definition])).
% 27.42/5.14 thf(f2385,definition,(
% 27.42/5.14 spl270_4 <=> (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 27.42/5.14 introduced(definition,[new_symbols(naming,[spl270_4])],[avatar_definition])).
% 27.42/5.14 thf(f5856,plain,(
% 27.42/5.14 ( ! [X0 : trm,X1 : trm] : ((none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X0))) | (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X1)))) ) | (spl270_2 | spl270_4)),
% 27.42/5.14 inference(subsumption_resolution,[status(thm)],[f5844,f2386])).
% 27.42/5.14 thf(f2386,plain,(
% 27.42/5.14 (none_fml != (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)) | spl270_4),
% 27.42/5.14 inference(avatar_component_clause,[status(thm)],[f2385])).
% 27.42/5.14 thf(f5844,plain,(
% 27.42/5.14 ( ! [X0 : trm,X1 : trm] : ((none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)) | (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X1))) | (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X0)))) ) | (spl270_2 | spl270_4)),
% 27.42/5.14 inference(trivial_inequality_removal,[status(thm)],[f5843])).
% 27.42/5.14 thf(f5843,plain,(
% 27.42/5.14 ( ! [X0 : trm,X1 : trm] : ((bot_bot_set_variable != bot_bot_set_variable) | (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X0))) | (none_fml = (uSubst516392804stappf @ sigma @ va @ (pred @ p @ X1))) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) ) | (spl270_2 | spl270_4)),
% 27.42/5.14 inference(superposition,[status(thm)],[f2705,f2026])).
% 27.42/5.14 thf(f2026,plain,(
% 27.42/5.14 ( ! [X2 : char,X3 : produc1418842292n_game,X0 : set_variable,X1 : trm] : ((none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2)) | (none_fml = (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) | (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (sK166 @ X3 @ X2 @ X0)) @ X0))) )),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f1418])).
% 27.42/5.14 thf(f1418,plain,(
% 27.42/5.14 ! [X0 : set_variable,X1 : trm,X2 : char,X3 : produc1418842292n_game] : ((none_fml = (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) | ((none_trm != (uSubst516392818stappt @ X3 @ X0 @ X1)) & ((none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2)) | ((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (sK166 @ X3 @ X2 @ X0)) @ X0)) & ((some_fml @ (sK166 @ X3 @ X2 @ X0)) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))))))),
% 27.42/5.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK166])],[f1061,f1417])).
% 27.42/5.14 thf(f1417,plain,(
% 27.42/5.14 ! [X0 : set_variable,X2 : char,X3 : produc1418842292n_game] : (? [X4 : fml] : ((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ X4) @ X0)) & ((some_fml @ X4) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))) => ((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ (sK166 @ X3 @ X2 @ X0)) @ X0)) & ((some_fml @ (sK166 @ X3 @ X2 @ X0)) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))))),
% 27.42/5.14 introduced(definition,[],[choice_axiom])).
% 27.42/5.14 thf(f1061,plain,(
% 27.42/5.14 ! [X0 : set_variable,X1 : trm,X2 : char,X3 : produc1418842292n_game] : ((none_fml = (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) | ((none_trm != (uSubst516392818stappt @ X3 @ X0 @ X1)) & ((none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2)) | ? [X4 : fml] : ((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ X4) @ X0)) & ((some_fml @ X4) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))))))),
% 27.42/5.14 inference(ennf_transformation,[status(thm)],[f488])).
% 27.42/5.14 thf(f488,plain,(
% 27.42/5.14 ! [X0 : set_variable,X1 : trm,X2 : char,X3 : produc1418842292n_game] : ((none_fml != (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) => ((none_trm != (uSubst516392818stappt @ X3 @ X0 @ X1)) & ((none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2)) | ? [X4 : fml] : ((bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ X4) @ X0)) & ((some_fml @ X4) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))))))),
% 27.42/5.14 inference(fool_elimination,[status(thm)],[f487])).
% 27.42/5.14 thf(f487,plain,(
% 27.42/5.14 ! [X0 : set_variable,X1 : trm,X2 : char,X3 : produc1418842292n_game] : ((none_fml != (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) => ((none_trm != (uSubst516392818stappt @ X3 @ X0 @ X1)) & (? [X4 : fml] : (((produc1250175341on_fml @ (^[X5 : char > option_trm] : (produc1615133358on_fml @ (^[X6 : char > option_trm] : (produc1420172399on_fml @ (^[X7 : char > option_fml, X8 : char > option_game] : (X7)))))) @ X3 @ X2) = (some_fml @ X4)) & (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ X4) @ X0))) | (none_fml = (produc1250175341on_fml @ (^[X9 : char > option_trm] : (produc1615133358on_fml @ (^[X10 : char > option_trm] : (produc1420172399on_fml @ (^[X11 : char > option_fml, X12 : char > option_game] : (X11)))))) @ X3 @ X2)))))),
% 27.42/5.14 inference(rectify,[status(thm)],[f140])).
% 27.42/5.14 thf(f140,axiom,(
% 27.42/5.14 ! [X30 : set_variable,X31 : trm,X28 : char,X27 : produc1418842292n_game] : ((none_fml != (uSubst516392804stappf @ X27 @ X30 @ (pred @ X28 @ X31))) => ((none_trm != (uSubst516392818stappt @ X27 @ X30 @ X31)) & (? [X63 : fml] : (((produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ X27 @ X28) = (some_fml @ X63)) & (bot_bot_set_variable = (inf_inf_set_variable @ (static_FVF @ X63) @ X30))) | (none_fml = (produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ X27 @ X28)))))),
% 27.42/5.14 file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_139_usubstappf__pred__conv)).
% 27.42/5.14 thf(f2705,plain,(
% 27.42/5.14 ( ! [X0 : set_variable,X1 : trm] : ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (sK166 @ sigma @ p @ X0)) @ va)) | (none_fml = (uSubst516392804stappf @ sigma @ X0 @ (pred @ p @ X1)))) ) | (spl270_2 | spl270_4)),
% 27.42/5.14 inference(forward_demodulation,[status(thm)],[f2704,f1593])).
% 27.42/5.14 thf(f1593,plain,(
% 27.42/5.14 ( ! [X0 : fml] : (((the_fml @ (some_fml @ X0)) = X0)) )),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f797])).
% 27.42/5.14 thf(f797,plain,(
% 27.42/5.14 ! [X0 : fml] : ((the_fml @ (some_fml @ X0)) = X0)),
% 27.42/5.14 inference(rectify,[status(thm)],[f131])).
% 27.42/5.14 thf(f131,axiom,(
% 27.42/5.14 ! [X40 : fml] : ((the_fml @ (some_fml @ X40)) = X40)),
% 27.42/5.14 file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_130_option_Osel)).
% 27.42/5.14 thf(f2704,plain,(
% 27.42/5.14 ( ! [X0 : set_variable,X1 : trm] : ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (some_fml @ (sK166 @ sigma @ p @ X0)))) @ va)) | (none_fml = (uSubst516392804stappf @ sigma @ X0 @ (pred @ p @ X1)))) ) | (spl270_2 | spl270_4)),
% 27.42/5.14 inference(subsumption_resolution,[status(thm)],[f2688,f2386])).
% 27.42/5.14 thf(f2688,plain,(
% 27.42/5.14 ( ! [X0 : set_variable,X1 : trm] : ((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (some_fml @ (sK166 @ sigma @ p @ X0)))) @ va)) | (none_fml = (uSubst516392804stappf @ sigma @ X0 @ (pred @ p @ X1))) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) ) | spl270_2),
% 27.42/5.14 inference(superposition,[status(thm)],[f2376,f2025])).
% 27.42/5.14 thf(f2025,plain,(
% 27.42/5.14 ( ! [X2 : char,X3 : produc1418842292n_game,X0 : set_variable,X1 : trm] : (((some_fml @ (sK166 @ X3 @ X2 @ X0)) = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2)) | (none_fml = (uSubst516392804stappf @ X3 @ X0 @ (pred @ X2 @ X1))) | (none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ X3 @ X2))) )),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f1418])).
% 27.42/5.14 thf(f2376,plain,(
% 27.42/5.14 (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) | spl270_2),
% 27.42/5.14 inference(avatar_component_clause,[status(thm)],[f2375])).
% 27.42/5.14 thf(f2409,plain,(
% 27.42/5.14 ~spl270_4),
% 27.42/5.14 inference(avatar_split_clause,[status(thm)],[f1873,f2385])).
% 27.42/5.14 thf(f1873,plain,(
% 27.42/5.14 (none_fml != (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f862])).
% 27.42/5.14 thf(f862,plain,(
% 27.42/5.14 (none_fml != (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 27.42/5.14 inference(flattening,[status(thm)],[f528])).
% 27.42/5.14 thf(f528,plain,(
% 27.42/5.14 ~(none_fml = (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))),
% 27.42/5.14 inference(fool_elimination,[status(thm)],[f527])).
% 27.42/5.14 thf(f527,plain,(
% 27.42/5.14 ~((produc1250175341on_fml @ (^[X0 : char > option_trm] : (produc1615133358on_fml @ (^[X1 : char > option_trm] : (produc1420172399on_fml @ (^[X2 : char > option_fml, X3 : char > option_game] : (X2)))))) @ sigma @ p) = none_fml)),
% 27.42/5.14 inference(rectify,[status(thm)],[f359])).
% 27.42/5.14 thf(f359,negated_conjecture,(
% 27.42/5.14 ~((produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ sigma @ p) = none_fml)),
% 27.42/5.14 inference(negated_conjecture,[status(cth)],[f358])).
% 27.42/5.14 thf(f358,conjecture,(
% 27.42/5.14 ((produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ sigma @ p) = none_fml)),
% 27.42/5.14 file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',conj_0)).
% 27.42/5.14 thf(f2401,plain,(
% 27.42/5.14 ~spl270_2),
% 27.42/5.14 inference(avatar_split_clause,[status(thm)],[f1936,f2375])).
% 27.42/5.14 thf(f1936,plain,(
% 27.42/5.14 (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 27.42/5.14 inference(cnf_transformation,[status(thm)],[f957])).
% 27.42/5.14 thf(f957,plain,(
% 27.42/5.14 (none_fml != (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))) & (bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va))),
% 27.42/5.14 inference(ennf_transformation,[status(thm)],[f771])).
% 27.42/5.14 thf(f771,plain,(
% 27.42/5.14 ~((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p))) @ va)) => (none_fml = (uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[Y0 : char > option_trm]: (produc1615133358on_fml @ (^[Y1 : char > option_trm]: (produc1420172399on_fml @ (^[Y2 : char > option_fml]: ((^[Y3 : char > option_game]: (Y2)))))))) @ sigma @ p)))))),
% 27.42/5.14 inference(fool_elimination,[status(thm)],[f770])).
% 27.42/5.14 thf(f770,plain,(
% 27.42/5.14 ~((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X0 : char > option_trm] : (produc1615133358on_fml @ (^[X1 : char > option_trm] : (produc1420172399on_fml @ (^[X2 : char > option_fml, X3 : char > option_game] : (X2)))))) @ sigma @ p))) @ va)) => ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X4 : char > option_trm] : (produc1615133358on_fml @ (^[X5 : char > option_trm] : (produc1420172399on_fml @ (^[X6 : char > option_fml, X7 : char > option_game] : (X6)))))) @ sigma @ p))) = none_fml))),
% 27.42/5.14 inference(rectify,[status(thm)],[f9])).
% 27.42/5.14 thf(f9,axiom,(
% 27.42/5.14 ~((bot_bot_set_variable != (inf_inf_set_variable @ (static_FVF @ (the_fml @ (produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ sigma @ p))) @ va)) => ((uSubst516392804stappf @ (uSubst1408967625substt @ (the_trm @ (uSubst516392818stappt @ sigma @ va @ theta))) @ bot_bot_set_variable @ (the_fml @ (produc1250175341on_fml @ (^[X8 : char > option_trm] : (produc1615133358on_fml @ (^[X9 : char > option_trm] : (produc1420172399on_fml @ (^[X10 : char > option_fml, X11 : char > option_game] : (X10)))))) @ sigma @ p))) = none_fml))),
% 27.42/5.14 file('/export/starexec/sandbox/tmp/tmp.MuaRRzv9n2/DTF2THF_16880.p',fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062)).
% 27.42/5.14 % SZS output end Proof for DTF2THF_16880
% 27.42/5.14 % (17330)------------------------------
% 27.42/5.14 % (17330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.14 % (17330)Termination reason: Refutation
% 27.42/5.14
% 27.42/5.14 % (17330)Memory used [KB]: 12920
% 27.42/5.14 % (17330)Time elapsed: 2.009 s
% 27.42/5.14 % (17330)Instructions burned: 6428 (million)
% 27.42/5.14 % (17330)------------------------------
% 27.42/5.14 % (17330)------------------------------
% 27.42/5.14 % (17208)Success in time 3.538 s
%------------------------------------------------------------------------------