%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP181^1 : 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:12 AM UTC 2026
% Result : Theorem 3.00s 1.93s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 102 ( 21 ~; 8 |; 0 &; 70 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 36 ( 35 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 411 ( 408 usr; 13 con; 0-5 aty)
% Number of variables : 37 ( 10 ^; 27 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
name: $tType ).
thf(type_def_6,type,
pi: $tType ).
thf(type_def_8,type,
late_freeRes: $tType ).
thf(type_def_9,type,
late_subject: $tType ).
thf(type_def_10,type,
late_residual: $tType ).
thf(type_def_11,type,
noption_name: $tType ).
thf(type_def_12,type,
noption_pi: $tType ).
thf(type_def_13,type,
noption_Late_freeRes: $tType ).
thf(type_def_14,type,
produc1141751126_pi_pi: $tType ).
thf(type_def_15,type,
noptio1575811931_pi_pi: $tType ).
thf(type_def_16,type,
produc1462499409ion_pi: $tType ).
thf(type_def_17,type,
produc405342261i_name: $tType ).
thf(type_def_18,type,
produc629157763_pi_pi: $tType ).
thf(type_def_19,type,
produc1834551554reeRes: $tType ).
thf(type_def_20,type,
produc1443308494i_name: $tType ).
thf(type_def_21,type,
produc1559976732_pi_pi: $tType ).
thf(type_def_22,type,
produc1961110975reeRes: $tType ).
thf(type_def_23,type,
produc53907987_pi_pi: $tType ).
thf(type_def_24,type,
produc367475239e_name: $tType ).
thf(type_def_25,type,
product_prod_name_pi: $tType ).
thf(type_def_26,type,
produc2008547984reeRes: $tType ).
thf(type_def_27,type,
product_prod_pi_name: $tType ).
thf(type_def_28,type,
product_prod_pi_pi: $tType ).
thf(type_def_29,type,
produc649380958reeRes: $tType ).
thf(type_def_30,type,
produc2052722628s_name: $tType ).
thf(type_def_31,type,
produc992857746Res_pi: $tType ).
thf(type_def_32,type,
produc1357834675reeRes: $tType ).
thf(type_def_33,type,
set_Pr1569510577ion_pi: $tType ).
thf(type_def_34,type,
set_Pr1294453099i_name: $tType ).
thf(type_def_35,type,
set_Pr1694908217_pi_pi: $tType ).
thf(type_def_36,type,
set_Pr305743074reeRes: $tType ).
thf(type_def_37,type,
set_Pr100209225_pi_pi: $tType ).
thf(type_def_38,type,
set_Pr1654044726_pi_pi: $tType ).
thf(type_def_39,type,
set_Pr1834926343_pi_pi: $tType ).
thf(type_def_40,type,
produc1217648014ion_pi: $tType ).
thf(func_def_0,type,
produc1217648014ion_pi: $tType ).
thf(func_def_1,type,
produc1961110975reeRes: $tType ).
thf(func_def_2,type,
set_Pr100209225_pi_pi: $tType ).
thf(func_def_3,type,
produc1443308494i_name: $tType ).
thf(func_def_4,type,
produc1559976732_pi_pi: $tType ).
thf(func_def_5,type,
produc53907987_pi_pi: $tType ).
thf(func_def_6,type,
set_Pr1569510577ion_pi: $tType ).
thf(func_def_7,type,
produc1462499409ion_pi: $tType ).
thf(func_def_8,type,
set_Pr305743074reeRes: $tType ).
thf(func_def_9,type,
noptio1575811931_pi_pi: $tType ).
thf(func_def_10,type,
set_Pr1294453099i_name: $tType ).
thf(func_def_11,type,
produc1834551554reeRes: $tType ).
thf(func_def_12,type,
set_Pr1694908217_pi_pi: $tType ).
thf(func_def_13,type,
set_Pr1654044726_pi_pi: $tType ).
thf(func_def_14,type,
produc405342261i_name: $tType ).
thf(func_def_15,type,
produc629157763_pi_pi: $tType ).
thf(func_def_16,type,
produc1141751126_pi_pi: $tType ).
thf(func_def_17,type,
produc1357834675reeRes: $tType ).
thf(func_def_18,type,
produc2052722628s_name: $tType ).
thf(func_def_19,type,
produc2008547984reeRes: $tType ).
thf(func_def_20,type,
produc992857746Res_pi: $tType ).
thf(func_def_21,type,
produc649380958reeRes: $tType ).
thf(func_def_22,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_23,type,
produc367475239e_name: $tType ).
thf(func_def_24,type,
product_prod_pi_name: $tType ).
thf(func_def_25,type,
product_prod_name_pi: $tType ).
thf(func_def_26,type,
product_prod_pi_pi: $tType ).
thf(func_def_27,type,
noption_Late_freeRes: $tType ).
thf(func_def_28,type,
noption_name: $tType ).
thf(func_def_29,type,
noption_pi: $tType ).
thf(func_def_30,type,
late_residual: $tType ).
thf(func_def_31,type,
late_subject: $tType ).
thf(func_def_32,type,
late_freeRes: $tType ).
thf(func_def_33,type,
name: $tType ).
thf(func_def_34,type,
pi: $tType ).
thf(func_def_35,type,
input: name > name > pi > pi ).
thf(func_def_36,type,
mismatch: name > name > pi > pi ).
thf(func_def_37,type,
output: name > name > pi > pi ).
thf(func_def_38,type,
par: pi > pi > pi ).
thf(func_def_39,type,
piNil: pi ).
thf(func_def_40,type,
res: name > pi > pi ).
thf(func_def_41,type,
sum: pi > pi > pi ).
thf(func_def_42,type,
tau: pi > pi ).
thf(func_def_43,type,
subs: pi > name > name > pi ).
thf(func_def_44,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_45,type,
late_TauR: late_freeRes ).
thf(func_def_46,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_47,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_48,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_49,type,
late_InputS: name > late_subject ).
thf(func_def_50,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_51,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(func_def_52,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_53,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(func_def_54,type,
abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi ).
thf(func_def_55,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(func_def_56,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_57,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(func_def_58,type,
fresh_2065563522_pi_pi: name > ( name > noptio1575811931_pi_pi ) > $o ).
thf(func_def_59,type,
fresh_name_name: name > name > $o ).
thf(func_def_60,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_61,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_62,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_63,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_64,type,
fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
thf(func_def_65,type,
fresh_453496559i_name: name > produc405342261i_name > $o ).
thf(func_def_66,type,
fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
thf(func_def_67,type,
fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
thf(func_def_68,type,
fresh_1513292180i_name: name > produc1443308494i_name > $o ).
thf(func_def_69,type,
fresh_1335311330_pi_pi: name > produc1559976732_pi_pi > $o ).
thf(func_def_70,type,
fresh_1729533561reeRes: name > produc1961110975reeRes > $o ).
thf(func_def_71,type,
fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o ).
thf(func_def_72,type,
fresh_441084397e_name: name > produc367475239e_name > $o ).
thf(func_def_73,type,
fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
thf(func_def_74,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(func_def_75,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(func_def_76,type,
fresh_261416607i_name: name > product_prod_pi_name > $o ).
thf(func_def_77,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(func_def_78,type,
fresh_1504024600reeRes: name > produc649380958reeRes > $o ).
thf(func_def_79,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(func_def_80,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(func_def_81,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(func_def_82,type,
ord_le1032043601ion_pi: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > $o ).
thf(func_def_83,type,
ord_le2082425291i_name: set_Pr1294453099i_name > set_Pr1294453099i_name > $o ).
thf(func_def_84,type,
ord_le1854926745_pi_pi: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > $o ).
thf(func_def_85,type,
ord_le1762471042reeRes: set_Pr305743074reeRes > set_Pr305743074reeRes > $o ).
thf(func_def_86,type,
ord_le211833513_pi_pi: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > $o ).
thf(func_def_87,type,
ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(func_def_88,type,
ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_89,type,
produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
thf(func_def_90,type,
produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
thf(func_def_91,type,
produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
thf(func_def_92,type,
produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
thf(func_def_93,type,
produc674047040ion_pi: ( name > noption_pi ) > produc1462499409ion_pi > produc1217648014ion_pi ).
thf(func_def_94,type,
produc1024533510i_name: ( name > noption_pi ) > produc405342261i_name > produc1443308494i_name ).
thf(func_def_95,type,
produc1189045204_pi_pi: ( name > noption_pi ) > produc629157763_pi_pi > produc1559976732_pi_pi ).
thf(func_def_96,type,
produc703114481reeRes: ( name > noption_pi ) > produc1834551554reeRes > produc1961110975reeRes ).
thf(func_def_97,type,
produc1275980869_pi_pi: ( name > noption_pi ) > produc1141751126_pi_pi > produc53907987_pi_pi ).
thf(func_def_98,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(func_def_99,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(func_def_100,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(func_def_101,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(func_def_102,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
thf(func_def_103,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(func_def_104,type,
produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes ).
thf(func_def_105,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(func_def_106,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(func_def_107,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(func_def_108,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(func_def_109,type,
id_name_noption_pi: set_Pr1569510577ion_pi ).
thf(func_def_110,type,
id_pi: set_Pr1834926343_pi_pi ).
thf(func_def_111,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(func_def_112,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(func_def_113,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(func_def_114,type,
member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
thf(func_def_115,type,
member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
thf(func_def_116,type,
member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
thf(func_def_117,type,
member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
thf(func_def_118,type,
member695660714_pi_pi: produc53907987_pi_pi > set_Pr100209225_pi_pi > $o ).
thf(func_def_119,type,
member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
thf(func_def_120,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_121,type,
p: pi ).
thf(func_def_122,type,
pq: pi ).
thf(func_def_123,type,
q: pi ).
thf(func_def_124,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_125,type,
a: late_subject ).
thf(func_def_126,type,
x: name ).
thf(func_def_127,type,
y: name ).
thf(func_def_146,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_147,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_148,type,
sP2: late_subject > name > pi > pi > pi > $o ).
thf(func_def_149,type,
sP3: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > $o ).
thf(func_def_150,type,
sP4: late_residual > name > pi > $o ).
thf(func_def_151,type,
sP5: name > pi > late_residual > $o ).
thf(func_def_152,type,
sP6: pi > set_Pr1834926343_pi_pi > name > pi > $o ).
thf(func_def_153,type,
sP7: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > $o ).
thf(func_def_154,type,
sP8: pi > set_Pr1834926343_pi_pi > pi > name > $o ).
thf(func_def_155,type,
sP9: name > pi > late_subject > name > pi > $o ).
thf(func_def_156,type,
sP10: pi > set_Pr1834926343_pi_pi > pi > pi > $o ).
thf(func_def_157,type,
sP11: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > $o ).
thf(func_def_158,type,
sP12: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > $o ).
thf(func_def_159,type,
sP13: name > set_Pr1834926343_pi_pi > pi > pi > $o ).
thf(func_def_160,type,
sP14: set_Pr1834926343_pi_pi > pi > pi > name > name > $o ).
thf(func_def_161,type,
sP15: pi > pi > set_Pr1834926343_pi_pi > name > $o ).
thf(func_def_162,type,
sP16: pi > set_Pr1834926343_pi_pi > pi > pi > name > $o ).
thf(func_def_163,type,
sP17: pi > set_Pr1834926343_pi_pi > pi > name > $o ).
thf(func_def_164,type,
sK18: ( produc1443308494i_name > $o ) > produc405342261i_name ).
thf(func_def_165,type,
sK19: ( produc1443308494i_name > $o ) > name > noption_pi ).
thf(func_def_166,type,
sK20: ( pi > late_residual > $o ) > pi ).
thf(func_def_167,type,
sK21: ( pi > late_residual > $o ) > pi ).
thf(func_def_168,type,
sK22: ( pi > late_residual > $o ) > late_freeRes ).
thf(func_def_169,type,
sK23: ( pi > late_residual > $o ) > late_subject ).
thf(func_def_170,type,
sK24: ( pi > late_residual > $o ) > name ).
thf(func_def_171,type,
sK25: ( pi > late_residual > $o ) > pi ).
thf(func_def_172,type,
sK26: ( pi > late_residual > $o ) > pi ).
thf(func_def_173,type,
sK27: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_174,type,
sK28: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_175,type,
sK29: product_prod_pi_pi > pi ).
thf(func_def_176,type,
sK30: product_prod_pi_pi > pi ).
thf(func_def_177,type,
sK31: product_prod_pi_pi > pi ).
thf(func_def_178,type,
sK32: ( produc1961110975reeRes > $o ) > name > noption_pi ).
thf(func_def_179,type,
sK33: ( produc1961110975reeRes > $o ) > produc1834551554reeRes ).
thf(func_def_180,type,
sK34: name > name ).
thf(func_def_181,type,
sK35: product_prod_pi_pi > pi ).
thf(func_def_182,type,
sK36: product_prod_pi_pi > pi ).
thf(func_def_183,type,
sK37: produc1462499409ion_pi > name > noption_pi ).
thf(func_def_184,type,
sK38: ( produc1141751126_pi_pi > late_residual > $o ) > produc1141751126_pi_pi ).
thf(func_def_185,type,
sK39: ( produc1141751126_pi_pi > late_residual > $o ) > late_subject ).
thf(func_def_186,type,
sK40: ( produc1141751126_pi_pi > late_residual > $o ) > pi ).
thf(func_def_187,type,
sK41: ( produc1141751126_pi_pi > late_residual > $o ) > name ).
thf(func_def_188,type,
sK42: ( produc1141751126_pi_pi > late_residual > $o ) > late_freeRes ).
thf(func_def_189,type,
sK43: ( produc1141751126_pi_pi > late_residual > $o ) > produc1141751126_pi_pi ).
thf(func_def_190,type,
sK44: ( produc1141751126_pi_pi > late_residual > $o ) > pi ).
thf(func_def_191,type,
sK45: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > product_prod_pi_pi ).
thf(func_def_192,type,
sK46: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_193,type,
sK47: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_194,type,
sK48: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_195,type,
sK49: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_196,type,
sK50: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_197,type,
sK51: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_198,type,
sK52: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_199,type,
sK53: produc1961110975reeRes > produc1834551554reeRes ).
thf(func_def_200,type,
sK54: produc1961110975reeRes > name > noption_pi ).
thf(func_def_201,type,
sK55: produc405342261i_name > name > noption_pi ).
thf(func_def_202,type,
sK56: produc405342261i_name > name ).
thf(func_def_203,type,
sK57: ( produc53907987_pi_pi > $o ) > product_prod_pi_pi ).
thf(func_def_204,type,
sK58: ( produc53907987_pi_pi > $o ) > name ).
thf(func_def_205,type,
sK59: ( produc53907987_pi_pi > $o ) > name > noption_pi ).
thf(func_def_206,type,
sK60: pi > pi > late_freeRes > set_Pr1834926343_pi_pi > pi ).
thf(func_def_207,type,
sK61: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_208,type,
sK62: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_209,type,
sK63: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_210,type,
sK64: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_211,type,
sK65: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_212,type,
sK66: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_213,type,
sK67: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_214,type,
sK68: produc629157763_pi_pi > name > noption_pi ).
thf(func_def_215,type,
sK69: produc629157763_pi_pi > pi ).
thf(func_def_216,type,
sK70: ( produc1141751126_pi_pi > late_residual > $o ) > produc1141751126_pi_pi ).
thf(func_def_217,type,
sK71: ( produc1141751126_pi_pi > late_residual > $o ) > late_subject ).
thf(func_def_218,type,
sK72: ( produc1141751126_pi_pi > late_residual > $o ) > name ).
thf(func_def_219,type,
sK73: ( produc1141751126_pi_pi > late_residual > $o ) > pi ).
thf(func_def_220,type,
sK74: ( produc1141751126_pi_pi > late_residual > $o ) > pi ).
thf(func_def_221,type,
sK75: ( produc1141751126_pi_pi > late_residual > $o ) > produc1141751126_pi_pi ).
thf(func_def_222,type,
sK76: ( produc1141751126_pi_pi > late_residual > $o ) > late_freeRes ).
thf(func_def_223,type,
sK77: produc53907987_pi_pi > name > noption_pi ).
thf(func_def_224,type,
sK78: produc53907987_pi_pi > produc1141751126_pi_pi ).
thf(func_def_225,type,
sK79: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_226,type,
sK80: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_227,type,
sK81: produc1141751126_pi_pi > name ).
thf(func_def_228,type,
sK82: produc1141751126_pi_pi > pi ).
thf(func_def_229,type,
sK83: produc1141751126_pi_pi > pi ).
thf(func_def_230,type,
sK84: late_subject > name > pi > pi > pi > pi ).
thf(func_def_231,type,
sK85: late_subject > name > pi > pi > pi > pi ).
thf(func_def_232,type,
sK86: late_subject > name > pi > pi > pi > late_subject ).
thf(func_def_233,type,
sK87: late_subject > name > pi > pi > pi > name ).
thf(func_def_234,type,
sK88: late_subject > name > pi > pi > pi > pi ).
thf(func_def_235,type,
sK89: pi > pi > name > pi > late_subject > late_subject ).
thf(func_def_236,type,
sK90: pi > pi > name > pi > late_subject > pi ).
thf(func_def_237,type,
sK91: pi > pi > name > pi > late_subject > pi ).
thf(func_def_238,type,
sK92: pi > pi > name > pi > late_subject > pi ).
thf(func_def_239,type,
sK93: pi > pi > name > pi > late_subject > name ).
thf(func_def_240,type,
sK94: pi > late_residual > name > name > pi ).
thf(func_def_241,type,
sK95: pi > late_residual > name > name > name ).
thf(func_def_242,type,
sK96: pi > late_residual > name > name > name ).
thf(func_def_243,type,
sK97: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > name ).
thf(func_def_244,type,
sK98: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > pi ).
thf(func_def_245,type,
sK99: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > late_subject ).
thf(func_def_246,type,
sK100: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_247,type,
sK101: pi > pi > set_Pr1834926343_pi_pi > late_freeRes ).
thf(func_def_248,type,
sK102: ( produc53907987_pi_pi > $o ) > produc1141751126_pi_pi ).
thf(func_def_249,type,
sK103: ( produc53907987_pi_pi > $o ) > name > noption_pi ).
thf(func_def_250,type,
sK104: ( produc1834551554reeRes > $o ) > name > noption_pi ).
thf(func_def_251,type,
sK105: ( produc1834551554reeRes > $o ) > late_freeRes ).
thf(func_def_252,type,
sK106: ( late_residual > $o ) > pi ).
thf(func_def_253,type,
sK107: ( late_residual > $o ) > late_freeRes ).
thf(func_def_254,type,
sK108: ( late_residual > $o ) > pi ).
thf(func_def_255,type,
sK109: ( late_residual > $o ) > late_subject ).
thf(func_def_256,type,
sK110: ( late_residual > $o ) > name ).
thf(func_def_257,type,
sK111: name > pi > late_residual > name ).
thf(func_def_258,type,
sK112: name > pi > late_residual > pi ).
thf(func_def_259,type,
sK113: name > pi > late_residual > name ).
thf(func_def_260,type,
sK114: name > pi > late_residual > pi ).
thf(func_def_261,type,
sK115: late_residual > name > pi > name ).
thf(func_def_262,type,
sK116: late_residual > name > pi > late_subject ).
thf(func_def_263,type,
sK117: late_residual > name > pi > pi ).
thf(func_def_264,type,
sK118: late_residual > name > pi > name ).
thf(func_def_265,type,
sK119: late_residual > name > pi > pi ).
thf(func_def_266,type,
sK120: pi > late_residual > name > pi ).
thf(func_def_267,type,
sK121: pi > late_residual > name > pi ).
thf(func_def_268,type,
sK122: pi > late_residual > name > name ).
thf(func_def_269,type,
sK123: pi > late_residual > name > late_freeRes ).
thf(func_def_270,type,
sK124: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_271,type,
sK125: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_272,type,
sK126: ( produc1141751126_pi_pi > $o ) > name ).
thf(func_def_273,type,
sK127: ( produc1141751126_pi_pi > $o ) > product_prod_pi_pi ).
thf(func_def_274,type,
sK128: produc1834551554reeRes > name > noption_pi ).
thf(func_def_275,type,
sK129: produc1834551554reeRes > late_freeRes ).
thf(func_def_276,type,
sK130: late_subject > name ).
thf(func_def_277,type,
sK131: late_subject > name ).
thf(func_def_278,type,
sK132: pi > set_Pr1834926343_pi_pi > name > pi > name ).
thf(func_def_279,type,
sK133: pi > set_Pr1834926343_pi_pi > name > pi > late_subject ).
thf(func_def_280,type,
sK134: pi > set_Pr1834926343_pi_pi > name > pi > pi ).
thf(func_def_281,type,
sK135: pi > set_Pr1834926343_pi_pi > pi > pi ).
thf(func_def_282,type,
sK136: pi > set_Pr1834926343_pi_pi > pi > late_freeRes ).
thf(func_def_283,type,
sK137: produc1834551554reeRes > name > noption_pi ).
thf(func_def_284,type,
sK138: produc1834551554reeRes > late_freeRes ).
thf(func_def_285,type,
sK139: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > product_prod_pi_pi ).
thf(func_def_286,type,
sK140: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > name ).
thf(func_def_287,type,
sK141: produc1141751126_pi_pi > product_prod_pi_pi ).
thf(func_def_288,type,
sK142: produc1141751126_pi_pi > name ).
thf(func_def_289,type,
sK143: produc629157763_pi_pi > pi ).
thf(func_def_290,type,
sK144: produc629157763_pi_pi > name > noption_pi ).
thf(func_def_291,type,
sK145: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_292,type,
sK146: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_293,type,
sK147: pi > set_Pr1834926343_pi_pi > pi > name > pi ).
thf(func_def_294,type,
sK148: pi > set_Pr1834926343_pi_pi > pi > name > late_freeRes ).
thf(func_def_295,type,
sK149: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > late_subject ).
thf(func_def_296,type,
sK150: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > pi ).
thf(func_def_297,type,
sK151: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > name ).
thf(func_def_298,type,
sK152: set_Pr1834926343_pi_pi > pi > pi > name > pi ).
thf(func_def_299,type,
sK153: set_Pr1834926343_pi_pi > pi > pi > name > name ).
thf(func_def_300,type,
sK154: ( product_prod_pi_pi > $o ) > ( product_prod_pi_pi > $o ) > product_prod_pi_pi ).
thf(func_def_301,type,
sK155: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > name > noption_pi ).
thf(func_def_302,type,
sK156: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > name > noption_pi ).
thf(func_def_303,type,
sK157: produc53907987_pi_pi > name > noption_pi ).
thf(func_def_304,type,
sK158: produc53907987_pi_pi > name ).
thf(func_def_305,type,
sK159: produc53907987_pi_pi > pi ).
thf(func_def_306,type,
sK160: produc53907987_pi_pi > pi ).
thf(func_def_307,type,
sK161: set_Pr305743074reeRes > set_Pr305743074reeRes > late_freeRes ).
thf(func_def_308,type,
sK162: set_Pr305743074reeRes > set_Pr305743074reeRes > name > noption_pi ).
thf(func_def_309,type,
sK163: ( produc1462499409ion_pi > $o ) > name > noption_pi ).
thf(func_def_310,type,
sK164: ( produc1462499409ion_pi > $o ) > name > noption_pi ).
thf(func_def_311,type,
sK165: produc1462499409ion_pi > name > noption_pi ).
thf(func_def_312,type,
sK166: produc1462499409ion_pi > name > noption_pi ).
thf(func_def_313,type,
sK167: ( late_freeRes > $o ) > name ).
thf(func_def_314,type,
sK168: ( late_freeRes > $o ) > name ).
thf(func_def_315,type,
sK169: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_316,type,
sK170: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_317,type,
sK171: name > pi > late_subject > name > pi > name ).
thf(func_def_318,type,
sK172: name > pi > late_subject > name > pi > pi ).
thf(func_def_319,type,
sK173: name > pi > late_subject > name > pi > name ).
thf(func_def_320,type,
sK174: name > pi > late_subject > name > pi > late_subject ).
thf(func_def_321,type,
sK175: name > pi > late_subject > name > pi > pi ).
thf(func_def_322,type,
sK176: name > late_subject > name > pi > pi > name ).
thf(func_def_323,type,
sK177: name > late_subject > name > pi > pi > pi ).
thf(func_def_324,type,
sK178: name > late_subject > name > pi > pi > name ).
thf(func_def_325,type,
sK179: name > late_subject > name > pi > pi > pi ).
thf(func_def_326,type,
sK180: pi > late_freeRes > name > ( pi > $o ) > pi ).
thf(func_def_327,type,
sK181: name > late_freeRes > pi > pi > name ).
thf(func_def_328,type,
sK182: name > late_freeRes > pi > pi > pi ).
thf(func_def_329,type,
sK183: name > late_freeRes > pi > pi > late_freeRes ).
thf(func_def_330,type,
sK184: name > late_freeRes > pi > pi > pi ).
thf(func_def_331,type,
sK185: pi > name ).
thf(func_def_332,type,
sK186: produc405342261i_name > name ).
thf(func_def_333,type,
sK187: produc405342261i_name > name > noption_pi ).
thf(func_def_334,type,
sK188: late_freeRes > name ).
thf(func_def_335,type,
sK189: ( produc1559976732_pi_pi > $o ) > name > noption_pi ).
thf(func_def_336,type,
sK190: ( produc1559976732_pi_pi > $o ) > produc629157763_pi_pi ).
thf(func_def_337,type,
sK191: ( name > late_residual > $o ) > name ).
thf(func_def_338,type,
sK192: ( name > late_residual > $o ) > late_subject ).
thf(func_def_339,type,
sK193: ( name > late_residual > $o ) > name ).
thf(func_def_340,type,
sK194: ( name > late_residual > $o ) > pi ).
thf(func_def_341,type,
sK195: ( name > late_residual > $o ) > pi ).
thf(func_def_342,type,
sK196: ( name > late_residual > $o ) > late_freeRes ).
thf(func_def_343,type,
sK197: ( name > late_residual > $o ) > name ).
thf(func_def_344,type,
sK198: ( late_subject > $o ) > name ).
thf(func_def_345,type,
sK199: ( late_subject > $o ) > name ).
thf(func_def_346,type,
sK200: pi > late_residual > pi ).
thf(func_def_347,type,
sK201: ( produc1141751126_pi_pi > $o ) > pi ).
thf(func_def_348,type,
sK202: ( produc1141751126_pi_pi > $o ) > pi ).
thf(func_def_349,type,
sK203: ( produc1141751126_pi_pi > $o ) > name ).
thf(func_def_350,type,
sK204: pi > set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(func_def_351,type,
sK205: pi > set_Pr1834926343_pi_pi > pi > pi > late_subject ).
thf(func_def_352,type,
sK206: pi > set_Pr1834926343_pi_pi > pi > pi > name ).
thf(func_def_353,type,
sK207: pi > set_Pr1834926343_pi_pi > pi > pi ).
thf(func_def_354,type,
sK208: pi > set_Pr1834926343_pi_pi > pi > late_freeRes ).
thf(func_def_355,type,
sK209: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > produc1141751126_pi_pi ).
thf(func_def_356,type,
sK210: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > name > noption_pi ).
thf(func_def_357,type,
sK211: produc1217648014ion_pi > name > noption_pi ).
thf(func_def_358,type,
sK212: produc1217648014ion_pi > produc1462499409ion_pi ).
thf(func_def_359,type,
sK213: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_360,type,
sK214: ( set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ) > set_Pr1834926343_pi_pi ).
thf(func_def_361,type,
sK215: ( produc1961110975reeRes > $o ) > name > noption_pi ).
thf(func_def_362,type,
sK216: ( produc1961110975reeRes > $o ) > produc1834551554reeRes ).
thf(func_def_363,type,
sK217: ( produc405342261i_name > $o ) > name ).
thf(func_def_364,type,
sK218: ( produc405342261i_name > $o ) > name > noption_pi ).
thf(func_def_365,type,
sK219: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_366,type,
sK220: ( product_prod_pi_pi > $o ) > pi ).
thf(func_def_367,type,
sK221: ( produc629157763_pi_pi > $o ) > name > noption_pi ).
thf(func_def_368,type,
sK222: ( produc629157763_pi_pi > $o ) > pi ).
thf(func_def_369,type,
sK223: produc1141751126_pi_pi > product_prod_pi_pi ).
thf(func_def_370,type,
sK224: produc1141751126_pi_pi > name ).
thf(func_def_371,type,
sK225: ( pi > late_residual > $o ) > name ).
thf(func_def_372,type,
sK226: ( pi > late_residual > $o ) > pi ).
thf(func_def_373,type,
sK227: ( pi > late_residual > $o ) > late_subject ).
thf(func_def_374,type,
sK228: ( pi > late_residual > $o ) > pi ).
thf(func_def_375,type,
sK229: ( pi > late_residual > $o ) > late_freeRes ).
thf(func_def_376,type,
sK230: ( pi > late_residual > $o ) > pi ).
thf(func_def_377,type,
sK231: ( pi > late_residual > $o ) > pi ).
thf(func_def_378,type,
sK232: ( produc405342261i_name > $o ) > name ).
thf(func_def_379,type,
sK233: ( produc405342261i_name > $o ) > name > noption_pi ).
thf(func_def_380,type,
sK234: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > pi ).
thf(func_def_381,type,
sK235: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > name ).
thf(func_def_382,type,
sK236: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > late_subject ).
thf(func_def_383,type,
sK237: set_Pr1834926343_pi_pi > pi > pi > late_freeRes ).
thf(func_def_384,type,
sK238: set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(func_def_385,type,
sK239: ( name > late_residual > $o ) > name ).
thf(func_def_386,type,
sK240: ( name > late_residual > $o ) > pi ).
thf(func_def_387,type,
sK241: ( name > late_residual > $o ) > late_subject ).
thf(func_def_388,type,
sK242: ( name > late_residual > $o ) > name ).
thf(func_def_389,type,
sK243: ( name > late_residual > $o ) > late_freeRes ).
thf(func_def_390,type,
sK244: ( name > late_residual > $o ) > pi ).
thf(func_def_391,type,
sK245: ( name > late_residual > $o ) > name ).
thf(func_def_392,type,
sK246: ( produc53907987_pi_pi > $o ) > name > noption_pi ).
thf(func_def_393,type,
sK247: ( produc53907987_pi_pi > $o ) > produc1141751126_pi_pi ).
thf(func_def_394,type,
sK248: pi > name > late_residual > name > name ).
thf(func_def_395,type,
sK249: pi > name > late_residual > name > name ).
thf(func_def_396,type,
sK250: pi > name > late_residual > name > pi ).
thf(func_def_397,type,
sK251: late_freeRes > name ).
thf(func_def_398,type,
sK252: late_freeRes > name ).
thf(func_def_399,type,
sK253: produc53907987_pi_pi > name > noption_pi ).
thf(func_def_400,type,
sK254: produc53907987_pi_pi > name ).
thf(func_def_401,type,
sK255: produc53907987_pi_pi > product_prod_pi_pi ).
thf(func_def_402,type,
sK256: pi > pi > set_Pr1834926343_pi_pi > name ).
thf(func_def_403,type,
sK257: pi > pi > set_Pr1834926343_pi_pi > late_subject ).
thf(func_def_404,type,
sK258: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_405,type,
sK259: pi > pi > set_Pr1834926343_pi_pi > late_freeRes ).
thf(func_def_406,type,
sK260: pi > pi > set_Pr1834926343_pi_pi > pi ).
thf(func_def_407,type,
sK261: produc1462499409ion_pi > name > noption_pi ).
thf(func_def_408,type,
sK262: produc1462499409ion_pi > name > noption_pi ).
thf(func_def_409,type,
sK263: ( produc1834551554reeRes > $o ) > late_freeRes ).
thf(func_def_410,type,
sK264: ( produc1834551554reeRes > $o ) > name > noption_pi ).
thf(func_def_411,type,
sK265: ( produc1559976732_pi_pi > $o ) > name > noption_pi ).
thf(func_def_412,type,
sK266: ( produc1559976732_pi_pi > $o ) > produc629157763_pi_pi ).
thf(func_def_413,type,
sK267: ( pi > $o ) > pi > name > pi > late_subject > pi ).
thf(func_def_414,type,
sK268: ( pi > $o ) > pi > name > pi > late_subject > pi ).
thf(func_def_415,type,
sK269: produc53907987_pi_pi > produc1141751126_pi_pi ).
thf(func_def_416,type,
sK270: produc53907987_pi_pi > name > noption_pi ).
thf(func_def_417,type,
sK271: ( produc629157763_pi_pi > $o ) > pi ).
thf(func_def_418,type,
sK272: ( produc629157763_pi_pi > $o ) > name > noption_pi ).
thf(func_def_419,type,
sK273: late_subject > pi > set_Pr1834926343_pi_pi > pi > name > pi ).
thf(func_def_420,type,
sK274: ( produc1141751126_pi_pi > $o ) > product_prod_pi_pi ).
thf(func_def_421,type,
sK275: ( produc1141751126_pi_pi > $o ) > name ).
thf(func_def_422,type,
sK276: produc1141751126_pi_pi > name ).
thf(func_def_423,type,
sK277: ( produc1462499409ion_pi > $o ) > name > noption_pi ).
thf(func_def_424,type,
sK278: ( produc1462499409ion_pi > $o ) > name > noption_pi ).
thf(func_def_425,type,
sK279: name > set_Pr1834926343_pi_pi > pi > pi > late_freeRes ).
thf(func_def_426,type,
sK280: name > set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(func_def_427,type,
sK281: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > name ).
thf(func_def_428,type,
sK282: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > pi ).
thf(func_def_429,type,
sK283: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > late_subject ).
thf(func_def_430,type,
sK284: set_Pr1834926343_pi_pi > name > pi > pi > name ).
thf(func_def_431,type,
sK285: set_Pr1834926343_pi_pi > name > pi > pi > pi ).
thf(func_def_432,type,
sK286: set_Pr1294453099i_name > set_Pr1294453099i_name > name > noption_pi ).
thf(func_def_433,type,
sK287: set_Pr1294453099i_name > set_Pr1294453099i_name > name ).
thf(func_def_434,type,
sK288: ( produc53907987_pi_pi > $o ) > pi ).
thf(func_def_435,type,
sK289: ( produc53907987_pi_pi > $o ) > name > noption_pi ).
thf(func_def_436,type,
sK290: ( produc53907987_pi_pi > $o ) > name ).
thf(func_def_437,type,
sK291: ( produc53907987_pi_pi > $o ) > pi ).
thf(func_def_438,type,
sK292: produc1443308494i_name > produc405342261i_name ).
thf(func_def_439,type,
sK293: produc1443308494i_name > name > noption_pi ).
thf(func_def_440,type,
sK294: pi > pi > set_Pr1834926343_pi_pi > name > pi ).
thf(func_def_441,type,
sK295: pi > pi > set_Pr1834926343_pi_pi > name > late_freeRes ).
thf(func_def_442,type,
sK296: set_Pr1834926343_pi_pi > pi > pi > name > name > pi ).
thf(func_def_443,type,
sK297: set_Pr1834926343_pi_pi > pi > pi > name > name > name ).
thf(func_def_444,type,
sK298: set_Pr1834926343_pi_pi > pi > pi > name > name > late_subject ).
thf(func_def_445,type,
sK299: name > set_Pr1834926343_pi_pi > pi > pi > name ).
thf(func_def_446,type,
sK300: name > set_Pr1834926343_pi_pi > pi > pi > pi ).
thf(func_def_447,type,
sK301: ( produc1443308494i_name > $o ) > name > noption_pi ).
thf(func_def_448,type,
sK302: ( produc1443308494i_name > $o ) > produc405342261i_name ).
thf(func_def_449,type,
sK303: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > name > noption_pi ).
thf(func_def_450,type,
sK304: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > pi ).
thf(func_def_451,type,
sK305: produc1559976732_pi_pi > name > noption_pi ).
thf(func_def_452,type,
sK306: produc1559976732_pi_pi > produc629157763_pi_pi ).
thf(func_def_453,type,
sK307: pi > set_Pr1834926343_pi_pi > pi > name > name ).
thf(func_def_454,type,
sK308: pi > set_Pr1834926343_pi_pi > pi > name > pi ).
thf(func_def_455,type,
sK309: pi > set_Pr1834926343_pi_pi > pi > pi > name > late_subject ).
thf(func_def_456,type,
sK310: pi > set_Pr1834926343_pi_pi > pi > pi > name > pi ).
thf(func_def_457,type,
sK311: pi > set_Pr1834926343_pi_pi > pi > pi > name > name ).
thf(func_def_458,type,
sK312: set_Pr1834926343_pi_pi > pi > name > pi > pi ).
thf(func_def_459,type,
sK313: set_Pr1834926343_pi_pi > pi > name > pi > late_freeRes ).
thf(func_def_461,type,
ph315:
!>[X0: $tType] : X0 ).
thf(f2496,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2495]) ).
thf(f2495,plain,
$false = $true,
inference(duplicate_literal_removal,[status(thm)],[f2493]) ).
thf(f2493,plain,
( ( $false = $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f2453,f1064]) ).
thf(f1064,plain,
! [X1: $o] :
( ( ( ~ X1 ) = $false )
| ( $false = X1 ) ),
introduced(definition,[],[logical_not_proxy_axiom]) ).
thf(f2453,plain,
( $true = ( ~ $true ) ),
inference(superposition,[status(thm)],[f2450,f2332]) ).
thf(f2332,plain,
! [X0: $tType,X2: X0] :
( $true
= ( X2 = X2 ) ),
inference(equality_resolution,[status(thm)],[f1061]) ).
thf(f1061,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( ( X1 = X2 )
= $true )
| ( X1 != X2 ) ),
introduced(definition,[],[equality_proxy_axiom]) ).
thf(f2450,plain,
( ( x != x )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2447]) ).
thf(f2447,plain,
( ( ( x != x )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2410,f2252]) ).
thf(f2252,plain,
( ( fresh_1376661020_pi_pi @ x @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1912,f2188]) ).
thf(f2188,plain,
y = x,
inference(cnf_transformation,[status(thm)],[f1101]) ).
thf(f1101,plain,
y = x,
inference(flattening,[status(thm)],[f776]) ).
thf(f776,plain,
~ ( ( y != x ) ),
inference(fool_elimination,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( ( y != x ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
y != x,
file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',conj_0) ).
thf(f1912,plain,
( ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f830]) ).
thf(f830,plain,
( ( fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f829]) ).
thf(f829,plain,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ),
file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_1_Bound_Ohyps_I5_J) ).
thf(f2410,plain,
! [X2: name,X0: name,X1: product_prod_pi_pi] :
( ( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
!= $true )
| ( $true
= ( X2 != X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2320]) ).
thf(f2320,plain,
! [X2: name,X0: name,X1: product_prod_pi_pi] :
( ( ( ^ [Y0: name,Y1: name] : ( Y0 != Y1 )
@ X2
@ X0 )
= $true )
| ( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2177,f1688]) ).
thf(f1688,plain,
( fresh_name_name
= ( ^ [Y0: name,Y1: name] : ( Y0 != Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f465]) ).
thf(f465,plain,
( fresh_name_name
= ( ^ [Y0: name,Y1: name] : ( Y0 != Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f464]) ).
thf(f464,plain,
( ( ^ [X0: name,X1: name] : ( X0 != X1 ) )
= fresh_name_name ),
inference(rectify,[status(thm)],[f274]) ).
thf(f274,axiom,
( ( ^ [X61: name,X62: name] : ( X61 != X62 ) )
= fresh_name_name ),
file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_273_name__fresh) ).
thf(f2177,plain,
! [X2: name,X0: name,X1: product_prod_pi_pi] :
( ( ( fresh_name_name @ X2 @ X0 )
= $true )
| ( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1313]) ).
thf(f1313,plain,
! [X0: name,X1: product_prod_pi_pi,X2: name] :
( ( ( fresh_name_name @ X2 @ X0 )
= $true )
| ( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f884]) ).
thf(f884,plain,
! [X0: name,X1: product_prod_pi_pi,X2: name] :
( ( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
= $true )
=> ( ( fresh_name_name @ X2 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f883]) ).
thf(f883,plain,
! [X0: name,X1: product_prod_pi_pi,X2: name] :
( ( fresh_1376661020_pi_pi @ X2 @ ( produc235456326_pi_pi @ X0 @ X1 ) )
=> ( fresh_name_name @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f32]) ).
thf(f32,axiom,
! [X1: name,X2: product_prod_pi_pi,X0: name] :
( ( fresh_1376661020_pi_pi @ X0 @ ( produc235456326_pi_pi @ X1 @ X2 ) )
=> ( fresh_name_name @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_31_fresh__prodD_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP181^1 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n025.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:29:12 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : ITP181^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.47 % Domain : Interactive Theorem Proving
% 0.31/0.47 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_189__3410182_1
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Des21]
% 0.31/0.47 % Names : Strong_Late_Sim_SC/prob_189__3410182_1 [Des21]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.31/0.47 % Syntax : Number of formulae : 481 ( 181 unt; 128 typ; 0 def)
% 0.31/0.47 % Number of atoms : 968 ( 372 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 16 ( 2 avg)
% 0.31/0.47 % Number of connectives : 3651 ( 172 ~; 10 |; 86 &;2926 @)
% 0.31/0.47 % ( 0 <=>; 457 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 27 ( 8 avg)
% 0.31/0.47 % Number of types : 36 ( 35 usr)
% 0.31/0.47 % Number of type conns : 366 ( 366 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 94 ( 93 usr; 11 con; 0-5 aty)
% 0.31/0.47 % Number of variables : 1441 ( 26 ^;1373 !; 42 ?;1441 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:23.843
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % Could-be-implicit typings (35)
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 0.31/0.47 produc1217648014ion_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.31/0.47 produc1961110975reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J,type,
% 0.31/0.47 set_Pr100209225_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 0.31/0.47 produc1443308494i_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 0.31/0.47 produc1559976732_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.31/0.47 produc53907987_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 0.31/0.47 set_Pr1569510577ion_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.31/0.47 produc1462499409ion_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.31/0.47 set_Pr305743074reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.31/0.47 noptio1575811931_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 0.31/0.47 set_Pr1294453099i_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.31/0.47 produc1834551554reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 0.31/0.47 set_Pr1694908217_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.31/0.47 set_Pr1654044726_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.31/0.47 produc405342261i_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.31/0.47 produc629157763_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.31/0.47 produc1141751126_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.31/0.47 produc1357834675reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.31/0.47 produc2052722628s_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.31/0.47 produc2008547984reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.31/0.47 produc992857746Res_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 0.31/0.47 produc649380958reeRes: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.31/0.47 set_Pr1834926343_pi_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.31/0.47 produc367475239e_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 0.31/0.47 product_prod_pi_name: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 0.31/0.47 product_prod_name_pi: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.31/0.47 product_prod_pi_pi: $tType ).
% 0.31/0.47
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% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.31/0.47 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.31/0.47 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.31/0.47 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.31/0.47 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Relation_OId_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.31/0.47 id_name_noption_pi: set_Pr1569510577ion_pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 0.31/0.47 id_pi: set_Pr1834926343_pi_pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.31/0.47 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.31/0.47 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.31/0.47 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.31/0.47 member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.31/0.47 member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.31/0.47 member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.31/0.47 member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.31/0.47 member695660714_pi_pi: produc53907987_pi_pi > set_Pr100209225_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.31/0.47 member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.31/0.47 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_P,type,
% 0.31/0.47 p: pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_PQ____,type,
% 0.31/0.47 pq: pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_Q,type,
% 0.31/0.47 q: pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_Rel,type,
% 0.31/0.47 rel: set_Pr1834926343_pi_pi ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_a____,type,
% 0.31/0.47 a: late_subject ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_x,type,
% 0.31/0.47 x: name ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_y____,type,
% 0.31/0.47 y: name ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (352)
% 0.31/0.47 thf(fact_0_Eqvt,axiom,
% 0.31/0.47 eqvt_pi @ rel ).
% 0.31/0.47
% 0.31/0.47 % Eqvt
% 0.31/0.47 thf(fact_1_Bound_Ohyps_I5_J,axiom,
% 0.31/0.47 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.31/0.47
% 0.31/0.47 % Bound.hyps(5)
% 0.31/0.47 thf(fact_2_Bound_Ohyps_I4_J,axiom,
% 0.31/0.47 fresh_717452603ubject @ y @ a ).
% 0.31/0.47
% 0.31/0.47 % Bound.hyps(4)
% 0.31/0.47 thf(fact_3_Bound_Ohyps_I3_J,axiom,
% 0.31/0.47 fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 0.31/0.47
% 0.31/0.47 % Bound.hyps(3)
% 0.31/0.47 thf(fact_4_Bound_Ohyps_I2_J,axiom,
% 0.31/0.47 fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 0.31/0.47
% 0.31/0.47 % Bound.hyps(2)
% 0.31/0.47 thf(fact_5_Bound_Ohyps_I1_J,axiom,
% 0.31/0.47 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 0.31/0.47
% 0.31/0.47 % Bound.hyps(1)
% 0.31/0.47 thf(fact_6_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.31/0.47 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.31/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_7_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: late_freeRes,Y: name] :
% 0.31/0.47 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.31/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_8_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: late_freeRes,Y: pi] :
% 0.31/0.47 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.31/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_9_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: late_freeRes] :
% 0.31/0.47 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X )
% 0.31/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_10_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: name] :
% 0.31/0.47 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X )
% 0.31/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_11_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: pi] :
% 0.31/0.47 ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X )
% 0.31/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_12_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: late_freeRes] :
% 0.31/0.47 ( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.31/0.47 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_13_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: name] :
% 0.31/0.47 ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.31/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_14_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: pi] :
% 0.31/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.31/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_15_fresh__prod,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.31/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X )
% 0.31/0.47 & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prod
% 0.31/0.47 thf(fact_16_pi_Ofresh_I7_J,axiom,
% 0.31/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.31/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.31/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.fresh(7)
% 0.31/0.47 thf(fact_17_transitions_OResB,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.31/0.47 => ( ( Y != X )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.31/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transitions.ResB
% 0.31/0.47 thf(fact_18_freshBoundDerivative_I1_J,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.47 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshBoundDerivative(1)
% 0.31/0.47 thf(fact_19_Late__Semantics_OResB,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.31/0.47 => ( ( Y != X )
% 0.31/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics.ResB
% 0.31/0.47 thf(fact_20_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: pi] :
% 0.31/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_21_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.31/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_22_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.31/0.47 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.31/0.47 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_23_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: name] :
% 0.31/0.47 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.31/0.47 => ( fresh_name_name @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_24_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.31/0.47 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_25_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.31/0.47 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_26_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_27_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
% 0.31/0.47 ( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
% 0.31/0.47 => ( fresh_1711070152reeRes @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_28_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
% 0.31/0.47 ( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
% 0.31/0.47 => ( fresh_453496559i_name @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_29_fresh__prodD_I2_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
% 0.31/0.47 ( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_253309757_pi_pi @ A @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(2)
% 0.31/0.47 thf(fact_30_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: pi] :
% 0.31/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_name_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_31_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.31/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_name_name @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_32_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 0.31/0.47 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_33_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: name] :
% 0.31/0.47 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_34_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: pi] :
% 0.31/0.47 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_35_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.31/0.47 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_36_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_37_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
% 0.31/0.47 ( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_38_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
% 0.31/0.47 ( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_39_fresh__prodD_I1_J,axiom,
% 0.31/0.47 ! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
% 0.31/0.47 ( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
% 0.31/0.47 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % fresh_prodD(1)
% 0.31/0.47 thf(fact_40_freshBoundDerivative_I2_J,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.47 => ( ( Y != X )
% 0.31/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshBoundDerivative(2)
% 0.31/0.47 thf(fact_41_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.31/0.47 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.31/0.47 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_42_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 0.31/0.47 ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 0.31/0.47 = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_43_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 0.31/0.47 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.31/0.47 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_44_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 0.31/0.47 ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.31/0.47 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_45_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 0.31/0.47 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.31/0.47 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_46_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 0.31/0.47 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.31/0.47 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_47_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( ( produc1275980869_pi_pi @ X1 @ X2 )
% 0.31/0.47 = ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_48_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: produc1834551554reeRes,Y1: name > noption_pi,Y2: produc1834551554reeRes] :
% 0.31/0.47 ( ( ( produc703114481reeRes @ X1 @ X2 )
% 0.31/0.47 = ( produc703114481reeRes @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_49_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: produc405342261i_name,Y1: name > noption_pi,Y2: produc405342261i_name] :
% 0.31/0.47 ( ( ( produc1024533510i_name @ X1 @ X2 )
% 0.31/0.47 = ( produc1024533510i_name @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_50_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: name > noption_pi,X2: produc629157763_pi_pi,Y1: name > noption_pi,Y2: produc629157763_pi_pi] :
% 0.31/0.47 ( ( ( produc1189045204_pi_pi @ X1 @ X2 )
% 0.31/0.47 = ( produc1189045204_pi_pi @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_51_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.31/0.47 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.31/0.47 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_52_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.31/0.47 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.31/0.47 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_53_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.31/0.47 ( ( ( produc1505598906reeRes @ A @ B )
% 0.31/0.47 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_54_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.31/0.47 ( ( ( produc540578151i_name @ A @ B )
% 0.31/0.47 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_55_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.31/0.47 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_56_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.31/0.47 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.31/0.47 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_57_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_58_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
% 0.31/0.47 ( ( ( produc703114481reeRes @ A @ B )
% 0.31/0.47 = ( produc703114481reeRes @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_59_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
% 0.31/0.47 ( ( ( produc1024533510i_name @ A @ B )
% 0.31/0.47 = ( produc1024533510i_name @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_60_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
% 0.31/0.47 ( ( ( produc1189045204_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1189045204_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_61_pi_Odistinct_I81_J,axiom,
% 0.31/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.31/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.31/0.47 != ( res @ Name @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(81)
% 0.31/0.47 thf(fact_62_freshResidual,axiom,
% 0.31/0.47 ! [P: pi,Rs: late_residual,X: name] :
% 0.31/0.47 ( ( late_transitions @ P @ Rs )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshResidual
% 0.31/0.47 thf(fact_63_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.31/0.47 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_64_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 0.31/0.47 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_65_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_66_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_67_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_68_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_69_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_70_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1961110975reeRes > $o,Prod: produc1961110975reeRes] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_71_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1443308494i_name > $o,Prod: produc1443308494i_name] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_72_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P: produc1559976732_pi_pi > $o,Prod: produc1559976732_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_73_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: product_prod_pi_pi] :
% 0.31/0.47 ~ ! [A3: pi,B3: pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_74_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1141751126_pi_pi] :
% 0.31/0.47 ~ ! [A3: name,B3: product_prod_pi_pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_75_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1834551554reeRes] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_76_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc405342261i_name] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: name] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_77_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc629157763_pi_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_78_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1462499409ion_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_79_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc53907987_pi_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_80_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1961110975reeRes] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: produc1834551554reeRes] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc703114481reeRes @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_81_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1443308494i_name] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: produc405342261i_name] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1024533510i_name @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_82_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1559976732_pi_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: produc629157763_pi_pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1189045204_pi_pi @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_83_Pair__inject,axiom,
% 0.31/0.47 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 0.31/0.47 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.31/0.47 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_84_Pair__inject,axiom,
% 0.31/0.47 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 0.31/0.47 ( ( ( produc235456326_pi_pi @ A @ B )
% 0.31/0.47 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_85_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 0.31/0.47 ( ( ( produc1505598906reeRes @ A @ B )
% 0.31/0.47 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_86_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 0.31/0.47 ( ( ( produc540578151i_name @ A @ B )
% 0.31/0.47 = ( produc540578151i_name @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_87_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 0.31/0.47 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_88_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 0.31/0.47 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.31/0.47 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_89_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( ( produc1275980869_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_90_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
% 0.31/0.47 ( ( ( produc703114481reeRes @ A @ B )
% 0.31/0.47 = ( produc703114481reeRes @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_91_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
% 0.31/0.47 ( ( ( produc1024533510i_name @ A @ B )
% 0.31/0.47 = ( produc1024533510i_name @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_92_Pair__inject,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
% 0.31/0.47 ( ( ( produc1189045204_pi_pi @ A @ B )
% 0.31/0.47 = ( produc1189045204_pi_pi @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_93_prod__cases,axiom,
% 0.31/0.47 ! [P: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 0.31/0.47 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_94_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
% 0.31/0.47 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_95_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1834551554reeRes > $o,P3: produc1834551554reeRes] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_96_prod__cases,axiom,
% 0.31/0.47 ! [P: produc405342261i_name > $o,P3: produc405342261i_name] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_97_prod__cases,axiom,
% 0.31/0.47 ! [P: produc629157763_pi_pi > $o,P3: produc629157763_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_98_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1462499409ion_pi > $o,P3: produc1462499409ion_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_99_prod__cases,axiom,
% 0.31/0.47 ! [P: produc53907987_pi_pi > $o,P3: produc53907987_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_100_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1961110975reeRes > $o,P3: produc1961110975reeRes] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_101_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1443308494i_name > $o,P3: produc1443308494i_name] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_102_prod__cases,axiom,
% 0.31/0.47 ! [P: produc1559976732_pi_pi > $o,P3: produc1559976732_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
% 0.31/0.47 => ( P @ P3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_103_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc1217648014ion_pi] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: produc1462499409ion_pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc674047040ion_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_104_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc1141751126_pi_pi] :
% 0.31/0.47 ? [X3: name,Y3: product_prod_pi_pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_105_surj__pair,axiom,
% 0.31/0.47 ! [P3: product_prod_pi_pi] :
% 0.31/0.47 ? [X3: pi,Y3: pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_106_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc1834551554reeRes] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: late_freeRes] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_107_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc53907987_pi_pi] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_108_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc405342261i_name] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: name] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc540578151i_name @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_109_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc629157763_pi_pi] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_110_surj__pair,axiom,
% 0.31/0.47 ! [P3: produc1462499409ion_pi] :
% 0.31/0.47 ? [X3: name > noption_pi,Y3: name > noption_pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 = ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_111_name__exists__fresh,axiom,
% 0.31/0.47 ! [X: late_freeRes] :
% 0.31/0.47 ~ ! [C: name] :
% 0.31/0.47 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 0.31/0.47
% 0.31/0.47 % name_exists_fresh
% 0.31/0.47 thf(fact_112_name__exists__fresh,axiom,
% 0.31/0.47 ! [X: produc1141751126_pi_pi] :
% 0.31/0.47 ~ ! [C: name] :
% 0.31/0.47 ~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% 0.31/0.47
% 0.31/0.47 % name_exists_fresh
% 0.31/0.47 thf(fact_113_name__exists__fresh,axiom,
% 0.31/0.47 ! [X: name] :
% 0.31/0.47 ~ ! [C: name] :
% 0.31/0.47 ~ ( fresh_name_name @ C @ X ) ).
% 0.31/0.47
% 0.31/0.47 % name_exists_fresh
% 0.31/0.47 thf(fact_114_name__exists__fresh,axiom,
% 0.31/0.47 ! [X: pi] :
% 0.31/0.47 ~ ! [C: name] :
% 0.31/0.47 ~ ( fresh_name_pi @ C @ X ) ).
% 0.31/0.47
% 0.31/0.47 % name_exists_fresh
% 0.31/0.47 thf(fact_115_pi_Oinject_I6_J,axiom,
% 0.31/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.31/0.47 ( ( ( sum @ X2 @ X1 )
% 0.31/0.47 = ( sum @ Y2 @ Y1 ) )
% 0.31/0.47 = ( ( X2 = Y2 )
% 0.31/0.47 & ( X1 = Y1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.inject(6)
% 0.31/0.47 thf(fact_116_prod__induct4,axiom,
% 0.31/0.47 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name,C: pi,D: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) )
% 0.31/0.47 => ( P @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct4
% 0.31/0.47 thf(fact_117_prod__induct3,axiom,
% 0.31/0.47 ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 0.31/0.47 ( ! [A3: name,B3: pi,C: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
% 0.31/0.47 => ( P @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct3
% 0.31/0.47 thf(fact_118_prod__induct3,axiom,
% 0.31/0.47 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 0.31/0.47 ( ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) )
% 0.31/0.47 => ( P @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct3
% 0.31/0.47 thf(fact_119_prod__cases4,axiom,
% 0.31/0.47 ! [Y: produc53907987_pi_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: name,C: pi,D: pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases4
% 0.31/0.47 thf(fact_120_prod__cases3,axiom,
% 0.31/0.47 ! [Y: produc1141751126_pi_pi] :
% 0.31/0.47 ~ ! [A3: name,B3: pi,C: pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases3
% 0.31/0.47 thf(fact_121_prod__cases3,axiom,
% 0.31/0.47 ! [Y: produc53907987_pi_pi] :
% 0.31/0.47 ~ ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases3
% 0.31/0.47 thf(fact_122_freshRes,axiom,
% 0.31/0.47 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshRes
% 0.31/0.47 thf(fact_123_Sum2,axiom,
% 0.31/0.47 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ Rs )
% 0.31/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/0.47
% 0.31/0.47 % Sum2
% 0.31/0.47 thf(fact_124_Sum1,axiom,
% 0.31/0.47 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ Rs )
% 0.31/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.31/0.47
% 0.31/0.47 % Sum1
% 0.31/0.47 thf(fact_125_sumCases_H,axiom,
% 0.31/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumCases'
% 0.31/0.47 thf(fact_126_sumCases,axiom,
% 0.31/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.31/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.31/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.31/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumCases
% 0.31/0.47 thf(fact_127_Id,axiom,
% 0.31/0.47 ord_le630093991_pi_pi @ id_pi @ rel ).
% 0.31/0.47
% 0.31/0.47 % Id
% 0.31/0.47 thf(fact_128_transitions_OPar2B,axiom,
% 0.31/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transitions.Par2B
% 0.31/0.47 thf(fact_129_transitions_OPar1B,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transitions.Par1B
% 0.31/0.47 thf(fact_130_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.31/0.47 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.31/0.47 = ( P @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_131_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( collec1051790738_pi_pi
% 0.31/0.47 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_132_parCasesB_H,axiom,
% 0.31/0.47 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.31/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.31/0.47 => ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Q3: pi] :
% 0.31/0.47 ( ( ( par @ P @ Q )
% 0.31/0.47 = ( par @ P4 @ Q3 ) )
% 0.31/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.31/0.47 = ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q3 ) ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P4 )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q3 )
% 0.31/0.47 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
% 0.31/0.47 => ~ ! [Q3: pi,A3: late_subject,X3: name,Q4: pi,P4: pi] :
% 0.31/0.47 ( ( ( par @ P @ Q )
% 0.31/0.47 = ( par @ P4 @ Q3 ) )
% 0.31/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.31/0.47 = ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 0.31/0.47 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P4 )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q3 )
% 0.31/0.47 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % parCasesB'
% 0.31/0.47 thf(fact_133_inputIneqTrans,axiom,
% 0.31/0.47 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.31/0.47 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.31/0.47 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % inputIneqTrans
% 0.31/0.47 thf(fact_134_resTauBoundTrans,axiom,
% 0.31/0.47 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % resTauBoundTrans
% 0.31/0.47 thf(fact_135_residual_Ostrong__inducts,axiom,
% 0.31/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
% 0.31/0.47 ( ( fresh_1641682979reeRes @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_inducts
% 0.31/0.47 thf(fact_136_residual_Ostrong__inducts,axiom,
% 0.31/0.47 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_inducts
% 0.31/0.47 thf(fact_137_residual_Ostrong__inducts,axiom,
% 0.31/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
% 0.31/0.47 ( ( fresh_name_name @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_inducts
% 0.31/0.47 thf(fact_138_residual_Ostrong__inducts,axiom,
% 0.31/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_inducts
% 0.31/0.47 thf(fact_139_residual_Ostrong__induct,axiom,
% 0.31/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
% 0.31/0.47 ( ( fresh_1641682979reeRes @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_induct
% 0.31/0.47 thf(fact_140_residual_Ostrong__induct,axiom,
% 0.31/0.47 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_induct
% 0.31/0.47 thf(fact_141_residual_Ostrong__induct,axiom,
% 0.31/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
% 0.31/0.47 ( ( fresh_name_name @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_induct
% 0.31/0.47 thf(fact_142_residual_Ostrong__induct,axiom,
% 0.31/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ Name2 @ Z2 )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.31/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.strong_induct
% 0.31/0.47 thf(fact_143_pi_Ofresh_I8_J,axiom,
% 0.31/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.31/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.31/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.fresh(8)
% 0.31/0.47 thf(fact_144_pi_Ofresh_I3_J,axiom,
% 0.31/0.47 ! [A: name,X1: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.31/0.47 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.fresh(3)
% 0.31/0.47 thf(fact_145_residual_Ofresh_I2_J,axiom,
% 0.31/0.47 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.31/0.47 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.31/0.47 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.31/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.fresh(2)
% 0.31/0.47 thf(fact_146_residual_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.31/0.47 ( ( ( late_FreeR @ X2 @ X1 )
% 0.31/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.31/0.47 = ( ( X2 = Y2 )
% 0.31/0.47 & ( X1 = Y1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.inject(2)
% 0.31/0.47 thf(fact_147_pi_Odistinct_I35_J,axiom,
% 0.31/0.47 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.31/0.47 ( ( tau @ Pi4 )
% 0.31/0.47 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(35)
% 0.31/0.47 thf(fact_148_pi_Odistinct_I43_J,axiom,
% 0.31/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.47 ( ( tau @ Pi4 )
% 0.31/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(43)
% 0.31/0.47 thf(fact_149_pi_Odistinct_I55_J,axiom,
% 0.31/0.47 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.47 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.31/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(55)
% 0.31/0.47 thf(fact_150_pi_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X1: pi,Y1: pi] :
% 0.31/0.47 ( ( ( tau @ X1 )
% 0.31/0.47 = ( tau @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.inject(2)
% 0.31/0.47 thf(fact_151_pi_Oinject_I7_J,axiom,
% 0.31/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.31/0.47 ( ( ( par @ X2 @ X1 )
% 0.31/0.47 = ( par @ Y2 @ Y1 ) )
% 0.31/0.47 = ( ( X2 = Y2 )
% 0.31/0.47 & ( X1 = Y1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.inject(7)
% 0.31/0.47 thf(fact_152_Par2F,axiom,
% 0.31/0.47 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Par2F
% 0.31/0.47 thf(fact_153_Par1F,axiom,
% 0.31/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Par1F
% 0.31/0.47 thf(fact_154_inputFreeTrans,axiom,
% 0.31/0.47 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % inputFreeTrans
% 0.31/0.47 thf(fact_155_resInputFreeTrans,axiom,
% 0.31/0.47 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % resInputFreeTrans
% 0.31/0.47 thf(fact_156_pi_Odistinct_I85_J,axiom,
% 0.31/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.31/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.31/0.47 != ( res @ Name @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(85)
% 0.31/0.47 thf(fact_157_pi_Odistinct_I79_J,axiom,
% 0.31/0.47 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.31/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(79)
% 0.31/0.47 thf(fact_158_residual_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.31/0.47 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 0.31/0.47 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.distinct(1)
% 0.31/0.47 thf(fact_159_residual_Oinducts,axiom,
% 0.31/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.31/0.47 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 0.31/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.31/0.47 => ( P @ Residual ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.inducts
% 0.31/0.47 thf(fact_160_pi_Odistinct_I57_J,axiom,
% 0.31/0.47 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.31/0.47 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.31/0.47 != ( res @ Name @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(57)
% 0.31/0.47 thf(fact_161_pi_Odistinct_I45_J,axiom,
% 0.31/0.47 ! [Pi4: pi,Name: name,Pi: pi] :
% 0.31/0.47 ( ( tau @ Pi4 )
% 0.31/0.47 != ( res @ Name @ Pi ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(45)
% 0.31/0.47 thf(fact_162_pi_Odistinct_I53_J,axiom,
% 0.31/0.47 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.47 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.31/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(53)
% 0.31/0.47 thf(fact_163_pi_Odistinct_I41_J,axiom,
% 0.31/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.47 ( ( tau @ Pi4 )
% 0.31/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.distinct(41)
% 0.31/0.47 thf(fact_164_resCasesF,axiom,
% 0.31/0.47 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.31/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.31/0.47 => ( ! [P5: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.31/0.47 => ( F @ ( res @ X @ P5 ) ) ) )
% 0.31/0.47 => ( F @ XP ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resCasesF
% 0.31/0.47 thf(fact_165_resCasesF_H,axiom,
% 0.31/0.47 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.31/0.47 ( ( ( res @ X @ P )
% 0.31/0.47 = ( res @ Y3 @ P4 ) )
% 0.31/0.47 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.31/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.31/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resCasesF'
% 0.31/0.47 thf(fact_166_ResF,axiom,
% 0.31/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 0.31/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ResF
% 0.31/0.47 thf(fact_167_freshFreeDerivative_I2_J,axiom,
% 0.31/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshFreeDerivative(2)
% 0.31/0.47 thf(fact_168_freshFreeDerivative_I1_J,axiom,
% 0.31/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.47 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freshFreeDerivative(1)
% 0.31/0.47 thf(fact_169_resTrans_I2_J,axiom,
% 0.31/0.47 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.31/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.31/0.47
% 0.31/0.47 % resTrans(2)
% 0.31/0.47 thf(fact_170_tauBoundTrans,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % tauBoundTrans
% 0.31/0.47 thf(fact_171_Late__Semantics_OPar1B,axiom,
% 0.31/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics.Par1B
% 0.31/0.47 thf(fact_172_Late__Semantics_OPar2B,axiom,
% 0.31/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics.Par2B
% 0.31/0.47 thf(fact_173_parCasesB,axiom,
% 0.31/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.31/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.47 => ( ! [P5: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 0.31/0.47 => ( Prop @ ( par @ P5 @ Q ) ) )
% 0.31/0.47 => ( ! [Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 0.31/0.47 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.31/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % parCasesB
% 0.31/0.47 thf(fact_174_IdI,axiom,
% 0.31/0.47 ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 0.31/0.47
% 0.31/0.47 % IdI
% 0.31/0.47 thf(fact_175_IdI,axiom,
% 0.31/0.47 ! [A: name > noption_pi] : ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ A ) @ id_name_noption_pi ) ).
% 0.31/0.47
% 0.31/0.47 % IdI
% 0.31/0.47 thf(fact_176_pair__in__Id__conv,axiom,
% 0.31/0.47 ! [A: pi,B: pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.31/0.47 = ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % pair_in_Id_conv
% 0.31/0.47 thf(fact_177_pair__in__Id__conv,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name > noption_pi] :
% 0.31/0.47 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 0.31/0.47 = ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % pair_in_Id_conv
% 0.31/0.47 thf(fact_178_subsetI,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ! [X3: product_prod_pi_pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ X3 @ A4 )
% 0.31/0.47 => ( member558706512_pi_pi @ X3 @ B4 ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_179_subset__antisym,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B4 @ A4 )
% 0.31/0.47 => ( A4 = B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_antisym
% 0.31/0.47 thf(fact_180_order__refl,axiom,
% 0.31/0.47 ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_181_IdE,axiom,
% 0.31/0.47 ! [P3: product_prod_pi_pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ P3 @ id_pi )
% 0.31/0.47 => ~ ! [X3: pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 != ( product_Pair_pi_pi @ X3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IdE
% 0.31/0.47 thf(fact_182_IdE,axiom,
% 0.31/0.47 ! [P3: produc1462499409ion_pi] :
% 0.31/0.47 ( ( member1632198138ion_pi @ P3 @ id_name_noption_pi )
% 0.31/0.47 => ~ ! [X3: name > noption_pi] :
% 0.31/0.47 ( P3
% 0.31/0.47 != ( produc1342893193ion_pi @ X3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % IdE
% 0.31/0.47 thf(fact_183_IdD,axiom,
% 0.31/0.47 ! [A: pi,B: pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.31/0.47 => ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % IdD
% 0.31/0.47 thf(fact_184_IdD,axiom,
% 0.31/0.47 ! [A: name > noption_pi,B: name > noption_pi] :
% 0.31/0.47 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 0.31/0.47 => ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % IdD
% 0.31/0.47 thf(fact_185_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
% 0.31/0.47 ( ! [X3: name,Y3: product_prod_pi_pi] :
% 0.31/0.47 ( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le797229014_pi_pi @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_186_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr305743074reeRes,S: set_Pr305743074reeRes] :
% 0.31/0.47 ( ! [X3: name > noption_pi,Y3: late_freeRes] :
% 0.31/0.47 ( ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le1762471042reeRes @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_187_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr100209225_pi_pi,S: set_Pr100209225_pi_pi] :
% 0.31/0.47 ( ! [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le211833513_pi_pi @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_188_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr1294453099i_name,S: set_Pr1294453099i_name] :
% 0.31/0.47 ( ! [X3: name > noption_pi,Y3: name] :
% 0.31/0.47 ( ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le2082425291i_name @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_189_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr1694908217_pi_pi,S: set_Pr1694908217_pi_pi] :
% 0.31/0.47 ( ! [X3: name > noption_pi,Y3: pi] :
% 0.31/0.47 ( ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le1854926745_pi_pi @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_190_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr1569510577ion_pi,S: set_Pr1569510577ion_pi] :
% 0.31/0.47 ( ! [X3: name > noption_pi,Y3: name > noption_pi] :
% 0.31/0.47 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le1032043601ion_pi @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_191_subrelI,axiom,
% 0.31/0.47 ! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ! [X3: pi,Y3: pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ R )
% 0.31/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ S ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ R @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % subrelI
% 0.31/0.47 thf(fact_192_dual__order_Oantisym,axiom,
% 0.31/0.47 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ B @ A )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( A = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.antisym
% 0.31/0.47 thf(fact_193_dual__order_Oeq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.31/0.47 = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ B5 @ A5 )
% 0.31/0.47 & ( ord_le630093991_pi_pi @ A5 @ B5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.eq_iff
% 0.31/0.47 thf(fact_194_dual__order_Otrans,axiom,
% 0.31/0.47 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ B @ A )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ C2 @ B )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ C2 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.trans
% 0.31/0.47 thf(fact_195_dual__order_Orefl,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.refl
% 0.31/0.47 thf(fact_196_order__trans,axiom,
% 0.31/0.47 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X @ Y )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ Y @ Z )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ X @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_trans
% 0.31/0.47 thf(fact_197_order__class_Oorder_Oantisym,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B @ A )
% 0.31/0.47 => ( A = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.antisym
% 0.31/0.47 thf(fact_198_ord__le__eq__trans,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( ( B = C2 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_trans
% 0.31/0.47 thf(fact_199_ord__eq__le__trans,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_trans
% 0.31/0.47 thf(fact_200_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.31/0.47 = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A5 @ B5 )
% 0.31/0.47 & ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.eq_iff
% 0.31/0.47 thf(fact_201_antisym__conv,axiom,
% 0.31/0.47 ! [Y: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ Y @ X )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv
% 0.31/0.47 thf(fact_202_order_Otrans,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.trans
% 0.31/0.47 thf(fact_203_eq__refl,axiom,
% 0.31/0.47 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( X = Y )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ X @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_refl
% 0.31/0.47 thf(fact_204_antisym,axiom,
% 0.31/0.47 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X @ Y )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ Y @ X )
% 0.31/0.47 => ( X = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym
% 0.31/0.47 thf(fact_205_eq__iff,axiom,
% 0.31/0.47 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.31/0.47 = ( ^ [X4: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X4 @ Y5 )
% 0.31/0.47 & ( ord_le630093991_pi_pi @ Y5 @ X4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_iff
% 0.31/0.47 thf(fact_206_ord__le__eq__subst,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( ( ( F2 @ B )
% 0.31/0.47 = C2 )
% 0.31/0.47 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_subst
% 0.31/0.47 thf(fact_207_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( F2 @ B ) )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.31/0.47 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_subst
% 0.31/0.47 thf(fact_208_order__subst2,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ ( F2 @ B ) @ C2 )
% 0.31/0.47 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_209_order__subst1,axiom,
% 0.31/0.47 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A @ ( F2 @ B ) )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.31/0.47 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_210_Collect__mono__iff,axiom,
% 0.31/0.47 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) )
% 0.31/0.47 = ( ! [X4: product_prod_pi_pi] :
% 0.31/0.47 ( ( P @ X4 )
% 0.31/0.47 => ( Q @ X4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_211_set__eq__subset,axiom,
% 0.31/0.47 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.31/0.47 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A6 @ B6 )
% 0.31/0.47 & ( ord_le630093991_pi_pi @ B6 @ A6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_eq_subset
% 0.31/0.47 thf(fact_212_subset__trans,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C3: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ B4 @ C3 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A4 @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_trans
% 0.31/0.47 thf(fact_213_Collect__mono,axiom,
% 0.31/0.47 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.31/0.47 ( ! [X3: product_prod_pi_pi] :
% 0.31/0.47 ( ( P @ X3 )
% 0.31/0.47 => ( Q @ X3 ) )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_214_subset__refl,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A4 @ A4 ) ).
% 0.31/0.47
% 0.31/0.47 % subset_refl
% 0.31/0.47 thf(fact_215_subset__iff,axiom,
% 0.31/0.47 ( ord_le630093991_pi_pi
% 0.31/0.47 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ! [T: product_prod_pi_pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ T @ A6 )
% 0.31/0.47 => ( member558706512_pi_pi @ T @ B6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_iff
% 0.31/0.47 thf(fact_216_equalityD2,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( A4 = B4 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityD2
% 0.31/0.47 thf(fact_217_equalityD1,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( A4 = B4 )
% 0.31/0.47 => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityD1
% 0.31/0.47 thf(fact_218_subset__eq,axiom,
% 0.31/0.47 ( ord_le630093991_pi_pi
% 0.31/0.47 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ! [X4: product_prod_pi_pi] :
% 0.31/0.47 ( ( member558706512_pi_pi @ X4 @ A6 )
% 0.31/0.47 => ( member558706512_pi_pi @ X4 @ B6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_eq
% 0.31/0.47 thf(fact_219_equalityE,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( A4 = B4 )
% 0.31/0.47 => ~ ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ~ ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % equalityE
% 0.31/0.47 thf(fact_220_subsetD,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C2: product_prod_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( ( member558706512_pi_pi @ C2 @ A4 )
% 0.31/0.47 => ( member558706512_pi_pi @ C2 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetD
% 0.31/0.47 thf(fact_221_in__mono,axiom,
% 0.31/0.47 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,X: product_prod_pi_pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( ( member558706512_pi_pi @ X @ A4 )
% 0.31/0.47 => ( member558706512_pi_pi @ X @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_mono
% 0.31/0.47 thf(fact_222_resInputBoundOutputTrans,axiom,
% 0.31/0.47 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % resInputBoundOutputTrans
% 0.31/0.47 thf(fact_223_resTauOutputTrans,axiom,
% 0.31/0.47 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % resTauOutputTrans
% 0.31/0.47 thf(fact_224_simCasesCont,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.31/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simCasesCont
% 0.31/0.47 thf(fact_225_simCasesCont,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.31/0.47 => ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.31/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simCasesCont
% 0.31/0.47 thf(fact_226_simCasesCont,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.31/0.47 => ( ( fresh_name_name @ X3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.31/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simCasesCont
% 0.31/0.47 thf(fact_227_simCasesCont,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ Q )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 0.31/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simCasesCont
% 0.31/0.47 thf(fact_228_residual_Ofresh_I1_J,axiom,
% 0.31/0.47 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 0.31/0.47 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.31/0.47 = ( ( fresh_717452603ubject @ A @ X32 )
% 0.31/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.fresh(1)
% 0.31/0.47 thf(fact_229_resCases_H,axiom,
% 0.31/0.47 ! [X: name,P: pi,Rs: late_residual] :
% 0.31/0.47 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.31/0.47 => ( ! [P4: pi,A3: name,B3: name] :
% 0.31/0.47 ( ( ( res @ X @ P )
% 0.31/0.47 = ( res @ B3 @ P4 ) )
% 0.31/0.47 => ! [P5: pi] :
% 0.31/0.47 ( ( Rs
% 0.31/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.31/0.47 => ( A3 = B3 ) ) ) )
% 0.31/0.47 => ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
% 0.31/0.47 ( ( ( res @ X @ P )
% 0.31/0.47 = ( res @ Y3 @ P4 ) )
% 0.31/0.47 => ( ( Rs
% 0.31/0.47 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.31/0.47 => ( ( Y3 != X3 )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P4 )
% 0.31/0.47 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
% 0.31/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 0.31/0.47 ( ( ( res @ X @ P )
% 0.31/0.47 = ( res @ Y3 @ P4 ) )
% 0.31/0.47 => ( ( Rs
% 0.31/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.31/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resCases'
% 0.31/0.47 thf(fact_230_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.31/0.47 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.31/0.47 ( ( ( late_OutputR @ X2 @ X1 )
% 0.31/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.31/0.47 = ( ( X2 = Y2 )
% 0.31/0.47 & ( X1 = Y1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics.freeRes.inject
% 0.31/0.47 thf(fact_231_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X1: name,Y1: name] :
% 0.31/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.31/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.31/0.47 = ( X1 = Y1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics.subject.inject(2)
% 0.31/0.47 thf(fact_232_subject_Ofresh_I2_J,axiom,
% 0.31/0.47 ! [A: name,X1: name] :
% 0.31/0.47 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.31/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % subject.fresh(2)
% 0.31/0.47 thf(fact_233_freeRes_Ofresh_I1_J,axiom,
% 0.31/0.47 ! [A: name,X2: name,X1: name] :
% 0.31/0.47 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X2 )
% 0.31/0.47 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % freeRes.fresh(1)
% 0.31/0.47 thf(fact_234_pi_Ofresh_I9_J,axiom,
% 0.31/0.47 ! [A: name,X1: name,X2: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.31/0.47 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.fresh(9)
% 0.31/0.47 thf(fact_235_pi_Ofresh_I4_J,axiom,
% 0.31/0.47 ! [A: name,X32: name,X1: name,X2: pi] :
% 0.31/0.47 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.31/0.47 = ( ( fresh_name_name @ A @ X32 )
% 0.31/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.fresh(4)
% 0.31/0.47 thf(fact_236_monotonic,axiom,
% 0.31/0.47 ! [P: pi,A4: set_Pr1834926343_pi_pi,P2: pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( strong743114133lation @ P @ A4 @ P2 )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( strong743114133lation @ P @ B4 @ P2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % monotonic
% 0.31/0.47 thf(fact_237_abs__fun__eq1,axiom,
% 0.31/0.47 ! [A: name,X: pi,Y: pi] :
% 0.31/0.47 ( ( ( abs_fun_name_pi @ A @ X )
% 0.31/0.47 = ( abs_fun_name_pi @ A @ Y ) )
% 0.31/0.47 = ( X = Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_fun_eq1
% 0.31/0.47 thf(fact_238_derivativeMonotonic,axiom,
% 0.31/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ( strong2129052853vative @ P @ Q @ A @ X @ A4 )
% 0.31/0.47 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 0.31/0.47 => ( strong2129052853vative @ P @ Q @ A @ X @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % derivativeMonotonic
% 0.31/0.47 thf(fact_239_pi_Oinject_I8_J,axiom,
% 0.31/0.47 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.31/0.47 ( ( ( res @ X1 @ X2 )
% 0.31/0.47 = ( res @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.31/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.inject(8)
% 0.31/0.47 thf(fact_240_residual_Oinject_I1_J,axiom,
% 0.31/0.47 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.31/0.47 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.31/0.47 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X32 = Y32 )
% 0.31/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.31/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % residual.inject(1)
% 0.31/0.47 thf(fact_241_abs__fresh_I1_J,axiom,
% 0.31/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.31/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_fresh(1)
% 0.31/0.47 thf(fact_242_abs__fresh_I1_J,axiom,
% 0.31/0.47 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_fresh(1)
% 0.31/0.47 thf(fact_243_abs__fresh_I1_J,axiom,
% 0.31/0.47 ! [B: name,A: name,X: name] :
% 0.31/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_fresh(1)
% 0.31/0.47 thf(fact_244_abs__fresh_I1_J,axiom,
% 0.31/0.47 ! [B: name,A: name,X: pi] :
% 0.31/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_fresh(1)
% 0.31/0.47 thf(fact_245_name__fresh__abs,axiom,
% 0.31/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.31/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % name_fresh_abs
% 0.31/0.47 thf(fact_246_name__fresh__abs,axiom,
% 0.31/0.47 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % name_fresh_abs
% 0.31/0.47 thf(fact_247_name__fresh__abs,axiom,
% 0.31/0.47 ! [B: name,A: name,X: name] :
% 0.31/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % name_fresh_abs
% 0.31/0.47 thf(fact_248_name__fresh__abs,axiom,
% 0.31/0.47 ! [B: name,A: name,X: pi] :
% 0.31/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.31/0.47 = ( ( B = A )
% 0.31/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % name_fresh_abs
% 0.31/0.47 thf(fact_249_pi_Oinject_I3_J,axiom,
% 0.31/0.47 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.31/0.47 ( ( ( input @ X32 @ X1 @ X2 )
% 0.31/0.47 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X32 = Y32 )
% 0.31/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.31/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % pi.inject(3)
% 0.31/0.47 thf(fact_250_simE_I1_J,axiom,
% 0.31/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.31/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.31/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.47 => ? [P5: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 0.31/0.47 & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simE(1)
% 0.31/0.47 thf(fact_251_Strong__Late__Sim_Oreflexive,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % Strong_Late_Sim.reflexive
% 0.31/0.47 thf(fact_252_Open,axiom,
% 0.31/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Open
% 0.31/0.47 thf(fact_253_derivativeReflexive,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,A: late_subject,X: name] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong2129052853vative @ P @ P @ A @ X @ Rel ) ) ).
% 0.31/0.47
% 0.31/0.47 % derivativeReflexive
% 0.31/0.47 thf(fact_254_simE_I2_J,axiom,
% 0.31/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.31/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.31/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.31/0.47 => ? [P5: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simE(2)
% 0.31/0.47 thf(fact_255_resSimCases,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [Q4: pi,A3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.31/0.47 => ( ( A3 != X )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.31/0.47 => ( ( X != Y3 )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ Y3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resSimCases
% 0.31/0.47 thf(fact_256_resSimCases,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [Q4: pi,A3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.31/0.47 => ( ( A3 != X )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.31/0.47 => ( ( X != Y3 )
% 0.31/0.47 => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resSimCases
% 0.31/0.47 thf(fact_257_resSimCases,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [Q4: pi,A3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.31/0.47 => ( ( A3 != X )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.31/0.47 => ( ( X != Y3 )
% 0.31/0.47 => ( ( fresh_name_name @ Y3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resSimCases
% 0.31/0.47 thf(fact_258_resSimCases,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.31/0.47 ( ( eqvt_pi @ Rel )
% 0.31/0.47 => ( ! [Q4: pi,A3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.31/0.47 => ( ( A3 != X )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.31/0.47 => ( ( X != Y3 )
% 0.31/0.47 => ( ( fresh_name_pi @ Y3 @ C3 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.31/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resSimCases
% 0.31/0.47 thf(fact_259_simCases,axiom,
% 0.31/0.47 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.31/0.47 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.31/0.47 => ( ( fresh_name_pi @ Y3 @ P )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.31/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 0.31/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.31/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.31/0.47 => ? [P6: pi] :
% 0.31/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simCases
% 0.31/0.47 thf(fact_260_simulation__def,axiom,
% 0.31/0.47 ( strong743114133lation
% 0.31/0.47 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.31/0.47 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 0.31/0.47 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 0.31/0.47 & ( fresh_name_pi @ X4 @ P7 ) )
% 0.31/0.47 => ? [P8: pi] :
% 0.31/0.47 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 0.31/0.47 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 0.31/0.47 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.31/0.47 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.31/0.47 => ? [P8: pi] :
% 0.31/0.47 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.31/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % simulation_def
% 0.31/0.47 thf(fact_261_resCasesB_H,axiom,
% 0.31/0.47 ! [X5: name,P: pi,A: late_subject,Y6: name,P2: pi] :
% 0.31/0.47 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y6 @ P2 ) )
% 0.31/0.47 => ( ! [P4: pi,A3: name,B3: name] :
% 0.31/0.47 ( ( ( res @ X5 @ P )
% 0.31/0.47 = ( res @ B3 @ P4 ) )
% 0.31/0.47 => ! [P5: pi] :
% 0.31/0.47 ( ( ( late_BoundR @ A @ Y6 @ P2 )
% 0.31/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 0.31/0.47 => ( A3 = B3 ) ) ) )
% 0.31/0.47 => ~ ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
% 0.31/0.47 ( ( ( res @ X5 @ P )
% 0.31/0.47 = ( res @ Y3 @ P4 ) )
% 0.31/0.47 => ( ( ( late_BoundR @ A @ Y6 @ P2 )
% 0.31/0.47 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 0.31/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 0.31/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.31/0.47 => ( ( Y3 != X3 )
% 0.31/0.47 => ( ( fresh_name_pi @ X3 @ P4 )
% 0.31/0.47 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % resCasesB'
% 0.31/0.47 thf(fact_262_tauOutputTrans,axiom,
% 0.31/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % tauOutputTrans
% 0.31/0.47 thf(fact_263_inputBoundOutputTrans,axiom,
% 0.31/0.47 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 0.31/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % inputBoundOutputTrans
% 0.31/0.47 thf(fact_264_sumIdempRight,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumIdempRight
% 0.31/0.47 thf(fact_265_sumAssocRight,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumAssocRight
% 0.31/0.47 thf(fact_266_sumIdempLeft,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumIdempLeft
% 0.31/0.47 thf(fact_267_sumAssocLeft,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R2 ) @ Rel @ ( sum @ P @ ( sum @ Q @ R2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumAssocLeft
% 0.31/0.47 thf(fact_268_sumSym,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumSym
% 0.31/0.47 thf(fact_269_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.31/0.47 ! [X2: name,Y2: name] :
% 0.31/0.47 ( ( ( late_BoundOutputS @ X2 )
% 0.31/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.31/0.47 = ( X2 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics1.subject.inject(2)
% 0.31/0.47 thf(fact_270_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.31/0.47 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.31/0.47 ( ( ( late_OutputR @ X11 @ X12 )
% 0.31/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.31/0.47 = ( ( X11 = Y11 )
% 0.31/0.47 & ( X12 = Y12 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Late_Semantics1.freeRes.inject
% 0.31/0.47 thf(fact_271_sumZeroRight,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sumZeroRight
% 0.31/0.47 thf(fact_272_sumZeroLeft,axiom,
% 0.31/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.47 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.47 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.31/0.47
% 0.31/0.48 % sumZeroLeft
% 0.31/0.48 thf(fact_273_name__fresh,axiom,
% 0.31/0.48 ( fresh_name_name
% 0.31/0.48 = ( ^ [A5: name,B5: name] : ( A5 != B5 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % name_fresh
% 0.31/0.48 thf(fact_274_pi_Ofresh_I1_J,axiom,
% 0.31/0.48 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.31/0.48
% 0.31/0.48 % pi.fresh(1)
% 0.31/0.48 thf(fact_275_zeroTrans,axiom,
% 0.31/0.48 ! [Rs: late_residual] :
% 0.31/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/0.48
% 0.31/0.48 % zeroTrans
% 0.31/0.48 thf(fact_276_nilCases_H,axiom,
% 0.31/0.48 ! [Rs: late_residual] :
% 0.31/0.48 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.31/0.48
% 0.31/0.48 % nilCases'
% 0.31/0.48 thf(fact_277_pi_Odistinct_I15_J,axiom,
% 0.31/0.48 ! [Name: name,Pi: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( res @ Name @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(15)
% 0.31/0.48 thf(fact_278_pi_Odistinct_I13_J,axiom,
% 0.31/0.48 ! [Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(13)
% 0.31/0.48 thf(fact_279_pi_Odistinct_I11_J,axiom,
% 0.31/0.48 ! [Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(11)
% 0.31/0.48 thf(fact_280_pi_Odistinct_I5_J,axiom,
% 0.31/0.48 ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(5)
% 0.31/0.48 thf(fact_281_pi_Odistinct_I3_J,axiom,
% 0.31/0.48 ! [Pi: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( tau @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(3)
% 0.31/0.48 thf(fact_282_nilSimRight,axiom,
% 0.31/0.48 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.31/0.48
% 0.31/0.48 % nilSimRight
% 0.31/0.48 thf(fact_283_resZeroTrans,axiom,
% 0.31/0.48 ! [X: name,Rs: late_residual] :
% 0.31/0.48 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.31/0.48
% 0.31/0.48 % resZeroTrans
% 0.31/0.48 thf(fact_284_nilSim_I2_J,axiom,
% 0.31/0.48 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.31/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % nilSim(2)
% 0.31/0.48 thf(fact_285_nilSim_I1_J,axiom,
% 0.31/0.48 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.31/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % nilSim(1)
% 0.31/0.48 thf(fact_286_inputCases_H,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.48 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.31/0.48 => ~ ! [X3: name,A3: name,P4: pi] :
% 0.31/0.48 ( ( ( A = A3 )
% 0.31/0.48 & ( ( abs_fun_name_pi @ B @ P )
% 0.31/0.48 = ( abs_fun_name_pi @ X3 @ P4 ) ) )
% 0.31/0.48 => ( ( Rs
% 0.31/0.48 = ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P4 ) )
% 0.31/0.48 => ( X3 = A3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inputCases'
% 0.31/0.48 thf(fact_287_subject_Ofresh_I1_J,axiom,
% 0.31/0.48 ! [A: name,X1: name] :
% 0.31/0.48 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.31/0.48 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.31/0.48
% 0.31/0.48 % subject.fresh(1)
% 0.31/0.48 thf(fact_288_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [X1: name,X2: name] :
% 0.31/0.48 ( ( late_InputS @ X1 )
% 0.31/0.48 != ( late_BoundOutputS @ X2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics1.subject.distinct(1)
% 0.31/0.48 thf(fact_289_subject_Oexhaust,axiom,
% 0.31/0.48 ! [Y: late_subject] :
% 0.31/0.48 ( ! [X13: name] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( late_InputS @ X13 ) )
% 0.31/0.48 => ~ ! [X22: name] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subject.exhaust
% 0.31/0.48 thf(fact_290_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [Name3: name,Name: name] :
% 0.31/0.48 ( ( late_InputS @ Name3 )
% 0.31/0.48 != ( late_BoundOutputS @ Name ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.subject.distinct(1)
% 0.31/0.48 thf(fact_291_subject_Oinducts,axiom,
% 0.31/0.48 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.31/0.48 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 0.31/0.48 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 0.31/0.48 => ( P @ Subject2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subject.inducts
% 0.31/0.48 thf(fact_292_Late__Semantics_OInput,axiom,
% 0.31/0.48 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.Input
% 0.31/0.48 thf(fact_293_transitions_OInput,axiom,
% 0.31/0.48 ! [X: name,A: name,P: pi] :
% 0.31/0.48 ( ( X != A )
% 0.31/0.48 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % transitions.Input
% 0.31/0.48 thf(fact_294_resOutputInputTrans,axiom,
% 0.31/0.48 ! [X: name,A: name,B: name,P: pi,C2: name,Y: name,P2: pi] :
% 0.31/0.48 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % resOutputInputTrans
% 0.31/0.48 thf(fact_295_resOutputOutputTrans,axiom,
% 0.31/0.48 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 0.31/0.48 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % resOutputOutputTrans
% 0.31/0.48 thf(fact_296_Late__Semantics_OClose1,axiom,
% 0.31/0.48 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.Close1
% 0.31/0.48 thf(fact_297_subst__identity,axiom,
% 0.31/0.48 ! [P: pi,A: name] :
% 0.31/0.48 ( ( subs @ P @ A @ A )
% 0.31/0.48 = P ) ).
% 0.31/0.48
% 0.31/0.48 % subst_identity
% 0.31/0.48 thf(fact_298_simps_I9_J,axiom,
% 0.31/0.48 ! [X: name,C2: name,D2: name,P: pi] :
% 0.31/0.48 ( ( X != C2 )
% 0.31/0.48 => ( ( X != D2 )
% 0.31/0.48 => ( ( subs @ ( res @ X @ P ) @ C2 @ D2 )
% 0.31/0.48 = ( res @ X @ ( subs @ P @ C2 @ D2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % simps(9)
% 0.31/0.48 thf(fact_299_simps_I8_J,axiom,
% 0.31/0.48 ! [P: pi,Q: pi,C2: name,D2: name] :
% 0.31/0.48 ( ( subs @ ( par @ P @ Q ) @ C2 @ D2 )
% 0.31/0.48 = ( par @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % simps(8)
% 0.31/0.48 thf(fact_300_substTrans,axiom,
% 0.31/0.48 ! [B: name,P: pi,A: name,C2: name] :
% 0.31/0.48 ( ( fresh_name_pi @ B @ P )
% 0.31/0.48 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 0.31/0.48 = ( subs @ P @ A @ C2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % substTrans
% 0.31/0.48 thf(fact_301_simps_I7_J,axiom,
% 0.31/0.48 ! [P: pi,Q: pi,C2: name,D2: name] :
% 0.31/0.48 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D2 )
% 0.31/0.48 = ( sum @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % simps(7)
% 0.31/0.48 thf(fact_302_simps_I2_J,axiom,
% 0.31/0.48 ! [P: pi,C2: name,D2: name] :
% 0.31/0.48 ( ( subs @ ( tau @ P ) @ C2 @ D2 )
% 0.31/0.48 = ( tau @ ( subs @ P @ C2 @ D2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % simps(2)
% 0.31/0.48 thf(fact_303_simps_I1_J,axiom,
% 0.31/0.48 ! [C2: name,D2: name] :
% 0.31/0.48 ( ( subs @ piNil @ C2 @ D2 )
% 0.31/0.48 = piNil ) ).
% 0.31/0.48
% 0.31/0.48 % simps(1)
% 0.31/0.48 thf(fact_304_freeRes_Ofresh_I2_J,axiom,
% 0.31/0.48 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.31/0.48
% 0.31/0.48 % freeRes.fresh(2)
% 0.31/0.48 thf(fact_305_pi_Ofresh_I2_J,axiom,
% 0.31/0.48 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.31/0.48 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 0.31/0.48 = ( ( fresh_name_name @ A @ X32 )
% 0.31/0.48 & ( fresh_name_name @ A @ X2 )
% 0.31/0.48 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.fresh(2)
% 0.31/0.48 thf(fact_306_resOutputTauTrans,axiom,
% 0.31/0.48 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 0.31/0.48 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % resOutputTauTrans
% 0.31/0.48 thf(fact_307_outputTauTrans,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,P2: pi] :
% 0.31/0.48 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputTauTrans
% 0.31/0.48 thf(fact_308_pi_Odistinct_I31_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( res @ Name @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(31)
% 0.31/0.48 thf(fact_309_pi_Odistinct_I29_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(29)
% 0.31/0.48 thf(fact_310_pi_Odistinct_I27_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(27)
% 0.31/0.48 thf(fact_311_pi_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.31/0.48 ( ( ( output @ X32 @ X2 @ X1 )
% 0.31/0.48 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.31/0.48 = ( ( X32 = Y32 )
% 0.31/0.48 & ( X2 = Y2 )
% 0.31/0.48 & ( X1 = Y1 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.inject(1)
% 0.31/0.48 thf(fact_312_freeRes_Oinducts,axiom,
% 0.31/0.48 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.31/0.48 ( ! [Name13: name,Name24: name] : ( P @ ( late_OutputR @ Name13 @ Name24 ) )
% 0.31/0.48 => ( ( P @ late_TauR )
% 0.31/0.48 => ( P @ FreeRes3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % freeRes.inducts
% 0.31/0.48 thf(fact_313_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name] :
% 0.31/0.48 ( ( late_OutputR @ Name12 @ Name23 )
% 0.31/0.48 != late_TauR ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.freeRes.distinct(1)
% 0.31/0.48 thf(fact_314_pi_Odistinct_I19_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( tau @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(19)
% 0.31/0.48 thf(fact_315_pi_Odistinct_I21_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(21)
% 0.31/0.48 thf(fact_316_pi_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( output @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(1)
% 0.31/0.48 thf(fact_317_fresh__fact2,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi] :
% 0.31/0.48 ( ( A != B )
% 0.31/0.48 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % fresh_fact2
% 0.31/0.48 thf(fact_318_fresh__fact1,axiom,
% 0.31/0.48 ! [A: name,P: pi,C2: name,B: name] :
% 0.31/0.48 ( ( fresh_name_pi @ A @ P )
% 0.31/0.48 => ( ( A != C2 )
% 0.31/0.48 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % fresh_fact1
% 0.31/0.48 thf(fact_319_forget,axiom,
% 0.31/0.48 ! [A: name,P: pi,B: name] :
% 0.31/0.48 ( ( fresh_name_pi @ A @ P )
% 0.31/0.48 => ( ( subs @ P @ A @ B )
% 0.31/0.48 = P ) ) ).
% 0.31/0.48
% 0.31/0.48 % forget
% 0.31/0.48 thf(fact_320_freeRes_Oexhaust,axiom,
% 0.31/0.48 ! [Y: late_freeRes] :
% 0.31/0.48 ( ! [X112: name,X122: name] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( late_OutputR @ X112 @ X122 ) )
% 0.31/0.48 => ( Y = late_TauR ) ) ).
% 0.31/0.48
% 0.31/0.48 % freeRes.exhaust
% 0.31/0.48 thf(fact_321_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [X11: name,X12: name] :
% 0.31/0.48 ( ( late_OutputR @ X11 @ X12 )
% 0.31/0.48 != late_TauR ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics1.freeRes.distinct(1)
% 0.31/0.48 thf(fact_322_substRes3,axiom,
% 0.31/0.48 ! [B: name,P: pi,A: name] :
% 0.31/0.48 ( ( fresh_name_pi @ B @ P )
% 0.31/0.48 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.31/0.48 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % substRes3
% 0.31/0.48 thf(fact_323_substRes2,axiom,
% 0.31/0.48 ! [B: name,P: pi,A: name] :
% 0.31/0.48 ( ( fresh_name_pi @ B @ P )
% 0.31/0.48 => ( ( res @ A @ P )
% 0.31/0.48 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % substRes2
% 0.31/0.48 thf(fact_324_resTrans_I1_J,axiom,
% 0.31/0.48 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.48 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.31/0.48
% 0.31/0.48 % resTrans(1)
% 0.31/0.48 thf(fact_325_outputBoundTrans,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,C2: late_subject,X: name,P2: pi] :
% 0.31/0.48 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C2 @ X @ P2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputBoundTrans
% 0.31/0.48 thf(fact_326_nilSim_I3_J,axiom,
% 0.31/0.48 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.31/0.48 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % nilSim(3)
% 0.31/0.48 thf(fact_327_Late__Semantics_OComm2,axiom,
% 0.31/0.48 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.Comm2
% 0.31/0.48 thf(fact_328_Late__Semantics_OComm1,axiom,
% 0.31/0.48 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.Comm1
% 0.31/0.48 thf(fact_329_Output,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % Output
% 0.31/0.48 thf(fact_330_outputIneqTrans,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,C2: name,D2: name,P2: pi] :
% 0.31/0.48 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D2 ) @ P2 ) )
% 0.31/0.48 => ~ ( ( A != C2 )
% 0.31/0.48 | ( B != D2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputIneqTrans
% 0.31/0.48 thf(fact_331_outputCases_H,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.31/0.48 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.31/0.48 => ~ ! [A3: name,B3: name,P4: pi] :
% 0.31/0.48 ( ( ( A = A3 )
% 0.31/0.48 & ( B = B3 )
% 0.31/0.48 & ( P = P4 ) )
% 0.31/0.48 => ( Rs
% 0.31/0.48 != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputCases'
% 0.31/0.48 thf(fact_332_outputCases,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.31/0.48 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.48 => ( ( ( Alpha
% 0.31/0.48 = ( late_OutputR @ A @ B ) )
% 0.31/0.48 => ( ( P = P2 )
% 0.31/0.48 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.31/0.48 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputCases
% 0.31/0.48 thf(fact_333_outputFreshTrans,axiom,
% 0.31/0.48 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.31/0.48 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.48 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 0.31/0.48 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % outputFreshTrans
% 0.31/0.48 thf(fact_334_transitions_OComm2,axiom,
% 0.31/0.48 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.48 => ( ( X != A )
% 0.31/0.48 => ( ( X != B )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P2 )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % transitions.Comm2
% 0.31/0.48 thf(fact_335_transitions_OComm1,axiom,
% 0.31/0.48 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.48 => ( ( X != A )
% 0.31/0.48 => ( ( X != B )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q2 )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % transitions.Comm1
% 0.31/0.48 thf(fact_336_Tau,axiom,
% 0.31/0.48 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.31/0.48
% 0.31/0.48 % Tau
% 0.31/0.48 thf(fact_337_tauCases_H,axiom,
% 0.31/0.48 ! [P: pi,Rs: late_residual] :
% 0.31/0.48 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.31/0.48 => ~ ! [P4: pi] :
% 0.31/0.48 ( ( ( tau @ P )
% 0.31/0.48 = ( tau @ P4 ) )
% 0.31/0.48 => ( Rs
% 0.31/0.48 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % tauCases'
% 0.31/0.48 thf(fact_338_tauCases,axiom,
% 0.31/0.48 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.31/0.48 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.31/0.48 => ( ( ( Alpha = late_TauR )
% 0.31/0.48 => ( ( P = P2 )
% 0.31/0.48 => ( Prop @ late_TauR @ P ) ) )
% 0.31/0.48 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % tauCases
% 0.31/0.48 thf(fact_339_transitions_OClose2,axiom,
% 0.31/0.48 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ Q )
% 0.31/0.48 => ( ( X != A )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P2 )
% 0.31/0.48 => ( ( Y != A )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.31/0.48 => ( ( X != Y )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % transitions.Close2
% 0.31/0.48 thf(fact_340_transitions_OClose1,axiom,
% 0.31/0.48 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ P )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ Q )
% 0.31/0.48 => ( ( X != A )
% 0.31/0.48 => ( ( fresh_name_pi @ X @ Q2 )
% 0.31/0.48 => ( ( Y != A )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ P2 )
% 0.31/0.48 => ( ( X != Y )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % transitions.Close1
% 0.31/0.48 thf(fact_341_Late__Semantics_OClose2,axiom,
% 0.31/0.48 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.31/0.48 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.31/0.48 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.31/0.48 => ( ( fresh_name_pi @ Y @ Q )
% 0.31/0.48 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Late_Semantics.Close2
% 0.31/0.48 thf(fact_342_mismatchIdRight,axiom,
% 0.31/0.48 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.31/0.48 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.48 => ( ( A != B )
% 0.31/0.48 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A @ B @ P ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mismatchIdRight
% 0.31/0.48 thf(fact_343_mismatchIdLeft,axiom,
% 0.31/0.48 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.31/0.48 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.31/0.48 => ( ( A != B )
% 0.31/0.48 => ( strong743114133lation @ ( mismatch @ A @ B @ P ) @ Rel @ P ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mismatchIdLeft
% 0.31/0.48 thf(fact_344_pi_Ofresh_I6_J,axiom,
% 0.31/0.48 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.31/0.48 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.31/0.48 = ( ( fresh_name_name @ A @ X32 )
% 0.31/0.48 & ( fresh_name_name @ A @ X2 )
% 0.31/0.48 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.fresh(6)
% 0.31/0.48 thf(fact_345_pi_Odistinct_I25_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( ( output @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(25)
% 0.31/0.48 thf(fact_346_pi_Odistinct_I9_J,axiom,
% 0.31/0.48 ! [Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( piNil
% 0.31/0.48 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(9)
% 0.31/0.48 thf(fact_347_pi_Odistinct_I71_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(71)
% 0.31/0.48 thf(fact_348_pi_Odistinct_I51_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( ( input @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(51)
% 0.31/0.48 thf(fact_349_pi_Odistinct_I39_J,axiom,
% 0.31/0.48 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 0.31/0.48 ( ( tau @ Pi4 )
% 0.31/0.48 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(39)
% 0.31/0.48 thf(fact_350_pi_Oinject_I5_J,axiom,
% 0.31/0.48 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.31/0.48 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.31/0.48 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.31/0.48 = ( ( X32 = Y32 )
% 0.31/0.48 & ( X2 = Y2 )
% 0.31/0.48 & ( X1 = Y1 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.inject(5)
% 0.31/0.48 thf(fact_351_pi_Odistinct_I73_J,axiom,
% 0.31/0.48 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.31/0.48 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 0.31/0.48 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % pi.distinct(73)
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 0.31/0.48 y != x ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.89/1.52 ---- Embedded in THF ---
% 2.89/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.53 %%% Generated on Tue Feb 24 08:29:13 EST 2026
% 2.89/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.53 %%% Logic specification used:
% 2.89/1.53 %%% thf(spec, logic, $$dhol).
% 2.89/1.53
% 2.89/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2DTF22043.p
% See solution above
% 2.89/1.53 ------------------------
% 2.89/1.59 ---- Cleaned THF ---
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 2.89/1.59 produc1217648014ion_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 2.89/1.59 produc1961110975reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J_J,type,
% 2.89/1.59 set_Pr100209225_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 2.89/1.59 produc1443308494i_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 2.89/1.59 produc1559976732_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 2.89/1.59 produc53907987_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 2.89/1.59 set_Pr1569510577ion_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 2.89/1.59 produc1462499409ion_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 2.89/1.59 set_Pr305743074reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Nominal__Onoption_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 2.89/1.59 noptio1575811931_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 2.89/1.59 set_Pr1294453099i_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 produc1834551554reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 2.89/1.59 set_Pr1694908217_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 2.89/1.59 set_Pr1654044726_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 2.89/1.59 produc405342261i_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 2.89/1.59 produc629157763_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.89/1.59 produc1141751126_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 produc1357834675reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 2.89/1.59 produc2052722628s_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 produc2008547984reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 2.89/1.59 produc992857746Res_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 produc649380958reeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.89/1.59 set_Pr1834926343_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 2.89/1.59 produc367475239e_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 2.89/1.59 product_prod_pi_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 2.89/1.59 product_prod_name_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.89/1.59 product_prod_pi_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 noption_Late_freeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 2.89/1.59 noption_name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 2.89/1.59 noption_pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 2.89/1.59 late_residual: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Late____Semantics__Osubject,type,
% 2.89/1.59 late_subject: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 2.89/1.59 late_freeRes: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Agent__Oname,type,
% 2.89/1.59 name: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(ty_n_t__Agent__Opi,type,
% 2.89/1.59 pi: $tType ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OInput,type,
% 2.89/1.59 input: name > name > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OMismatch,type,
% 2.89/1.59 mismatch: name > name > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OOutput,type,
% 2.89/1.59 output: name > name > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OPar,type,
% 2.89/1.59 par: pi > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OPiNil,type,
% 2.89/1.59 piNil: pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_ORes,type,
% 2.89/1.59 res: name > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OSum,type,
% 2.89/1.59 sum: pi > pi > pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_Agent_Opi_OTau,type,
% 2.89/1.59 tau: pi > pi ).
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% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 2.89/1.59 member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 2.89/1.59 member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 2.89/1.59 member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 2.89/1.59 member695660714_pi_pi: produc53907987_pi_pi > set_Pr100209225_pi_pi > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.89/1.59 member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.89/1.59 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_P,type,
% 2.89/1.59 p: pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_PQ____,type,
% 2.89/1.59 pq: pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_Q,type,
% 2.89/1.59 q: pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_Rel,type,
% 2.89/1.59 rel: set_Pr1834926343_pi_pi ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_a____,type,
% 2.89/1.59 a: late_subject ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_x,type,
% 2.89/1.59 x: name ).
% 2.89/1.59
% 2.89/1.59 thf(sy_v_y____,type,
% 2.89/1.59 y: name ).
% 2.89/1.59
% 2.89/1.59 thf(fact_0_Eqvt,axiom,
% 2.89/1.59 eqvt_pi @ rel ).
% 2.89/1.59
% 2.89/1.59 thf(fact_1_Bound_Ohyps_I5_J,axiom,
% 2.89/1.59 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_2_Bound_Ohyps_I4_J,axiom,
% 2.89/1.59 fresh_717452603ubject @ y @ a ).
% 2.89/1.59
% 2.89/1.59 thf(fact_3_Bound_Ohyps_I3_J,axiom,
% 2.89/1.59 fresh_name_pi @ y @ ( res @ x @ ( sum @ p @ q ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_4_Bound_Ohyps_I2_J,axiom,
% 2.89/1.59 fresh_name_pi @ y @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_5_Bound_Ohyps_I1_J,axiom,
% 2.89/1.59 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_BoundR @ a @ y @ pq ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_6_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 2.89/1.59 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.89/1.59 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_7_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: late_freeRes,Y: name] :
% 2.89/1.59 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.89/1.59 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_8_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: late_freeRes,Y: pi] :
% 2.89/1.59 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_1641682979reeRes @ A @ X )
% 2.89/1.59 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_9_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: late_freeRes] :
% 2.89/1.59 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X )
% 2.89/1.59 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_10_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: name] :
% 2.89/1.59 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X )
% 2.89/1.59 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_11_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: pi] :
% 2.89/1.59 ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X )
% 2.89/1.59 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_12_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: late_freeRes] :
% 2.89/1.59 ( ( fresh_1504024600reeRes @ A @ ( produc1638681944reeRes @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_pi @ A @ X )
% 2.89/1.59 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_13_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: name] :
% 2.89/1.59 ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_pi @ A @ X )
% 2.89/1.59 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_14_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: pi] :
% 2.89/1.59 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_pi @ A @ X )
% 2.89/1.59 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_15_fresh__prod,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.89/1.59 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X )
% 2.89/1.59 & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_16_pi_Ofresh_I7_J,axiom,
% 2.89/1.59 ! [A: name,X2: pi,X1: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 2.89/1.59 = ( ( fresh_name_pi @ A @ X2 )
% 2.89/1.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_17_transitions_OResB,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Y @ A )
% 2.89/1.59 => ( ( Y != X )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A )
% 2.89/1.59 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_18_freshBoundDerivative_I1_J,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.59 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_19_Late__Semantics_OResB,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Y @ A )
% 2.89/1.59 => ( ( Y != X )
% 2.89/1.59 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_20_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: pi] :
% 2.89/1.59 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_name_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_21_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.89/1.59 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_22_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 2.89/1.59 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 2.89/1.59 => ( fresh_1641682979reeRes @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_23_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: name] :
% 2.89/1.59 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 2.89/1.59 => ( fresh_name_name @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_24_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: pi] :
% 2.89/1.59 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_name_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_25_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 2.89/1.59 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_26_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_1376661020_pi_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_27_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
% 2.89/1.59 ( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
% 2.89/1.59 => ( fresh_1711070152reeRes @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_28_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
% 2.89/1.59 ( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
% 2.89/1.59 => ( fresh_453496559i_name @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_29_fresh__prodD_I2_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
% 2.89/1.59 ( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_253309757_pi_pi @ A @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_30_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: pi] :
% 2.89/1.59 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_name_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_31_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.89/1.59 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_name_name @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_32_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: late_freeRes] :
% 2.89/1.59 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_33_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: name] :
% 2.89/1.59 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_34_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: pi] :
% 2.89/1.59 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_35_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 2.89/1.59 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_36_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_975559885_pi_pi @ A @ ( produc1275980869_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_37_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc1834551554reeRes] :
% 2.89/1.59 ( ( fresh_1729533561reeRes @ A @ ( produc703114481reeRes @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_38_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc405342261i_name] :
% 2.89/1.59 ( ( fresh_1513292180i_name @ A @ ( produc1024533510i_name @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_39_fresh__prodD_I1_J,axiom,
% 2.89/1.59 ! [A: name,X: name > noption_pi,Y: produc629157763_pi_pi] :
% 2.89/1.59 ( ( fresh_1335311330_pi_pi @ A @ ( produc1189045204_pi_pi @ X @ Y ) )
% 2.89/1.59 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_40_freshBoundDerivative_I2_J,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.59 => ( ( Y != X )
% 2.89/1.59 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_41_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 2.89/1.59 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 2.89/1.59 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_42_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name,X2: product_prod_pi_pi,Y1: name,Y2: product_prod_pi_pi] :
% 2.89/1.59 ( ( ( produc235456326_pi_pi @ X1 @ X2 )
% 2.89/1.59 = ( produc235456326_pi_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_43_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y2: late_freeRes] :
% 2.89/1.59 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 2.89/1.59 = ( produc1505598906reeRes @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_44_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y2: name] :
% 2.89/1.59 ( ( ( produc540578151i_name @ X1 @ X2 )
% 2.89/1.59 = ( produc540578151i_name @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_45_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y2: pi] :
% 2.89/1.59 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 2.89/1.59 = ( produc1820286517_pi_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_46_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y2: name > noption_pi] :
% 2.89/1.59 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 2.89/1.59 = ( produc1342893193ion_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_47_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: produc1141751126_pi_pi,Y1: name > noption_pi,Y2: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( ( produc1275980869_pi_pi @ X1 @ X2 )
% 2.89/1.59 = ( produc1275980869_pi_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_48_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: produc1834551554reeRes,Y1: name > noption_pi,Y2: produc1834551554reeRes] :
% 2.89/1.59 ( ( ( produc703114481reeRes @ X1 @ X2 )
% 2.89/1.59 = ( produc703114481reeRes @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_49_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: produc405342261i_name,Y1: name > noption_pi,Y2: produc405342261i_name] :
% 2.89/1.59 ( ( ( produc1024533510i_name @ X1 @ X2 )
% 2.89/1.59 = ( produc1024533510i_name @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_50_prod_Oinject,axiom,
% 2.89/1.59 ! [X1: name > noption_pi,X2: produc629157763_pi_pi,Y1: name > noption_pi,Y2: produc629157763_pi_pi] :
% 2.89/1.59 ( ( ( produc1189045204_pi_pi @ X1 @ X2 )
% 2.89/1.59 = ( produc1189045204_pi_pi @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X1 = Y1 )
% 2.89/1.59 & ( X2 = Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_51_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 2.89/1.59 ( ( ( product_Pair_pi_pi @ A @ B )
% 2.89/1.59 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_52_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 2.89/1.59 ( ( ( produc235456326_pi_pi @ A @ B )
% 2.89/1.59 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_53_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 2.89/1.59 ( ( ( produc1505598906reeRes @ A @ B )
% 2.89/1.59 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_54_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 2.89/1.59 ( ( ( produc540578151i_name @ A @ B )
% 2.89/1.59 = ( produc540578151i_name @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_55_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 2.89/1.59 ( ( ( produc1820286517_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_56_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 2.89/1.59 ( ( ( produc1342893193ion_pi @ A @ B )
% 2.89/1.59 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_57_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( ( produc1275980869_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_58_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
% 2.89/1.59 ( ( ( produc703114481reeRes @ A @ B )
% 2.89/1.59 = ( produc703114481reeRes @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_59_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
% 2.89/1.59 ( ( ( produc1024533510i_name @ A @ B )
% 2.89/1.59 = ( produc1024533510i_name @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_60_old_Oprod_Oinject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
% 2.89/1.59 ( ( ( produc1189045204_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1189045204_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 = ( ( A = A2 )
% 2.89/1.59 & ( B = B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_61_pi_Odistinct_I81_J,axiom,
% 2.89/1.59 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.89/1.59 ( ( sum @ Pi1 @ Pi2 )
% 2.89/1.59 != ( res @ Name @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_62_freshResidual,axiom,
% 2.89/1.59 ! [P: pi,Rs: late_residual,X: name] :
% 2.89/1.59 ( ( late_transitions @ P @ Rs )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_63_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 2.89/1.59 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_64_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1141751126_pi_pi > $o,Prod: produc1141751126_pi_pi] :
% 2.89/1.59 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_65_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_66_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_67_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_68_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_69_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc53907987_pi_pi > $o,Prod: produc53907987_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_70_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1961110975reeRes > $o,Prod: produc1961110975reeRes] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_71_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1443308494i_name > $o,Prod: produc1443308494i_name] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_72_old_Oprod_Oinducts,axiom,
% 2.89/1.59 ! [P: produc1559976732_pi_pi > $o,Prod: produc1559976732_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ Prod ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_73_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: product_prod_pi_pi] :
% 2.89/1.59 ~ ! [A3: pi,B3: pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( product_Pair_pi_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_74_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1141751126_pi_pi] :
% 2.89/1.59 ~ ! [A3: name,B3: product_prod_pi_pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc235456326_pi_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_75_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1834551554reeRes] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: late_freeRes] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1505598906reeRes @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_76_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc405342261i_name] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: name] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc540578151i_name @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_77_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc629157763_pi_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1820286517_pi_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_78_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1462499409ion_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: name > noption_pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1342893193ion_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_79_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc53907987_pi_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1275980869_pi_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_80_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1961110975reeRes] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: produc1834551554reeRes] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc703114481reeRes @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_81_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1443308494i_name] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: produc405342261i_name] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1024533510i_name @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_82_old_Oprod_Oexhaust,axiom,
% 2.89/1.59 ! [Y: produc1559976732_pi_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: produc629157763_pi_pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1189045204_pi_pi @ A3 @ B3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_83_Pair__inject,axiom,
% 2.89/1.59 ! [A: pi,B: pi,A2: pi,B2: pi] :
% 2.89/1.59 ( ( ( product_Pair_pi_pi @ A @ B )
% 2.89/1.59 = ( product_Pair_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_84_Pair__inject,axiom,
% 2.89/1.59 ! [A: name,B: product_prod_pi_pi,A2: name,B2: product_prod_pi_pi] :
% 2.89/1.59 ( ( ( produc235456326_pi_pi @ A @ B )
% 2.89/1.59 = ( produc235456326_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_85_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: late_freeRes,A2: name > noption_pi,B2: late_freeRes] :
% 2.89/1.59 ( ( ( produc1505598906reeRes @ A @ B )
% 2.89/1.59 = ( produc1505598906reeRes @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_86_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name,A2: name > noption_pi,B2: name] :
% 2.89/1.59 ( ( ( produc540578151i_name @ A @ B )
% 2.89/1.59 = ( produc540578151i_name @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_87_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: pi,A2: name > noption_pi,B2: pi] :
% 2.89/1.59 ( ( ( produc1820286517_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1820286517_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_88_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name > noption_pi,A2: name > noption_pi,B2: name > noption_pi] :
% 2.89/1.59 ( ( ( produc1342893193ion_pi @ A @ B )
% 2.89/1.59 = ( produc1342893193ion_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_89_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc1141751126_pi_pi,A2: name > noption_pi,B2: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( ( produc1275980869_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1275980869_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_90_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc1834551554reeRes,A2: name > noption_pi,B2: produc1834551554reeRes] :
% 2.89/1.59 ( ( ( produc703114481reeRes @ A @ B )
% 2.89/1.59 = ( produc703114481reeRes @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_91_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc405342261i_name,A2: name > noption_pi,B2: produc405342261i_name] :
% 2.89/1.59 ( ( ( produc1024533510i_name @ A @ B )
% 2.89/1.59 = ( produc1024533510i_name @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_92_Pair__inject,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: produc629157763_pi_pi,A2: name > noption_pi,B2: produc629157763_pi_pi] :
% 2.89/1.59 ( ( ( produc1189045204_pi_pi @ A @ B )
% 2.89/1.59 = ( produc1189045204_pi_pi @ A2 @ B2 ) )
% 2.89/1.59 => ~ ( ( A = A2 )
% 2.89/1.59 => ( B != B2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_93_prod__cases,axiom,
% 2.89/1.59 ! [P: product_prod_pi_pi > $o,P3: product_prod_pi_pi] :
% 2.89/1.59 ( ! [A3: pi,B3: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_94_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1141751126_pi_pi > $o,P3: produc1141751126_pi_pi] :
% 2.89/1.59 ( ! [A3: name,B3: product_prod_pi_pi] : ( P @ ( produc235456326_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_95_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1834551554reeRes > $o,P3: produc1834551554reeRes] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_96_prod__cases,axiom,
% 2.89/1.59 ! [P: produc405342261i_name > $o,P3: produc405342261i_name] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name] : ( P @ ( produc540578151i_name @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_97_prod__cases,axiom,
% 2.89/1.59 ! [P: produc629157763_pi_pi > $o,P3: produc629157763_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_98_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1462499409ion_pi > $o,P3: produc1462499409ion_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_99_prod__cases,axiom,
% 2.89/1.59 ! [P: produc53907987_pi_pi > $o,P3: produc53907987_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc1141751126_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_100_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1961110975reeRes > $o,P3: produc1961110975reeRes] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc1834551554reeRes] : ( P @ ( produc703114481reeRes @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_101_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1443308494i_name > $o,P3: produc1443308494i_name] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc405342261i_name] : ( P @ ( produc1024533510i_name @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_102_prod__cases,axiom,
% 2.89/1.59 ! [P: produc1559976732_pi_pi > $o,P3: produc1559976732_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: produc629157763_pi_pi] : ( P @ ( produc1189045204_pi_pi @ A3 @ B3 ) )
% 2.89/1.59 => ( P @ P3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_103_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc1217648014ion_pi] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: produc1462499409ion_pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc674047040ion_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_104_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc1141751126_pi_pi] :
% 2.89/1.59 ? [X3: name,Y3: product_prod_pi_pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc235456326_pi_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_105_surj__pair,axiom,
% 2.89/1.59 ! [P3: product_prod_pi_pi] :
% 2.89/1.59 ? [X3: pi,Y3: pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( product_Pair_pi_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_106_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc1834551554reeRes] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: late_freeRes] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc1505598906reeRes @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_107_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc53907987_pi_pi] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc1275980869_pi_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_108_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc405342261i_name] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: name] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc540578151i_name @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_109_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc629157763_pi_pi] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc1820286517_pi_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_110_surj__pair,axiom,
% 2.89/1.59 ! [P3: produc1462499409ion_pi] :
% 2.89/1.59 ? [X3: name > noption_pi,Y3: name > noption_pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 = ( produc1342893193ion_pi @ X3 @ Y3 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_111_name__exists__fresh,axiom,
% 2.89/1.59 ! [X: late_freeRes] :
% 2.89/1.59 ~ ! [C: name] :
% 2.89/1.59 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_112_name__exists__fresh,axiom,
% 2.89/1.59 ! [X: produc1141751126_pi_pi] :
% 2.89/1.59 ~ ! [C: name] :
% 2.89/1.59 ~ ( fresh_1376661020_pi_pi @ C @ X ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_113_name__exists__fresh,axiom,
% 2.89/1.59 ! [X: name] :
% 2.89/1.59 ~ ! [C: name] :
% 2.89/1.59 ~ ( fresh_name_name @ C @ X ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_114_name__exists__fresh,axiom,
% 2.89/1.59 ! [X: pi] :
% 2.89/1.59 ~ ! [C: name] :
% 2.89/1.59 ~ ( fresh_name_pi @ C @ X ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_115_pi_Oinject_I6_J,axiom,
% 2.89/1.59 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.89/1.59 ( ( ( sum @ X2 @ X1 )
% 2.89/1.59 = ( sum @ Y2 @ Y1 ) )
% 2.89/1.59 = ( ( X2 = Y2 )
% 2.89/1.59 & ( X1 = Y1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_116_prod__induct4,axiom,
% 2.89/1.59 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name,C: pi,D: pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) )
% 2.89/1.59 => ( P @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_117_prod__induct3,axiom,
% 2.89/1.59 ! [P: produc1141751126_pi_pi > $o,X: produc1141751126_pi_pi] :
% 2.89/1.59 ( ! [A3: name,B3: pi,C: pi] : ( P @ ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) )
% 2.89/1.59 => ( P @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_118_prod__induct3,axiom,
% 2.89/1.59 ! [P: produc53907987_pi_pi > $o,X: produc53907987_pi_pi] :
% 2.89/1.59 ( ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] : ( P @ ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) )
% 2.89/1.59 => ( P @ X ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_119_prod__cases4,axiom,
% 2.89/1.59 ! [Y: produc53907987_pi_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: name,C: pi,D: pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ ( product_Pair_pi_pi @ C @ D ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_120_prod__cases3,axiom,
% 2.89/1.59 ! [Y: produc1141751126_pi_pi] :
% 2.89/1.59 ~ ! [A3: name,B3: pi,C: pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc235456326_pi_pi @ A3 @ ( product_Pair_pi_pi @ B3 @ C ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_121_prod__cases3,axiom,
% 2.89/1.59 ! [Y: produc53907987_pi_pi] :
% 2.89/1.59 ~ ! [A3: name > noption_pi,B3: name,C: product_prod_pi_pi] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( produc1275980869_pi_pi @ A3 @ ( produc235456326_pi_pi @ B3 @ C ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_122_freshRes,axiom,
% 2.89/1.59 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_123_Sum2,axiom,
% 2.89/1.59 ! [Q: pi,Rs: late_residual,P: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ Rs )
% 2.89/1.59 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_124_Sum1,axiom,
% 2.89/1.59 ! [P: pi,Rs: late_residual,Q: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ Rs )
% 2.89/1.59 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_125_sumCases_H,axiom,
% 2.89/1.59 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.89/1.59 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.89/1.59 => ( ~ ( late_transitions @ P @ Rs )
% 2.89/1.59 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_126_sumCases,axiom,
% 2.89/1.59 ! [P: pi,Q: pi,Rs: late_residual] :
% 2.89/1.59 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 2.89/1.59 => ( ~ ( late_transitions @ P @ Rs )
% 2.89/1.59 => ( late_transitions @ Q @ Rs ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_127_Id,axiom,
% 2.89/1.59 ord_le630093991_pi_pi @ id_pi @ rel ).
% 2.89/1.59
% 2.89/1.59 thf(fact_128_transitions_OPar2B,axiom,
% 2.89/1.59 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_129_transitions_OPar1B,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_130_mem__Collect__eq,axiom,
% 2.89/1.59 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 2.89/1.59 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 2.89/1.59 = ( P @ A ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_131_Collect__mem__eq,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( collec1051790738_pi_pi
% 2.89/1.59 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A4 ) )
% 2.89/1.59 = A4 ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_132_parCasesB_H,axiom,
% 2.89/1.59 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 2.89/1.59 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.89/1.59 => ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Q3: pi] :
% 2.89/1.59 ( ( ( par @ P @ Q )
% 2.89/1.59 = ( par @ P4 @ Q3 ) )
% 2.89/1.59 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.89/1.59 = ( late_BoundR @ A3 @ X3 @ ( par @ P5 @ Q3 ) ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P4 )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q3 )
% 2.89/1.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) )
% 2.89/1.59 => ~ ! [Q3: pi,A3: late_subject,X3: name,Q4: pi,P4: pi] :
% 2.89/1.59 ( ( ( par @ P @ Q )
% 2.89/1.59 = ( par @ P4 @ Q3 ) )
% 2.89/1.59 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 2.89/1.59 = ( late_BoundR @ A3 @ X3 @ ( par @ P4 @ Q4 ) ) )
% 2.89/1.59 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P4 )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q3 )
% 2.89/1.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_133_inputIneqTrans,axiom,
% 2.89/1.59 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 2.89/1.59 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 2.89/1.59 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_134_resTauBoundTrans,axiom,
% 2.89/1.59 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_135_residual_Ostrong__inducts,axiom,
% 2.89/1.59 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
% 2.89/1.59 ( ( fresh_1641682979reeRes @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_136_residual_Ostrong__inducts,axiom,
% 2.89/1.59 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_137_residual_Ostrong__inducts,axiom,
% 2.89/1.59 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
% 2.89/1.59 ( ( fresh_name_name @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_138_residual_Ostrong__inducts,axiom,
% 2.89/1.59 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_139_residual_Ostrong__induct,axiom,
% 2.89/1.59 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
% 2.89/1.59 ( ( fresh_1641682979reeRes @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_140_residual_Ostrong__induct,axiom,
% 2.89/1.59 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_1376661020_pi_pi @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_141_residual_Ostrong__induct,axiom,
% 2.89/1.59 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
% 2.89/1.59 ( ( fresh_name_name @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_142_residual_Ostrong__induct,axiom,
% 2.89/1.59 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ Name2 @ Z2 )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 2.89/1.59 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Z @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_143_pi_Ofresh_I8_J,axiom,
% 2.89/1.59 ! [A: name,X2: pi,X1: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 2.89/1.59 = ( ( fresh_name_pi @ A @ X2 )
% 2.89/1.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_144_pi_Ofresh_I3_J,axiom,
% 2.89/1.59 ! [A: name,X1: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 2.89/1.59 = ( fresh_name_pi @ A @ X1 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_145_residual_Ofresh_I2_J,axiom,
% 2.89/1.59 ! [A: name,X2: late_freeRes,X1: pi] :
% 2.89/1.59 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 2.89/1.59 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 2.89/1.59 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_146_residual_Oinject_I2_J,axiom,
% 2.89/1.59 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.89/1.59 ( ( ( late_FreeR @ X2 @ X1 )
% 2.89/1.59 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.89/1.59 = ( ( X2 = Y2 )
% 2.89/1.59 & ( X1 = Y1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_147_pi_Odistinct_I35_J,axiom,
% 2.89/1.59 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.89/1.59 ( ( tau @ Pi4 )
% 2.89/1.59 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_148_pi_Odistinct_I43_J,axiom,
% 2.89/1.59 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( ( tau @ Pi4 )
% 2.89/1.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_149_pi_Odistinct_I55_J,axiom,
% 2.89/1.59 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.89/1.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_150_pi_Oinject_I2_J,axiom,
% 2.89/1.59 ! [X1: pi,Y1: pi] :
% 2.89/1.59 ( ( ( tau @ X1 )
% 2.89/1.59 = ( tau @ Y1 ) )
% 2.89/1.59 = ( X1 = Y1 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_151_pi_Oinject_I7_J,axiom,
% 2.89/1.59 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.89/1.59 ( ( ( par @ X2 @ X1 )
% 2.89/1.59 = ( par @ Y2 @ Y1 ) )
% 2.89/1.59 = ( ( X2 = Y2 )
% 2.89/1.59 & ( X1 = Y1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_152_Par2F,axiom,
% 2.89/1.59 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_153_Par1F,axiom,
% 2.89/1.59 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_154_inputFreeTrans,axiom,
% 2.89/1.59 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_155_resInputFreeTrans,axiom,
% 2.89/1.59 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_156_pi_Odistinct_I85_J,axiom,
% 2.89/1.59 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 2.89/1.59 ( ( par @ Pi1 @ Pi2 )
% 2.89/1.59 != ( res @ Name @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_157_pi_Odistinct_I79_J,axiom,
% 2.89/1.59 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( ( sum @ Pi1 @ Pi2 )
% 2.89/1.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_158_residual_Odistinct_I1_J,axiom,
% 2.89/1.59 ! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 2.89/1.59 ( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
% 2.89/1.59 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_159_residual_Oinducts,axiom,
% 2.89/1.59 ! [P: late_residual > $o,Residual: late_residual] :
% 2.89/1.59 ( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
% 2.89/1.59 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 2.89/1.59 => ( P @ Residual ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_160_pi_Odistinct_I57_J,axiom,
% 2.89/1.59 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 2.89/1.59 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.89/1.59 != ( res @ Name @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_161_pi_Odistinct_I45_J,axiom,
% 2.89/1.59 ! [Pi4: pi,Name: name,Pi: pi] :
% 2.89/1.59 ( ( tau @ Pi4 )
% 2.89/1.59 != ( res @ Name @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_162_pi_Odistinct_I53_J,axiom,
% 2.89/1.59 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.89/1.59 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_163_pi_Odistinct_I41_J,axiom,
% 2.89/1.59 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( ( tau @ Pi4 )
% 2.89/1.59 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_164_resCasesF,axiom,
% 2.89/1.59 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 2.89/1.59 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.89/1.59 => ( ! [P5: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 2.89/1.59 => ( F @ ( res @ X @ P5 ) ) ) )
% 2.89/1.59 => ( F @ XP ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_165_resCasesF_H,axiom,
% 2.89/1.59 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.89/1.59 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.59 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.89/1.59 ( ( ( res @ X @ P )
% 2.89/1.59 = ( res @ Y3 @ P4 ) )
% 2.89/1.59 => ( ( ( late_FreeR @ Alpha @ P2 )
% 2.89/1.59 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.89/1.59 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_166_ResF,axiom,
% 2.89/1.59 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 2.89/1.59 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_167_freshFreeDerivative_I2_J,axiom,
% 2.89/1.59 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.59 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_168_freshFreeDerivative_I1_J,axiom,
% 2.89/1.59 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.59 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_169_resTrans_I2_J,axiom,
% 2.89/1.59 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_170_tauBoundTrans,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_171_Late__Semantics_OPar1B,axiom,
% 2.89/1.59 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_172_Late__Semantics_OPar2B,axiom,
% 2.89/1.59 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_173_parCasesB,axiom,
% 2.89/1.59 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 2.89/1.59 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.59 => ( ! [P5: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 2.89/1.59 => ( Prop @ ( par @ P5 @ Q ) ) )
% 2.89/1.59 => ( ! [Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 2.89/1.59 => ( Prop @ ( par @ P @ Q4 ) ) )
% 2.89/1.59 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_174_IdI,axiom,
% 2.89/1.59 ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_175_IdI,axiom,
% 2.89/1.59 ! [A: name > noption_pi] : ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ A ) @ id_name_noption_pi ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_176_pair__in__Id__conv,axiom,
% 2.89/1.59 ! [A: pi,B: pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 2.89/1.59 = ( A = B ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_177_pair__in__Id__conv,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name > noption_pi] :
% 2.89/1.59 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 2.89/1.59 = ( A = B ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_178_subsetI,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ! [X3: product_prod_pi_pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ X3 @ A4 )
% 2.89/1.59 => ( member558706512_pi_pi @ X3 @ B4 ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_179_subset__antisym,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B4 @ A4 )
% 2.89/1.59 => ( A4 = B4 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_180_order__refl,axiom,
% 2.89/1.59 ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_181_IdE,axiom,
% 2.89/1.59 ! [P3: product_prod_pi_pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ P3 @ id_pi )
% 2.89/1.59 => ~ ! [X3: pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 != ( product_Pair_pi_pi @ X3 @ X3 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_182_IdE,axiom,
% 2.89/1.59 ! [P3: produc1462499409ion_pi] :
% 2.89/1.59 ( ( member1632198138ion_pi @ P3 @ id_name_noption_pi )
% 2.89/1.59 => ~ ! [X3: name > noption_pi] :
% 2.89/1.59 ( P3
% 2.89/1.59 != ( produc1342893193ion_pi @ X3 @ X3 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_183_IdD,axiom,
% 2.89/1.59 ! [A: pi,B: pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 2.89/1.59 => ( A = B ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_184_IdD,axiom,
% 2.89/1.59 ! [A: name > noption_pi,B: name > noption_pi] :
% 2.89/1.59 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 2.89/1.59 => ( A = B ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_185_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr1654044726_pi_pi,S: set_Pr1654044726_pi_pi] :
% 2.89/1.59 ( ! [X3: name,Y3: product_prod_pi_pi] :
% 2.89/1.59 ( ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member540268543_pi_pi @ ( produc235456326_pi_pi @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le797229014_pi_pi @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_186_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr305743074reeRes,S: set_Pr305743074reeRes] :
% 2.89/1.59 ( ! [X3: name > noption_pi,Y3: late_freeRes] :
% 2.89/1.59 ( ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member2081207979reeRes @ ( produc1505598906reeRes @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le1762471042reeRes @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_187_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr100209225_pi_pi,S: set_Pr100209225_pi_pi] :
% 2.89/1.59 ( ! [X3: name > noption_pi,Y3: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member695660714_pi_pi @ ( produc1275980869_pi_pi @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le211833513_pi_pi @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_188_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr1294453099i_name,S: set_Pr1294453099i_name] :
% 2.89/1.59 ( ! [X3: name > noption_pi,Y3: name] :
% 2.89/1.59 ( ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member1353687244i_name @ ( produc540578151i_name @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le2082425291i_name @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_189_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr1694908217_pi_pi,S: set_Pr1694908217_pi_pi] :
% 2.89/1.59 ( ! [X3: name > noption_pi,Y3: pi] :
% 2.89/1.59 ( ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le1854926745_pi_pi @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_190_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr1569510577ion_pi,S: set_Pr1569510577ion_pi] :
% 2.89/1.59 ( ! [X3: name > noption_pi,Y3: name > noption_pi] :
% 2.89/1.59 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le1032043601ion_pi @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_191_subrelI,axiom,
% 2.89/1.59 ! [R: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ! [X3: pi,Y3: pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ R )
% 2.89/1.59 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X3 @ Y3 ) @ S ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ R @ S ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_192_dual__order_Oantisym,axiom,
% 2.89/1.59 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ B @ A )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( A = B ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_193_dual__order_Oeq__iff,axiom,
% 2.89/1.59 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 2.89/1.59 = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ B5 @ A5 )
% 2.89/1.59 & ( ord_le630093991_pi_pi @ A5 @ B5 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_194_dual__order_Otrans,axiom,
% 2.89/1.59 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ B @ A )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ C2 @ B )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ C2 @ A ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_195_dual__order_Orefl,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_196_order__trans,axiom,
% 2.89/1.59 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X @ Y )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ Y @ Z )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ X @ Z ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_197_order__class_Oorder_Oantisym,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B @ A )
% 2.89/1.59 => ( A = B ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_198_ord__le__eq__trans,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( ( B = C2 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_199_ord__eq__le__trans,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( A = B )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_200_order__class_Oorder_Oeq__iff,axiom,
% 2.89/1.59 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 2.89/1.59 = ( ^ [A5: set_Pr1834926343_pi_pi,B5: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A5 @ B5 )
% 2.89/1.59 & ( ord_le630093991_pi_pi @ B5 @ A5 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_201_antisym__conv,axiom,
% 2.89/1.59 ! [Y: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ Y @ X )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ X @ Y )
% 2.89/1.59 = ( X = Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_202_order_Otrans,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_203_eq__refl,axiom,
% 2.89/1.59 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( X = Y )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ X @ Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_204_antisym,axiom,
% 2.89/1.59 ! [X: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X @ Y )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ Y @ X )
% 2.89/1.59 => ( X = Y ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_205_eq__iff,axiom,
% 2.89/1.59 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 2.89/1.59 = ( ^ [X4: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X4 @ Y5 )
% 2.89/1.59 & ( ord_le630093991_pi_pi @ Y5 @ X4 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_206_ord__le__eq__subst,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( ( ( F2 @ B )
% 2.89/1.59 = C2 )
% 2.89/1.59 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_207_ord__eq__le__subst,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( A
% 2.89/1.59 = ( F2 @ B ) )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 2.89/1.59 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_208_order__subst2,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ B )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ ( F2 @ B ) @ C2 )
% 2.89/1.59 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_209_order__subst1,axiom,
% 2.89/1.59 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A @ ( F2 @ B ) )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 2.89/1.59 => ( ! [X3: set_Pr1834926343_pi_pi,Y3: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ X3 @ Y3 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_210_Collect__mono__iff,axiom,
% 2.89/1.59 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) )
% 2.89/1.59 = ( ! [X4: product_prod_pi_pi] :
% 2.89/1.59 ( ( P @ X4 )
% 2.89/1.59 => ( Q @ X4 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_211_set__eq__subset,axiom,
% 2.89/1.59 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 2.89/1.59 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A6 @ B6 )
% 2.89/1.59 & ( ord_le630093991_pi_pi @ B6 @ A6 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_212_subset__trans,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C3: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ B4 @ C3 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A4 @ C3 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_213_Collect__mono,axiom,
% 2.89/1.59 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 2.89/1.59 ( ! [X3: product_prod_pi_pi] :
% 2.89/1.59 ( ( P @ X3 )
% 2.89/1.59 => ( Q @ X3 ) )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_214_subset__refl,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A4 @ A4 ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_215_subset__iff,axiom,
% 2.89/1.59 ( ord_le630093991_pi_pi
% 2.89/1.59 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ! [T: product_prod_pi_pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ T @ A6 )
% 2.89/1.59 => ( member558706512_pi_pi @ T @ B6 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_216_equalityD2,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( A4 = B4 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_217_equalityD1,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( A4 = B4 )
% 2.89/1.59 => ( ord_le630093991_pi_pi @ A4 @ B4 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_218_subset__eq,axiom,
% 2.89/1.59 ( ord_le630093991_pi_pi
% 2.89/1.59 = ( ^ [A6: set_Pr1834926343_pi_pi,B6: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ! [X4: product_prod_pi_pi] :
% 2.89/1.59 ( ( member558706512_pi_pi @ X4 @ A6 )
% 2.89/1.59 => ( member558706512_pi_pi @ X4 @ B6 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_219_equalityE,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( A4 = B4 )
% 2.89/1.59 => ~ ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ~ ( ord_le630093991_pi_pi @ B4 @ A4 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_220_subsetD,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,C2: product_prod_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( ( member558706512_pi_pi @ C2 @ A4 )
% 2.89/1.59 => ( member558706512_pi_pi @ C2 @ B4 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_221_in__mono,axiom,
% 2.89/1.59 ! [A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi,X: product_prod_pi_pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( ( member558706512_pi_pi @ X @ A4 )
% 2.89/1.59 => ( member558706512_pi_pi @ X @ B4 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_222_resInputBoundOutputTrans,axiom,
% 2.89/1.59 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_223_resTauOutputTrans,axiom,
% 2.89/1.59 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_224_simCasesCont,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 2.89/1.59 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_225_simCasesCont,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 2.89/1.59 => ( ( fresh_1376661020_pi_pi @ X3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 2.89/1.59 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_226_simCasesCont,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 2.89/1.59 => ( ( fresh_name_name @ X3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 2.89/1.59 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_227_simCasesCont,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [A3: late_subject,X3: name,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ Q )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X3 @ A3 )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X3 @ Rel ) ) ) ) ) ) )
% 2.89/1.59 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_228_residual_Ofresh_I1_J,axiom,
% 2.89/1.59 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 2.89/1.59 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 2.89/1.59 = ( ( fresh_717452603ubject @ A @ X32 )
% 2.89/1.59 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_229_resCases_H,axiom,
% 2.89/1.59 ! [X: name,P: pi,Rs: late_residual] :
% 2.89/1.59 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 2.89/1.59 => ( ! [P4: pi,A3: name,B3: name] :
% 2.89/1.59 ( ( ( res @ X @ P )
% 2.89/1.59 = ( res @ B3 @ P4 ) )
% 2.89/1.59 => ! [P5: pi] :
% 2.89/1.59 ( ( Rs
% 2.89/1.59 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 2.89/1.59 => ( A3 = B3 ) ) ) )
% 2.89/1.59 => ( ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
% 2.89/1.59 ( ( ( res @ X @ P )
% 2.89/1.59 = ( res @ Y3 @ P4 ) )
% 2.89/1.59 => ( ( Rs
% 2.89/1.59 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 2.89/1.59 => ( ( Y3 != X3 )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P4 )
% 2.89/1.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) )
% 2.89/1.59 => ~ ! [P4: pi,Alpha2: late_freeRes,P5: pi,Y3: name] :
% 2.89/1.59 ( ( ( res @ X @ P )
% 2.89/1.59 = ( res @ Y3 @ P4 ) )
% 2.89/1.59 => ( ( Rs
% 2.89/1.59 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P5 ) ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P5 ) )
% 2.89/1.59 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_230_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.89/1.59 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 2.89/1.59 ( ( ( late_OutputR @ X2 @ X1 )
% 2.89/1.59 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.89/1.59 = ( ( X2 = Y2 )
% 2.89/1.59 & ( X1 = Y1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_231_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.89/1.59 ! [X1: name,Y1: name] :
% 2.89/1.59 ( ( ( late_BoundOutputS @ X1 )
% 2.89/1.59 = ( late_BoundOutputS @ Y1 ) )
% 2.89/1.59 = ( X1 = Y1 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_232_subject_Ofresh_I2_J,axiom,
% 2.89/1.59 ! [A: name,X1: name] :
% 2.89/1.59 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 2.89/1.59 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_233_freeRes_Ofresh_I1_J,axiom,
% 2.89/1.59 ! [A: name,X2: name,X1: name] :
% 2.89/1.59 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X2 )
% 2.89/1.59 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_234_pi_Ofresh_I9_J,axiom,
% 2.89/1.59 ! [A: name,X1: name,X2: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 2.89/1.59 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_235_pi_Ofresh_I4_J,axiom,
% 2.89/1.59 ! [A: name,X32: name,X1: name,X2: pi] :
% 2.89/1.59 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 2.89/1.59 = ( ( fresh_name_name @ A @ X32 )
% 2.89/1.59 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_236_monotonic,axiom,
% 2.89/1.59 ! [P: pi,A4: set_Pr1834926343_pi_pi,P2: pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( strong743114133lation @ P @ A4 @ P2 )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( strong743114133lation @ P @ B4 @ P2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_237_abs__fun__eq1,axiom,
% 2.89/1.59 ! [A: name,X: pi,Y: pi] :
% 2.89/1.59 ( ( ( abs_fun_name_pi @ A @ X )
% 2.89/1.59 = ( abs_fun_name_pi @ A @ Y ) )
% 2.89/1.59 = ( X = Y ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_238_derivativeMonotonic,axiom,
% 2.89/1.59 ! [P: pi,Q: pi,A: late_subject,X: name,A4: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ( strong2129052853vative @ P @ Q @ A @ X @ A4 )
% 2.89/1.59 => ( ( ord_le630093991_pi_pi @ A4 @ B4 )
% 2.89/1.59 => ( strong2129052853vative @ P @ Q @ A @ X @ B4 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_239_pi_Oinject_I8_J,axiom,
% 2.89/1.59 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 2.89/1.59 ( ( ( res @ X1 @ X2 )
% 2.89/1.59 = ( res @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.89/1.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_240_residual_Oinject_I1_J,axiom,
% 2.89/1.59 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 2.89/1.59 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 2.89/1.59 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X32 = Y32 )
% 2.89/1.59 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.89/1.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_241_abs__fresh_I1_J,axiom,
% 2.89/1.59 ! [B: name,A: name,X: late_freeRes] :
% 2.89/1.59 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_242_abs__fresh_I1_J,axiom,
% 2.89/1.59 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_243_abs__fresh_I1_J,axiom,
% 2.89/1.59 ! [B: name,A: name,X: name] :
% 2.89/1.59 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_name_name @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_244_abs__fresh_I1_J,axiom,
% 2.89/1.59 ! [B: name,A: name,X: pi] :
% 2.89/1.59 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_name_pi @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_245_name__fresh__abs,axiom,
% 2.89/1.59 ! [B: name,A: name,X: late_freeRes] :
% 2.89/1.59 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_246_name__fresh__abs,axiom,
% 2.89/1.59 ! [B: name,A: name,X: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( fresh_2065563522_pi_pi @ B @ ( abs_fu385186459_pi_pi @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_1376661020_pi_pi @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_247_name__fresh__abs,axiom,
% 2.89/1.59 ! [B: name,A: name,X: name] :
% 2.89/1.59 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_name_name @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_248_name__fresh__abs,axiom,
% 2.89/1.59 ! [B: name,A: name,X: pi] :
% 2.89/1.59 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 2.89/1.59 = ( ( B = A )
% 2.89/1.59 | ( fresh_name_pi @ B @ X ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_249_pi_Oinject_I3_J,axiom,
% 2.89/1.59 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 2.89/1.59 ( ( ( input @ X32 @ X1 @ X2 )
% 2.89/1.59 = ( input @ Y32 @ Y1 @ Y2 ) )
% 2.89/1.59 = ( ( X32 = Y32 )
% 2.89/1.59 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 2.89/1.59 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_250_simE_I1_J,axiom,
% 2.89/1.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 2.89/1.59 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.89/1.59 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.59 => ? [P5: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P5 ) )
% 2.89/1.59 & ( strong2129052853vative @ P5 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_251_Strong__Late__Sim_Oreflexive,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_252_Open,axiom,
% 2.89/1.59 ! [P: pi,A: name,B: name,P2: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.89/1.59 => ( ( A != B )
% 2.89/1.59 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_253_derivativeReflexive,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi,A: late_subject,X: name] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong2129052853vative @ P @ P @ A @ X @ Rel ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_254_simE_I2_J,axiom,
% 2.89/1.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 2.89/1.59 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.89/1.59 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.89/1.59 => ? [P5: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P5 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q2 ) @ Rel ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_255_resSimCases,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [Q4: pi,A3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.89/1.59 => ( ( A3 != X )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.89/1.59 => ( ( X != Y3 )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ Y3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_256_resSimCases,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [Q4: pi,A3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.89/1.59 => ( ( A3 != X )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.89/1.59 => ( ( X != Y3 )
% 2.89/1.59 => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_257_resSimCases,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [Q4: pi,A3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.89/1.59 => ( ( A3 != X )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.89/1.59 => ( ( X != Y3 )
% 2.89/1.59 => ( ( fresh_name_name @ Y3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_258_resSimCases,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 2.89/1.59 ( ( eqvt_pi @ Rel )
% 2.89/1.59 => ( ! [Q4: pi,A3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.89/1.59 => ( ( A3 != X )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.89/1.59 => ( ( X != Y3 )
% 2.89/1.59 => ( ( fresh_name_pi @ Y3 @ C3 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.89/1.59 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_259_simCases,axiom,
% 2.89/1.59 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 2.89/1.59 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.89/1.59 => ( ( fresh_name_pi @ Y3 @ P )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.89/1.59 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 2.89/1.59 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.89/1.59 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.89/1.59 => ? [P6: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_260_simulation__def,axiom,
% 2.89/1.59 ( strong743114133lation
% 2.89/1.59 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 2.89/1.59 ( ! [A5: late_subject,X4: name,Q6: pi] :
% 2.89/1.59 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A5 @ X4 @ Q6 ) )
% 2.89/1.59 & ( fresh_name_pi @ X4 @ P7 ) )
% 2.89/1.59 => ? [P8: pi] :
% 2.89/1.59 ( ( late_transitions @ P7 @ ( late_BoundR @ A5 @ X4 @ P8 ) )
% 2.89/1.59 & ( strong2129052853vative @ P8 @ Q6 @ A5 @ X4 @ Rel2 ) ) )
% 2.89/1.59 & ! [Alpha3: late_freeRes,Q6: pi] :
% 2.89/1.59 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 2.89/1.59 => ? [P8: pi] :
% 2.89/1.59 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 2.89/1.59 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_261_resCasesB_H,axiom,
% 2.89/1.59 ! [X5: name,P: pi,A: late_subject,Y6: name,P2: pi] :
% 2.89/1.59 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y6 @ P2 ) )
% 2.89/1.59 => ( ! [P4: pi,A3: name,B3: name] :
% 2.89/1.59 ( ( ( res @ X5 @ P )
% 2.89/1.59 = ( res @ B3 @ P4 ) )
% 2.89/1.59 => ! [P5: pi] :
% 2.89/1.59 ( ( ( late_BoundR @ A @ Y6 @ P2 )
% 2.89/1.59 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B3 @ P5 ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P5 ) )
% 2.89/1.59 => ( A3 = B3 ) ) ) )
% 2.89/1.59 => ~ ! [P4: pi,A3: late_subject,X3: name,P5: pi,Y3: name] :
% 2.89/1.59 ( ( ( res @ X5 @ P )
% 2.89/1.59 = ( res @ Y3 @ P4 ) )
% 2.89/1.59 => ( ( ( late_BoundR @ A @ Y6 @ P2 )
% 2.89/1.59 = ( late_BoundR @ A3 @ X3 @ ( res @ Y3 @ P5 ) ) )
% 2.89/1.59 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X3 @ P5 ) )
% 2.89/1.59 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 2.89/1.59 => ( ( Y3 != X3 )
% 2.89/1.59 => ( ( fresh_name_pi @ X3 @ P4 )
% 2.89/1.59 => ~ ( fresh_717452603ubject @ X3 @ A3 ) ) ) ) ) ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_262_tauOutputTrans,axiom,
% 2.89/1.59 ! [P: pi,A: name,B: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_263_inputBoundOutputTrans,axiom,
% 2.89/1.59 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_264_sumIdempRight,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_265_sumAssocRight,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R2 ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_266_sumIdempLeft,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_267_sumAssocLeft,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R2: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R2 ) @ Rel @ ( sum @ P @ ( sum @ Q @ R2 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_268_sumSym,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_269_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.89/1.59 ! [X2: name,Y2: name] :
% 2.89/1.59 ( ( ( late_BoundOutputS @ X2 )
% 2.89/1.59 = ( late_BoundOutputS @ Y2 ) )
% 2.89/1.59 = ( X2 = Y2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_270_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.89/1.59 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 2.89/1.59 ( ( ( late_OutputR @ X11 @ X12 )
% 2.89/1.59 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.89/1.59 = ( ( X11 = Y11 )
% 2.89/1.59 & ( X12 = Y12 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_271_sumZeroRight,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_272_sumZeroLeft,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.59 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_273_name__fresh,axiom,
% 2.89/1.59 ( fresh_name_name
% 2.89/1.59 = ( ^ [A5: name,B5: name] : ( A5 != B5 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_274_pi_Ofresh_I1_J,axiom,
% 2.89/1.59 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_275_zeroTrans,axiom,
% 2.89/1.59 ! [Rs: late_residual] :
% 2.89/1.59 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_276_nilCases_H,axiom,
% 2.89/1.59 ! [Rs: late_residual] :
% 2.89/1.59 ~ ( late_transitions @ piNil @ Rs ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_277_pi_Odistinct_I15_J,axiom,
% 2.89/1.59 ! [Name: name,Pi: pi] :
% 2.89/1.59 ( piNil
% 2.89/1.59 != ( res @ Name @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_278_pi_Odistinct_I13_J,axiom,
% 2.89/1.59 ! [Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( piNil
% 2.89/1.59 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_279_pi_Odistinct_I11_J,axiom,
% 2.89/1.59 ! [Pi12: pi,Pi22: pi] :
% 2.89/1.59 ( piNil
% 2.89/1.59 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_280_pi_Odistinct_I5_J,axiom,
% 2.89/1.59 ! [Name1: name,Name22: name,Pi: pi] :
% 2.89/1.59 ( piNil
% 2.89/1.59 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_281_pi_Odistinct_I3_J,axiom,
% 2.89/1.59 ! [Pi: pi] :
% 2.89/1.59 ( piNil
% 2.89/1.59 != ( tau @ Pi ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_282_nilSimRight,axiom,
% 2.89/1.59 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_283_resZeroTrans,axiom,
% 2.89/1.59 ! [X: name,Rs: late_residual] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_284_nilSim_I2_J,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 2.89/1.59 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_285_nilSim_I1_J,axiom,
% 2.89/1.59 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 2.89/1.59 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_286_inputCases_H,axiom,
% 2.89/1.59 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.89/1.59 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 2.89/1.59 => ~ ! [X3: name,A3: name,P4: pi] :
% 2.89/1.59 ( ( ( A = A3 )
% 2.89/1.59 & ( ( abs_fun_name_pi @ B @ P )
% 2.89/1.59 = ( abs_fun_name_pi @ X3 @ P4 ) ) )
% 2.89/1.59 => ( ( Rs
% 2.89/1.59 = ( late_BoundR @ ( late_InputS @ A3 ) @ X3 @ P4 ) )
% 2.89/1.59 => ( X3 = A3 ) ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_287_subject_Ofresh_I1_J,axiom,
% 2.89/1.59 ! [A: name,X1: name] :
% 2.89/1.59 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 2.89/1.59 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_288_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.89/1.59 ! [X1: name,X2: name] :
% 2.89/1.59 ( ( late_InputS @ X1 )
% 2.89/1.59 != ( late_BoundOutputS @ X2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_289_subject_Oexhaust,axiom,
% 2.89/1.59 ! [Y: late_subject] :
% 2.89/1.59 ( ! [X13: name] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( late_InputS @ X13 ) )
% 2.89/1.59 => ~ ! [X22: name] :
% 2.89/1.59 ( Y
% 2.89/1.59 != ( late_BoundOutputS @ X22 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_290_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.89/1.59 ! [Name3: name,Name: name] :
% 2.89/1.59 ( ( late_InputS @ Name3 )
% 2.89/1.59 != ( late_BoundOutputS @ Name ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_291_subject_Oinducts,axiom,
% 2.89/1.59 ! [P: late_subject > $o,Subject2: late_subject] :
% 2.89/1.59 ( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
% 2.89/1.59 => ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
% 2.89/1.59 => ( P @ Subject2 ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_292_Late__Semantics_OInput,axiom,
% 2.89/1.59 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_293_transitions_OInput,axiom,
% 2.89/1.59 ! [X: name,A: name,P: pi] :
% 2.89/1.59 ( ( X != A )
% 2.89/1.59 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_294_resOutputInputTrans,axiom,
% 2.89/1.59 ! [X: name,A: name,B: name,P: pi,C2: name,Y: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_295_resOutputOutputTrans,axiom,
% 2.89/1.59 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 2.89/1.59 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 2.89/1.59
% 2.89/1.59 thf(fact_296_Late__Semantics_OClose1,axiom,
% 2.89/1.59 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.89/1.59 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_297_subst__identity,axiom,
% 2.89/1.60 ! [P: pi,A: name] :
% 2.89/1.60 ( ( subs @ P @ A @ A )
% 2.89/1.60 = P ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_298_simps_I9_J,axiom,
% 2.89/1.60 ! [X: name,C2: name,D2: name,P: pi] :
% 2.89/1.60 ( ( X != C2 )
% 2.89/1.60 => ( ( X != D2 )
% 2.89/1.60 => ( ( subs @ ( res @ X @ P ) @ C2 @ D2 )
% 2.89/1.60 = ( res @ X @ ( subs @ P @ C2 @ D2 ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_299_simps_I8_J,axiom,
% 2.89/1.60 ! [P: pi,Q: pi,C2: name,D2: name] :
% 2.89/1.60 ( ( subs @ ( par @ P @ Q ) @ C2 @ D2 )
% 2.89/1.60 = ( par @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_300_substTrans,axiom,
% 2.89/1.60 ! [B: name,P: pi,A: name,C2: name] :
% 2.89/1.60 ( ( fresh_name_pi @ B @ P )
% 2.89/1.60 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 2.89/1.60 = ( subs @ P @ A @ C2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_301_simps_I7_J,axiom,
% 2.89/1.60 ! [P: pi,Q: pi,C2: name,D2: name] :
% 2.89/1.60 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D2 )
% 2.89/1.60 = ( sum @ ( subs @ P @ C2 @ D2 ) @ ( subs @ Q @ C2 @ D2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_302_simps_I2_J,axiom,
% 2.89/1.60 ! [P: pi,C2: name,D2: name] :
% 2.89/1.60 ( ( subs @ ( tau @ P ) @ C2 @ D2 )
% 2.89/1.60 = ( tau @ ( subs @ P @ C2 @ D2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_303_simps_I1_J,axiom,
% 2.89/1.60 ! [C2: name,D2: name] :
% 2.89/1.60 ( ( subs @ piNil @ C2 @ D2 )
% 2.89/1.60 = piNil ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_304_freeRes_Ofresh_I2_J,axiom,
% 2.89/1.60 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_305_pi_Ofresh_I2_J,axiom,
% 2.89/1.60 ! [A: name,X32: name,X2: name,X1: pi] :
% 2.89/1.60 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 2.89/1.60 = ( ( fresh_name_name @ A @ X32 )
% 2.89/1.60 & ( fresh_name_name @ A @ X2 )
% 2.89/1.60 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_306_resOutputTauTrans,axiom,
% 2.89/1.60 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 2.89/1.60 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_307_outputTauTrans,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,P2: pi] :
% 2.89/1.60 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_308_pi_Odistinct_I31_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( res @ Name @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_309_pi_Odistinct_I29_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_310_pi_Odistinct_I27_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_311_pi_Oinject_I1_J,axiom,
% 2.89/1.60 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.89/1.60 ( ( ( output @ X32 @ X2 @ X1 )
% 2.89/1.60 = ( output @ Y32 @ Y2 @ Y1 ) )
% 2.89/1.60 = ( ( X32 = Y32 )
% 2.89/1.60 & ( X2 = Y2 )
% 2.89/1.60 & ( X1 = Y1 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_312_freeRes_Oinducts,axiom,
% 2.89/1.60 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.89/1.60 ( ! [Name13: name,Name24: name] : ( P @ ( late_OutputR @ Name13 @ Name24 ) )
% 2.89/1.60 => ( ( P @ late_TauR )
% 2.89/1.60 => ( P @ FreeRes3 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_313_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name] :
% 2.89/1.60 ( ( late_OutputR @ Name12 @ Name23 )
% 2.89/1.60 != late_TauR ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_314_pi_Odistinct_I19_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( tau @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_315_pi_Odistinct_I21_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( input @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_316_pi_Odistinct_I1_J,axiom,
% 2.89/1.60 ! [Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( piNil
% 2.89/1.60 != ( output @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_317_fresh__fact2,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi] :
% 2.89/1.60 ( ( A != B )
% 2.89/1.60 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_318_fresh__fact1,axiom,
% 2.89/1.60 ! [A: name,P: pi,C2: name,B: name] :
% 2.89/1.60 ( ( fresh_name_pi @ A @ P )
% 2.89/1.60 => ( ( A != C2 )
% 2.89/1.60 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_319_forget,axiom,
% 2.89/1.60 ! [A: name,P: pi,B: name] :
% 2.89/1.60 ( ( fresh_name_pi @ A @ P )
% 2.89/1.60 => ( ( subs @ P @ A @ B )
% 2.89/1.60 = P ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_320_freeRes_Oexhaust,axiom,
% 2.89/1.60 ! [Y: late_freeRes] :
% 2.89/1.60 ( ! [X112: name,X122: name] :
% 2.89/1.60 ( Y
% 2.89/1.60 != ( late_OutputR @ X112 @ X122 ) )
% 2.89/1.60 => ( Y = late_TauR ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_321_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.89/1.60 ! [X11: name,X12: name] :
% 2.89/1.60 ( ( late_OutputR @ X11 @ X12 )
% 2.89/1.60 != late_TauR ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_322_substRes3,axiom,
% 2.89/1.60 ! [B: name,P: pi,A: name] :
% 2.89/1.60 ( ( fresh_name_pi @ B @ P )
% 2.89/1.60 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 2.89/1.60 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_323_substRes2,axiom,
% 2.89/1.60 ! [B: name,P: pi,A: name] :
% 2.89/1.60 ( ( fresh_name_pi @ B @ P )
% 2.89/1.60 => ( ( res @ A @ P )
% 2.89/1.60 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_324_resTrans_I1_J,axiom,
% 2.89/1.60 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 2.89/1.60 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_325_outputBoundTrans,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,C2: late_subject,X: name,P2: pi] :
% 2.89/1.60 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C2 @ X @ P2 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_326_nilSim_I3_J,axiom,
% 2.89/1.60 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 2.89/1.60 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_327_Late__Semantics_OComm2,axiom,
% 2.89/1.60 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_328_Late__Semantics_OComm1,axiom,
% 2.89/1.60 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_329_Output,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_330_outputIneqTrans,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,C2: name,D2: name,P2: pi] :
% 2.89/1.60 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D2 ) @ P2 ) )
% 2.89/1.60 => ~ ( ( A != C2 )
% 2.89/1.60 | ( B != D2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_331_outputCases_H,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 2.89/1.60 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 2.89/1.60 => ~ ! [A3: name,B3: name,P4: pi] :
% 2.89/1.60 ( ( ( A = A3 )
% 2.89/1.60 & ( B = B3 )
% 2.89/1.60 & ( P = P4 ) )
% 2.89/1.60 => ( Rs
% 2.89/1.60 != ( late_FreeR @ ( late_OutputR @ A3 @ B3 ) @ P4 ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_332_outputCases,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.89/1.60 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.60 => ( ( ( Alpha
% 2.89/1.60 = ( late_OutputR @ A @ B ) )
% 2.89/1.60 => ( ( P = P2 )
% 2.89/1.60 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 2.89/1.60 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_333_outputFreshTrans,axiom,
% 2.89/1.60 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 2.89/1.60 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.60 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 2.89/1.60 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_334_transitions_OComm2,axiom,
% 2.89/1.60 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.60 => ( ( X != A )
% 2.89/1.60 => ( ( X != B )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P2 )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_335_transitions_OComm1,axiom,
% 2.89/1.60 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.60 => ( ( X != A )
% 2.89/1.60 => ( ( X != B )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q2 )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_336_Tau,axiom,
% 2.89/1.60 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_337_tauCases_H,axiom,
% 2.89/1.60 ! [P: pi,Rs: late_residual] :
% 2.89/1.60 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 2.89/1.60 => ~ ! [P4: pi] :
% 2.89/1.60 ( ( ( tau @ P )
% 2.89/1.60 = ( tau @ P4 ) )
% 2.89/1.60 => ( Rs
% 2.89/1.60 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_338_tauCases,axiom,
% 2.89/1.60 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 2.89/1.60 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 2.89/1.60 => ( ( ( Alpha = late_TauR )
% 2.89/1.60 => ( ( P = P2 )
% 2.89/1.60 => ( Prop @ late_TauR @ P ) ) )
% 2.89/1.60 => ( Prop @ Alpha @ P2 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_339_transitions_OClose2,axiom,
% 2.89/1.60 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ Q )
% 2.89/1.60 => ( ( X != A )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P2 )
% 2.89/1.60 => ( ( Y != A )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ Q2 )
% 2.89/1.60 => ( ( X != Y )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_340_transitions_OClose1,axiom,
% 2.89/1.60 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ P )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ Q )
% 2.89/1.60 => ( ( X != A )
% 2.89/1.60 => ( ( fresh_name_pi @ X @ Q2 )
% 2.89/1.60 => ( ( Y != A )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ P2 )
% 2.89/1.60 => ( ( X != Y )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_341_Late__Semantics_OClose2,axiom,
% 2.89/1.60 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 2.89/1.60 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 2.89/1.60 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.89/1.60 => ( ( fresh_name_pi @ Y @ Q )
% 2.89/1.60 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_342_mismatchIdRight,axiom,
% 2.89/1.60 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 2.89/1.60 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.60 => ( ( A != B )
% 2.89/1.60 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A @ B @ P ) ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_343_mismatchIdLeft,axiom,
% 2.89/1.60 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 2.89/1.60 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 2.89/1.60 => ( ( A != B )
% 2.89/1.60 => ( strong743114133lation @ ( mismatch @ A @ B @ P ) @ Rel @ P ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_344_pi_Ofresh_I6_J,axiom,
% 2.89/1.60 ! [A: name,X32: name,X2: name,X1: pi] :
% 2.89/1.60 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 2.89/1.60 = ( ( fresh_name_name @ A @ X32 )
% 2.89/1.60 & ( fresh_name_name @ A @ X2 )
% 2.89/1.60 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_345_pi_Odistinct_I25_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( ( output @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_346_pi_Odistinct_I9_J,axiom,
% 2.89/1.60 ! [Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( piNil
% 2.89/1.60 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_347_pi_Odistinct_I71_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.60 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( sum @ Pi12 @ Pi22 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_348_pi_Odistinct_I51_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( ( input @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_349_pi_Odistinct_I39_J,axiom,
% 2.89/1.60 ! [Pi4: pi,Name1: name,Name22: name,Pi: pi] :
% 2.89/1.60 ( ( tau @ Pi4 )
% 2.89/1.60 != ( mismatch @ Name1 @ Name22 @ Pi ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_350_pi_Oinject_I5_J,axiom,
% 2.89/1.60 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 2.89/1.60 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 2.89/1.60 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 2.89/1.60 = ( ( X32 = Y32 )
% 2.89/1.60 & ( X2 = Y2 )
% 2.89/1.60 & ( X1 = Y1 ) ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(fact_351_pi_Odistinct_I73_J,axiom,
% 2.89/1.60 ! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 2.89/1.60 ( ( mismatch @ Name12 @ Name23 @ Pi4 )
% 2.89/1.60 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.89/1.60
% 2.89/1.60 thf(conj_0,conjecture,
% 2.89/1.60 y != x ).
% 2.89/1.60 ------------------------
% 3.00/1.62 % (22377)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_22043 for (2999ds/2Mi)
% 3.00/1.62 % (22379)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/18Mi)
% 3.00/1.62 % (22377)Instruction limit reached!
% 3.00/1.62 % (22377)------------------------------
% 3.00/1.62 % (22377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.62 % (22377)Termination reason: Unknown
% 3.00/1.62 % (22377)Termination phase: shuffling
% 3.00/1.62
% 3.00/1.62 % (22377)Memory used [KB]: 1535
% 3.00/1.62 % (22377)Time elapsed: 0.003 s
% 3.00/1.62 % (22377)Instructions burned: 3 (million)
% 3.00/1.62 % (22377)------------------------------
% 3.00/1.62 % (22377)------------------------------
% 3.00/1.63 % (22379)Instruction limit reached!
% 3.00/1.63 % (22379)------------------------------
% 3.00/1.63 % (22379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (22379)Termination reason: Unknown
% 3.00/1.63 % (22379)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (22379)Memory used [KB]: 1791
% 3.00/1.63 % (22379)Time elapsed: 0.008 s
% 3.00/1.63 % (22379)Instructions burned: 18 (million)
% 3.00/1.63 % (22379)------------------------------
% 3.00/1.63 % (22379)------------------------------
% 3.00/1.63 % (22373)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/183Mi)
% 3.00/1.63 % (22374)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_22043 for (2999ds/4Mi)
% 3.00/1.63 % (22375)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_22043 for (2999ds/27Mi)
% 3.00/1.63 % (22376)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/2Mi)
% 3.00/1.63 % (22378)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_22043 for (2999ds/275Mi)
% 3.00/1.63 % (22376)Instruction limit reached!
% 3.00/1.63 % (22376)------------------------------
% 3.00/1.63 % (22376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (22376)Termination reason: Unknown
% 3.00/1.63 % (22376)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (22376)Memory used [KB]: 1535
% 3.00/1.63 % (22376)Time elapsed: 0.004 s
% 3.00/1.63 % (22376)Instructions burned: 3 (million)
% 3.00/1.63 % (22376)------------------------------
% 3.00/1.63 % (22376)------------------------------
% 3.00/1.63 % (22374)Instruction limit reached!
% 3.00/1.63 % (22374)------------------------------
% 3.00/1.63 % (22374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (22374)Termination reason: Unknown
% 3.00/1.63 % (22374)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (22374)Memory used [KB]: 1663
% 3.00/1.63 % (22374)Time elapsed: 0.005 s
% 3.00/1.63 % (22374)Instructions burned: 5 (million)
% 3.00/1.63 % (22374)------------------------------
% 3.00/1.63 % (22374)------------------------------
% 3.00/1.63 % (22380)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/3Mi)
% 3.00/1.63 % (22380)Instruction limit reached!
% 3.00/1.63 % (22380)------------------------------
% 3.00/1.63 % (22380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.63 % (22380)Termination reason: Unknown
% 3.00/1.63 % (22380)Termination phase: shuffling
% 3.00/1.63
% 3.00/1.63 % (22380)Memory used [KB]: 1535
% 3.00/1.63 % (22380)Time elapsed: 0.003 s
% 3.00/1.63 % (22380)Instructions burned: 5 (million)
% 3.00/1.63 % (22380)------------------------------
% 3.00/1.63 % (22380)------------------------------
% 3.00/1.64 % (22381)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_22043 for (2999ds/37Mi)
% 3.00/1.64 % (22384)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_22043 for (2999ds/1041Mi)
% 3.00/1.64 % (22375)Instruction limit reached!
% 3.00/1.64 % (22375)------------------------------
% 3.00/1.64 % (22375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.64 % (22375)Termination reason: Unknown
% 3.00/1.64 % (22375)Termination phase: shuffling
% 3.00/1.64
% 3.00/1.64 % (22375)Memory used [KB]: 2046
% 3.00/1.64 % (22375)Time elapsed: 0.019 s
% 3.00/1.64 % (22375)Instructions burned: 28 (million)
% 3.00/1.64 % (22375)------------------------------
% 3.00/1.64 % (22375)------------------------------
% 3.00/1.65 % (22382)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_22043 for (2999ds/15Mi)
% 3.00/1.65 % (22383)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_22043 for (2999ds/3Mi)
% 3.00/1.65 % (22381)Instruction limit reached!
% 3.00/1.65 % (22381)------------------------------
% 3.00/1.65 % (22381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (22381)Termination reason: Unknown
% 3.00/1.65 % (22381)Termination phase: shuffling
% 3.00/1.65
% 3.00/1.65 % (22381)Memory used [KB]: 2302
% 3.00/1.65 % (22381)Time elapsed: 0.013 s
% 3.00/1.65 % (22381)Instructions burned: 38 (million)
% 3.00/1.65 % (22381)------------------------------
% 3.00/1.65 % (22381)------------------------------
% 3.00/1.65 % (22383)Instruction limit reached!
% 3.00/1.65 % (22383)------------------------------
% 3.00/1.65 % (22383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.65 % (22383)Termination reason: Unknown
% 3.00/1.65 % (22383)Termination phase: shuffling
% 3.00/1.65
% 3.00/1.65 % (22383)Memory used [KB]: 1535
% 3.00/1.65 % (22383)Time elapsed: 0.004 s
% 3.00/1.65 % (22383)Instructions burned: 3 (million)
% 3.00/1.65 % (22383)------------------------------
% 3.00/1.65 % (22383)------------------------------
% 3.00/1.66 % (22382)Instruction limit reached!
% 3.00/1.66 % (22382)------------------------------
% 3.00/1.66 % (22382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.66 % (22382)Termination reason: Unknown
% 3.00/1.66 % (22382)Termination phase: shuffling
% 3.00/1.66
% 3.00/1.66 % (22382)Memory used [KB]: 1791
% 3.00/1.66 % (22382)Time elapsed: 0.011 s
% 3.00/1.66 % (22382)Instructions burned: 15 (million)
% 3.00/1.66 % (22382)------------------------------
% 3.00/1.66 % (22382)------------------------------
% 3.00/1.66 % (22386)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/16Mi)
% 3.00/1.66 % (22378)Refutation not found, incomplete strategy
% 3.00/1.66 % (22378)------------------------------
% 3.00/1.66 % (22378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.66 % (22378)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.66
% 3.00/1.66
% 3.00/1.66 % (22378)Memory used [KB]: 6524
% 3.00/1.66 % (22378)Time elapsed: 0.035 s
% 3.00/1.66 % (22378)Instructions burned: 58 (million)
% 3.00/1.66 % (22378)------------------------------
% 3.00/1.66 % (22378)------------------------------
% 3.00/1.66 % (22385)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/7Mi)
% 3.00/1.66 % (22386)Instruction limit reached!
% 3.00/1.66 % (22386)------------------------------
% 3.00/1.66 % (22386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.66 % (22386)Termination reason: Unknown
% 3.00/1.66 % (22386)Termination phase: shuffling
% 3.00/1.66
% 3.00/1.66 % (22386)Memory used [KB]: 1791
% 3.00/1.66 % (22386)Time elapsed: 0.007 s
% 3.00/1.66 % (22386)Instructions burned: 16 (million)
% 3.00/1.66 % (22386)------------------------------
% 3.00/1.66 % (22386)------------------------------
% 3.00/1.67 % (22387)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_22043 for (2999ds/3Mi)
% 3.00/1.67 % (22385)Instruction limit reached!
% 3.00/1.67 % (22385)------------------------------
% 3.00/1.67 % (22385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.67 % (22385)Termination reason: Unknown
% 3.00/1.67 % (22385)Termination phase: shuffling
% 3.00/1.67
% 3.00/1.67 % (22385)Memory used [KB]: 1663
% 3.00/1.67 % (22385)Time elapsed: 0.007 s
% 3.00/1.67 % (22385)Instructions burned: 8 (million)
% 3.00/1.67 % (22385)------------------------------
% 3.00/1.67 % (22385)------------------------------
% 3.00/1.67 % (22387)Instruction limit reached!
% 3.00/1.67 % (22387)------------------------------
% 3.00/1.67 % (22387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.67 % (22387)Termination reason: Unknown
% 3.00/1.67 % (22387)Termination phase: shuffling
% 3.00/1.67
% 3.00/1.67 % (22387)Memory used [KB]: 1535
% 3.00/1.67 % (22387)Time elapsed: 0.004 s
% 3.00/1.67 % (22387)Instructions burned: 3 (million)
% 3.00/1.67 % (22387)------------------------------
% 3.00/1.67 % (22387)------------------------------
% 3.00/1.67 % (22388)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_22043 for (2999ds/3Mi)
% 3.00/1.67 % (22390)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/3Mi)
% 3.00/1.67 % (22390)Instruction limit reached!
% 3.00/1.67 % (22390)------------------------------
% 3.00/1.67 % (22390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.67 % (22390)Termination reason: Unknown
% 3.00/1.67 % (22390)Termination phase: shuffling
% 3.00/1.67
% 3.00/1.67 % (22390)Memory used [KB]: 1535
% 3.00/1.67 % (22390)Time elapsed: 0.002 s
% 3.00/1.67 % (22390)Instructions burned: 3 (million)
% 3.00/1.67 % (22390)------------------------------
% 3.00/1.67 % (22390)------------------------------
% 3.00/1.68 % (22388)Instruction limit reached!
% 3.00/1.68 % (22388)------------------------------
% 3.00/1.68 % (22388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.68 % (22388)Termination reason: Unknown
% 3.00/1.68 % (22388)Termination phase: shuffling
% 3.00/1.68
% 3.00/1.68 % (22388)Memory used [KB]: 1535
% 3.00/1.68 % (22388)Time elapsed: 0.004 s
% 3.00/1.68 % (22388)Instructions burned: 3 (million)
% 3.00/1.68 % (22388)------------------------------
% 3.00/1.68 % (22388)------------------------------
% 3.00/1.68 % (22392)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/18Mi)
% 3.00/1.68 % (22389)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/7Mi)
% 3.00/1.68 % (22391)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/4Mi)
% 3.00/1.68 % (22391)Instruction limit reached!
% 3.00/1.68 % (22391)------------------------------
% 3.00/1.68 % (22391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.68 % (22391)Termination reason: Unknown
% 3.00/1.68 % (22391)Termination phase: shuffling
% 3.00/1.68
% 3.00/1.68 % (22391)Memory used [KB]: 1535
% 3.00/1.68 % (22391)Time elapsed: 0.003 s
% 3.00/1.68 % (22391)Instructions burned: 4 (million)
% 3.00/1.68 % (22391)------------------------------
% 3.00/1.68 % (22391)------------------------------
% 3.00/1.68 % (22389)Instruction limit reached!
% 3.00/1.68 % (22389)------------------------------
% 3.00/1.68 % (22389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.68 % (22389)Termination reason: Unknown
% 3.00/1.68 % (22389)Termination phase: shuffling
% 3.00/1.68
% 3.00/1.68 % (22389)Memory used [KB]: 1663
% 3.00/1.68 % (22389)Time elapsed: 0.006 s
% 3.00/1.68 % (22389)Instructions burned: 7 (million)
% 3.00/1.68 % (22389)------------------------------
% 3.00/1.68 % (22389)------------------------------
% 3.00/1.68 % (22393)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/710Mi)
% 3.00/1.69 % (22392)Instruction limit reached!
% 3.00/1.69 % (22392)------------------------------
% 3.00/1.69 % (22392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.69 % (22392)Termination reason: Unknown
% 3.00/1.69 % (22392)Termination phase: shuffling
% 3.00/1.69
% 3.00/1.69 % (22392)Memory used [KB]: 1918
% 3.00/1.69 % (22392)Time elapsed: 0.008 s
% 3.00/1.69 % (22392)Instructions burned: 19 (million)
% 3.00/1.69 % (22392)------------------------------
% 3.00/1.69 % (22392)------------------------------
% 3.00/1.69 % (22395)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_22043 for (2999ds/902Mi)
% 3.00/1.69 % (22394)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/6Mi)
% 3.00/1.69 % (22373)Instruction limit reached!
% 3.00/1.69 % (22373)------------------------------
% 3.00/1.69 % (22373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.69 % (22373)Termination reason: Unknown
% 3.00/1.69 % (22373)Termination phase: Saturation
% 3.00/1.69
% 3.00/1.69 % (22373)Memory used [KB]: 7547
% 3.00/1.69 % (22373)Time elapsed: 0.068 s
% 3.00/1.69 % (22373)Instructions burned: 185 (million)
% 3.00/1.69 % (22373)------------------------------
% 3.00/1.69 % (22373)------------------------------
% 3.00/1.70 % (22397)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/5Mi)
% 3.00/1.70 % (22394)Instruction limit reached!
% 3.00/1.70 % (22394)------------------------------
% 3.00/1.70 % (22394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.70 % (22394)Termination reason: Unknown
% 3.00/1.70 % (22394)Termination phase: shuffling
% 3.00/1.70
% 3.00/1.70 % (22394)Memory used [KB]: 1535
% 3.00/1.70 % (22394)Time elapsed: 0.006 s
% 3.00/1.70 % (22394)Instructions burned: 7 (million)
% 3.00/1.70 % (22394)------------------------------
% 3.00/1.70 % (22394)------------------------------
% 3.00/1.70 % (22397)Instruction limit reached!
% 3.00/1.70 % (22397)------------------------------
% 3.00/1.70 % (22397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.70 % (22397)Termination reason: Unknown
% 3.00/1.70 % (22397)Termination phase: shuffling
% 3.00/1.70
% 3.00/1.70 % (22397)Memory used [KB]: 1663
% 3.00/1.70 % (22397)Time elapsed: 0.004 s
% 3.00/1.70 % (22397)Instructions burned: 7 (million)
% 3.00/1.70 % (22397)------------------------------
% 3.00/1.70 % (22397)------------------------------
% 3.00/1.70 % (22396)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_22043 for (2999ds/21Mi)
% 3.00/1.70 % (22393)Refutation not found, incomplete strategy
% 3.00/1.70 % (22393)------------------------------
% 3.00/1.70 % (22393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.70 % (22393)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.70
% 3.00/1.70
% 3.00/1.70 % (22393)Memory used [KB]: 6652
% 3.00/1.70 % (22393)Time elapsed: 0.019 s
% 3.00/1.70 % (22393)Instructions burned: 60 (million)
% 3.00/1.70 % (22393)------------------------------
% 3.00/1.70 % (22393)------------------------------
% 3.00/1.70 % (22398)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_22043 for (2999ds/6Mi)
% 3.00/1.71 % (22398)Instruction limit reached!
% 3.00/1.71 % (22398)------------------------------
% 3.00/1.71 % (22398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.71 % (22398)Termination reason: Unknown
% 3.00/1.71 % (22398)Termination phase: shuffling
% 3.00/1.71
% 3.00/1.71 % (22398)Memory used [KB]: 1663
% 3.00/1.71 % (22398)Time elapsed: 0.004 s
% 3.00/1.71 % (22398)Instructions burned: 7 (million)
% 3.00/1.71 % (22398)------------------------------
% 3.00/1.71 % (22398)------------------------------
% 3.00/1.71 % (22396)Instruction limit reached!
% 3.00/1.71 % (22396)------------------------------
% 3.00/1.71 % (22396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.71 % (22396)Termination reason: Unknown
% 3.00/1.71 % (22396)Termination phase: shuffling
% 3.00/1.71
% 3.00/1.71 % (22396)Memory used [KB]: 1918
% 3.00/1.71 % (22396)Time elapsed: 0.010 s
% 3.00/1.71 % (22396)Instructions burned: 23 (million)
% 3.00/1.71 % (22396)------------------------------
% 3.00/1.71 % (22396)------------------------------
% 3.00/1.71 % (22400)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_22043 for (2999ds/779Mi)
% 3.00/1.71 % (22401)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_22043 for (2999ds/19Mi)
% 3.00/1.71 % (22399)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/377Mi)
% 3.00/1.72 % (22402)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/879Mi)
% 3.00/1.72 % (22401)Instruction limit reached!
% 3.00/1.72 % (22401)------------------------------
% 3.00/1.72 % (22401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.72 % (22401)Termination reason: Unknown
% 3.00/1.72 % (22401)Termination phase: shuffling
% 3.00/1.72
% 3.00/1.72 % (22401)Memory used [KB]: 2046
% 3.00/1.72 % (22401)Time elapsed: 0.007 s
% 3.00/1.72 % (22401)Instructions burned: 22 (million)
% 3.00/1.72 % (22401)------------------------------
% 3.00/1.72 % (22401)------------------------------
% 3.00/1.72 % (22403)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22043 for (2999ds/17Mi)
% 3.00/1.72 % (22403)Instruction limit reached!
% 3.00/1.72 % (22403)------------------------------
% 3.00/1.72 % (22403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.72 % (22403)Termination reason: Unknown
% 3.00/1.72 % (22403)Termination phase: shuffling
% 3.00/1.72
% 3.00/1.72 % (22403)Memory used [KB]: 1791
% 3.00/1.72 % (22403)Time elapsed: 0.007 s
% 3.00/1.72 % (22403)Instructions burned: 17 (million)
% 3.00/1.72 % (22403)------------------------------
% 3.00/1.72 % (22403)------------------------------
% 3.00/1.73 % (22404)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22043 for (2998ds/3Mi)
% 3.00/1.73 % (22404)Instruction limit reached!
% 3.00/1.73 % (22404)------------------------------
% 3.00/1.73 % (22404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.73 % (22404)Termination reason: Unknown
% 3.00/1.73 % (22404)Termination phase: shuffling
% 3.00/1.73
% 3.00/1.73 % (22404)Memory used [KB]: 1535
% 3.00/1.73 % (22404)Time elapsed: 0.003 s
% 3.00/1.73 % (22404)Instructions burned: 5 (million)
% 3.00/1.73 % (22404)------------------------------
% 3.00/1.73 % (22404)------------------------------
% 3.00/1.73 % (22405)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22043 for (2998ds/30Mi)
% 3.00/1.74 % (22402)Refutation not found, incomplete strategy
% 3.00/1.74 % (22402)------------------------------
% 3.00/1.74 % (22402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.74 % (22402)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.74
% 3.00/1.74
% 3.00/1.74 % (22402)Memory used [KB]: 6652
% 3.00/1.74 % (22402)Time elapsed: 0.024 s
% 3.00/1.74 % (22402)Instructions burned: 69 (million)
% 3.00/1.74 % (22402)------------------------------
% 3.00/1.74 % (22402)------------------------------
% 3.00/1.74 % (22406)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22043 for (2998ds/127Mi)
% 3.00/1.74 % (22405)Instruction limit reached!
% 3.00/1.74 % (22405)------------------------------
% 3.00/1.74 % (22405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.74 % (22405)Termination reason: Unknown
% 3.00/1.74 % (22405)Termination phase: shuffling
% 3.00/1.74
% 3.00/1.74 % (22405)Memory used [KB]: 2046
% 3.00/1.74 % (22405)Time elapsed: 0.012 s
% 3.00/1.74 % (22405)Instructions burned: 30 (million)
% 3.00/1.74 % (22405)------------------------------
% 3.00/1.74 % (22405)------------------------------
% 3.00/1.75 % (22407)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22043 for (2998ds/100Mi)
% 3.00/1.75 % (22408)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_22043 for (2998ds/3Mi)
% 3.00/1.76 % (22408)Instruction limit reached!
% 3.00/1.76 % (22408)------------------------------
% 3.00/1.76 % (22408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.76 % (22408)Termination reason: Unknown
% 3.00/1.76 % (22408)Termination phase: shuffling
% 3.00/1.76
% 3.00/1.76 % (22408)Memory used [KB]: 1535
% 3.00/1.76 % (22408)Time elapsed: 0.003 s
% 3.00/1.76 % (22408)Instructions burned: 3 (million)
% 3.00/1.76 % (22408)------------------------------
% 3.00/1.76 % (22408)------------------------------
% 3.00/1.77 % (22409)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_22043 for (2998ds/20Mi)
% 3.00/1.77 % (22409)Instruction limit reached!
% 3.00/1.77 % (22409)------------------------------
% 3.00/1.77 % (22409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.77 % (22409)Termination reason: Unknown
% 3.00/1.77 % (22409)Termination phase: shuffling
% 3.00/1.77
% 3.00/1.77 % (22409)Memory used [KB]: 1918
% 3.00/1.77 % (22409)Time elapsed: 0.009 s
% 3.00/1.77 % (22409)Instructions burned: 20 (million)
% 3.00/1.77 % (22409)------------------------------
% 3.00/1.77 % (22409)------------------------------
% 3.00/1.77 % (22406)Instruction limit reached!
% 3.00/1.77 % (22406)------------------------------
% 3.00/1.77 % (22406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.77 % (22406)Termination reason: Unknown
% 3.00/1.77 % (22406)Termination phase: Property scanning
% 3.00/1.77
% 3.00/1.77 % (22406)Memory used [KB]: 2942
% 3.00/1.77 % (22406)Time elapsed: 0.037 s
% 3.00/1.77 % (22406)Instructions burned: 130 (million)
% 3.00/1.77 % (22406)------------------------------
% 3.00/1.77 % (22406)------------------------------
% 3.00/1.78 % (22407)Instruction limit reached!
% 3.00/1.78 % (22407)------------------------------
% 3.00/1.78 % (22407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.78 % (22407)Termination reason: Unknown
% 3.00/1.78 % (22407)Termination phase: Property scanning
% 3.00/1.78
% 3.00/1.78 % (22407)Memory used [KB]: 2942
% 3.00/1.78 % (22407)Time elapsed: 0.031 s
% 3.00/1.78 % (22407)Instructions burned: 103 (million)
% 3.00/1.78 % (22407)------------------------------
% 3.00/1.78 % (22407)------------------------------
% 3.00/1.78 % (22410)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_22043 for (2998ds/86Mi)
% 3.00/1.78 % (22411)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_22043 for (2998ds/107Mi)
% 3.00/1.79 % (22412)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_22043 for (2998ds/39Mi)
% 3.00/1.80 % (22412)Instruction limit reached!
% 3.00/1.80 % (22412)------------------------------
% 3.00/1.80 % (22412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.80 % (22412)Termination reason: Unknown
% 3.00/1.80 % (22412)Termination phase: shuffling
% 3.00/1.80
% 3.00/1.80 % (22412)Memory used [KB]: 2302
% 3.00/1.80 % (22412)Time elapsed: 0.014 s
% 3.00/1.80 % (22412)Instructions burned: 41 (million)
% 3.00/1.80 % (22412)------------------------------
% 3.00/1.80 % (22412)------------------------------
% 3.00/1.81 % (22413)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_22043 for (2997ds/448Mi)
% 3.00/1.81 % (22410)Instruction limit reached!
% 3.00/1.81 % (22410)------------------------------
% 3.00/1.81 % (22410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.81 % (22410)Termination reason: Unknown
% 3.00/1.81 % (22410)Termination phase: Property scanning
% 3.00/1.81
% 3.00/1.81 % (22410)Memory used [KB]: 2942
% 3.00/1.81 % (22410)Time elapsed: 0.030 s
% 3.00/1.81 % (22410)Instructions burned: 89 (million)
% 3.00/1.81 % (22410)------------------------------
% 3.00/1.81 % (22410)------------------------------
% 3.00/1.82 % (22411)Instruction limit reached!
% 3.00/1.82 % (22411)------------------------------
% 3.00/1.82 % (22411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.82 % (22411)Termination reason: Unknown
% 3.00/1.82 % (22411)Termination phase: Property scanning
% 3.00/1.82
% 3.00/1.82 % (22411)Memory used [KB]: 2814
% 3.00/1.82 % (22411)Time elapsed: 0.032 s
% 3.00/1.82 % (22411)Instructions burned: 109 (million)
% 3.00/1.82 % (22411)------------------------------
% 3.00/1.82 % (22411)------------------------------
% 3.00/1.82 % (22414)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_22043 for (2997ds/46Mi)
% 3.00/1.82 % (22415)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_22043 for (2997ds/98Mi)
% 3.00/1.84 % (22414)Instruction limit reached!
% 3.00/1.84 % (22414)------------------------------
% 3.00/1.84 % (22414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.84 % (22414)Termination reason: Unknown
% 3.00/1.84 % (22414)Termination phase: Property scanning
% 3.00/1.84
% 3.00/1.84 % (22414)Memory used [KB]: 2046
% 3.00/1.84 % (22414)Time elapsed: 0.016 s
% 3.00/1.84 % (22414)Instructions burned: 47 (million)
% 3.00/1.84 % (22414)------------------------------
% 3.00/1.84 % (22414)------------------------------
% 3.00/1.84 % (22399)Instruction limit reached!
% 3.00/1.84 % (22399)------------------------------
% 3.00/1.84 % (22399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.84 % (22399)Termination reason: Unknown
% 3.00/1.84 % (22399)Termination phase: Saturation
% 3.00/1.84
% 3.00/1.84 % (22399)Memory used [KB]: 9466
% 3.00/1.84 % (22399)Time elapsed: 0.130 s
% 3.00/1.84 % (22399)Instructions burned: 377 (million)
% 3.00/1.84 % (22399)------------------------------
% 3.00/1.84 % (22399)------------------------------
% 3.00/1.85 % (22416)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_22043 for (2997ds/507Mi)
% 3.00/1.85 % (22415)Instruction limit reached!
% 3.00/1.85 % (22415)------------------------------
% 3.00/1.85 % (22415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.85 % (22415)Termination reason: Unknown
% 3.00/1.85 % (22415)Termination phase: Property scanning
% 3.00/1.85
% 3.00/1.85 % (22415)Memory used [KB]: 2942
% 3.00/1.85 % (22415)Time elapsed: 0.028 s
% 3.00/1.85 % (22415)Instructions burned: 101 (million)
% 3.00/1.85 % (22415)------------------------------
% 3.00/1.85 % (22415)------------------------------
% 3.00/1.85 % (22417)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_22043 for (2997ds/149Mi)
% 3.00/1.86 % (22418)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22043 for (2997ds/39Mi)
% 3.00/1.87 % (22418)Instruction limit reached!
% 3.00/1.87 % (22418)------------------------------
% 3.00/1.87 % (22418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.87 % (22418)Termination reason: Unknown
% 3.00/1.87 % (22418)Termination phase: Property scanning
% 3.00/1.87
% 3.00/1.87 % (22418)Memory used [KB]: 2046
% 3.00/1.87 % (22418)Time elapsed: 0.013 s
% 3.00/1.87 % (22418)Instructions burned: 40 (million)
% 3.00/1.87 % (22418)------------------------------
% 3.00/1.87 % (22418)------------------------------
% 3.00/1.88 % (22419)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_22043 for (2997ds/6Mi)
% 3.00/1.88 % (22419)Instruction limit reached!
% 3.00/1.88 % (22419)------------------------------
% 3.00/1.88 % (22419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.88 % (22419)Termination reason: Unknown
% 3.00/1.88 % (22419)Termination phase: shuffling
% 3.00/1.88
% 3.00/1.88 % (22419)Memory used [KB]: 1663
% 3.00/1.88 % (22419)Time elapsed: 0.003 s
% 3.00/1.88 % (22419)Instructions burned: 6 (million)
% 3.00/1.88 % (22419)------------------------------
% 3.00/1.88 % (22419)------------------------------
% 3.00/1.89 % (22420)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_22043 for (2997ds/1087Mi)
% 3.00/1.90 % (22417)Instruction limit reached!
% 3.00/1.90 % (22417)------------------------------
% 3.00/1.90 % (22417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.90 % (22417)Termination reason: Unknown
% 3.00/1.90 % (22417)Termination phase: Property scanning
% 3.00/1.90
% 3.00/1.90 % (22417)Memory used [KB]: 2942
% 3.00/1.90 % (22417)Time elapsed: 0.045 s
% 3.00/1.90 % (22417)Instructions burned: 150 (million)
% 3.00/1.90 % (22417)------------------------------
% 3.00/1.90 % (22417)------------------------------
% 3.00/1.91 % (22421)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22043 for (2996ds/47Mi)
% 3.00/1.91 % (22420)Refutation not found, incomplete strategy
% 3.00/1.91 % (22420)------------------------------
% 3.00/1.91 % (22420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.91 % (22420)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.91
% 3.00/1.91
% 3.00/1.91 % (22420)Memory used [KB]: 6652
% 3.00/1.91 % (22420)Time elapsed: 0.019 s
% 3.00/1.91 % (22420)Instructions burned: 61 (million)
% 3.00/1.91 % (22420)------------------------------
% 3.00/1.91 % (22420)------------------------------
% 3.00/1.92 % (22421)Instruction limit reached!
% 3.00/1.92 % (22421)------------------------------
% 3.00/1.92 % (22421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.92 % (22421)Termination reason: Unknown
% 3.00/1.92 % (22421)Termination phase: Property scanning
% 3.00/1.92
% 3.00/1.92 % (22421)Memory used [KB]: 2046
% 3.00/1.92 % (22421)Time elapsed: 0.017 s
% 3.00/1.92 % (22421)Instructions burned: 47 (million)
% 3.00/1.92 % (22421)------------------------------
% 3.00/1.92 % (22421)------------------------------
% 3.00/1.92 % (22422)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_22043 for (2996ds/44Mi)
% 3.00/1.93 % (22416)First to succeed.
% 3.00/1.93 % (22416)Refutation found. Thanks to Tanya!
% 3.00/1.93 % SZS status Theorem for DTF2THF_22043
% 3.00/1.93 % SZS output start Proof for DTF2THF_22043
% 3.00/1.93 thf(type_def_5, type, name: $tType).
% 3.00/1.93 thf(type_def_6, type, pi: $tType).
% 3.00/1.93 thf(type_def_8, type, late_freeRes: $tType).
% 3.00/1.93 thf(type_def_9, type, late_subject: $tType).
% 3.00/1.93 thf(type_def_10, type, late_residual: $tType).
% 3.00/1.93 thf(type_def_11, type, noption_name: $tType).
% 3.00/1.93 thf(type_def_12, type, noption_pi: $tType).
% 3.00/1.93 thf(type_def_13, type, noption_Late_freeRes: $tType).
% 3.00/1.93 thf(type_def_14, type, produc1141751126_pi_pi: $tType).
% 3.00/1.93 thf(type_def_15, type, noptio1575811931_pi_pi: $tType).
% 3.00/1.93 thf(type_def_16, type, produc1462499409ion_pi: $tType).
% 3.00/1.93 thf(type_def_17, type, produc405342261i_name: $tType).
% 3.00/1.93 thf(type_def_18, type, produc629157763_pi_pi: $tType).
% 3.00/1.93 thf(type_def_19, type, produc1834551554reeRes: $tType).
% 3.00/1.93 thf(type_def_20, type, produc1443308494i_name: $tType).
% 3.00/1.93 thf(type_def_21, type, produc1559976732_pi_pi: $tType).
% 3.00/1.93 thf(type_def_22, type, produc1961110975reeRes: $tType).
% 3.00/1.93 thf(type_def_23, type, produc53907987_pi_pi: $tType).
% 3.00/1.93 thf(type_def_24, type, produc367475239e_name: $tType).
% 3.00/1.93 thf(type_def_25, type, product_prod_name_pi: $tType).
% 3.00/1.93 thf(type_def_26, type, produc2008547984reeRes: $tType).
% 3.00/1.93 thf(type_def_27, type, product_prod_pi_name: $tType).
% 3.00/1.93 thf(type_def_28, type, product_prod_pi_pi: $tType).
% 3.00/1.93 thf(type_def_29, type, produc649380958reeRes: $tType).
% 3.00/1.93 thf(type_def_30, type, produc2052722628s_name: $tType).
% 3.00/1.93 thf(type_def_31, type, produc992857746Res_pi: $tType).
% 3.00/1.93 thf(type_def_32, type, produc1357834675reeRes: $tType).
% 3.00/1.93 thf(type_def_33, type, set_Pr1569510577ion_pi: $tType).
% 3.00/1.93 thf(type_def_34, type, set_Pr1294453099i_name: $tType).
% 3.00/1.93 thf(type_def_35, type, set_Pr1694908217_pi_pi: $tType).
% 3.00/1.93 thf(type_def_36, type, set_Pr305743074reeRes: $tType).
% 3.00/1.93 thf(type_def_37, type, set_Pr100209225_pi_pi: $tType).
% 3.00/1.93 thf(type_def_38, type, set_Pr1654044726_pi_pi: $tType).
% 3.00/1.93 thf(type_def_39, type, set_Pr1834926343_pi_pi: $tType).
% 3.00/1.93 thf(type_def_40, type, produc1217648014ion_pi: $tType).
% 3.00/1.93 thf(func_def_0, type, produc1217648014ion_pi: $tType).
% 3.00/1.93 thf(func_def_1, type, produc1961110975reeRes: $tType).
% 3.00/1.93 thf(func_def_2, type, set_Pr100209225_pi_pi: $tType).
% 3.00/1.93 thf(func_def_3, type, produc1443308494i_name: $tType).
% 3.00/1.93 thf(func_def_4, type, produc1559976732_pi_pi: $tType).
% 3.00/1.93 thf(func_def_5, type, produc53907987_pi_pi: $tType).
% 3.00/1.93 thf(func_def_6, type, set_Pr1569510577ion_pi: $tType).
% 3.00/1.93 thf(func_def_7, type, produc1462499409ion_pi: $tType).
% 3.00/1.93 thf(func_def_8, type, set_Pr305743074reeRes: $tType).
% 3.00/1.93 thf(func_def_9, type, noptio1575811931_pi_pi: $tType).
% 3.00/1.93 thf(func_def_10, type, set_Pr1294453099i_name: $tType).
% 3.00/1.93 thf(func_def_11, type, produc1834551554reeRes: $tType).
% 3.00/1.93 thf(func_def_12, type, set_Pr1694908217_pi_pi: $tType).
% 3.00/1.93 thf(func_def_13, type, set_Pr1654044726_pi_pi: $tType).
% 3.00/1.93 thf(func_def_14, type, produc405342261i_name: $tType).
% 3.00/1.93 thf(func_def_15, type, produc629157763_pi_pi: $tType).
% 3.00/1.93 thf(func_def_16, type, produc1141751126_pi_pi: $tType).
% 3.00/1.93 thf(func_def_17, type, produc1357834675reeRes: $tType).
% 3.00/1.93 thf(func_def_18, type, produc2052722628s_name: $tType).
% 3.00/1.93 thf(func_def_19, type, produc2008547984reeRes: $tType).
% 3.00/1.93 thf(func_def_20, type, produc992857746Res_pi: $tType).
% 3.00/1.93 thf(func_def_21, type, produc649380958reeRes: $tType).
% 3.00/1.93 thf(func_def_22, type, set_Pr1834926343_pi_pi: $tType).
% 3.00/1.93 thf(func_def_23, type, produc367475239e_name: $tType).
% 3.00/1.93 thf(func_def_24, type, product_prod_pi_name: $tType).
% 3.00/1.93 thf(func_def_25, type, product_prod_name_pi: $tType).
% 3.00/1.93 thf(func_def_26, type, product_prod_pi_pi: $tType).
% 3.00/1.93 thf(func_def_27, type, noption_Late_freeRes: $tType).
% 3.00/1.93 thf(func_def_28, type, noption_name: $tType).
% 3.00/1.93 thf(func_def_29, type, noption_pi: $tType).
% 3.00/1.93 thf(func_def_30, type, late_residual: $tType).
% 3.00/1.93 thf(func_def_31, type, late_subject: $tType).
% 3.00/1.93 thf(func_def_32, type, late_freeRes: $tType).
% 3.00/1.93 thf(func_def_33, type, name: $tType).
% 3.00/1.93 thf(func_def_34, type, pi: $tType).
% 3.00/1.93 thf(func_def_35, type, input: name > name > pi > pi).
% 3.00/1.93 thf(func_def_36, type, mismatch: name > name > pi > pi).
% 3.00/1.93 thf(func_def_37, type, output: name > name > pi > pi).
% 3.00/1.93 thf(func_def_38, type, par: pi > pi > pi).
% 3.00/1.93 thf(func_def_39, type, piNil: pi).
% 3.00/1.93 thf(func_def_40, type, res: name > pi > pi).
% 3.00/1.93 thf(func_def_41, type, sum: pi > pi > pi).
% 3.00/1.93 thf(func_def_42, type, tau: pi > pi).
% 3.00/1.93 thf(func_def_43, type, subs: pi > name > name > pi).
% 3.00/1.93 thf(func_def_44, type, late_OutputR: name > name > late_freeRes).
% 3.00/1.93 thf(func_def_45, type, late_TauR: late_freeRes).
% 3.00/1.93 thf(func_def_46, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.00/1.93 thf(func_def_47, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.00/1.93 thf(func_def_48, type, late_BoundOutputS: name > late_subject).
% 3.00/1.93 thf(func_def_49, type, late_InputS: name > late_subject).
% 3.00/1.93 thf(func_def_50, type, late_transitions: pi > late_residual > $o).
% 3.00/1.93 thf(func_def_51, type, abs_fun_name_name: name > name > name > noption_name).
% 3.00/1.93 thf(func_def_52, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 3.00/1.93 thf(func_def_53, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 3.00/1.93 thf(func_def_54, type, abs_fu385186459_pi_pi: name > produc1141751126_pi_pi > name > noptio1575811931_pi_pi).
% 3.00/1.93 thf(func_def_55, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 3.00/1.93 thf(func_def_56, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 3.00/1.93 thf(func_def_57, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 3.00/1.93 thf(func_def_58, type, fresh_2065563522_pi_pi: name > (name > noptio1575811931_pi_pi) > $o).
% 3.00/1.93 thf(func_def_59, type, fresh_name_name: name > name > $o).
% 3.00/1.93 thf(func_def_60, type, fresh_name_pi: name > pi > $o).
% 3.00/1.93 thf(func_def_61, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.00/1.93 thf(func_def_62, type, fresh_81631222sidual: name > late_residual > $o).
% 3.00/1.93 thf(func_def_63, type, fresh_717452603ubject: name > late_subject > $o).
% 3.00/1.93 thf(func_def_64, type, fresh_225680151ion_pi: name > produc1462499409ion_pi > $o).
% 3.00/1.93 thf(func_def_65, type, fresh_453496559i_name: name > produc405342261i_name > $o).
% 3.00/1.93 thf(func_def_66, type, fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o).
% 3.00/1.93 thf(func_def_67, type, fresh_1711070152reeRes: name > produc1834551554reeRes > $o).
% 3.00/1.93 thf(func_def_68, type, fresh_1513292180i_name: name > produc1443308494i_name > $o).
% 3.00/1.93 thf(func_def_69, type, fresh_1335311330_pi_pi: name > produc1559976732_pi_pi > $o).
% 3.00/1.93 thf(func_def_70, type, fresh_1729533561reeRes: name > produc1961110975reeRes > $o).
% 3.00/1.93 thf(func_def_71, type, fresh_975559885_pi_pi: name > produc53907987_pi_pi > $o).
% 3.00/1.93 thf(func_def_72, type, fresh_441084397e_name: name > produc367475239e_name > $o).
% 3.00/1.93 thf(func_def_73, type, fresh_93646139ame_pi: name > product_prod_name_pi > $o).
% 3.00/1.93 thf(func_def_74, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 3.00/1.93 thf(func_def_75, type, fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o).
% 3.00/1.93 thf(func_def_76, type, fresh_261416607i_name: name > product_prod_pi_name > $o).
% 3.00/1.93 thf(func_def_77, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 3.00/1.93 thf(func_def_78, type, fresh_1504024600reeRes: name > produc649380958reeRes > $o).
% 3.00/1.93 thf(func_def_79, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 3.00/1.93 thf(func_def_80, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 3.00/1.93 thf(func_def_81, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 3.00/1.93 thf(func_def_82, type, ord_le1032043601ion_pi: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > $o).
% 3.00/1.93 thf(func_def_83, type, ord_le2082425291i_name: set_Pr1294453099i_name > set_Pr1294453099i_name > $o).
% 3.00/1.93 thf(func_def_84, type, ord_le1854926745_pi_pi: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > $o).
% 3.00/1.93 thf(func_def_85, type, ord_le1762471042reeRes: set_Pr305743074reeRes > set_Pr305743074reeRes > $o).
% 3.00/1.93 thf(func_def_86, type, ord_le211833513_pi_pi: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > $o).
% 3.00/1.93 thf(func_def_87, type, ord_le797229014_pi_pi: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > $o).
% 3.00/1.93 thf(func_def_88, type, ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.00/1.93 thf(func_def_89, type, produc1342893193ion_pi: (name > noption_pi) > (name > noption_pi) > produc1462499409ion_pi).
% 3.00/1.93 thf(func_def_90, type, produc540578151i_name: (name > noption_pi) > name > produc405342261i_name).
% 3.00/1.93 thf(func_def_91, type, produc1820286517_pi_pi: (name > noption_pi) > pi > produc629157763_pi_pi).
% 3.00/1.93 thf(func_def_92, type, produc1505598906reeRes: (name > noption_pi) > late_freeRes > produc1834551554reeRes).
% 3.00/1.93 thf(func_def_93, type, produc674047040ion_pi: (name > noption_pi) > produc1462499409ion_pi > produc1217648014ion_pi).
% 3.00/1.93 thf(func_def_94, type, produc1024533510i_name: (name > noption_pi) > produc405342261i_name > produc1443308494i_name).
% 3.00/1.93 thf(func_def_95, type, produc1189045204_pi_pi: (name > noption_pi) > produc629157763_pi_pi > produc1559976732_pi_pi).
% 3.00/1.93 thf(func_def_96, type, produc703114481reeRes: (name > noption_pi) > produc1834551554reeRes > produc1961110975reeRes).
% 3.00/1.93 thf(func_def_97, type, produc1275980869_pi_pi: (name > noption_pi) > produc1141751126_pi_pi > produc53907987_pi_pi).
% 3.00/1.93 thf(func_def_98, type, produc1570949143e_name: name > name > produc367475239e_name).
% 3.00/1.93 thf(func_def_99, type, product_Pair_name_pi: name > pi > product_prod_name_pi).
% 3.00/1.93 thf(func_def_100, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 3.00/1.93 thf(func_def_101, type, produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_102, type, product_Pair_pi_name: pi > name > product_prod_pi_name).
% 3.00/1.93 thf(func_def_103, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_104, type, produc1638681944reeRes: pi > late_freeRes > produc649380958reeRes).
% 3.00/1.93 thf(func_def_105, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 3.00/1.93 thf(func_def_106, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 3.00/1.93 thf(func_def_107, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 3.00/1.93 thf(func_def_108, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 3.00/1.93 thf(func_def_109, type, id_name_noption_pi: set_Pr1569510577ion_pi).
% 3.00/1.93 thf(func_def_110, type, id_pi: set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_111, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_112, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 3.00/1.93 thf(func_def_113, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 3.00/1.93 thf(func_def_114, type, member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o).
% 3.00/1.93 thf(func_def_115, type, member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o).
% 3.00/1.93 thf(func_def_116, type, member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o).
% 3.00/1.93 thf(func_def_117, type, member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o).
% 3.00/1.93 thf(func_def_118, type, member695660714_pi_pi: produc53907987_pi_pi > set_Pr100209225_pi_pi > $o).
% 3.00/1.93 thf(func_def_119, type, member540268543_pi_pi: produc1141751126_pi_pi > set_Pr1654044726_pi_pi > $o).
% 3.00/1.93 thf(func_def_120, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.00/1.93 thf(func_def_121, type, p: pi).
% 3.00/1.93 thf(func_def_122, type, pq: pi).
% 3.00/1.93 thf(func_def_123, type, q: pi).
% 3.00/1.93 thf(func_def_124, type, rel: set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_125, type, a: late_subject).
% 3.00/1.93 thf(func_def_126, type, x: name).
% 3.00/1.93 thf(func_def_127, type, y: name).
% 3.00/1.93 thf(func_def_146, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.00/1.93 thf(func_def_147, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.00/1.93 thf(func_def_148, type, sP2: late_subject > name > pi > pi > pi > $o).
% 3.00/1.93 thf(func_def_149, type, sP3: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > $o).
% 3.00/1.93 thf(func_def_150, type, sP4: late_residual > name > pi > $o).
% 3.00/1.93 thf(func_def_151, type, sP5: name > pi > late_residual > $o).
% 3.00/1.93 thf(func_def_152, type, sP6: pi > set_Pr1834926343_pi_pi > name > pi > $o).
% 3.00/1.93 thf(func_def_153, type, sP7: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > $o).
% 3.00/1.93 thf(func_def_154, type, sP8: pi > set_Pr1834926343_pi_pi > pi > name > $o).
% 3.00/1.93 thf(func_def_155, type, sP9: name > pi > late_subject > name > pi > $o).
% 3.00/1.93 thf(func_def_156, type, sP10: pi > set_Pr1834926343_pi_pi > pi > pi > $o).
% 3.00/1.93 thf(func_def_157, type, sP11: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > $o).
% 3.00/1.93 thf(func_def_158, type, sP12: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > $o).
% 3.00/1.93 thf(func_def_159, type, sP13: name > set_Pr1834926343_pi_pi > pi > pi > $o).
% 3.00/1.93 thf(func_def_160, type, sP14: set_Pr1834926343_pi_pi > pi > pi > name > name > $o).
% 3.00/1.93 thf(func_def_161, type, sP15: pi > pi > set_Pr1834926343_pi_pi > name > $o).
% 3.00/1.93 thf(func_def_162, type, sP16: pi > set_Pr1834926343_pi_pi > pi > pi > name > $o).
% 3.00/1.93 thf(func_def_163, type, sP17: pi > set_Pr1834926343_pi_pi > pi > name > $o).
% 3.00/1.93 thf(func_def_164, type, sK18: (produc1443308494i_name > $o) > produc405342261i_name).
% 3.00/1.93 thf(func_def_165, type, sK19: (produc1443308494i_name > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_166, type, sK20: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_167, type, sK21: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_168, type, sK22: (pi > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_169, type, sK23: (pi > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_170, type, sK24: (pi > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_171, type, sK25: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_172, type, sK26: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_173, type, sK27: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_174, type, sK28: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_175, type, sK29: product_prod_pi_pi > pi).
% 3.00/1.93 thf(func_def_176, type, sK30: product_prod_pi_pi > pi).
% 3.00/1.93 thf(func_def_177, type, sK31: product_prod_pi_pi > pi).
% 3.00/1.93 thf(func_def_178, type, sK32: (produc1961110975reeRes > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_179, type, sK33: (produc1961110975reeRes > $o) > produc1834551554reeRes).
% 3.00/1.93 thf(func_def_180, type, sK34: name > name).
% 3.00/1.93 thf(func_def_181, type, sK35: product_prod_pi_pi > pi).
% 3.00/1.93 thf(func_def_182, type, sK36: product_prod_pi_pi > pi).
% 3.00/1.93 thf(func_def_183, type, sK37: produc1462499409ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_184, type, sK38: (produc1141751126_pi_pi > late_residual > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_185, type, sK39: (produc1141751126_pi_pi > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_186, type, sK40: (produc1141751126_pi_pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_187, type, sK41: (produc1141751126_pi_pi > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_188, type, sK42: (produc1141751126_pi_pi > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_189, type, sK43: (produc1141751126_pi_pi > late_residual > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_190, type, sK44: (produc1141751126_pi_pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_191, type, sK45: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_192, type, sK46: (late_freeRes > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_193, type, sK47: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_194, type, sK48: (late_freeRes > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_195, type, sK49: (late_freeRes > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_196, type, sK50: (late_freeRes > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_197, type, sK51: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_198, type, sK52: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_199, type, sK53: produc1961110975reeRes > produc1834551554reeRes).
% 3.00/1.93 thf(func_def_200, type, sK54: produc1961110975reeRes > name > noption_pi).
% 3.00/1.93 thf(func_def_201, type, sK55: produc405342261i_name > name > noption_pi).
% 3.00/1.93 thf(func_def_202, type, sK56: produc405342261i_name > name).
% 3.00/1.93 thf(func_def_203, type, sK57: (produc53907987_pi_pi > $o) > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_204, type, sK58: (produc53907987_pi_pi > $o) > name).
% 3.00/1.93 thf(func_def_205, type, sK59: (produc53907987_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_206, type, sK60: pi > pi > late_freeRes > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_207, type, sK61: (late_freeRes > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_208, type, sK62: (late_freeRes > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_209, type, sK63: (late_freeRes > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_210, type, sK64: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_211, type, sK65: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_212, type, sK66: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_213, type, sK67: (late_freeRes > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_214, type, sK68: produc629157763_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_215, type, sK69: produc629157763_pi_pi > pi).
% 3.00/1.93 thf(func_def_216, type, sK70: (produc1141751126_pi_pi > late_residual > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_217, type, sK71: (produc1141751126_pi_pi > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_218, type, sK72: (produc1141751126_pi_pi > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_219, type, sK73: (produc1141751126_pi_pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_220, type, sK74: (produc1141751126_pi_pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_221, type, sK75: (produc1141751126_pi_pi > late_residual > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_222, type, sK76: (produc1141751126_pi_pi > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_223, type, sK77: produc53907987_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_224, type, sK78: produc53907987_pi_pi > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_225, type, sK79: (product_prod_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_226, type, sK80: (product_prod_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_227, type, sK81: produc1141751126_pi_pi > name).
% 3.00/1.93 thf(func_def_228, type, sK82: produc1141751126_pi_pi > pi).
% 3.00/1.93 thf(func_def_229, type, sK83: produc1141751126_pi_pi > pi).
% 3.00/1.93 thf(func_def_230, type, sK84: late_subject > name > pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_231, type, sK85: late_subject > name > pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_232, type, sK86: late_subject > name > pi > pi > pi > late_subject).
% 3.00/1.93 thf(func_def_233, type, sK87: late_subject > name > pi > pi > pi > name).
% 3.00/1.93 thf(func_def_234, type, sK88: late_subject > name > pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_235, type, sK89: pi > pi > name > pi > late_subject > late_subject).
% 3.00/1.93 thf(func_def_236, type, sK90: pi > pi > name > pi > late_subject > pi).
% 3.00/1.93 thf(func_def_237, type, sK91: pi > pi > name > pi > late_subject > pi).
% 3.00/1.93 thf(func_def_238, type, sK92: pi > pi > name > pi > late_subject > pi).
% 3.00/1.93 thf(func_def_239, type, sK93: pi > pi > name > pi > late_subject > name).
% 3.00/1.93 thf(func_def_240, type, sK94: pi > late_residual > name > name > pi).
% 3.00/1.93 thf(func_def_241, type, sK95: pi > late_residual > name > name > name).
% 3.00/1.93 thf(func_def_242, type, sK96: pi > late_residual > name > name > name).
% 3.00/1.93 thf(func_def_243, type, sK97: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > name).
% 3.00/1.93 thf(func_def_244, type, sK98: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > pi).
% 3.00/1.93 thf(func_def_245, type, sK99: set_Pr1834926343_pi_pi > pi > pi > late_freeRes > late_subject).
% 3.00/1.93 thf(func_def_246, type, sK100: pi > pi > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_247, type, sK101: pi > pi > set_Pr1834926343_pi_pi > late_freeRes).
% 3.00/1.93 thf(func_def_248, type, sK102: (produc53907987_pi_pi > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_249, type, sK103: (produc53907987_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_250, type, sK104: (produc1834551554reeRes > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_251, type, sK105: (produc1834551554reeRes > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_252, type, sK106: (late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_253, type, sK107: (late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_254, type, sK108: (late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_255, type, sK109: (late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_256, type, sK110: (late_residual > $o) > name).
% 3.00/1.93 thf(func_def_257, type, sK111: name > pi > late_residual > name).
% 3.00/1.93 thf(func_def_258, type, sK112: name > pi > late_residual > pi).
% 3.00/1.93 thf(func_def_259, type, sK113: name > pi > late_residual > name).
% 3.00/1.93 thf(func_def_260, type, sK114: name > pi > late_residual > pi).
% 3.00/1.93 thf(func_def_261, type, sK115: late_residual > name > pi > name).
% 3.00/1.93 thf(func_def_262, type, sK116: late_residual > name > pi > late_subject).
% 3.00/1.93 thf(func_def_263, type, sK117: late_residual > name > pi > pi).
% 3.00/1.93 thf(func_def_264, type, sK118: late_residual > name > pi > name).
% 3.00/1.93 thf(func_def_265, type, sK119: late_residual > name > pi > pi).
% 3.00/1.93 thf(func_def_266, type, sK120: pi > late_residual > name > pi).
% 3.00/1.93 thf(func_def_267, type, sK121: pi > late_residual > name > pi).
% 3.00/1.93 thf(func_def_268, type, sK122: pi > late_residual > name > name).
% 3.00/1.93 thf(func_def_269, type, sK123: pi > late_residual > name > late_freeRes).
% 3.00/1.93 thf(func_def_270, type, sK124: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_271, type, sK125: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_272, type, sK126: (produc1141751126_pi_pi > $o) > name).
% 3.00/1.93 thf(func_def_273, type, sK127: (produc1141751126_pi_pi > $o) > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_274, type, sK128: produc1834551554reeRes > name > noption_pi).
% 3.00/1.93 thf(func_def_275, type, sK129: produc1834551554reeRes > late_freeRes).
% 3.00/1.93 thf(func_def_276, type, sK130: late_subject > name).
% 3.00/1.93 thf(func_def_277, type, sK131: late_subject > name).
% 3.00/1.93 thf(func_def_278, type, sK132: pi > set_Pr1834926343_pi_pi > name > pi > name).
% 3.00/1.93 thf(func_def_279, type, sK133: pi > set_Pr1834926343_pi_pi > name > pi > late_subject).
% 3.00/1.93 thf(func_def_280, type, sK134: pi > set_Pr1834926343_pi_pi > name > pi > pi).
% 3.00/1.93 thf(func_def_281, type, sK135: pi > set_Pr1834926343_pi_pi > pi > pi).
% 3.00/1.93 thf(func_def_282, type, sK136: pi > set_Pr1834926343_pi_pi > pi > late_freeRes).
% 3.00/1.93 thf(func_def_283, type, sK137: produc1834551554reeRes > name > noption_pi).
% 3.00/1.93 thf(func_def_284, type, sK138: produc1834551554reeRes > late_freeRes).
% 3.00/1.93 thf(func_def_285, type, sK139: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_286, type, sK140: set_Pr1654044726_pi_pi > set_Pr1654044726_pi_pi > name).
% 3.00/1.93 thf(func_def_287, type, sK141: produc1141751126_pi_pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_288, type, sK142: produc1141751126_pi_pi > name).
% 3.00/1.93 thf(func_def_289, type, sK143: produc629157763_pi_pi > pi).
% 3.00/1.93 thf(func_def_290, type, sK144: produc629157763_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_291, type, sK145: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_292, type, sK146: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_293, type, sK147: pi > set_Pr1834926343_pi_pi > pi > name > pi).
% 3.00/1.93 thf(func_def_294, type, sK148: pi > set_Pr1834926343_pi_pi > pi > name > late_freeRes).
% 3.00/1.93 thf(func_def_295, type, sK149: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > late_subject).
% 3.00/1.93 thf(func_def_296, type, sK150: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > pi).
% 3.00/1.93 thf(func_def_297, type, sK151: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > name > pi > name).
% 3.00/1.93 thf(func_def_298, type, sK152: set_Pr1834926343_pi_pi > pi > pi > name > pi).
% 3.00/1.93 thf(func_def_299, type, sK153: set_Pr1834926343_pi_pi > pi > pi > name > name).
% 3.00/1.93 thf(func_def_300, type, sK154: (product_prod_pi_pi > $o) > (product_prod_pi_pi > $o) > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_301, type, sK155: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_302, type, sK156: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_303, type, sK157: produc53907987_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_304, type, sK158: produc53907987_pi_pi > name).
% 3.00/1.93 thf(func_def_305, type, sK159: produc53907987_pi_pi > pi).
% 3.00/1.93 thf(func_def_306, type, sK160: produc53907987_pi_pi > pi).
% 3.00/1.93 thf(func_def_307, type, sK161: set_Pr305743074reeRes > set_Pr305743074reeRes > late_freeRes).
% 3.00/1.93 thf(func_def_308, type, sK162: set_Pr305743074reeRes > set_Pr305743074reeRes > name > noption_pi).
% 3.00/1.93 thf(func_def_309, type, sK163: (produc1462499409ion_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_310, type, sK164: (produc1462499409ion_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_311, type, sK165: produc1462499409ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_312, type, sK166: produc1462499409ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_313, type, sK167: (late_freeRes > $o) > name).
% 3.00/1.93 thf(func_def_314, type, sK168: (late_freeRes > $o) > name).
% 3.00/1.93 thf(func_def_315, type, sK169: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_316, type, sK170: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_317, type, sK171: name > pi > late_subject > name > pi > name).
% 3.00/1.93 thf(func_def_318, type, sK172: name > pi > late_subject > name > pi > pi).
% 3.00/1.93 thf(func_def_319, type, sK173: name > pi > late_subject > name > pi > name).
% 3.00/1.93 thf(func_def_320, type, sK174: name > pi > late_subject > name > pi > late_subject).
% 3.00/1.93 thf(func_def_321, type, sK175: name > pi > late_subject > name > pi > pi).
% 3.00/1.93 thf(func_def_322, type, sK176: name > late_subject > name > pi > pi > name).
% 3.00/1.93 thf(func_def_323, type, sK177: name > late_subject > name > pi > pi > pi).
% 3.00/1.93 thf(func_def_324, type, sK178: name > late_subject > name > pi > pi > name).
% 3.00/1.93 thf(func_def_325, type, sK179: name > late_subject > name > pi > pi > pi).
% 3.00/1.93 thf(func_def_326, type, sK180: pi > late_freeRes > name > (pi > $o) > pi).
% 3.00/1.93 thf(func_def_327, type, sK181: name > late_freeRes > pi > pi > name).
% 3.00/1.93 thf(func_def_328, type, sK182: name > late_freeRes > pi > pi > pi).
% 3.00/1.93 thf(func_def_329, type, sK183: name > late_freeRes > pi > pi > late_freeRes).
% 3.00/1.93 thf(func_def_330, type, sK184: name > late_freeRes > pi > pi > pi).
% 3.00/1.93 thf(func_def_331, type, sK185: pi > name).
% 3.00/1.93 thf(func_def_332, type, sK186: produc405342261i_name > name).
% 3.00/1.93 thf(func_def_333, type, sK187: produc405342261i_name > name > noption_pi).
% 3.00/1.93 thf(func_def_334, type, sK188: late_freeRes > name).
% 3.00/1.93 thf(func_def_335, type, sK189: (produc1559976732_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_336, type, sK190: (produc1559976732_pi_pi > $o) > produc629157763_pi_pi).
% 3.00/1.93 thf(func_def_337, type, sK191: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_338, type, sK192: (name > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_339, type, sK193: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_340, type, sK194: (name > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_341, type, sK195: (name > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_342, type, sK196: (name > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_343, type, sK197: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_344, type, sK198: (late_subject > $o) > name).
% 3.00/1.93 thf(func_def_345, type, sK199: (late_subject > $o) > name).
% 3.00/1.93 thf(func_def_346, type, sK200: pi > late_residual > pi).
% 3.00/1.93 thf(func_def_347, type, sK201: (produc1141751126_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_348, type, sK202: (produc1141751126_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_349, type, sK203: (produc1141751126_pi_pi > $o) > name).
% 3.00/1.93 thf(func_def_350, type, sK204: pi > set_Pr1834926343_pi_pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_351, type, sK205: pi > set_Pr1834926343_pi_pi > pi > pi > late_subject).
% 3.00/1.93 thf(func_def_352, type, sK206: pi > set_Pr1834926343_pi_pi > pi > pi > name).
% 3.00/1.93 thf(func_def_353, type, sK207: pi > set_Pr1834926343_pi_pi > pi > pi).
% 3.00/1.93 thf(func_def_354, type, sK208: pi > set_Pr1834926343_pi_pi > pi > late_freeRes).
% 3.00/1.93 thf(func_def_355, type, sK209: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_356, type, sK210: set_Pr100209225_pi_pi > set_Pr100209225_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_357, type, sK211: produc1217648014ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_358, type, sK212: produc1217648014ion_pi > produc1462499409ion_pi).
% 3.00/1.93 thf(func_def_359, type, sK213: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_360, type, sK214: (set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi) > set_Pr1834926343_pi_pi).
% 3.00/1.93 thf(func_def_361, type, sK215: (produc1961110975reeRes > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_362, type, sK216: (produc1961110975reeRes > $o) > produc1834551554reeRes).
% 3.00/1.93 thf(func_def_363, type, sK217: (produc405342261i_name > $o) > name).
% 3.00/1.93 thf(func_def_364, type, sK218: (produc405342261i_name > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_365, type, sK219: (product_prod_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_366, type, sK220: (product_prod_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_367, type, sK221: (produc629157763_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_368, type, sK222: (produc629157763_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_369, type, sK223: produc1141751126_pi_pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_370, type, sK224: produc1141751126_pi_pi > name).
% 3.00/1.93 thf(func_def_371, type, sK225: (pi > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_372, type, sK226: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_373, type, sK227: (pi > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_374, type, sK228: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_375, type, sK229: (pi > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_376, type, sK230: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_377, type, sK231: (pi > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_378, type, sK232: (produc405342261i_name > $o) > name).
% 3.00/1.93 thf(func_def_379, type, sK233: (produc405342261i_name > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_380, type, sK234: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > pi).
% 3.00/1.93 thf(func_def_381, type, sK235: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > name).
% 3.00/1.93 thf(func_def_382, type, sK236: pi > set_Pr1834926343_pi_pi > produc1141751126_pi_pi > pi > late_subject).
% 3.00/1.93 thf(func_def_383, type, sK237: set_Pr1834926343_pi_pi > pi > pi > late_freeRes).
% 3.00/1.93 thf(func_def_384, type, sK238: set_Pr1834926343_pi_pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_385, type, sK239: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_386, type, sK240: (name > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_387, type, sK241: (name > late_residual > $o) > late_subject).
% 3.00/1.93 thf(func_def_388, type, sK242: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_389, type, sK243: (name > late_residual > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_390, type, sK244: (name > late_residual > $o) > pi).
% 3.00/1.93 thf(func_def_391, type, sK245: (name > late_residual > $o) > name).
% 3.00/1.93 thf(func_def_392, type, sK246: (produc53907987_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_393, type, sK247: (produc53907987_pi_pi > $o) > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_394, type, sK248: pi > name > late_residual > name > name).
% 3.00/1.93 thf(func_def_395, type, sK249: pi > name > late_residual > name > name).
% 3.00/1.93 thf(func_def_396, type, sK250: pi > name > late_residual > name > pi).
% 3.00/1.93 thf(func_def_397, type, sK251: late_freeRes > name).
% 3.00/1.93 thf(func_def_398, type, sK252: late_freeRes > name).
% 3.00/1.93 thf(func_def_399, type, sK253: produc53907987_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_400, type, sK254: produc53907987_pi_pi > name).
% 3.00/1.93 thf(func_def_401, type, sK255: produc53907987_pi_pi > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_402, type, sK256: pi > pi > set_Pr1834926343_pi_pi > name).
% 3.00/1.93 thf(func_def_403, type, sK257: pi > pi > set_Pr1834926343_pi_pi > late_subject).
% 3.00/1.93 thf(func_def_404, type, sK258: pi > pi > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_405, type, sK259: pi > pi > set_Pr1834926343_pi_pi > late_freeRes).
% 3.00/1.93 thf(func_def_406, type, sK260: pi > pi > set_Pr1834926343_pi_pi > pi).
% 3.00/1.93 thf(func_def_407, type, sK261: produc1462499409ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_408, type, sK262: produc1462499409ion_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_409, type, sK263: (produc1834551554reeRes > $o) > late_freeRes).
% 3.00/1.93 thf(func_def_410, type, sK264: (produc1834551554reeRes > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_411, type, sK265: (produc1559976732_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_412, type, sK266: (produc1559976732_pi_pi > $o) > produc629157763_pi_pi).
% 3.00/1.93 thf(func_def_413, type, sK267: (pi > $o) > pi > name > pi > late_subject > pi).
% 3.00/1.93 thf(func_def_414, type, sK268: (pi > $o) > pi > name > pi > late_subject > pi).
% 3.00/1.93 thf(func_def_415, type, sK269: produc53907987_pi_pi > produc1141751126_pi_pi).
% 3.00/1.93 thf(func_def_416, type, sK270: produc53907987_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_417, type, sK271: (produc629157763_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_418, type, sK272: (produc629157763_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_419, type, sK273: late_subject > pi > set_Pr1834926343_pi_pi > pi > name > pi).
% 3.00/1.93 thf(func_def_420, type, sK274: (produc1141751126_pi_pi > $o) > product_prod_pi_pi).
% 3.00/1.93 thf(func_def_421, type, sK275: (produc1141751126_pi_pi > $o) > name).
% 3.00/1.93 thf(func_def_422, type, sK276: produc1141751126_pi_pi > name).
% 3.00/1.93 thf(func_def_423, type, sK277: (produc1462499409ion_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_424, type, sK278: (produc1462499409ion_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_425, type, sK279: name > set_Pr1834926343_pi_pi > pi > pi > late_freeRes).
% 3.00/1.93 thf(func_def_426, type, sK280: name > set_Pr1834926343_pi_pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_427, type, sK281: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > name).
% 3.00/1.93 thf(func_def_428, type, sK282: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > pi).
% 3.00/1.93 thf(func_def_429, type, sK283: pi > set_Pr1834926343_pi_pi > pi > late_freeRes > name > late_subject).
% 3.00/1.93 thf(func_def_430, type, sK284: set_Pr1834926343_pi_pi > name > pi > pi > name).
% 3.00/1.93 thf(func_def_431, type, sK285: set_Pr1834926343_pi_pi > name > pi > pi > pi).
% 3.00/1.93 thf(func_def_432, type, sK286: set_Pr1294453099i_name > set_Pr1294453099i_name > name > noption_pi).
% 3.00/1.93 thf(func_def_433, type, sK287: set_Pr1294453099i_name > set_Pr1294453099i_name > name).
% 3.00/1.93 thf(func_def_434, type, sK288: (produc53907987_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_435, type, sK289: (produc53907987_pi_pi > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_436, type, sK290: (produc53907987_pi_pi > $o) > name).
% 3.00/1.93 thf(func_def_437, type, sK291: (produc53907987_pi_pi > $o) > pi).
% 3.00/1.93 thf(func_def_438, type, sK292: produc1443308494i_name > produc405342261i_name).
% 3.00/1.93 thf(func_def_439, type, sK293: produc1443308494i_name > name > noption_pi).
% 3.00/1.93 thf(func_def_440, type, sK294: pi > pi > set_Pr1834926343_pi_pi > name > pi).
% 3.00/1.93 thf(func_def_441, type, sK295: pi > pi > set_Pr1834926343_pi_pi > name > late_freeRes).
% 3.00/1.93 thf(func_def_442, type, sK296: set_Pr1834926343_pi_pi > pi > pi > name > name > pi).
% 3.00/1.93 thf(func_def_443, type, sK297: set_Pr1834926343_pi_pi > pi > pi > name > name > name).
% 3.00/1.93 thf(func_def_444, type, sK298: set_Pr1834926343_pi_pi > pi > pi > name > name > late_subject).
% 3.00/1.93 thf(func_def_445, type, sK299: name > set_Pr1834926343_pi_pi > pi > pi > name).
% 3.00/1.93 thf(func_def_446, type, sK300: name > set_Pr1834926343_pi_pi > pi > pi > pi).
% 3.00/1.93 thf(func_def_447, type, sK301: (produc1443308494i_name > $o) > name > noption_pi).
% 3.00/1.93 thf(func_def_448, type, sK302: (produc1443308494i_name > $o) > produc405342261i_name).
% 3.00/1.93 thf(func_def_449, type, sK303: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_450, type, sK304: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > pi).
% 3.00/1.93 thf(func_def_451, type, sK305: produc1559976732_pi_pi > name > noption_pi).
% 3.00/1.93 thf(func_def_452, type, sK306: produc1559976732_pi_pi > produc629157763_pi_pi).
% 3.00/1.93 thf(func_def_453, type, sK307: pi > set_Pr1834926343_pi_pi > pi > name > name).
% 3.00/1.93 thf(func_def_454, type, sK308: pi > set_Pr1834926343_pi_pi > pi > name > pi).
% 3.00/1.93 thf(func_def_455, type, sK309: pi > set_Pr1834926343_pi_pi > pi > pi > name > late_subject).
% 3.00/1.93 thf(func_def_456, type, sK310: pi > set_Pr1834926343_pi_pi > pi > pi > name > pi).
% 3.00/1.93 thf(func_def_457, type, sK311: pi > set_Pr1834926343_pi_pi > pi > pi > name > name).
% 3.00/1.93 thf(func_def_458, type, sK312: set_Pr1834926343_pi_pi > pi > name > pi > pi).
% 3.00/1.93 thf(func_def_459, type, sK313: set_Pr1834926343_pi_pi > pi > name > pi > late_freeRes).
% 3.00/1.93 thf(func_def_461, type, ph315: !>[X0: $tType]:(X0)).
% 3.00/1.93 thf(f2496,plain,(
% 3.00/1.93 $false),
% 3.00/1.93 inference(trivial_inequality_removal,[status(thm)],[f2495])).
% 3.00/1.93 thf(f2495,plain,(
% 3.00/1.93 ($false = $true)),
% 3.00/1.93 inference(duplicate_literal_removal,[status(thm)],[f2493])).
% 3.00/1.93 thf(f2493,plain,(
% 3.00/1.93 ($false = $true) | ($false = $true)),
% 3.00/1.93 inference(superposition,[status(thm)],[f2453,f1064])).
% 3.00/1.93 thf(f1064,plain,(
% 3.00/1.93 ( ! [X1 : $o] : (((~ X1) = $false) | ($false = X1)) )),
% 3.00/1.93 introduced(definition,[],[logical_not_proxy_axiom])).
% 3.00/1.93 thf(f2453,plain,(
% 3.00/1.93 ($true = (~ $true))),
% 3.00/1.93 inference(superposition,[status(thm)],[f2450,f2332])).
% 3.00/1.93 thf(f2332,plain,(
% 3.00/1.93 ( ! [X0 : $tType,X2 : X0] : (($true = (X2 = X2))) )),
% 3.00/1.93 inference(equality_resolution,[status(thm)],[f1061])).
% 3.00/1.93 thf(f1061,plain,(
% 3.00/1.93 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((X1 = X2) = $true) | (X1 != X2)) )),
% 3.00/1.93 introduced(definition,[],[equality_proxy_axiom])).
% 3.00/1.93 thf(f2450,plain,(
% 3.00/1.93 ((~ (x = x)) = $true)),
% 3.00/1.93 inference(trivial_inequality_removal,[status(thm)],[f2447])).
% 3.00/1.93 thf(f2447,plain,(
% 3.00/1.93 ((~ (x = x)) = $true) | ($true != $true)),
% 3.00/1.93 inference(superposition,[status(thm)],[f2410,f2252])).
% 3.00/1.93 thf(f2252,plain,(
% 3.00/1.93 ((fresh_1376661020_pi_pi @ x @ (produc235456326_pi_pi @ x @ (product_Pair_pi_pi @ p @ q))) = $true)),
% 3.00/1.93 inference(definition_unfolding,[status(thm)],[f1912,f2188])).
% 3.00/1.93 thf(f2188,plain,(
% 3.00/1.93 (y = x)),
% 3.00/1.93 inference(cnf_transformation,[status(thm)],[f1101])).
% 3.00/1.93 thf(f1101,plain,(
% 3.00/1.93 (y = x)),
% 3.00/1.93 inference(flattening,[status(thm)],[f776])).
% 3.00/1.93 thf(f776,plain,(
% 3.00/1.93 ~(y != x)),
% 3.00/1.93 inference(fool_elimination,[status(thm)],[f354])).
% 3.00/1.93 thf(f354,negated_conjecture,(
% 3.00/1.93 ~(y != x)),
% 3.00/1.93 inference(negated_conjecture,[status(cth)],[f353])).
% 3.00/1.93 thf(f353,conjecture,(
% 3.00/1.93 (y != x)),
% 3.00/1.93 file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',conj_0)).
% 3.00/1.93 thf(f1912,plain,(
% 3.00/1.93 ((fresh_1376661020_pi_pi @ y @ (produc235456326_pi_pi @ x @ (product_Pair_pi_pi @ p @ q))) = $true)),
% 3.00/1.93 inference(cnf_transformation,[status(thm)],[f830])).
% 3.00/1.93 thf(f830,plain,(
% 3.00/1.93 ((fresh_1376661020_pi_pi @ y @ (produc235456326_pi_pi @ x @ (product_Pair_pi_pi @ p @ q))) = $true)),
% 3.00/1.93 inference(fool_elimination,[status(thm)],[f829])).
% 3.00/1.93 thf(f829,plain,(
% 3.00/1.93 (fresh_1376661020_pi_pi @ y @ (produc235456326_pi_pi @ x @ (product_Pair_pi_pi @ p @ q)))),
% 3.00/1.93 inference(rectify,[status(thm)],[f2])).
% 3.00/1.93 thf(f2,axiom,(
% 3.00/1.93 (fresh_1376661020_pi_pi @ y @ (produc235456326_pi_pi @ x @ (product_Pair_pi_pi @ p @ q)))),
% 3.00/1.93 file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_1_Bound_Ohyps_I5_J)).
% 3.00/1.93 thf(f2410,plain,(
% 3.00/1.93 ( ! [X2 : name,X0 : name,X1 : product_prod_pi_pi] : (((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) != $true) | ($true = (~ (X2 = X0)))) )),
% 3.00/1.93 inference(beta_eta_normalization,[status(thm)],[f2320])).
% 3.00/1.93 thf(f2320,plain,(
% 3.00/1.93 ( ! [X2 : name,X0 : name,X1 : product_prod_pi_pi] : ((((^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))) @ X2 @ X0) = $true) | ((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) != $true)) )),
% 3.00/1.93 inference(definition_unfolding,[status(thm)],[f2177,f1688])).
% 3.00/1.93 thf(f1688,plain,(
% 3.00/1.93 (fresh_name_name = (^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))))),
% 3.00/1.93 inference(cnf_transformation,[status(thm)],[f465])).
% 3.00/1.93 thf(f465,plain,(
% 3.00/1.93 (fresh_name_name = (^[Y0 : name]: ((^[Y1 : name]: (~ (Y0 = Y1))))))),
% 3.00/1.93 inference(fool_elimination,[status(thm)],[f464])).
% 3.00/1.93 thf(f464,plain,(
% 3.00/1.93 ((^[X0 : name, X1 : name] : ((X0 != X1))) = fresh_name_name)),
% 3.00/1.93 inference(rectify,[status(thm)],[f274])).
% 3.00/1.93 thf(f274,axiom,(
% 3.00/1.93 ((^[X61 : name, X62 : name] : ((X61 != X62))) = fresh_name_name)),
% 3.00/1.93 file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_273_name__fresh)).
% 3.00/1.93 thf(f2177,plain,(
% 3.00/1.93 ( ! [X2 : name,X0 : name,X1 : product_prod_pi_pi] : (((fresh_name_name @ X2 @ X0) = $true) | ((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) != $true)) )),
% 3.00/1.93 inference(cnf_transformation,[status(thm)],[f1313])).
% 3.00/1.93 thf(f1313,plain,(
% 3.00/1.93 ! [X0 : name,X1 : product_prod_pi_pi,X2 : name] : (((fresh_name_name @ X2 @ X0) = $true) | ((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) != $true))),
% 3.00/1.93 inference(ennf_transformation,[status(thm)],[f884])).
% 3.00/1.93 thf(f884,plain,(
% 3.00/1.93 ! [X0 : name,X1 : product_prod_pi_pi,X2 : name] : (((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) = $true) => ((fresh_name_name @ X2 @ X0) = $true))),
% 3.00/1.93 inference(fool_elimination,[status(thm)],[f883])).
% 3.00/1.93 thf(f883,plain,(
% 3.00/1.93 ! [X0 : name,X1 : product_prod_pi_pi,X2 : name] : ((fresh_1376661020_pi_pi @ X2 @ (produc235456326_pi_pi @ X0 @ X1)) => (fresh_name_name @ X2 @ X0))),
% 3.00/1.93 inference(rectify,[status(thm)],[f32])).
% 3.00/1.93 thf(f32,axiom,(
% 3.00/1.93 ! [X1 : name,X2 : product_prod_pi_pi,X0 : name] : ((fresh_1376661020_pi_pi @ X0 @ (produc235456326_pi_pi @ X1 @ X2)) => (fresh_name_name @ X0 @ X1))),
% 3.00/1.93 file('/export/starexec/sandbox/tmp/tmp.EKtkV0nSOw/DTF2THF_22043.p',fact_31_fresh__prodD_I1_J)).
% 3.00/1.93 % SZS output end Proof for DTF2THF_22043
% 3.00/1.93 % (22416)------------------------------
% 3.00/1.93 % (22416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.00/1.93 % (22416)Termination reason: Refutation
% 3.00/1.93
% 3.00/1.93 % (22416)Memory used [KB]: 9210
% 3.00/1.93 % (22416)Time elapsed: 0.083 s
% 3.00/1.93 % (22416)Instructions burned: 280 (million)
% 3.00/1.93 % (22416)------------------------------
% 3.00/1.93 % (22416)------------------------------
% 3.00/1.93 % (22372)Success in time 0.332 s
%------------------------------------------------------------------------------