%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP191^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 08:56:17 AM UTC 2026
% Result : ContradictoryAxioms 3.07s 1.77s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 78 ( 10 ~; 0 |; 0 &; 60 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 164 ( 160 usr; 21 con; 0-5 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 24 ( 10 ^; 14 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
name: $tType ).
thf(type_def_6,type,
pi: $tType ).
thf(type_def_8,type,
produc367475239e_name: $tType ).
thf(type_def_9,type,
product_unit: $tType ).
thf(type_def_10,type,
pi_Rep: $tType ).
thf(type_def_11,type,
late_freeRes: $tType ).
thf(type_def_12,type,
late_subject: $tType ).
thf(type_def_13,type,
late_residual: $tType ).
thf(type_def_14,type,
late_residual_Rep: $tType ).
thf(type_def_15,type,
noption_pi: $tType ).
thf(type_def_16,type,
list_name_noption_pi: $tType ).
thf(type_def_17,type,
list_name: $tType ).
thf(type_def_18,type,
list_pi: $tType ).
thf(type_def_19,type,
list_pi_Rep: $tType ).
thf(type_def_20,type,
list_Late_freeRes: $tType ).
thf(type_def_21,type,
list_Late_subject: $tType ).
thf(type_def_22,type,
list_P227219501e_name: $tType ).
thf(type_def_23,type,
produc1141751126_pi_pi: $tType ).
thf(type_def_24,type,
list_P431515740_pi_pi: $tType ).
thf(type_def_25,type,
list_Product_unit: $tType ).
thf(type_def_26,type,
product_prod_name_pi: $tType ).
thf(type_def_27,type,
produc546891580t_unit: $tType ).
thf(type_def_28,type,
product_prod_pi_name: $tType ).
thf(type_def_29,type,
product_prod_pi_pi: $tType ).
thf(type_def_30,type,
produc1028309998t_unit: $tType ).
thf(type_def_31,type,
produc135724498t_name: $tType ).
thf(type_def_32,type,
produc738223008nit_pi: $tType ).
thf(type_def_33,type,
produc971140967t_unit: $tType ).
thf(type_def_34,type,
late_freeRes_Rep: $tType ).
thf(type_def_35,type,
late_subject_Rep: $tType ).
thf(type_def_36,type,
produc2052722628s_name: $tType ).
thf(type_def_37,type,
produc992857746Res_pi: $tType ).
thf(type_def_38,type,
produc1777919905pi_Rep: $tType ).
thf(type_def_39,type,
produc1357834675reeRes: $tType ).
thf(type_def_40,type,
produc214645451ubject: $tType ).
thf(type_def_41,type,
produc1998742700t_name: $tType ).
thf(type_def_42,type,
produc140253050ect_pi: $tType ).
thf(type_def_43,type,
produc257012921pi_Rep: $tType ).
thf(type_def_44,type,
produc355105483reeRes: $tType ).
thf(type_def_45,type,
produc1359399907ubject: $tType ).
thf(type_def_46,type,
set_name: $tType ).
thf(type_def_47,type,
set_pi: $tType ).
thf(type_def_48,type,
set_pi_Rep: $tType ).
thf(type_def_49,type,
set_Late_freeRes: $tType ).
thf(type_def_50,type,
set_Late_subject: $tType ).
thf(type_def_51,type,
set_Pr1834926343_pi_pi: $tType ).
thf(type_def_52,type,
produc1212344719pi_Rep: $tType ).
thf(type_def_53,type,
set_Pr443758855e_name: $tType ).
thf(type_def_54,type,
set_Pr1131282415pi_Rep: $tType ).
thf(type_def_55,type,
set_Pr1780909331reeRes: $tType ).
thf(type_def_56,type,
set_Pr806375235ubject: $tType ).
thf(func_def_0,type,
list_P431515740_pi_pi: $tType ).
thf(func_def_1,type,
set_Pr806375235ubject: $tType ).
thf(func_def_2,type,
set_Pr1780909331reeRes: $tType ).
thf(func_def_3,type,
produc1141751126_pi_pi: $tType ).
thf(func_def_4,type,
produc1359399907ubject: $tType ).
thf(func_def_5,type,
produc355105483reeRes: $tType ).
thf(func_def_6,type,
produc214645451ubject: $tType ).
thf(func_def_7,type,
produc1357834675reeRes: $tType ).
thf(func_def_8,type,
set_Pr1131282415pi_Rep: $tType ).
thf(func_def_9,type,
produc971140967t_unit: $tType ).
thf(func_def_10,type,
produc257012921pi_Rep: $tType ).
thf(func_def_11,type,
produc1777919905pi_Rep: $tType ).
thf(func_def_12,type,
list_name_noption_pi: $tType ).
thf(func_def_13,type,
list_P227219501e_name: $tType ).
thf(func_def_14,type,
set_Pr443758855e_name: $tType ).
thf(func_def_15,type,
produc1998742700t_name: $tType ).
thf(func_def_16,type,
produc2052722628s_name: $tType ).
thf(func_def_17,type,
produc140253050ect_pi: $tType ).
thf(func_def_18,type,
produc992857746Res_pi: $tType ).
thf(func_def_19,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_20,type,
produc135724498t_name: $tType ).
thf(func_def_21,type,
produc1212344719pi_Rep: $tType ).
thf(func_def_22,type,
produc546891580t_unit: $tType ).
thf(func_def_23,type,
produc738223008nit_pi: $tType ).
thf(func_def_24,type,
produc1028309998t_unit: $tType ).
thf(func_def_25,type,
produc367475239e_name: $tType ).
thf(func_def_26,type,
product_prod_pi_name: $tType ).
thf(func_def_27,type,
product_prod_name_pi: $tType ).
thf(func_def_28,type,
product_prod_pi_pi: $tType ).
thf(func_def_29,type,
list_Late_subject: $tType ).
thf(func_def_30,type,
list_Late_freeRes: $tType ).
thf(func_def_31,type,
set_Late_subject: $tType ).
thf(func_def_32,type,
set_Late_freeRes: $tType ).
thf(func_def_33,type,
list_Product_unit: $tType ).
thf(func_def_34,type,
list_pi_Rep: $tType ).
thf(func_def_35,type,
late_residual_Rep: $tType ).
thf(func_def_36,type,
noption_pi: $tType ).
thf(func_def_37,type,
late_subject_Rep: $tType ).
thf(func_def_38,type,
late_freeRes_Rep: $tType ).
thf(func_def_39,type,
set_pi_Rep: $tType ).
thf(func_def_40,type,
list_name: $tType ).
thf(func_def_41,type,
set_name: $tType ).
thf(func_def_42,type,
list_pi: $tType ).
thf(func_def_43,type,
late_residual: $tType ).
thf(func_def_44,type,
late_subject: $tType ).
thf(func_def_45,type,
late_freeRes: $tType ).
thf(func_def_46,type,
set_pi: $tType ).
thf(func_def_47,type,
product_unit: $tType ).
thf(func_def_48,type,
pi_Rep: $tType ).
thf(func_def_49,type,
name: $tType ).
thf(func_def_50,type,
pi: $tType ).
thf(func_def_51,type,
input: name > name > pi > pi ).
thf(func_def_52,type,
par: pi > pi > pi ).
thf(func_def_53,type,
res: name > pi > pi ).
thf(func_def_54,type,
swap_name: produc367475239e_name > name > name ).
thf(func_def_55,type,
subs: pi > name > name > pi ).
thf(func_def_56,type,
defaul1399868459t_unit: product_unit ).
thf(func_def_57,type,
if_name: $o > name > name > name ).
thf(func_def_58,type,
if_pi: $o > pi > pi > pi ).
thf(func_def_59,type,
if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).
thf(func_def_60,type,
if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).
thf(func_def_61,type,
if_Late_subject: $o > late_subject > late_subject > late_subject ).
thf(func_def_62,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_63,type,
late_TauR: late_freeRes ).
thf(func_def_64,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_65,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_66,type,
late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
thf(func_def_67,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_68,type,
late_InputS: name > late_subject ).
thf(func_def_69,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_70,type,
cons_name_noption_pi: ( name > noption_pi ) > list_name_noption_pi > list_name_noption_pi ).
thf(func_def_71,type,
cons_name: name > list_name > list_name ).
thf(func_def_72,type,
cons_pi: pi > list_pi > list_pi ).
thf(func_def_73,type,
cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).
thf(func_def_74,type,
cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).
thf(func_def_75,type,
cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).
thf(func_def_76,type,
cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).
thf(func_def_77,type,
cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi ).
thf(func_def_78,type,
cons_Product_unit: product_unit > list_Product_unit > list_Product_unit ).
thf(func_def_79,type,
nil_Pr743626285e_name: list_P227219501e_name ).
thf(func_def_80,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_81,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_82,type,
fresh_name_name: name > name > $o ).
thf(func_def_83,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_84,type,
fresh_name_pi_Rep: name > pi_Rep > $o ).
thf(func_def_85,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_86,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_87,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_88,type,
fresh_1135477378ion_pi: name > list_name_noption_pi > $o ).
thf(func_def_89,type,
fresh_name_list_name: name > list_name > $o ).
thf(func_def_90,type,
fresh_name_list_pi: name > list_pi > $o ).
thf(func_def_91,type,
fresh_922791155e_name: name > list_P227219501e_name > $o ).
thf(func_def_92,type,
fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o ).
thf(func_def_93,type,
fresh_1732817625t_unit: name > list_Product_unit > $o ).
thf(func_def_94,type,
fresh_441084397e_name: name > produc367475239e_name > $o ).
thf(func_def_95,type,
fresh_93646139ame_pi: name > product_prod_name_pi > $o ).
thf(func_def_96,type,
fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o ).
thf(func_def_97,type,
fresh_90540034t_unit: name > produc546891580t_unit > $o ).
thf(func_def_98,type,
fresh_261416607i_name: name > product_prod_pi_name > $o ).
thf(func_def_99,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(func_def_100,type,
fresh_997779380t_unit: name > produc1028309998t_unit > $o ).
thf(func_def_101,type,
fresh_1826856600t_name: name > produc135724498t_name > $o ).
thf(func_def_102,type,
fresh_707692390nit_pi: name > produc738223008nit_pi > $o ).
thf(func_def_103,type,
fresh_994967853t_unit: name > produc971140967t_unit > $o ).
thf(func_def_104,type,
fresh_1143631827t_unit: name > product_unit > $o ).
thf(func_def_105,type,
perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).
thf(func_def_106,type,
perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).
thf(func_def_107,type,
perm_n1667196784ion_pi: list_P227219501e_name > ( name > noption_pi ) > name > noption_pi ).
thf(func_def_108,type,
perm_n1333244520reeRes: list_P227219501e_name > ( pi > late_freeRes ) > pi > late_freeRes ).
thf(func_def_109,type,
perm_n190055296ubject: list_P227219501e_name > ( pi > late_subject ) > pi > late_subject ).
thf(func_def_110,type,
perm_n1841560599reeRes: list_P227219501e_name > ( pi_Rep > late_freeRes ) > pi_Rep > late_freeRes ).
thf(func_def_111,type,
perm_n698371375ubject: list_P227219501e_name > ( pi_Rep > late_subject ) > pi_Rep > late_subject ).
thf(func_def_112,type,
perm_n1446290985reeRes: list_P227219501e_name > ( late_freeRes > late_freeRes ) > late_freeRes > late_freeRes ).
thf(func_def_113,type,
perm_n303101761ubject: list_P227219501e_name > ( late_freeRes > late_subject ) > late_freeRes > late_subject ).
thf(func_def_114,type,
perm_n443561793reeRes: list_P227219501e_name > ( late_subject > late_freeRes ) > late_subject > late_freeRes ).
thf(func_def_115,type,
perm_n1447856217ubject: list_P227219501e_name > ( late_subject > late_subject ) > late_subject > late_subject ).
thf(func_def_116,type,
perm_name_o: list_P227219501e_name > $o > $o ).
thf(func_def_117,type,
perm_name_name: list_P227219501e_name > name > name ).
thf(func_def_118,type,
perm_name_pi: list_P227219501e_name > pi > pi ).
thf(func_def_119,type,
perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep ).
thf(func_def_120,type,
perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes ).
thf(func_def_121,type,
perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep ).
thf(func_def_122,type,
perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).
thf(func_def_123,type,
perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep ).
thf(func_def_124,type,
perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject ).
thf(func_def_125,type,
perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep ).
thf(func_def_126,type,
perm_name_list_name: list_P227219501e_name > list_name > list_name ).
thf(func_def_127,type,
perm_name_list_pi: list_P227219501e_name > list_pi > list_pi ).
thf(func_def_128,type,
perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).
thf(func_def_129,type,
perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).
thf(func_def_130,type,
perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).
thf(func_def_131,type,
perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).
thf(func_def_132,type,
perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).
thf(func_def_133,type,
perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).
thf(func_def_134,type,
perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).
thf(func_def_135,type,
perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
thf(func_def_136,type,
perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
thf(func_def_137,type,
perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
thf(func_def_138,type,
perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
thf(func_def_139,type,
perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
thf(func_def_140,type,
perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
thf(func_def_141,type,
perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
thf(func_def_142,type,
perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
thf(func_def_143,type,
perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
thf(func_def_144,type,
perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit ).
thf(func_def_145,type,
perm_name_set_name: list_P227219501e_name > set_name > set_name ).
thf(func_def_146,type,
perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
thf(func_def_147,type,
perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
thf(func_def_148,type,
perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
thf(func_def_149,type,
perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
thf(func_def_150,type,
perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
thf(func_def_151,type,
swap_name2: produc367475239e_name > name > name ).
thf(func_def_152,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(func_def_153,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(func_def_154,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(func_def_155,type,
produc1785453612t_unit: name > product_unit > produc546891580t_unit ).
thf(func_def_156,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
thf(func_def_157,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(func_def_158,type,
produc1831798878t_unit: pi > product_unit > produc1028309998t_unit ).
thf(func_def_159,type,
produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
thf(func_def_160,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(func_def_161,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(func_def_162,type,
produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
thf(func_def_163,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(func_def_164,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(func_def_165,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(func_def_166,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(func_def_167,type,
produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
thf(func_def_168,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(func_def_169,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(func_def_170,type,
produc421428802t_name: product_unit > name > produc135724498t_name ).
thf(func_def_171,type,
produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi ).
thf(func_def_172,type,
produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
thf(func_def_173,type,
product_Unity: product_unit ).
thf(func_def_174,type,
eqvt_name: set_Pr443758855e_name > $o ).
thf(func_def_175,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(func_def_176,type,
eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
thf(func_def_177,type,
eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
thf(func_def_178,type,
eqvt_Late_subject: set_Pr806375235ubject > $o ).
thf(func_def_179,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(func_def_180,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(func_def_181,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(func_def_182,type,
member_name: name > set_name > $o ).
thf(func_def_183,type,
member_pi: pi > set_pi > $o ).
thf(func_def_184,type,
member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
thf(func_def_185,type,
member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
thf(func_def_186,type,
member_Late_subject: late_subject > set_Late_subject > $o ).
thf(func_def_187,type,
member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
thf(func_def_188,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_189,type,
member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
thf(func_def_190,type,
member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
thf(func_def_191,type,
member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
thf(func_def_192,type,
p: pi ).
thf(func_def_193,type,
pq: pi ).
thf(func_def_194,type,
p2: pi ).
thf(func_def_195,type,
q: pi ).
thf(func_def_196,type,
q2: pi ).
thf(func_def_197,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_198,type,
aa: late_subject ).
thf(func_def_199,type,
ab: name ).
thf(func_def_200,type,
b: name ).
thf(func_def_201,type,
c: name ).
thf(func_def_202,type,
x: name ).
thf(func_def_203,type,
xPQ: pi ).
thf(func_def_204,type,
y: name ).
thf(func_def_205,type,
ya: name ).
thf(func_def_229,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_230,type,
sK2: name > name ).
thf(func_def_231,type,
sK3: product_unit > name ).
thf(func_def_232,type,
sK4: pi > name ).
thf(func_def_233,type,
sK5: produc1141751126_pi_pi > name ).
thf(f1839,plain,
$false,
inference(equality_resolution,[status(thm)],[f1838]) ).
thf(f1838,plain,
! [X2: name,X1: name] :
( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ X1 @ X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f1835]) ).
thf(f1835,plain,
! [X2: name,X1: name] :
( $false
= ( ( late_OutputR @ ab @ x )
= ( late_OutputR @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f1834]) ).
thf(f1834,plain,
! [X2: name,X1: name] :
( $true
= ( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1833]) ).
thf(f1833,plain,
! [X2: name,X1: name] :
( $true
= ( ^ [Y0: name] :
( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1832]) ).
thf(f1832,plain,
! [X1: name] :
( ( !! @ name
@ ^ [Y0: name] :
( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1831]) ).
thf(f1831,plain,
! [X1: name] :
( ( ^ [Y0: name] :
( !! @ name
@ ^ [Y1: name] :
( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1499]) ).
thf(f1499,plain,
( $true
= ( !! @ name
@ ^ [Y0: name] :
( !! @ name
@ ^ [Y1: name] :
( ( late_OutputR @ ab @ x )
!= ( late_OutputR @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1418,f1230]) ).
thf(f1230,plain,
( ( late_OutputR @ ab @ x )
= late_TauR ),
inference(cnf_transformation,[status(thm)],[f611]) ).
thf(f611,plain,
( ( late_OutputR @ ab @ x )
= late_TauR ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( late_OutputR @ ab @ x )
= late_TauR ),
file('/export/starexec/sandbox2/tmp/tmp.dCSmdHGfAN/DTF2THF_8414.p',fact_1_cComm1_Ohyps_I9_J) ).
thf(f1418,plain,
( $true
= ( !! @ name
@ ^ [Y0: name] :
( !! @ name
@ ^ [Y1: name] :
( late_TauR
!= ( late_OutputR @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f590]) ).
thf(f590,plain,
( $true
= ( !! @ name
@ ^ [Y0: name] :
( !! @ name
@ ^ [Y1: name] :
( late_TauR
!= ( late_OutputR @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f589]) ).
thf(f589,plain,
! [X0: name,X1: name] :
( late_TauR
!= ( late_OutputR @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f325]) ).
thf(f325,axiom,
! [X87: name,X86: name] :
( late_TauR
!= ( late_OutputR @ X86 @ X87 ) ),
file('/export/starexec/sandbox2/tmp/tmp.dCSmdHGfAN/DTF2THF_8414.p',fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP191^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:29:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : ITP191^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.46 % Domain : Interactive Theorem Proving
% 0.27/0.46 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_894__3417700_1
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Des21]
% 0.27/0.46 % Names : Strong_Late_Sim_SC/prob_894__3417700_1 [Des21]
% 0.27/0.46
% 0.27/0.46 % Status : ContradictoryAxioms
% 0.27/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.27 v7.5.0
% 0.27/0.46 % Syntax : Number of formulae : 568 ( 217 unt; 206 typ; 0 def)
% 0.27/0.46 % Number of atoms : 990 ( 367 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 16 ( 2 avg)
% 0.27/0.46 % Number of connectives : 4476 ( 96 ~; 1 |; 65 &;3860 @)
% 0.27/0.46 % ( 0 <=>; 454 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 27 ( 7 avg)
% 0.27/0.46 % Number of types : 52 ( 51 usr)
% 0.27/0.46 % Number of type conns : 350 ( 350 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 158 ( 155 usr; 20 con; 0-5 aty)
% 0.27/0.46 % Number of variables : 1309 ( 7 ^;1275 !; 27 ?;1309 :)
% 0.27/0.46 % SPC : TH0_CAX_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:44.830
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % Could-be-implicit typings (51)
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 0.27/0.46 list_P431515740_pi_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J,type,
% 0.27/0.46 set_Pr806375235ubject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.27/0.46 set_Pr1780909331reeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.46 produc1141751126_pi_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.27/0.46 produc1359399907ubject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.46 produc355105483reeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.27/0.46 produc214645451ubject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.46 produc1357834675reeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J_J,type,
% 0.27/0.46 set_Pr1131282415pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 produc971140967t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.46 produc257012921pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.46 produc1777919905pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.27/0.46 list_name_noption_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.27/0.46 list_P227219501e_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.27/0.46 set_Pr443758855e_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.27/0.46 produc1998742700t_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.27/0.46 produc2052722628s_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.27/0.46 produc140253050ect_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.27/0.46 produc992857746Res_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.46 set_Pr1834926343_pi_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Agent__Oname_J,type,
% 0.27/0.46 produc135724498t_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.46 produc1212344719pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 produc546891580t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Agent__Opi_J,type,
% 0.27/0.46 produc738223008nit_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Product____Type__Ounit_J,type,
% 0.27/0.46 produc1028309998t_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.27/0.46 produc367475239e_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 0.27/0.46 product_prod_pi_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 0.27/0.46 product_prod_name_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.46 product_prod_pi_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
% 0.27/0.46 list_Late_subject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 0.27/0.46 list_Late_freeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.27/0.46 set_Late_subject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.27/0.46 set_Late_freeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Ounit_J,type,
% 0.27/0.46 list_Product_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 0.27/0.46 list_pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 0.27/0.46 late_residual_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.27/0.46 noption_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 0.27/0.46 late_subject_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 0.27/0.46 late_freeRes_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 0.27/0.46 set_pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 0.27/0.46 list_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 0.27/0.46 set_name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 0.27/0.46 list_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.27/0.46 late_residual: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.27/0.46 late_subject: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.27/0.46 late_freeRes: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
% 0.27/0.46 set_pi: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Product____Type__Ounit,type,
% 0.27/0.46 product_unit: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Agent__Opi____Rep,type,
% 0.27/0.46 pi_Rep: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Agent__Oname,type,
% 0.27/0.46 name: $tType ).
% 0.27/0.46
% 0.27/0.46 thf(ty_n_t__Agent__Opi,type,
% 0.27/0.46 pi: $tType ).
% 0.27/0.46
% 0.27/0.46 % Explicit typings (155)
% 0.27/0.46 thf(sy_c_Agent_Opi_OInput,type,
% 0.27/0.46 input: name > name > pi > pi ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Agent_Opi_OPar,type,
% 0.27/0.46 par: pi > pi > pi ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Agent_Opi_ORes,type,
% 0.27/0.46 res: name > pi > pi ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Agent_Orec_Oswap__name,type,
% 0.27/0.46 swap_name: produc367475239e_name > name > name ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_Agent_Osubs,type,
% 0.27/0.46 subs: pi > name > name > pi ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_HOL_Odefault__class_Odefault_001t__Product____Type__Ounit,type,
% 0.27/0.46 defaul1399868459t_unit: product_unit ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_If_001t__Agent__Oname,type,
% 0.27/0.46 if_name: $o > name > name > name ).
% 0.27/0.46
% 0.27/0.46 thf(sy_c_If_001t__Agent__Opi,type,
% 0.27/0.46 if_pi: $o > pi > pi > pi ).
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% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.47 perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.47 perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.27/0.47 perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Ounit,type,
% 0.27/0.47 perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
% 0.27/0.47 perm_name_set_name: list_P227219501e_name > set_name > set_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
% 0.27/0.47 perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 0.27/0.47 perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.27/0.47 perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.27/0.47 perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.27/0.47 perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
% 0.27/0.47 swap_name2: produc367475239e_name > name > name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.27/0.47 produc1570949143e_name: name > name > produc367475239e_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.27/0.47 product_Pair_name_pi: name > pi > product_prod_name_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.47 produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Ounit,type,
% 0.27/0.47 produc1785453612t_unit: name > product_unit > produc546891580t_unit ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
% 0.27/0.47 product_Pair_pi_name: pi > name > product_prod_pi_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.27/0.47 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Product____Type__Ounit,type,
% 0.27/0.47 produc1831798878t_unit: pi > product_unit > produc1028309998t_unit ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
% 0.27/0.47 produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.27/0.47 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.27/0.47 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi____Rep,type,
% 0.27/0.47 produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.47 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 0.27/0.47 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.27/0.47 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.27/0.47 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 0.27/0.47 produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.47 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.27/0.47 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Oname,type,
% 0.27/0.47 produc421428802t_name: product_unit > name > produc135724498t_name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Opi,type,
% 0.27/0.47 produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 0.27/0.47 produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Product__Type_OUnity,type,
% 0.27/0.47 product_Unity: product_unit ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
% 0.27/0.47 eqvt_name: set_Pr443758855e_name > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.27/0.47 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
% 0.27/0.47 eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.47 eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
% 0.27/0.47 eqvt_Late_subject: set_Pr806375235ubject > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.47 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.27/0.47 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.27/0.47 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Agent__Oname,type,
% 0.27/0.47 member_name: name > set_name > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Agent__Opi,type,
% 0.27/0.47 member_pi: pi > set_pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 0.27/0.47 member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 0.27/0.47 member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 0.27/0.47 member_Late_subject: late_subject > set_Late_subject > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.27/0.47 member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.27/0.47 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 0.27/0.47 member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.27/0.47 member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.27/0.47 member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_P,type,
% 0.27/0.47 p: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_PQ____,type,
% 0.27/0.47 pq: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_P_H____,type,
% 0.27/0.47 p2: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Q,type,
% 0.27/0.47 q: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Q_H____,type,
% 0.27/0.47 q2: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_Rel,type,
% 0.27/0.47 rel: set_Pr1834926343_pi_pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_aa____,type,
% 0.27/0.47 aa: late_subject ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_ab____,type,
% 0.27/0.47 ab: name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_b____,type,
% 0.27/0.47 b: name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_c____,type,
% 0.27/0.47 c: name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_x,type,
% 0.27/0.47 x: name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_xPQ____,type,
% 0.27/0.47 xPQ: pi ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_y____,type,
% 0.27/0.47 y: name ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_ya____,type,
% 0.27/0.47 ya: name ).
% 0.27/0.47
% 0.27/0.47 % Relevant facts (350)
% 0.27/0.47 thf(fact_0_cComm1_Ohyps_I5_J,axiom,
% 0.27/0.47 ya != b ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(5)
% 0.27/0.47 thf(fact_1_cComm1_Ohyps_I9_J,axiom,
% 0.27/0.47 ( ( late_OutputR @ ab @ x )
% 0.27/0.47 = late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(9)
% 0.27/0.47 thf(fact_2_cOpen_Ohyps_I2_J,axiom,
% 0.27/0.47 ab != x ).
% 0.27/0.47
% 0.27/0.47 % cOpen.hyps(2)
% 0.27/0.47 thf(fact_3_cComm1_Ohyps_I6_J,axiom,
% 0.27/0.47 ya != c ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(6)
% 0.27/0.47 thf(fact_4_cOpen_Ohyps_I3_J,axiom,
% 0.27/0.47 ( aa
% 0.27/0.47 = ( late_BoundOutputS @ ab ) ) ).
% 0.27/0.47
% 0.27/0.47 % cOpen.hyps(3)
% 0.27/0.47 thf(fact_5_assms_I3_J,axiom,
% 0.27/0.47 eqvt_pi @ rel ).
% 0.27/0.47
% 0.27/0.47 % assms(3)
% 0.27/0.47 thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.27/0.47 y != x ).
% 0.27/0.47
% 0.27/0.47 % \<open>y__ \<noteq> x\<close>
% 0.27/0.47 thf(fact_7_Bound_Ohyps_I1_J,axiom,
% 0.27/0.47 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ) ).
% 0.27/0.47
% 0.27/0.47 % Bound.hyps(1)
% 0.27/0.47 thf(fact_8_assms_I1_J,axiom,
% 0.27/0.47 fresh_name_pi @ x @ p ).
% 0.27/0.47
% 0.27/0.47 % assms(1)
% 0.27/0.47 thf(fact_9_cComm1_Ohyps_I3_J,axiom,
% 0.27/0.47 fresh_name_pi @ ya @ p ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(3)
% 0.27/0.47 thf(fact_10_cComm1_Ohyps_I4_J,axiom,
% 0.27/0.47 fresh_name_pi @ ya @ q ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(4)
% 0.27/0.47 thf(fact_11_cComm1_Ohyps_I7_J,axiom,
% 0.27/0.47 fresh_name_pi @ ya @ q2 ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(7)
% 0.27/0.47 thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 0.27/0.47 fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 0.27/0.47
% 0.27/0.47 % Bound.hyps(3)
% 0.27/0.47 thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 0.27/0.47 fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 0.27/0.47
% 0.27/0.47 % Bound.hyps(2)
% 0.27/0.47 thf(fact_14_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3,axiom,
% 0.27/0.47 ! [A: name,P: pi,X: name] :
% 0.27/0.47 ( ( subs @ ( res @ A @ P ) @ X @ A )
% 0.27/0.47 = ( res @ X @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ A ) @ nil_Pr743626285e_name ) @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Strong_Late_Sim_SC_Mirabelle_ygjvazaixl.substRes3
% 0.27/0.47 thf(fact_15_cComm1_Ohyps_I1_J,axiom,
% 0.27/0.47 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ) ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(1)
% 0.27/0.47 thf(fact_16_perm__swap_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(1)
% 0.27/0.47 thf(fact_17_perm__swap_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(1)
% 0.27/0.47 thf(fact_18_perm__swap_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(1)
% 0.27/0.47 thf(fact_19_perm__swap_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(1)
% 0.27/0.47 thf(fact_20_perm__swap_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(1)
% 0.27/0.47 thf(fact_21_name__id,axiom,
% 0.27/0.47 ! [A: name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_id
% 0.27/0.47 thf(fact_22_name__id,axiom,
% 0.27/0.47 ! [A: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_id
% 0.27/0.47 thf(fact_23_name__id,axiom,
% 0.27/0.47 ! [A: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_id
% 0.27/0.47 thf(fact_24_name__id,axiom,
% 0.27/0.47 ! [A: name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_id
% 0.27/0.47 thf(fact_25_name__id,axiom,
% 0.27/0.47 ! [A: name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_id
% 0.27/0.47 thf(fact_26_name__swap,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap
% 0.27/0.47 thf(fact_27_name__swap,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap
% 0.27/0.47 thf(fact_28_name__swap,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap
% 0.27/0.47 thf(fact_29_name__swap,axiom,
% 0.27/0.47 ! [A: name,B: name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap
% 0.27/0.47 thf(fact_30_name__swap,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap
% 0.27/0.47 thf(fact_31_name__swap__bij,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap_bij
% 0.27/0.47 thf(fact_32_name__swap__bij,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap_bij
% 0.27/0.47 thf(fact_33_name__swap__bij,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap_bij
% 0.27/0.47 thf(fact_34_name__swap__bij,axiom,
% 0.27/0.47 ! [A: name,B: name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap_bij
% 0.27/0.47 thf(fact_35_name__swap__bij,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_swap_bij
% 0.27/0.47 thf(fact_36_cOpen_Ohyps_I1_J,axiom,
% 0.27/0.47 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ) ).
% 0.27/0.47
% 0.27/0.47 % cOpen.hyps(1)
% 0.27/0.47 thf(fact_37_pi_Operm_I8_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi @ ( par @ X2 @ X1 ) )
% 0.27/0.47 = ( par @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.perm(8)
% 0.27/0.47 thf(fact_38_simps_I8_J,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,C: name,D: name] :
% 0.27/0.47 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.27/0.47 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(8)
% 0.27/0.47 thf(fact_39_simps_I9_J,axiom,
% 0.27/0.47 ! [X: name,C: name,D: name,P: pi] :
% 0.27/0.47 ( ( X != C )
% 0.27/0.47 => ( ( X != D )
% 0.27/0.47 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.27/0.47 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simps(9)
% 0.27/0.47 thf(fact_40_pt__name1,axiom,
% 0.27/0.47 ! [X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % pt_name1
% 0.27/0.47 thf(fact_41_pt__name1,axiom,
% 0.27/0.47 ! [X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % pt_name1
% 0.27/0.47 thf(fact_42_pt__name1,axiom,
% 0.27/0.47 ! [X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % pt_name1
% 0.27/0.47 thf(fact_43_pt__name1,axiom,
% 0.27/0.47 ! [X: name] :
% 0.27/0.47 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % pt_name1
% 0.27/0.47 thf(fact_44_pt__name1,axiom,
% 0.27/0.47 ! [X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % pt_name1
% 0.27/0.47 thf(fact_45_cComm1_Ohyps_I2_J,axiom,
% 0.27/0.47 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ) ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(2)
% 0.27/0.47 thf(fact_46__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 0.27/0.47 fresh_name_pi @ y @ ( par @ p @ q ) ).
% 0.27/0.47
% 0.27/0.47 % \<open>y__ \<sharp> P \<parallel> Q\<close>
% 0.27/0.47 thf(fact_47_subst__identity,axiom,
% 0.27/0.47 ! [P: pi,A: name] :
% 0.27/0.47 ( ( subs @ P @ A @ A )
% 0.27/0.47 = P ) ).
% 0.27/0.47
% 0.27/0.47 % subst_identity
% 0.27/0.47 thf(fact_48_pi__perm__empty,axiom,
% 0.27/0.47 ! [Pi_Rep: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 0.27/0.47 = Pi_Rep ) ).
% 0.27/0.47
% 0.27/0.47 % pi_perm_empty
% 0.27/0.47 thf(fact_49__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062,axiom,
% 0.27/0.47 fresh_name_pi @ y @ p ).
% 0.27/0.47
% 0.27/0.47 % \<open>y__ \<sharp> P\<close>
% 0.27/0.47 thf(fact_50__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.27/0.47 fresh_name_pi @ y @ q ).
% 0.27/0.47
% 0.27/0.47 % \<open>y__ \<sharp> Q\<close>
% 0.27/0.47 thf(fact_51_pi_Ofresh_I8_J,axiom,
% 0.27/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.27/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.27/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(8)
% 0.27/0.47 thf(fact_52_pi_Operm_I9_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 0.27/0.47 = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.perm(9)
% 0.27/0.47 thf(fact_53_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: late_subject,B: name] :
% 0.27/0.47 ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.47 => ( ( fresh_717452603ubject @ B @ X )
% 0.27/0.47 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_54_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: late_freeRes,B: name] :
% 0.27/0.47 ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.27/0.47 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_55_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: pi_Rep,B: name] :
% 0.27/0.47 ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.27/0.47 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_56_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,B: name] :
% 0.27/0.47 ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ B @ X )
% 0.27/0.47 => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_57_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.27/0.47 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_58_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: name,B: name] :
% 0.27/0.47 ( ( fresh_name_name @ A @ X )
% 0.27/0.47 => ( ( fresh_name_name @ B @ X )
% 0.27/0.47 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_59_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: pi,B: name] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi @ B @ X )
% 0.27/0.47 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_60_perm__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: name > noption_pi,B: name] :
% 0.27/0.47 ( ( fresh_543891186ion_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_543891186ion_pi @ B @ X )
% 0.27/0.47 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_fresh_fresh
% 0.27/0.47 thf(fact_61_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: late_subject,B: name] :
% 0.27/0.47 ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.47 => ( ( fresh_717452603ubject @ B @ X )
% 0.27/0.47 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_62_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: late_freeRes,B: name] :
% 0.27/0.47 ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.27/0.47 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_63_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: pi_Rep,B: name] :
% 0.27/0.47 ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.27/0.47 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_64_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,B: name] :
% 0.27/0.47 ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ B @ X )
% 0.27/0.47 => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_65_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 0.27/0.47 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_66_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: name,B: name] :
% 0.27/0.47 ( ( fresh_name_name @ A @ X )
% 0.27/0.47 => ( ( fresh_name_name @ B @ X )
% 0.27/0.47 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_67_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: pi,B: name] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi @ B @ X )
% 0.27/0.47 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_68_name__fresh__fresh,axiom,
% 0.27/0.47 ! [A: name,X: name > noption_pi,B: name] :
% 0.27/0.47 ( ( fresh_543891186ion_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_543891186ion_pi @ B @ X )
% 0.27/0.47 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.27/0.47 = X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh_fresh
% 0.27/0.47 thf(fact_69_Bound_Ohyps_I4_J,axiom,
% 0.27/0.47 fresh_717452603ubject @ y @ aa ).
% 0.27/0.47
% 0.27/0.47 % Bound.hyps(4)
% 0.27/0.47 thf(fact_70_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.47 => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_71_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.47 => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_72_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.47 => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_73_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: product_unit] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_74_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.47 => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_75_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: name] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_name_name @ A @ X )
% 0.27/0.47 => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_76_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_77_fresh__perm__app,axiom,
% 0.27/0.47 ! [A: name,Pi: list_P227219501e_name,X: name > noption_pi] :
% 0.27/0.47 ( ( fresh_922791155e_name @ A @ Pi )
% 0.27/0.47 => ( ( fresh_543891186ion_pi @ A @ X )
% 0.27/0.47 => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_perm_app
% 0.27/0.47 thf(fact_78_name__exists__fresh,axiom,
% 0.27/0.47 ! [X: product_unit] :
% 0.27/0.47 ~ ! [C2: name] :
% 0.27/0.47 ~ ( fresh_1143631827t_unit @ C2 @ X ) ).
% 0.27/0.47
% 0.27/0.47 % name_exists_fresh
% 0.27/0.47 thf(fact_79_name__exists__fresh,axiom,
% 0.27/0.47 ! [X: produc1141751126_pi_pi] :
% 0.27/0.47 ~ ! [C2: name] :
% 0.27/0.47 ~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% 0.27/0.47
% 0.27/0.47 % name_exists_fresh
% 0.27/0.47 thf(fact_80_name__exists__fresh,axiom,
% 0.27/0.47 ! [X: name] :
% 0.27/0.47 ~ ! [C2: name] :
% 0.27/0.47 ~ ( fresh_name_name @ C2 @ X ) ).
% 0.27/0.47
% 0.27/0.47 % name_exists_fresh
% 0.27/0.47 thf(fact_81_name__exists__fresh,axiom,
% 0.27/0.47 ! [X: pi] :
% 0.27/0.47 ~ ! [C2: name] :
% 0.27/0.47 ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.27/0.47
% 0.27/0.47 % name_exists_fresh
% 0.27/0.47 thf(fact_82_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 0.27/0.47 = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_83_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 0.27/0.47 = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_84_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 0.27/0.47 = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_85_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: product_unit] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_1143631827t_unit @ A @ X ) )
% 0.27/0.47 = ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_86_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
% 0.27/0.47 = ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_87_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 0.27/0.47 = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_88_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 0.27/0.47 = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_89_fresh__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( fresh_543891186ion_pi @ A @ X ) )
% 0.27/0.47 = ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_eqvt
% 0.27/0.47 thf(fact_90_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.27/0.47 ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 0.27/0.47 = ( fresh_717452603ubject @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_91_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.27/0.47 ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 0.27/0.47 = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_92_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.27/0.47 ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 0.27/0.47 = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_93_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: product_unit] :
% 0.27/0.47 ( ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) )
% 0.27/0.47 = ( fresh_1143631827t_unit @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_94_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
% 0.27/0.47 = ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_95_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.27/0.47 ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 0.27/0.47 = ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_96_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 0.27/0.47 = ( fresh_name_pi @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_97_fresh__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 0.27/0.47 ( ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) )
% 0.27/0.47 = ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_bij
% 0.27/0.47 thf(fact_98_freshRes,axiom,
% 0.27/0.47 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshRes
% 0.27/0.47 thf(fact_99_fresh__fact2,axiom,
% 0.27/0.47 ! [A: name,B: name,P: pi] :
% 0.27/0.47 ( ( A != B )
% 0.27/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_fact2
% 0.27/0.47 thf(fact_100_fresh__fact1,axiom,
% 0.27/0.47 ! [A: name,P: pi,C: name,B: name] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ P )
% 0.27/0.47 => ( ( A != C )
% 0.27/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_fact1
% 0.27/0.47 thf(fact_101_forget,axiom,
% 0.27/0.47 ! [A: name,P: pi,B: name] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ P )
% 0.27/0.47 => ( ( subs @ P @ A @ B )
% 0.27/0.47 = P ) ) ).
% 0.27/0.47
% 0.27/0.47 % forget
% 0.27/0.47 thf(fact_102_name__calc_I2_J,axiom,
% 0.27/0.47 ! [X: name] :
% 0.27/0.47 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % name_calc(2)
% 0.27/0.47 thf(fact_103_mem__Collect__eq,axiom,
% 0.27/0.47 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.27/0.47 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.27/0.47 = ( P @ A ) ) ).
% 0.27/0.47
% 0.27/0.47 % mem_Collect_eq
% 0.27/0.47 thf(fact_104_Collect__mem__eq,axiom,
% 0.27/0.47 ! [A2: set_Pr1834926343_pi_pi] :
% 0.27/0.47 ( ( collec1051790738_pi_pi
% 0.27/0.47 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A2 ) )
% 0.27/0.47 = A2 ) ).
% 0.27/0.47
% 0.27/0.47 % Collect_mem_eq
% 0.27/0.47 thf(fact_105_Agent_OsubstRes3,axiom,
% 0.27/0.47 ! [B: name,P: pi,A: name] :
% 0.27/0.47 ( ( fresh_name_pi @ B @ P )
% 0.27/0.47 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.27/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Agent.substRes3
% 0.27/0.47 thf(fact_106_substRes2,axiom,
% 0.27/0.47 ! [B: name,P: pi,A: name] :
% 0.27/0.47 ( ( fresh_name_pi @ B @ P )
% 0.27/0.47 => ( ( res @ A @ P )
% 0.27/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % substRes2
% 0.27/0.47 thf(fact_107_eqvt__subs,axiom,
% 0.27/0.47 ! [P2: list_P227219501e_name,P: pi,A: name,B: name] :
% 0.27/0.47 ( ( perm_name_pi @ P2 @ ( subs @ P @ A @ B ) )
% 0.27/0.47 = ( subs @ ( perm_name_pi @ P2 @ P ) @ ( perm_name_name @ P2 @ A ) @ ( perm_name_name @ P2 @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvt_subs
% 0.27/0.47 thf(fact_108_swap__simps_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 0.27/0.47 = B ) ).
% 0.27/0.47
% 0.27/0.47 % swap_simps(1)
% 0.27/0.47 thf(fact_109_swap__simps_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 0.27/0.47 = A ) ).
% 0.27/0.47
% 0.27/0.47 % swap_simps(2)
% 0.27/0.47 thf(fact_110_swap__simps_I3_J,axiom,
% 0.27/0.47 ! [A: name,C: name,B: name] :
% 0.27/0.47 ( ( A != C )
% 0.27/0.47 => ( ( B != C )
% 0.27/0.47 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
% 0.27/0.47 = C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % swap_simps(3)
% 0.27/0.47 thf(fact_111_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: late_subject,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_717452603ubject @ A @ X )
% 0.27/0.47 => ( ( fresh_717452603ubject @ C @ X )
% 0.27/0.47 => ( fresh_717452603ubject @ C @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_112_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: late_freeRes,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ C @ X )
% 0.27/0.47 => ( fresh_1641682979reeRes @ C @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_113_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: pi_Rep,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi_Rep @ C @ X )
% 0.27/0.47 => ( fresh_name_pi_Rep @ C @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_114_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: product_unit,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ C @ X )
% 0.27/0.47 => ( fresh_1143631827t_unit @ C @ ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_115_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: produc1141751126_pi_pi,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ C @ X )
% 0.27/0.47 => ( fresh_1376661020_pi_pi @ C @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_116_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: name,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_name_name @ A @ X )
% 0.27/0.47 => ( ( fresh_name_name @ C @ X )
% 0.27/0.47 => ( fresh_name_name @ C @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_117_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: pi,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_name_pi @ C @ X )
% 0.27/0.47 => ( fresh_name_pi @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_118_fresh__aux,axiom,
% 0.27/0.47 ! [C: name,A: name,X: name > noption_pi,B: name] :
% 0.27/0.47 ( ( C != A )
% 0.27/0.47 => ( ( fresh_543891186ion_pi @ A @ X )
% 0.27/0.47 => ( ( fresh_543891186ion_pi @ C @ X )
% 0.27/0.47 => ( fresh_543891186ion_pi @ C @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_aux
% 0.27/0.47 thf(fact_119_cp__name__name1,axiom,
% 0.27/0.47 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cp_name_name1
% 0.27/0.47 thf(fact_120_cp__name__name1,axiom,
% 0.27/0.47 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cp_name_name1
% 0.27/0.47 thf(fact_121_cp__name__name1,axiom,
% 0.27/0.47 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cp_name_name1
% 0.27/0.47 thf(fact_122_cp__name__name1,axiom,
% 0.27/0.47 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 0.27/0.47 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cp_name_name1
% 0.27/0.47 thf(fact_123_cp__name__name1,axiom,
% 0.27/0.47 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 0.27/0.47 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cp_name_name1
% 0.27/0.47 thf(fact_124_name__perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_perm_compose
% 0.27/0.47 thf(fact_125_name__perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_perm_compose
% 0.27/0.47 thf(fact_126_name__perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_perm_compose
% 0.27/0.47 thf(fact_127_name__perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_perm_compose
% 0.27/0.47 thf(fact_128_name__perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_perm_compose
% 0.27/0.47 thf(fact_129_perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_compose
% 0.27/0.47 thf(fact_130_perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_compose
% 0.27/0.47 thf(fact_131_perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_compose
% 0.27/0.47 thf(fact_132_perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_compose
% 0.27/0.47 thf(fact_133_perm__compose,axiom,
% 0.27/0.47 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.27/0.47 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_compose
% 0.27/0.47 thf(fact_134_perm__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_bij
% 0.27/0.47 thf(fact_135_perm__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_bij
% 0.27/0.47 thf(fact_136_perm__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.27/0.47 ( ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_bij
% 0.27/0.47 thf(fact_137_perm__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.27/0.47 ( ( ( perm_name_name @ Pi @ X )
% 0.27/0.47 = ( perm_name_name @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_bij
% 0.27/0.47 thf(fact_138_perm__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.27/0.47 ( ( ( perm_name_pi @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_bij
% 0.27/0.47 thf(fact_139_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_140_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_141_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_142_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_143_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_144_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_145_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_146_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_147_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_148_perm__app,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.27/0.47 = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_app
% 0.27/0.47 thf(fact_149_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X4: set_Pr1834926343_pi_pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X4 ) )
% 0.27/0.47 = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_150_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,X4: set_Late_subject] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X4 ) )
% 0.27/0.47 = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_151_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,X4: set_Late_freeRes] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X4 ) )
% 0.27/0.47 = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_152_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi_Rep,X4: set_pi_Rep] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X4 ) )
% 0.27/0.47 = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_153_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: name,X4: set_name] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member_name @ X @ X4 ) )
% 0.27/0.47 = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_154_in__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi,X4: set_pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( member_pi @ X @ X4 ) )
% 0.27/0.47 = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X4 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % in_eqvt
% 0.27/0.47 thf(fact_155_eq__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.27/0.47 = ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_eqvt
% 0.27/0.47 thf(fact_156_eq__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.27/0.47 = ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_eqvt
% 0.27/0.47 thf(fact_157_eq__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.27/0.47 = ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_eqvt
% 0.27/0.47 thf(fact_158_eq__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.27/0.47 = ( ( perm_name_name @ Pi @ X )
% 0.27/0.47 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_eqvt
% 0.27/0.47 thf(fact_159_eq__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.27/0.47 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.27/0.47 = ( ( perm_name_pi @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eq_eqvt
% 0.27/0.47 thf(fact_160_pi_Oinject_I7_J,axiom,
% 0.27/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.27/0.47 ( ( ( par @ X2 @ X1 )
% 0.27/0.47 = ( par @ Y2 @ Y1 ) )
% 0.27/0.47 = ( ( X2 = Y2 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.inject(7)
% 0.27/0.47 thf(fact_161_alphaRes,axiom,
% 0.27/0.47 ! [C: name,P: pi,A: name] :
% 0.27/0.47 ( ( fresh_name_pi @ C @ P )
% 0.27/0.47 => ( ( res @ A @ P )
% 0.27/0.47 = ( res @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % alphaRes
% 0.27/0.47 thf(fact_162_injPermSubst,axiom,
% 0.27/0.47 ! [B: name,P: pi,A: name] :
% 0.27/0.47 ( ( fresh_name_pi @ B @ P )
% 0.27/0.47 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ P )
% 0.27/0.47 = ( subs @ P @ A @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % injPermSubst
% 0.27/0.47 thf(fact_163_renaming,axiom,
% 0.27/0.47 ! [C: name,P: pi,A: name,B: name] :
% 0.27/0.47 ( ( fresh_name_pi @ C @ P )
% 0.27/0.47 => ( ( subs @ P @ A @ B )
% 0.27/0.47 = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ P ) @ C @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % renaming
% 0.27/0.47 thf(fact_164_pi_Odistinct_I85_J,axiom,
% 0.27/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 0.27/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.27/0.47 != ( res @ Name @ Pi3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(85)
% 0.27/0.47 thf(fact_165_perm__swap_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_subject] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(2)
% 0.27/0.47 thf(fact_166_perm__swap_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: late_freeRes] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(2)
% 0.27/0.47 thf(fact_167_perm__swap_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi_Rep] :
% 0.27/0.47 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(2)
% 0.27/0.47 thf(fact_168_perm__swap_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(2)
% 0.27/0.47 thf(fact_169_perm__swap_I2_J,axiom,
% 0.27/0.47 ! [A: name,B: name,X: pi] :
% 0.27/0.47 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % perm_swap(2)
% 0.27/0.47 thf(fact_170_transitions_OClose2,axiom,
% 0.27/0.47 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.47 => ( ( X != A )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P3 )
% 0.27/0.47 => ( ( Y != A )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.27/0.47 => ( ( X != Y )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Close2
% 0.27/0.47 thf(fact_171_transitions_OClose1,axiom,
% 0.27/0.47 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.47 => ( ( X != A )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.27/0.47 => ( ( Y != A )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P3 )
% 0.27/0.47 => ( ( X != Y )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Close1
% 0.27/0.47 thf(fact_172_Late__Semantics_OClose2,axiom,
% 0.27/0.47 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Close2
% 0.27/0.47 thf(fact_173_Late__Semantics_OClose1,axiom,
% 0.27/0.47 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Close1
% 0.27/0.47 thf(fact_174_transitions_OComm2,axiom,
% 0.27/0.47 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( X != A )
% 0.27/0.47 => ( ( X != B )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P3 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Comm2
% 0.27/0.47 thf(fact_175_transitions_OComm1,axiom,
% 0.27/0.47 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( X != A )
% 0.27/0.47 => ( ( X != B )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Comm1
% 0.27/0.47 thf(fact_176_Late__Semantics_OComm2,axiom,
% 0.27/0.47 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Comm2
% 0.27/0.47 thf(fact_177_Late__Semantics_OComm1,axiom,
% 0.27/0.47 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Comm1
% 0.27/0.47 thf(fact_178_alphaBoundResidual,axiom,
% 0.27/0.47 ! [X5: name,P: pi,A: late_subject,X: name] :
% 0.27/0.47 ( ( fresh_name_pi @ X5 @ P )
% 0.27/0.47 => ( ( late_BoundR @ A @ X @ P )
% 0.27/0.47 = ( late_BoundR @ A @ X5 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X5 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % alphaBoundResidual
% 0.27/0.47 thf(fact_179_freeRes__perm__empty,axiom,
% 0.27/0.47 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.27/0.47 ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 0.27/0.47 = FreeRes_Rep ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes_perm_empty
% 0.27/0.47 thf(fact_180_subject__perm__empty,axiom,
% 0.27/0.47 ! [Subject_Rep: late_subject_Rep] :
% 0.27/0.47 ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 0.27/0.47 = Subject_Rep ) ).
% 0.27/0.47
% 0.27/0.47 % subject_perm_empty
% 0.27/0.47 thf(fact_181_residual__perm__empty,axiom,
% 0.27/0.47 ! [Residual_Rep: late_residual_Rep] :
% 0.27/0.47 ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 0.27/0.47 = Residual_Rep ) ).
% 0.27/0.47
% 0.27/0.47 % residual_perm_empty
% 0.27/0.47 thf(fact_182_freeRes_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A: name,X2: name,X1: name] :
% 0.27/0.47 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X2 )
% 0.27/0.47 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.fresh(1)
% 0.27/0.47 thf(fact_183_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.27/0.47 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.27/0.47 ( ( ( late_OutputR @ X2 @ X1 )
% 0.27/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.27/0.47 = ( ( X2 = Y2 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.freeRes.inject
% 0.27/0.47 thf(fact_184_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X1: name,Y1: name] :
% 0.27/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.27/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.subject.inject(2)
% 0.27/0.47 thf(fact_185_freeRes_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.fresh(2)
% 0.27/0.47 thf(fact_186_freeRes_Operm_I2_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ late_TauR )
% 0.27/0.47 = late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.perm(2)
% 0.27/0.47 thf(fact_187_cComm1_Ohyps_I8_J,axiom,
% 0.27/0.47 fresh_1143631827t_unit @ ya @ product_Unity ).
% 0.27/0.47
% 0.27/0.47 % cComm1.hyps(8)
% 0.27/0.47 thf(fact_188_residual_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.27/0.47 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.27/0.47 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.27/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.fresh(2)
% 0.27/0.47 thf(fact_189_substTrans,axiom,
% 0.27/0.47 ! [B: name,P: pi,A: name,C: name] :
% 0.27/0.47 ( ( fresh_name_pi @ B @ P )
% 0.27/0.47 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.27/0.47 = ( subs @ P @ A @ C ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % substTrans
% 0.27/0.47 thf(fact_190_residual_Operm_I2_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 0.27/0.47 ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 0.27/0.47 = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.perm(2)
% 0.27/0.47 thf(fact_191_freeRes_Operm_I1_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 0.27/0.47 ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 0.27/0.47 = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.perm(1)
% 0.27/0.47 thf(fact_192_subject_Operm_I1_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X1: name] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 0.27/0.47 = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.perm(1)
% 0.27/0.47 thf(fact_193_subject_Operm_I2_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X1: name] :
% 0.27/0.47 ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.47 = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.perm(2)
% 0.27/0.47 thf(fact_194_subject_Ofresh_I2_J,axiom,
% 0.27/0.47 ! [A: name,X1: name] :
% 0.27/0.47 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.27/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.fresh(2)
% 0.27/0.47 thf(fact_195_subject_Ofresh_I1_J,axiom,
% 0.27/0.47 ! [A: name,X1: name] :
% 0.27/0.47 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.27/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.fresh(1)
% 0.27/0.47 thf(fact_196_residual_Operm_I1_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 0.27/0.47 ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.27/0.47 = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.perm(1)
% 0.27/0.47 thf(fact_197_name__bij,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.27/0.47 ( ( ( perm_name_name @ Pi @ X )
% 0.27/0.47 = ( perm_name_name @ Pi @ Y ) )
% 0.27/0.47 = ( X = Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_bij
% 0.27/0.47 thf(fact_198_freshResidual,axiom,
% 0.27/0.47 ! [P: pi,Rs: late_residual,X: name] :
% 0.27/0.47 ( ( late_transitions @ P @ Rs )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshResidual
% 0.27/0.47 thf(fact_199_resCasesF,axiom,
% 0.27/0.47 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.27/0.47 => ( ! [P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.27/0.47 => ( F2 @ ( res @ X @ P4 ) ) ) )
% 0.27/0.47 => ( F2 @ XP ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesF
% 0.27/0.47 thf(fact_200_resCasesF_H,axiom,
% 0.27/0.47 ! [X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.27/0.47 ( ( ( res @ X @ P )
% 0.27/0.47 = ( res @ Y3 @ P5 ) )
% 0.27/0.47 => ( ( ( late_FreeR @ Alpha @ P3 )
% 0.27/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.27/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesF'
% 0.27/0.47 thf(fact_201_ResF,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 0.27/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P3 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % ResF
% 0.27/0.47 thf(fact_202_Late__Semantics_OResB,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.27/0.47 => ( ( Y != X )
% 0.27/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.ResB
% 0.27/0.47 thf(fact_203_freshFreeDerivative_I1_J,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshFreeDerivative(1)
% 0.27/0.47 thf(fact_204_freshBoundDerivative_I1_J,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshBoundDerivative(1)
% 0.27/0.47 thf(fact_205_transitions_OResB,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.27/0.47 => ( ( Y != X )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.ResB
% 0.27/0.47 thf(fact_206_parCasesB_H,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.27/0.47 => ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Q3: pi] :
% 0.27/0.47 ( ( ( par @ P @ Q )
% 0.27/0.47 = ( par @ P5 @ Q3 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.27/0.47 = ( late_BoundR @ A3 @ X6 @ ( par @ P4 @ Q3 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P5 )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q3 )
% 0.27/0.47 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) )
% 0.27/0.47 => ~ ! [Q3: pi,A3: late_subject,X6: name,Q4: pi,P5: pi] :
% 0.27/0.47 ( ( ( par @ P @ Q )
% 0.27/0.47 = ( par @ P5 @ Q3 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 0.27/0.47 = ( late_BoundR @ A3 @ X6 @ ( par @ P5 @ Q4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P5 )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q3 )
% 0.27/0.47 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parCasesB'
% 0.27/0.47 thf(fact_207_transitions_OPar1B,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Par1B
% 0.27/0.47 thf(fact_208_transitions_OPar2B,axiom,
% 0.27/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Par2B
% 0.27/0.47 thf(fact_209_resCases_H,axiom,
% 0.27/0.47 ! [X: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.27/0.47 => ( ! [P5: pi,A3: name,B2: name] :
% 0.27/0.47 ( ( ( res @ X @ P )
% 0.27/0.47 = ( res @ B2 @ P5 ) )
% 0.27/0.47 => ! [P4: pi] :
% 0.27/0.47 ( ( Rs
% 0.27/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
% 0.27/0.47 => ( A3 = B2 ) ) ) )
% 0.27/0.47 => ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
% 0.27/0.47 ( ( ( res @ X @ P )
% 0.27/0.47 = ( res @ Y3 @ P5 ) )
% 0.27/0.47 => ( ( Rs
% 0.27/0.47 = ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.47 => ( ( Y3 != X6 )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P5 )
% 0.27/0.47 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) )
% 0.27/0.47 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 0.27/0.47 ( ( ( res @ X @ P )
% 0.27/0.47 = ( res @ Y3 @ P5 ) )
% 0.27/0.47 => ( ( Rs
% 0.27/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 0.27/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCases'
% 0.27/0.47 thf(fact_210_residual_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.27/0.47 ( ( ( late_FreeR @ X2 @ X1 )
% 0.27/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.27/0.47 = ( ( X2 = Y2 )
% 0.27/0.47 & ( X1 = Y1 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.inject(2)
% 0.27/0.47 thf(fact_211_resCasesB_H,axiom,
% 0.27/0.47 ! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
% 0.27/0.47 => ( ! [P5: pi,A3: name,B2: name] :
% 0.27/0.47 ( ( ( res @ X5 @ P )
% 0.27/0.47 = ( res @ B2 @ P5 ) )
% 0.27/0.47 => ! [P4: pi] :
% 0.27/0.47 ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.27/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
% 0.27/0.47 => ( A3 = B2 ) ) ) )
% 0.27/0.47 => ~ ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
% 0.27/0.47 ( ( ( res @ X5 @ P )
% 0.27/0.47 = ( res @ Y3 @ P5 ) )
% 0.27/0.47 => ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 0.27/0.47 = ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
% 0.27/0.47 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.27/0.47 => ( ( Y3 != X6 )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P5 )
% 0.27/0.47 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesB'
% 0.27/0.47 thf(fact_212_residual_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 0.27/0.47 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 0.27/0.47 != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.distinct(1)
% 0.27/0.47 thf(fact_213_residual_Oinducts,axiom,
% 0.27/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.inducts
% 0.27/0.47 thf(fact_214_eqvt,axiom,
% 0.27/0.47 ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( late_transitions @ X1 @ X2 )
% 0.27/0.47 => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvt
% 0.27/0.47 thf(fact_215_freeRes_Oinducts,axiom,
% 0.27/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.27/0.47 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 0.27/0.47 => ( ( P @ late_TauR )
% 0.27/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.inducts
% 0.27/0.47 thf(fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Name12: name,Name23: name] :
% 0.27/0.47 ( ( late_OutputR @ Name12 @ Name23 )
% 0.27/0.47 != late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.27/0.47 thf(fact_217_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [Name2: name,Name: name] :
% 0.27/0.47 ( ( late_InputS @ Name2 )
% 0.27/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.subject.distinct(1)
% 0.27/0.47 thf(fact_218_subject_Oinducts,axiom,
% 0.27/0.47 ! [P: late_subject > $o,Subject: late_subject] :
% 0.27/0.47 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.27/0.47 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.27/0.47 => ( P @ Subject ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.inducts
% 0.27/0.47 thf(fact_219_resCasesB,axiom,
% 0.27/0.47 ! [Y: name,P: pi,A: late_subject,X: name,YP: pi,F2: late_subject > pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ YP ) )
% 0.27/0.47 => ( ( X != Y )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ! [B2: name,P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P4 ) )
% 0.27/0.47 => ( ( B2 != Y )
% 0.27/0.47 => ( ( A
% 0.27/0.47 = ( late_BoundOutputS @ B2 ) )
% 0.27/0.47 => ( F2 @ ( late_BoundOutputS @ B2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P4 ) ) ) ) )
% 0.27/0.47 => ( ! [P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.27/0.47 => ( F2 @ A @ ( res @ Y @ P4 ) ) ) )
% 0.27/0.47 => ( F2 @ A @ YP ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resCasesB
% 0.27/0.47 thf(fact_220_Par1F,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Par1F
% 0.27/0.47 thf(fact_221_Par2F,axiom,
% 0.27/0.47 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Par2F
% 0.27/0.47 thf(fact_222_freshBoundDerivative_I2_J,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( ( Y != X )
% 0.27/0.47 => ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshBoundDerivative(2)
% 0.27/0.47 thf(fact_223_residual_Ostrong__inducts,axiom,
% 0.27/0.47 ! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
% 0.27/0.47 ( ( fresh_1143631827t_unit @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_inducts
% 0.27/0.47 thf(fact_224_residual_Ostrong__inducts,axiom,
% 0.27/0.47 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_inducts
% 0.27/0.47 thf(fact_225_residual_Ostrong__inducts,axiom,
% 0.27/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.27/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_inducts
% 0.27/0.47 thf(fact_226_residual_Ostrong__inducts,axiom,
% 0.27/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_inducts
% 0.27/0.47 thf(fact_227_residual_Ostrong__induct,axiom,
% 0.27/0.47 ! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
% 0.27/0.47 ( ( fresh_1143631827t_unit @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_induct
% 0.27/0.47 thf(fact_228_residual_Ostrong__induct,axiom,
% 0.27/0.47 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_induct
% 0.27/0.47 thf(fact_229_residual_Ostrong__induct,axiom,
% 0.27/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.27/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_induct
% 0.27/0.47 thf(fact_230_residual_Ostrong__induct,axiom,
% 0.27/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.27/0.47 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.27/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.27/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.27/0.47 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 0.27/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual.strong_induct
% 0.27/0.47 thf(fact_231_freshFreeDerivative_I2_J,axiom,
% 0.27/0.47 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( fresh_name_pi @ Y @ P3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % freshFreeDerivative(2)
% 0.27/0.47 thf(fact_232_Late__Semantics_OPar1B,axiom,
% 0.27/0.47 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Par1B
% 0.27/0.47 thf(fact_233_Late__Semantics_OPar2B,axiom,
% 0.27/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Par2B
% 0.27/0.47 thf(fact_234_parCasesB,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.27/0.47 => ( ! [P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.47 => ( Prop @ ( par @ P4 @ Q ) ) )
% 0.27/0.47 => ( ! [Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 0.27/0.47 => ( Prop @ ( par @ P @ Q4 ) ) )
% 0.27/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parCasesB
% 0.27/0.47 thf(fact_235_Open,axiom,
% 0.27/0.47 ! [P: pi,A: name,B: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.27/0.47 => ( ( A != B )
% 0.27/0.47 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Open
% 0.27/0.47 thf(fact_236_derivativeEqvtI2,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 0.27/0.47 => ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % derivativeEqvtI2
% 0.27/0.47 thf(fact_237_derivativeEqvtI,axiom,
% 0.27/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 0.27/0.47 => ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % derivativeEqvtI
% 0.27/0.47 thf(fact_238_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,Y: product_unit] :
% 0.27/0.47 ( ( fresh_994967853t_unit @ A @ ( produc1076565719t_unit @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_239_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,Y: name] :
% 0.27/0.47 ( ( fresh_1826856600t_name @ A @ ( produc421428802t_name @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_240_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,Y: pi] :
% 0.27/0.47 ( ( fresh_707692390nit_pi @ A @ ( produc1806354576nit_pi @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_241_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: product_unit] :
% 0.27/0.47 ( ( fresh_90540034t_unit @ A @ ( produc1785453612t_unit @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X )
% 0.27/0.47 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_242_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: pi] :
% 0.27/0.47 ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X )
% 0.27/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_243_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: pi,Y: product_unit] :
% 0.27/0.47 ( ( fresh_997779380t_unit @ A @ ( produc1831798878t_unit @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_244_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: pi,Y: name] :
% 0.27/0.47 ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_245_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: name] :
% 0.27/0.47 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X )
% 0.27/0.47 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_246_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: pi,Y: pi] :
% 0.27/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_247_fresh__prod,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X )
% 0.27/0.47 & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prod
% 0.27/0.47 thf(fact_248_Res,axiom,
% 0.27/0.47 ! [Y: name,R: pi,S: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ Y @ R )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 0.27/0.47
% 0.27/0.47 % Res
% 0.27/0.47 thf(fact_249_ScopeExt,axiom,
% 0.27/0.47 ! [Y: name,R: pi,Z: name,S: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ Y @ R )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 0.27/0.47
% 0.27/0.47 % ScopeExt
% 0.27/0.47 thf(fact_250_fresh__list__cons,axiom,
% 0.27/0.47 ! [A: name,X: product_unit,Xs: list_Product_unit] :
% 0.27/0.47 ( ( fresh_1732817625t_unit @ A @ ( cons_Product_unit @ X @ Xs ) )
% 0.27/0.47 = ( ( fresh_1143631827t_unit @ A @ X )
% 0.27/0.47 & ( fresh_1732817625t_unit @ A @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_list_cons
% 0.27/0.47 thf(fact_251_fresh__list__cons,axiom,
% 0.27/0.47 ! [A: name,X: produc1141751126_pi_pi,Xs: list_P431515740_pi_pi] :
% 0.27/0.47 ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs ) )
% 0.27/0.47 = ( ( fresh_1376661020_pi_pi @ A @ X )
% 0.27/0.47 & ( fresh_1958133282_pi_pi @ A @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_list_cons
% 0.27/0.47 thf(fact_252_fresh__list__cons,axiom,
% 0.27/0.47 ! [A: name,X: name,Xs: list_name] :
% 0.27/0.47 ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs ) )
% 0.27/0.47 = ( ( fresh_name_name @ A @ X )
% 0.27/0.47 & ( fresh_name_list_name @ A @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_list_cons
% 0.27/0.47 thf(fact_253_fresh__list__cons,axiom,
% 0.27/0.47 ! [A: name,X: pi,Xs: list_pi] :
% 0.27/0.47 ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs ) )
% 0.27/0.47 = ( ( fresh_name_pi @ A @ X )
% 0.27/0.47 & ( fresh_name_list_pi @ A @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_list_cons
% 0.27/0.47 thf(fact_254_fresh__list__cons,axiom,
% 0.27/0.47 ! [A: name,X: name > noption_pi,Xs: list_name_noption_pi] :
% 0.27/0.47 ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ X @ Xs ) )
% 0.27/0.47 = ( ( fresh_543891186ion_pi @ A @ X )
% 0.27/0.47 & ( fresh_1135477378ion_pi @ A @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_list_cons
% 0.27/0.47 thf(fact_255_Bound_Ohyps_I5_J,axiom,
% 0.27/0.47 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 0.27/0.47
% 0.27/0.47 % Bound.hyps(5)
% 0.27/0.47 thf(fact_256_name__fresh,axiom,
% 0.27/0.47 ( fresh_name_name
% 0.27/0.47 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_fresh
% 0.27/0.47 thf(fact_257_fresh__unit,axiom,
% 0.27/0.47 ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_unit
% 0.27/0.47 thf(fact_258_freshUnit,axiom,
% 0.27/0.47 ! [Y: name] : ( fresh_1143631827t_unit @ Y @ product_Unity ) ).
% 0.27/0.47
% 0.27/0.47 % freshUnit
% 0.27/0.47 thf(fact_259_allE__Nil,axiom,
% 0.27/0.47 ! [P: list_P227219501e_name > $o] :
% 0.27/0.47 ( ! [X_1: list_P227219501e_name] : ( P @ X_1 )
% 0.27/0.47 => ( P @ nil_Pr743626285e_name ) ) ).
% 0.27/0.47
% 0.27/0.47 % allE_Nil
% 0.27/0.47 thf(fact_260_abs__fun__if,axiom,
% 0.27/0.47 ! [C: $o,Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( C
% 0.27/0.47 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 0.27/0.47 & ( ~ C
% 0.27/0.47 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fun_if
% 0.27/0.47 thf(fact_261_abs__fun__if,axiom,
% 0.27/0.47 ! [C: $o,Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( C
% 0.27/0.47 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 0.27/0.47 & ( ~ C
% 0.27/0.47 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fun_if
% 0.27/0.47 thf(fact_262_abs__fun__if,axiom,
% 0.27/0.47 ! [C: $o,Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.27/0.47 ( ( C
% 0.27/0.47 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 0.27/0.47 & ( ~ C
% 0.27/0.47 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fun_if
% 0.27/0.47 thf(fact_263_abs__fun__if,axiom,
% 0.27/0.47 ! [C: $o,Pi: list_P227219501e_name,X: name,Y: name] :
% 0.27/0.47 ( ( C
% 0.27/0.47 => ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_name @ Pi @ X ) ) )
% 0.27/0.47 & ( ~ C
% 0.27/0.47 => ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_name @ Pi @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fun_if
% 0.27/0.47 thf(fact_264_abs__fun__if,axiom,
% 0.27/0.47 ! [C: $o,Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.27/0.47 ( ( C
% 0.27/0.47 => ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_pi @ Pi @ X ) ) )
% 0.27/0.47 & ( ~ C
% 0.27/0.47 => ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
% 0.27/0.47 = ( perm_name_pi @ Pi @ Y ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % abs_fun_if
% 0.27/0.47 thf(fact_265_pt__bij3,axiom,
% 0.27/0.47 ! [X: late_subject,Y: late_subject,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ( perm_n1559866809ubject @ Pi @ X )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pt_bij3
% 0.27/0.47 thf(fact_266_pt__bij3,axiom,
% 0.27/0.47 ! [X: late_freeRes,Y: late_freeRes,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ( perm_n336613537reeRes @ Pi @ X )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pt_bij3
% 0.27/0.47 thf(fact_267_pt__bij3,axiom,
% 0.27/0.47 ! [X: pi_Rep,Y: pi_Rep,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ( perm_name_pi_Rep @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pt_bij3
% 0.27/0.47 thf(fact_268_pt__bij3,axiom,
% 0.27/0.47 ! [X: name,Y: name,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ( perm_name_name @ Pi @ X )
% 0.27/0.47 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pt_bij3
% 0.27/0.47 thf(fact_269_pt__bij3,axiom,
% 0.27/0.47 ! [X: pi,Y: pi,Pi: list_P227219501e_name] :
% 0.27/0.47 ( ( X = Y )
% 0.27/0.47 => ( ( perm_name_pi @ Pi @ X )
% 0.27/0.47 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pt_bij3
% 0.27/0.47 thf(fact_270_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y ) )
% 0.27/0.47 = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_271_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_freeRes] :
% 0.27/0.47 ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y ) )
% 0.27/0.47 = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_272_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi_Rep] :
% 0.27/0.47 ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y ) )
% 0.27/0.47 = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_273_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: name] :
% 0.27/0.47 ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y ) )
% 0.27/0.47 = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_274_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi] :
% 0.27/0.47 ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y ) )
% 0.27/0.47 = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_275_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_subject] :
% 0.27/0.47 ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y ) )
% 0.27/0.47 = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_276_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y ) )
% 0.27/0.47 = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_277_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi_Rep] :
% 0.27/0.47 ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y ) )
% 0.27/0.47 = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_278_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: name] :
% 0.27/0.47 ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y ) )
% 0.27/0.47 = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_279_perm__prod_Osimps,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi] :
% 0.27/0.47 ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.27/0.47 = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % perm_prod.simps
% 0.27/0.47 thf(fact_280_fresh__prodD_I2_J,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: name] :
% 0.27/0.47 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.27/0.47 => ( fresh_name_name @ A @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(2)
% 0.27/0.47 thf(fact_281_fresh__prodD_I2_J,axiom,
% 0.27/0.47 ! [A: name,X: pi,Y: pi] :
% 0.27/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.47 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(2)
% 0.27/0.47 thf(fact_282_fresh__prodD_I2_J,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.47 => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(2)
% 0.27/0.47 thf(fact_283_fresh__prodD_I1_J,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: name] :
% 0.27/0.47 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.27/0.47 => ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(1)
% 0.27/0.47 thf(fact_284_fresh__prodD_I1_J,axiom,
% 0.27/0.47 ! [A: name,X: pi,Y: pi] :
% 0.27/0.47 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.27/0.47 => ( fresh_name_pi @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(1)
% 0.27/0.47 thf(fact_285_fresh__prodD_I1_J,axiom,
% 0.27/0.47 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 0.27/0.47 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 0.27/0.47 => ( fresh_name_name @ A @ X ) ) ).
% 0.27/0.47
% 0.27/0.47 % fresh_prodD(1)
% 0.27/0.47 thf(fact_286_if__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 0.27/0.47 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 0.27/0.47 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % if_eqvt
% 0.27/0.47 thf(fact_287_if__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 0.27/0.47 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 0.27/0.47 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % if_eqvt
% 0.27/0.47 thf(fact_288_if__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 0.27/0.47 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 0.27/0.47 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % if_eqvt
% 0.27/0.47 thf(fact_289_if__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 0.27/0.47 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_name @ Pi @ C1 ) ) )
% 0.27/0.47 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % if_eqvt
% 0.27/0.47 thf(fact_290_if__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 0.27/0.47 ( ( ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_pi @ Pi @ C1 ) ) )
% 0.27/0.47 & ( ~ ( perm_name_o @ Pi @ B )
% 0.27/0.47 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.27/0.47 = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % if_eqvt
% 0.27/0.47 thf(fact_291_cons__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_subject,Xs: list_Late_subject] :
% 0.27/0.47 ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs ) )
% 0.27/0.47 = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cons_eqvt
% 0.27/0.47 thf(fact_292_cons__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: late_freeRes,Xs: list_Late_freeRes] :
% 0.27/0.47 ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs ) )
% 0.27/0.47 = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cons_eqvt
% 0.27/0.47 thf(fact_293_cons__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi_Rep,Xs: list_pi_Rep] :
% 0.27/0.47 ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs ) )
% 0.27/0.47 = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cons_eqvt
% 0.27/0.47 thf(fact_294_cons__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: name,Xs: list_name] :
% 0.27/0.47 ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs ) )
% 0.27/0.47 = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cons_eqvt
% 0.27/0.47 thf(fact_295_cons__eqvt,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X: pi,Xs: list_pi] :
% 0.27/0.47 ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs ) )
% 0.27/0.47 = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % cons_eqvt
% 0.27/0.47 thf(fact_296_resSimCases,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: product_unit] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [Q4: pi,A3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.27/0.47 => ( ( A3 != X )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.47 => ( ( X != Y3 )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ Y3 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resSimCases
% 0.27/0.47 thf(fact_297_resSimCases,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [Q4: pi,A3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.27/0.47 => ( ( A3 != X )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.47 => ( ( X != Y3 )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resSimCases
% 0.27/0.47 thf(fact_298_resSimCases,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [Q4: pi,A3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.27/0.47 => ( ( A3 != X )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.47 => ( ( X != Y3 )
% 0.27/0.47 => ( ( fresh_name_name @ Y3 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resSimCases
% 0.27/0.47 thf(fact_299_resSimCases,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [Q4: pi,A3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 0.27/0.47 => ( ( A3 != X )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.27/0.47 => ( ( X != Y3 )
% 0.27/0.47 => ( ( fresh_name_pi @ Y3 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 0.27/0.47 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % resSimCases
% 0.27/0.47 thf(fact_300_simCasesCont,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: product_unit] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 0.27/0.47 => ( ( fresh_1143631827t_unit @ X6 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCasesCont
% 0.27/0.47 thf(fact_301_simCasesCont,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 0.27/0.47 => ( ( fresh_1376661020_pi_pi @ X6 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCasesCont
% 0.27/0.47 thf(fact_302_simCasesCont,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 0.27/0.47 => ( ( fresh_name_name @ X6 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCasesCont
% 0.27/0.47 thf(fact_303_simCasesCont,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ P )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ Q )
% 0.27/0.47 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 0.27/0.47 => ( ( fresh_name_pi @ X6 @ C3 )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCasesCont
% 0.27/0.47 thf(fact_304_eqvtRelI,axiom,
% 0.27/0.47 ! [Rel: set_Pr806375235ubject,P: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( eqvt_Late_subject @ Rel )
% 0.27/0.47 => ( ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel )
% 0.27/0.47 => ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelI
% 0.27/0.47 thf(fact_305_eqvtRelI,axiom,
% 0.27/0.47 ! [Rel: set_Pr1780909331reeRes,P: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( eqvt_Late_freeRes @ Rel )
% 0.27/0.47 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel )
% 0.27/0.47 => ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelI
% 0.27/0.47 thf(fact_306_eqvtRelI,axiom,
% 0.27/0.47 ! [Rel: set_Pr1131282415pi_Rep,P: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( eqvt_pi_Rep @ Rel )
% 0.27/0.47 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel )
% 0.27/0.47 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelI
% 0.27/0.47 thf(fact_307_eqvtRelI,axiom,
% 0.27/0.47 ! [Rel: set_Pr443758855e_name,P: name,Q: name,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( eqvt_name @ Rel )
% 0.27/0.47 => ( ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel )
% 0.27/0.47 => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelI
% 0.27/0.47 thf(fact_308_eqvtRelI,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,Perm: list_P227219501e_name] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelI
% 0.27/0.47 thf(fact_309_eqvtRelE,axiom,
% 0.27/0.47 ! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P: late_subject,Q: late_subject] :
% 0.27/0.47 ( ( eqvt_Late_subject @ Rel )
% 0.27/0.47 => ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
% 0.27/0.47 => ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelE
% 0.27/0.47 thf(fact_310_eqvtRelE,axiom,
% 0.27/0.47 ! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P: late_freeRes,Q: late_freeRes] :
% 0.27/0.47 ( ( eqvt_Late_freeRes @ Rel )
% 0.27/0.47 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
% 0.27/0.47 => ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelE
% 0.27/0.47 thf(fact_311_eqvtRelE,axiom,
% 0.27/0.47 ! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P: pi_Rep,Q: pi_Rep] :
% 0.27/0.47 ( ( eqvt_pi_Rep @ Rel )
% 0.27/0.47 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
% 0.27/0.47 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelE
% 0.27/0.47 thf(fact_312_eqvtRelE,axiom,
% 0.27/0.47 ! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P: name,Q: name] :
% 0.27/0.47 ( ( eqvt_name @ Rel )
% 0.27/0.47 => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
% 0.27/0.47 => ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelE
% 0.27/0.47 thf(fact_313_eqvtRelE,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P: pi,Q: pi] :
% 0.27/0.47 ( ( eqvt_pi @ Rel )
% 0.27/0.47 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvtRelE
% 0.27/0.47 thf(fact_314_parSym,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.27/0.47 ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.27/0.47 => ( ! [R2: pi,S2: pi,X6: name] :
% 0.27/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ R2 ) @ ( res @ X6 @ S2 ) ) @ Rel ) )
% 0.27/0.47 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parSym
% 0.27/0.47 thf(fact_315_simE_I2_J,axiom,
% 0.27/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.27/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.27/0.47 => ? [P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q2 ) @ Rel ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simE(2)
% 0.27/0.47 thf(fact_316_eqvt__def,axiom,
% 0.27/0.47 ( eqvt_pi
% 0.27/0.47 = ( ^ [Rel2: set_Pr1834926343_pi_pi] :
% 0.27/0.47 ! [X3: product_prod_pi_pi,Perm2: list_P227219501e_name] :
% 0.27/0.47 ( ( member558706512_pi_pi @ X3 @ Rel2 )
% 0.27/0.47 => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X3 ) @ Rel2 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % eqvt_def
% 0.27/0.47 thf(fact_317_parAssocLeft,axiom,
% 0.27/0.47 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.27/0.47 ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 0.27/0.47 => ( ! [S2: pi,T: pi,X6: name] :
% 0.27/0.47 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ S2 ) @ ( res @ X6 @ T ) ) @ Rel ) )
% 0.27/0.47 => ( ! [S2: pi,T: pi,U: pi,X6: name] :
% 0.27/0.47 ( ( fresh_name_pi @ X6 @ S2 )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X6 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.27/0.47 => ( ! [S2: pi,T: pi,U: pi,X6: name] :
% 0.27/0.47 ( ( fresh_name_pi @ X6 @ U )
% 0.27/0.47 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X6 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X6 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.27/0.47 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % parAssocLeft
% 0.27/0.47 thf(fact_318_simE_I1_J,axiom,
% 0.27/0.47 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.27/0.47 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.27/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.27/0.47 => ? [P4: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 0.27/0.47 & ( strong2129052853vative @ P4 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simE(1)
% 0.27/0.47 thf(fact_319_simCases,axiom,
% 0.27/0.47 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.27/0.47 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 0.27/0.47 => ( ( fresh_name_pi @ Y3 @ P )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 0.27/0.47 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 0.27/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 0.27/0.47 => ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 0.27/0.47 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simCases
% 0.27/0.47 thf(fact_320_simulation__def,axiom,
% 0.27/0.47 ( strong743114133lation
% 0.27/0.47 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.27/0.47 ( ! [A4: late_subject,X3: name,Q6: pi] :
% 0.27/0.47 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A4 @ X3 @ Q6 ) )
% 0.27/0.47 & ( fresh_name_pi @ X3 @ P7 ) )
% 0.27/0.47 => ? [P8: pi] :
% 0.27/0.47 ( ( late_transitions @ P7 @ ( late_BoundR @ A4 @ X3 @ P8 ) )
% 0.27/0.47 & ( strong2129052853vative @ P8 @ Q6 @ A4 @ X3 @ Rel2 ) ) )
% 0.27/0.47 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.27/0.47 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.27/0.47 => ? [P8: pi] :
% 0.27/0.47 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 0.27/0.47 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % simulation_def
% 0.27/0.47 thf(fact_321_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X2: name,Y2: name] :
% 0.27/0.47 ( ( ( late_BoundOutputS @ X2 )
% 0.27/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.27/0.47 = ( X2 = Y2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.inject(2)
% 0.27/0.47 thf(fact_322_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.27/0.47 ! [X1: name,Y1: name] :
% 0.27/0.47 ( ( ( late_InputS @ X1 )
% 0.27/0.47 = ( late_InputS @ Y1 ) )
% 0.27/0.47 = ( X1 = Y1 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.inject(1)
% 0.27/0.47 thf(fact_323_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.27/0.47 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.27/0.47 ( ( ( late_OutputR @ X11 @ X12 )
% 0.27/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.27/0.47 = ( ( X11 = Y11 )
% 0.27/0.47 & ( X12 = Y12 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.freeRes.inject
% 0.27/0.47 thf(fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X11: name,X12: name] :
% 0.27/0.47 ( ( late_OutputR @ X11 @ X12 )
% 0.27/0.47 != late_TauR ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.27/0.47 thf(fact_325_freeRes_Oexhaust,axiom,
% 0.27/0.47 ! [Y: late_freeRes] :
% 0.27/0.47 ( ! [X112: name,X122: name] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( late_OutputR @ X112 @ X122 ) )
% 0.27/0.47 => ( Y = late_TauR ) ) ).
% 0.27/0.47
% 0.27/0.47 % freeRes.exhaust
% 0.27/0.47 thf(fact_326_subject_Oexhaust,axiom,
% 0.27/0.47 ! [Y: late_subject] :
% 0.27/0.47 ( ! [X13: name] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( late_InputS @ X13 ) )
% 0.27/0.47 => ~ ! [X22: name] :
% 0.27/0.47 ( Y
% 0.27/0.47 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subject.exhaust
% 0.27/0.47 thf(fact_327_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.27/0.47 ! [X1: name,X2: name] :
% 0.27/0.47 ( ( late_InputS @ X1 )
% 0.27/0.47 != ( late_BoundOutputS @ X2 ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics1.subject.distinct(1)
% 0.27/0.47 thf(fact_328_inputCases,axiom,
% 0.27/0.47 ! [A: name,X: name,P: pi,B: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.27/0.47 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ YP ) )
% 0.27/0.47 => ( ( Y != A )
% 0.27/0.47 => ( ( Y != X )
% 0.27/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.27/0.47 => ( ( ( B
% 0.27/0.47 = ( late_InputS @ A ) )
% 0.27/0.47 => ( ( YP
% 0.27/0.47 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) )
% 0.27/0.47 => ( Prop @ ( late_InputS @ A ) @ Y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) ) ) )
% 0.27/0.47 => ( Prop @ B @ Y @ YP ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputCases
% 0.27/0.47 thf(fact_329_list_Oinject,axiom,
% 0.27/0.47 ! [X21: produc367475239e_name,X222: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 0.27/0.47 ( ( ( cons_P1213805021e_name @ X21 @ X222 )
% 0.27/0.47 = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % list.inject
% 0.27/0.47 thf(fact_330_pi_Operm_I4_J,axiom,
% 0.27/0.47 ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 0.27/0.47 ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 0.27/0.47 = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.perm(4)
% 0.27/0.47 thf(fact_331_pi_Odistinct_I57_J,axiom,
% 0.27/0.47 ! [Name12: name,Name23: name,Pi: pi,Name: name,Pi3: pi] :
% 0.27/0.47 ( ( input @ Name12 @ Name23 @ Pi )
% 0.27/0.47 != ( res @ Name @ Pi3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(57)
% 0.27/0.47 thf(fact_332_pi_Odistinct_I55_J,axiom,
% 0.27/0.47 ! [Name12: name,Name23: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.27/0.47 ( ( input @ Name12 @ Name23 @ Pi )
% 0.27/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.distinct(55)
% 0.27/0.47 thf(fact_333_resTrans_I2_J,axiom,
% 0.27/0.47 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.27/0.47
% 0.27/0.47 % resTrans(2)
% 0.27/0.47 thf(fact_334_inputFreeTrans,axiom,
% 0.27/0.47 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputFreeTrans
% 0.27/0.47 thf(fact_335_resInputFreeTrans,axiom,
% 0.27/0.47 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resInputFreeTrans
% 0.27/0.47 thf(fact_336_old_Ounit_Oinducts,axiom,
% 0.27/0.47 ! [P: product_unit > $o,Unit: product_unit] :
% 0.27/0.47 ( ( P @ product_Unity )
% 0.27/0.47 => ( P @ Unit ) ) ).
% 0.27/0.47
% 0.27/0.47 % old.unit.inducts
% 0.27/0.47 thf(fact_337_old_Ounit_Oexhaust,axiom,
% 0.27/0.47 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.27/0.47
% 0.27/0.47 % old.unit.exhaust
% 0.27/0.47 thf(fact_338_inputBoundOutputTrans,axiom,
% 0.27/0.47 ! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputBoundOutputTrans
% 0.27/0.47 thf(fact_339_Late__Semantics_OInput,axiom,
% 0.27/0.47 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.27/0.47
% 0.27/0.47 % Late_Semantics.Input
% 0.27/0.47 thf(fact_340_transitions_OInput,axiom,
% 0.27/0.47 ! [X: name,A: name,P: pi] :
% 0.27/0.47 ( ( X != A )
% 0.27/0.47 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % transitions.Input
% 0.27/0.47 thf(fact_341_inputIneqTrans,axiom,
% 0.27/0.47 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
% 0.27/0.47 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 0.27/0.47 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.27/0.47
% 0.27/0.47 % inputIneqTrans
% 0.27/0.47 thf(fact_342_resInputBoundOutputTrans,axiom,
% 0.27/0.47 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
% 0.27/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 0.27/0.47
% 0.27/0.47 % resInputBoundOutputTrans
% 0.27/0.47 thf(fact_343_alphaInput,axiom,
% 0.27/0.47 ! [C: name,P: pi,A: name,X: name] :
% 0.27/0.47 ( ( fresh_name_pi @ C @ P )
% 0.27/0.47 => ( ( input @ A @ X @ P )
% 0.27/0.47 = ( input @ A @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % alphaInput
% 0.27/0.47 thf(fact_344_default__unit__def,axiom,
% 0.27/0.47 defaul1399868459t_unit = product_Unity ).
% 0.27/0.47
% 0.27/0.47 % default_unit_def
% 0.27/0.47 thf(fact_345_residual__Rep_Oinject_I2_J,axiom,
% 0.27/0.47 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 0.27/0.47 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 0.27/0.47 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.27/0.47 = ( ( X21 = Y21 )
% 0.27/0.47 & ( X222 = Y22 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % residual_Rep.inject(2)
% 0.27/0.47 thf(fact_346_name__calc_I1_J,axiom,
% 0.27/0.47 ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 0.27/0.47 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 0.27/0.47 = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_calc(1)
% 0.27/0.47 thf(fact_347_name__calc_I3_J,axiom,
% 0.27/0.47 ! [A: name,C: name,B: name] :
% 0.27/0.47 ( ( ( A = C )
% 0.27/0.47 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 0.27/0.47 = B ) )
% 0.27/0.47 & ( ( A != C )
% 0.27/0.47 => ( ( ( B = C )
% 0.27/0.47 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 0.27/0.47 = A ) )
% 0.27/0.47 & ( ( B != C )
% 0.27/0.47 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 0.27/0.47 = C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % name_calc(3)
% 0.27/0.47 thf(fact_348_Agent_Oswap__name__def,axiom,
% 0.27/0.47 swap_name2 = swap_name ).
% 0.27/0.47
% 0.27/0.47 % Agent.swap_name_def
% 0.27/0.47 thf(fact_349_pi_Ofresh_I9_J,axiom,
% 0.27/0.47 ! [A: name,X1: name,X2: pi] :
% 0.27/0.47 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.27/0.47 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % pi.fresh(9)
% 0.27/0.47
% 0.27/0.47 % Helper facts (11)
% 0.27/0.47 thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 0.27/0.47 ! [X: pi,Y: pi] :
% 0.27/0.47 ( ( if_pi @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 0.27/0.47 ! [X: pi,Y: pi] :
% 0.27/0.47 ( ( if_pi @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.47 ! [X: name,Y: name] :
% 0.27/0.47 ( ( if_name @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.27/0.47 ! [X: name,Y: name] :
% 0.27/0.47 ( ( if_name @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.27/0.47 ! [X: pi_Rep,Y: pi_Rep] :
% 0.27/0.47 ( ( if_pi_Rep @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.27/0.47 ! [X: pi_Rep,Y: pi_Rep] :
% 0.27/0.47 ( ( if_pi_Rep @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.27/0.47 ! [X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( if_Late_freeRes @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.27/0.47 ! [X: late_freeRes,Y: late_freeRes] :
% 0.27/0.47 ( ( if_Late_freeRes @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.47 ! [P: $o] :
% 0.27/0.47 ( ( P = $true )
% 0.27/0.47 | ( P = $false ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.47 ! [X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( if_Late_subject @ $false @ X @ Y )
% 0.27/0.47 = Y ) ).
% 0.27/0.47
% 0.27/0.47 thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.27/0.47 ! [X: late_subject,Y: late_subject] :
% 0.27/0.47 ( ( if_Late_subject @ $true @ X @ Y )
% 0.27/0.47 = X ) ).
% 0.27/0.47
% 0.27/0.47 % Conjectures (1)
% 0.27/0.47 thf(conj_0,conjecture,
% 0.27/0.47 ? [P6: pi] :
% 0.27/0.47 ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ P6 ) )
% 0.27/0.47 & ( strong2129052853vative @ P6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.92/1.54 ---- Embedded in THF ---
% 2.92/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.92/1.54 %%% Generated on Tue Feb 24 08:29:41 EST 2026
% 2.92/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.92/1.54 %%% Logic specification used:
% 2.92/1.54 %%% thf(spec, logic, $$dhol).
% 2.92/1.54
% 2.92/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.dCSmdHGfAN/DTF2DTF8414.p
% See solution above
% 2.92/1.54 ------------------------
% 2.92/1.58 ---- Cleaned THF ---
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J_J,type,
% 2.92/1.58 list_P431515740_pi_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J_J,type,
% 2.92/1.58 set_Pr806375235ubject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J_J,type,
% 2.92/1.58 set_Pr1780909331reeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.92/1.58 produc1141751126_pi_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 2.92/1.58 produc1359399907ubject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 produc355105483reeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 2.92/1.58 produc214645451ubject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 produc1357834675reeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J_J,type,
% 2.92/1.58 set_Pr1131282415pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
% 2.92/1.58 produc971140967t_unit: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 2.92/1.58 produc257012921pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 2.92/1.58 produc1777919905pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 2.92/1.58 list_name_noption_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 2.92/1.58 list_P227219501e_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 2.92/1.58 set_Pr443758855e_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 2.92/1.58 produc1998742700t_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 2.92/1.58 produc2052722628s_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 2.92/1.58 produc140253050ect_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 2.92/1.58 produc992857746Res_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.92/1.58 set_Pr1834926343_pi_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Agent__Oname_J,type,
% 2.92/1.58 produc135724498t_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 2.92/1.58 produc1212344719pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Ounit_J,type,
% 2.92/1.58 produc546891580t_unit: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Agent__Opi_J,type,
% 2.92/1.58 produc738223008nit_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Product____Type__Ounit_J,type,
% 2.92/1.58 produc1028309998t_unit: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 2.92/1.58 produc367475239e_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Oname_J,type,
% 2.92/1.58 product_prod_pi_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Opi_J,type,
% 2.92/1.58 product_prod_name_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.92/1.58 product_prod_pi_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
% 2.92/1.58 list_Late_subject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 list_Late_freeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 2.92/1.58 set_Late_subject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 set_Late_freeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Product____Type__Ounit_J,type,
% 2.92/1.58 list_Product_unit: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 2.92/1.58 list_pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 2.92/1.58 late_residual_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 2.92/1.58 noption_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 2.92/1.58 late_subject_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 2.92/1.58 late_freeRes_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 2.92/1.58 set_pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 2.92/1.58 list_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 2.92/1.58 set_name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 2.92/1.58 list_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 2.92/1.58 late_residual: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__Osubject,type,
% 2.92/1.58 late_subject: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 2.92/1.58 late_freeRes: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
% 2.92/1.58 set_pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Product____Type__Ounit,type,
% 2.92/1.58 product_unit: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Agent__Opi____Rep,type,
% 2.92/1.58 pi_Rep: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Agent__Oname,type,
% 2.92/1.58 name: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(ty_n_t__Agent__Opi,type,
% 2.92/1.58 pi: $tType ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Agent_Opi_OInput,type,
% 2.92/1.58 input: name > name > pi > pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Agent_Opi_OPar,type,
% 2.92/1.58 par: pi > pi > pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Agent_Opi_ORes,type,
% 2.92/1.58 res: name > pi > pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Agent_Orec_Oswap__name,type,
% 2.92/1.58 swap_name: produc367475239e_name > name > name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Agent_Osubs,type,
% 2.92/1.58 subs: pi > name > name > pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_HOL_Odefault__class_Odefault_001t__Product____Type__Ounit,type,
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% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 2.92/1.58 perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 2.92/1.58 perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 2.92/1.58 perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 2.92/1.58 perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Ounit,type,
% 2.92/1.58 perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
% 2.92/1.58 perm_name_set_name: list_P227219501e_name > set_name > set_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
% 2.92/1.58 perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 2.92/1.58 perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 2.92/1.58 perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 2.92/1.58 perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
% 2.92/1.58 swap_name2: produc367475239e_name > name > name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 2.92/1.58 produc1570949143e_name: name > name > produc367475239e_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
% 2.92/1.58 product_Pair_name_pi: name > pi > product_prod_name_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.92/1.58 produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Ounit,type,
% 2.92/1.58 produc1785453612t_unit: name > product_unit > produc546891580t_unit ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
% 2.92/1.58 product_Pair_pi_name: pi > name > product_prod_pi_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 2.92/1.58 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Product____Type__Ounit,type,
% 2.92/1.58 produc1831798878t_unit: pi > product_unit > produc1028309998t_unit ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
% 2.92/1.58 produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 2.92/1.58 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 2.92/1.58 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi____Rep,type,
% 2.92/1.58 produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 2.92/1.58 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 2.92/1.58 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 2.92/1.58 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 2.92/1.58 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 2.92/1.58 produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 2.92/1.58 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 2.92/1.58 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Oname,type,
% 2.92/1.58 produc421428802t_name: product_unit > name > produc135724498t_name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Opi,type,
% 2.92/1.58 produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 2.92/1.58 produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Product__Type_OUnity,type,
% 2.92/1.58 product_Unity: product_unit ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
% 2.92/1.58 eqvt_name: set_Pr443758855e_name > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 2.92/1.58 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
% 2.92/1.58 eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
% 2.92/1.58 eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
% 2.92/1.58 eqvt_Late_subject: set_Pr806375235ubject > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.92/1.58 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 2.92/1.58 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 2.92/1.58 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Agent__Oname,type,
% 2.92/1.58 member_name: name > set_name > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Agent__Opi,type,
% 2.92/1.58 member_pi: pi > set_pi > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 2.92/1.58 member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 2.92/1.58 member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 2.92/1.58 member_Late_subject: late_subject > set_Late_subject > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 2.92/1.58 member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 2.92/1.58 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
% 2.92/1.58 member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 2.92/1.58 member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 2.92/1.58 member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_P,type,
% 2.92/1.58 p: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_PQ____,type,
% 2.92/1.58 pq: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_P_H____,type,
% 2.92/1.58 p2: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_Q,type,
% 2.92/1.58 q: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_Q_H____,type,
% 2.92/1.58 q2: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_Rel,type,
% 2.92/1.58 rel: set_Pr1834926343_pi_pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_aa____,type,
% 2.92/1.58 aa: late_subject ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_ab____,type,
% 2.92/1.58 ab: name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_b____,type,
% 2.92/1.58 b: name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_c____,type,
% 2.92/1.58 c: name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_x,type,
% 2.92/1.58 x: name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_xPQ____,type,
% 2.92/1.58 xPQ: pi ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_y____,type,
% 2.92/1.58 y: name ).
% 2.92/1.58
% 2.92/1.58 thf(sy_v_ya____,type,
% 2.92/1.58 ya: name ).
% 2.92/1.58
% 2.92/1.58 thf(fact_0_cComm1_Ohyps_I5_J,axiom,
% 2.92/1.58 ya != b ).
% 2.92/1.58
% 2.92/1.58 thf(fact_1_cComm1_Ohyps_I9_J,axiom,
% 2.92/1.58 ( ( late_OutputR @ ab @ x )
% 2.92/1.58 = late_TauR ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_2_cOpen_Ohyps_I2_J,axiom,
% 2.92/1.58 ab != x ).
% 2.92/1.58
% 2.92/1.58 thf(fact_3_cComm1_Ohyps_I6_J,axiom,
% 2.92/1.58 ya != c ).
% 2.92/1.58
% 2.92/1.58 thf(fact_4_cOpen_Ohyps_I3_J,axiom,
% 2.92/1.58 ( aa
% 2.92/1.58 = ( late_BoundOutputS @ ab ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_5_assms_I3_J,axiom,
% 2.92/1.58 eqvt_pi @ rel ).
% 2.92/1.58
% 2.92/1.58 thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062,axiom,
% 2.92/1.58 y != x ).
% 2.92/1.58
% 2.92/1.58 thf(fact_7_Bound_Ohyps_I1_J,axiom,
% 2.92/1.58 late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_8_assms_I1_J,axiom,
% 2.92/1.58 fresh_name_pi @ x @ p ).
% 2.92/1.58
% 2.92/1.58 thf(fact_9_cComm1_Ohyps_I3_J,axiom,
% 2.92/1.58 fresh_name_pi @ ya @ p ).
% 2.92/1.58
% 2.92/1.58 thf(fact_10_cComm1_Ohyps_I4_J,axiom,
% 2.92/1.58 fresh_name_pi @ ya @ q ).
% 2.92/1.58
% 2.92/1.58 thf(fact_11_cComm1_Ohyps_I7_J,axiom,
% 2.92/1.58 fresh_name_pi @ ya @ q2 ).
% 2.92/1.58
% 2.92/1.58 thf(fact_12_Bound_Ohyps_I3_J,axiom,
% 2.92/1.58 fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_13_Bound_Ohyps_I2_J,axiom,
% 2.92/1.58 fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_14_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3,axiom,
% 2.92/1.58 ! [A: name,P: pi,X: name] :
% 2.92/1.58 ( ( subs @ ( res @ A @ P ) @ X @ A )
% 2.92/1.58 = ( res @ X @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ A ) @ nil_Pr743626285e_name ) @ P ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_15_cComm1_Ohyps_I1_J,axiom,
% 2.92/1.58 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_16_perm__swap_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_17_perm__swap_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_18_perm__swap_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_19_perm__swap_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_20_perm__swap_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_21_name__id,axiom,
% 2.92/1.58 ! [A: name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_22_name__id,axiom,
% 2.92/1.58 ! [A: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_23_name__id,axiom,
% 2.92/1.58 ! [A: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_24_name__id,axiom,
% 2.92/1.58 ! [A: name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_25_name__id,axiom,
% 2.92/1.58 ! [A: name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_26_name__swap,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_27_name__swap,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_28_name__swap,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_29_name__swap,axiom,
% 2.92/1.58 ! [A: name,B: name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_30_name__swap,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_31_name__swap__bij,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_32_name__swap__bij,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_33_name__swap__bij,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_34_name__swap__bij,axiom,
% 2.92/1.58 ! [A: name,B: name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_35_name__swap__bij,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_36_cOpen_Ohyps_I1_J,axiom,
% 2.92/1.58 late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_37_pi_Operm_I8_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi @ ( par @ X2 @ X1 ) )
% 2.92/1.58 = ( par @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_38_simps_I8_J,axiom,
% 2.92/1.58 ! [P: pi,Q: pi,C: name,D: name] :
% 2.92/1.58 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 2.92/1.58 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_39_simps_I9_J,axiom,
% 2.92/1.58 ! [X: name,C: name,D: name,P: pi] :
% 2.92/1.58 ( ( X != C )
% 2.92/1.58 => ( ( X != D )
% 2.92/1.58 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 2.92/1.58 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_40_pt__name1,axiom,
% 2.92/1.58 ! [X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_41_pt__name1,axiom,
% 2.92/1.58 ! [X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_42_pt__name1,axiom,
% 2.92/1.58 ! [X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_43_pt__name1,axiom,
% 2.92/1.58 ! [X: name] :
% 2.92/1.58 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_44_pt__name1,axiom,
% 2.92/1.58 ! [X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_45_cComm1_Ohyps_I2_J,axiom,
% 2.92/1.58 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_46__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062,axiom,
% 2.92/1.58 fresh_name_pi @ y @ ( par @ p @ q ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_47_subst__identity,axiom,
% 2.92/1.58 ! [P: pi,A: name] :
% 2.92/1.58 ( ( subs @ P @ A @ A )
% 2.92/1.58 = P ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_48_pi__perm__empty,axiom,
% 2.92/1.58 ! [Pi_Rep: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 2.92/1.58 = Pi_Rep ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_49__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062,axiom,
% 2.92/1.58 fresh_name_pi @ y @ p ).
% 2.92/1.58
% 2.92/1.58 thf(fact_50__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062,axiom,
% 2.92/1.58 fresh_name_pi @ y @ q ).
% 2.92/1.58
% 2.92/1.58 thf(fact_51_pi_Ofresh_I8_J,axiom,
% 2.92/1.58 ! [A: name,X2: pi,X1: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 2.92/1.58 = ( ( fresh_name_pi @ A @ X2 )
% 2.92/1.58 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_52_pi_Operm_I9_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 2.92/1.58 = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_53_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: late_subject,B: name] :
% 2.92/1.58 ( ( fresh_717452603ubject @ A @ X )
% 2.92/1.58 => ( ( fresh_717452603ubject @ B @ X )
% 2.92/1.58 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_54_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: late_freeRes,B: name] :
% 2.92/1.58 ( ( fresh_1641682979reeRes @ A @ X )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ B @ X )
% 2.92/1.58 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_55_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: pi_Rep,B: name] :
% 2.92/1.58 ( ( fresh_name_pi_Rep @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi_Rep @ B @ X )
% 2.92/1.58 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_56_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,B: name] :
% 2.92/1.58 ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ B @ X )
% 2.92/1.58 => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_57_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 2.92/1.58 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_58_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: name,B: name] :
% 2.92/1.58 ( ( fresh_name_name @ A @ X )
% 2.92/1.58 => ( ( fresh_name_name @ B @ X )
% 2.92/1.58 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_59_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: pi,B: name] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi @ B @ X )
% 2.92/1.58 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_60_perm__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: name > noption_pi,B: name] :
% 2.92/1.58 ( ( fresh_543891186ion_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_543891186ion_pi @ B @ X )
% 2.92/1.58 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_61_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: late_subject,B: name] :
% 2.92/1.58 ( ( fresh_717452603ubject @ A @ X )
% 2.92/1.58 => ( ( fresh_717452603ubject @ B @ X )
% 2.92/1.58 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_62_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: late_freeRes,B: name] :
% 2.92/1.58 ( ( fresh_1641682979reeRes @ A @ X )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ B @ X )
% 2.92/1.58 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_63_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: pi_Rep,B: name] :
% 2.92/1.58 ( ( fresh_name_pi_Rep @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi_Rep @ B @ X )
% 2.92/1.58 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_64_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,B: name] :
% 2.92/1.58 ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ B @ X )
% 2.92/1.58 => ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_65_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: produc1141751126_pi_pi,B: name] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ B @ X )
% 2.92/1.58 => ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_66_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: name,B: name] :
% 2.92/1.58 ( ( fresh_name_name @ A @ X )
% 2.92/1.58 => ( ( fresh_name_name @ B @ X )
% 2.92/1.58 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_67_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: pi,B: name] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi @ B @ X )
% 2.92/1.58 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_68_name__fresh__fresh,axiom,
% 2.92/1.58 ! [A: name,X: name > noption_pi,B: name] :
% 2.92/1.58 ( ( fresh_543891186ion_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_543891186ion_pi @ B @ X )
% 2.92/1.58 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 2.92/1.58 = X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_69_Bound_Ohyps_I4_J,axiom,
% 2.92/1.58 fresh_717452603ubject @ y @ aa ).
% 2.92/1.58
% 2.92/1.58 thf(fact_70_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_717452603ubject @ A @ X )
% 2.92/1.58 => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_71_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ A @ X )
% 2.92/1.58 => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_72_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_name_pi_Rep @ A @ X )
% 2.92/1.58 => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_73_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: product_unit] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 => ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_74_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 2.92/1.58 => ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_75_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: name] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_name_name @ A @ X )
% 2.92/1.58 => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_76_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_77_fresh__perm__app,axiom,
% 2.92/1.58 ! [A: name,Pi: list_P227219501e_name,X: name > noption_pi] :
% 2.92/1.58 ( ( fresh_922791155e_name @ A @ Pi )
% 2.92/1.58 => ( ( fresh_543891186ion_pi @ A @ X )
% 2.92/1.58 => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_78_name__exists__fresh,axiom,
% 2.92/1.58 ! [X: product_unit] :
% 2.92/1.58 ~ ! [C2: name] :
% 2.92/1.58 ~ ( fresh_1143631827t_unit @ C2 @ X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_79_name__exists__fresh,axiom,
% 2.92/1.58 ! [X: produc1141751126_pi_pi] :
% 2.92/1.58 ~ ! [C2: name] :
% 2.92/1.58 ~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_80_name__exists__fresh,axiom,
% 2.92/1.58 ! [X: name] :
% 2.92/1.58 ~ ! [C2: name] :
% 2.92/1.58 ~ ( fresh_name_name @ C2 @ X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_81_name__exists__fresh,axiom,
% 2.92/1.58 ! [X: pi] :
% 2.92/1.58 ~ ! [C2: name] :
% 2.92/1.58 ~ ( fresh_name_pi @ C2 @ X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_82_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 2.92/1.58 = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_83_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 2.92/1.58 = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_84_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 2.92/1.58 = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_85_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: product_unit] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_1143631827t_unit @ A @ X ) )
% 2.92/1.58 = ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_86_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
% 2.92/1.58 = ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_87_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 2.92/1.58 = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_88_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 2.92/1.58 = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_89_fresh__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( fresh_543891186ion_pi @ A @ X ) )
% 2.92/1.58 = ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_90_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 2.92/1.58 ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 2.92/1.58 = ( fresh_717452603ubject @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_91_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 2.92/1.58 ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 2.92/1.58 = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_92_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 2.92/1.58 ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 2.92/1.58 = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_93_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: product_unit] :
% 2.92/1.58 ( ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) )
% 2.92/1.58 = ( fresh_1143631827t_unit @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_94_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
% 2.92/1.58 = ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_95_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 2.92/1.58 ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 2.92/1.58 = ( fresh_name_name @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_96_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 2.92/1.58 = ( fresh_name_pi @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_97_fresh__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 2.92/1.58 ( ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) )
% 2.92/1.58 = ( fresh_543891186ion_pi @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_98_freshRes,axiom,
% 2.92/1.58 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_99_fresh__fact2,axiom,
% 2.92/1.58 ! [A: name,B: name,P: pi] :
% 2.92/1.58 ( ( A != B )
% 2.92/1.58 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_100_fresh__fact1,axiom,
% 2.92/1.58 ! [A: name,P: pi,C: name,B: name] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ P )
% 2.92/1.58 => ( ( A != C )
% 2.92/1.58 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_101_forget,axiom,
% 2.92/1.58 ! [A: name,P: pi,B: name] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ P )
% 2.92/1.58 => ( ( subs @ P @ A @ B )
% 2.92/1.58 = P ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_102_name__calc_I2_J,axiom,
% 2.92/1.58 ! [X: name] :
% 2.92/1.58 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_103_mem__Collect__eq,axiom,
% 2.92/1.58 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 2.92/1.58 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 2.92/1.58 = ( P @ A ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_104_Collect__mem__eq,axiom,
% 2.92/1.58 ! [A2: set_Pr1834926343_pi_pi] :
% 2.92/1.58 ( ( collec1051790738_pi_pi
% 2.92/1.58 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A2 ) )
% 2.92/1.58 = A2 ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_105_Agent_OsubstRes3,axiom,
% 2.92/1.58 ! [B: name,P: pi,A: name] :
% 2.92/1.58 ( ( fresh_name_pi @ B @ P )
% 2.92/1.58 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 2.92/1.58 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_106_substRes2,axiom,
% 2.92/1.58 ! [B: name,P: pi,A: name] :
% 2.92/1.58 ( ( fresh_name_pi @ B @ P )
% 2.92/1.58 => ( ( res @ A @ P )
% 2.92/1.58 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_107_eqvt__subs,axiom,
% 2.92/1.58 ! [P2: list_P227219501e_name,P: pi,A: name,B: name] :
% 2.92/1.58 ( ( perm_name_pi @ P2 @ ( subs @ P @ A @ B ) )
% 2.92/1.58 = ( subs @ ( perm_name_pi @ P2 @ P ) @ ( perm_name_name @ P2 @ A ) @ ( perm_name_name @ P2 @ B ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_108_swap__simps_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 2.92/1.58 = B ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_109_swap__simps_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 2.92/1.58 = A ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_110_swap__simps_I3_J,axiom,
% 2.92/1.58 ! [A: name,C: name,B: name] :
% 2.92/1.58 ( ( A != C )
% 2.92/1.58 => ( ( B != C )
% 2.92/1.58 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
% 2.92/1.58 = C ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_111_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: late_subject,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_717452603ubject @ A @ X )
% 2.92/1.58 => ( ( fresh_717452603ubject @ C @ X )
% 2.92/1.58 => ( fresh_717452603ubject @ C @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_112_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: late_freeRes,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ A @ X )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ C @ X )
% 2.92/1.58 => ( fresh_1641682979reeRes @ C @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_113_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: pi_Rep,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_name_pi_Rep @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi_Rep @ C @ X )
% 2.92/1.58 => ( fresh_name_pi_Rep @ C @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_114_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: product_unit,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ C @ X )
% 2.92/1.58 => ( fresh_1143631827t_unit @ C @ ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_115_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: produc1141751126_pi_pi,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ C @ X )
% 2.92/1.58 => ( fresh_1376661020_pi_pi @ C @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_116_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: name,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_name_name @ A @ X )
% 2.92/1.58 => ( ( fresh_name_name @ C @ X )
% 2.92/1.58 => ( fresh_name_name @ C @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_117_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: pi,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_name_pi @ C @ X )
% 2.92/1.58 => ( fresh_name_pi @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_118_fresh__aux,axiom,
% 2.92/1.58 ! [C: name,A: name,X: name > noption_pi,B: name] :
% 2.92/1.58 ( ( C != A )
% 2.92/1.58 => ( ( fresh_543891186ion_pi @ A @ X )
% 2.92/1.58 => ( ( fresh_543891186ion_pi @ C @ X )
% 2.92/1.58 => ( fresh_543891186ion_pi @ C @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_119_cp__name__name1,axiom,
% 2.92/1.58 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_120_cp__name__name1,axiom,
% 2.92/1.58 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_121_cp__name__name1,axiom,
% 2.92/1.58 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_122_cp__name__name1,axiom,
% 2.92/1.58 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 2.92/1.58 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_123_cp__name__name1,axiom,
% 2.92/1.58 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 2.92/1.58 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_124_name__perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_125_name__perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_126_name__perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_127_name__perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_128_name__perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_129_perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_130_perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_131_perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_132_perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_133_perm__compose,axiom,
% 2.92/1.58 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 2.92/1.58 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_134_perm__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( ( perm_n1559866809ubject @ Pi @ X )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_135_perm__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( ( perm_n336613537reeRes @ Pi @ X )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_136_perm__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 2.92/1.58 ( ( ( perm_name_pi_Rep @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_137_perm__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 2.92/1.58 ( ( ( perm_name_name @ Pi @ X )
% 2.92/1.58 = ( perm_name_name @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_138_perm__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 2.92/1.58 ( ( ( perm_name_pi @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_139_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_140_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_141_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_142_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_143_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_144_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_145_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_146_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_147_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_148_perm__app,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 2.92/1.58 = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_149_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X4: set_Pr1834926343_pi_pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X4 ) )
% 2.92/1.58 = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_150_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,X4: set_Late_subject] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X4 ) )
% 2.92/1.58 = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_151_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,X4: set_Late_freeRes] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X4 ) )
% 2.92/1.58 = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_152_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi_Rep,X4: set_pi_Rep] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X4 ) )
% 2.92/1.58 = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_153_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: name,X4: set_name] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member_name @ X @ X4 ) )
% 2.92/1.58 = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_154_in__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi,X4: set_pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( member_pi @ X @ X4 ) )
% 2.92/1.58 = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X4 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_155_eq__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 2.92/1.58 = ( ( perm_n1559866809ubject @ Pi @ X )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_156_eq__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 2.92/1.58 = ( ( perm_n336613537reeRes @ Pi @ X )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_157_eq__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 2.92/1.58 = ( ( perm_name_pi_Rep @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_158_eq__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 2.92/1.58 = ( ( perm_name_name @ Pi @ X )
% 2.92/1.58 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_159_eq__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 2.92/1.58 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 2.92/1.58 = ( ( perm_name_pi @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_160_pi_Oinject_I7_J,axiom,
% 2.92/1.58 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 2.92/1.58 ( ( ( par @ X2 @ X1 )
% 2.92/1.58 = ( par @ Y2 @ Y1 ) )
% 2.92/1.58 = ( ( X2 = Y2 )
% 2.92/1.58 & ( X1 = Y1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_161_alphaRes,axiom,
% 2.92/1.58 ! [C: name,P: pi,A: name] :
% 2.92/1.58 ( ( fresh_name_pi @ C @ P )
% 2.92/1.58 => ( ( res @ A @ P )
% 2.92/1.58 = ( res @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_162_injPermSubst,axiom,
% 2.92/1.58 ! [B: name,P: pi,A: name] :
% 2.92/1.58 ( ( fresh_name_pi @ B @ P )
% 2.92/1.58 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ P )
% 2.92/1.58 = ( subs @ P @ A @ B ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_163_renaming,axiom,
% 2.92/1.58 ! [C: name,P: pi,A: name,B: name] :
% 2.92/1.58 ( ( fresh_name_pi @ C @ P )
% 2.92/1.58 => ( ( subs @ P @ A @ B )
% 2.92/1.58 = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ P ) @ C @ B ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_164_pi_Odistinct_I85_J,axiom,
% 2.92/1.58 ! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
% 2.92/1.58 ( ( par @ Pi1 @ Pi2 )
% 2.92/1.58 != ( res @ Name @ Pi3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_165_perm__swap_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_subject] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_166_perm__swap_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: late_freeRes] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_167_perm__swap_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi_Rep] :
% 2.92/1.58 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_168_perm__swap_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_169_perm__swap_I2_J,axiom,
% 2.92/1.58 ! [A: name,B: name,X: pi] :
% 2.92/1.58 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_170_transitions_OClose2,axiom,
% 2.92/1.58 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ Q )
% 2.92/1.58 => ( ( X != A )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P3 )
% 2.92/1.58 => ( ( Y != A )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ Q2 )
% 2.92/1.58 => ( ( X != Y )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_171_transitions_OClose1,axiom,
% 2.92/1.58 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ Q )
% 2.92/1.58 => ( ( X != A )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q2 )
% 2.92/1.58 => ( ( Y != A )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P3 )
% 2.92/1.58 => ( ( X != Y )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_172_Late__Semantics_OClose2,axiom,
% 2.92/1.58 ! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ Q )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_173_Late__Semantics_OClose1,axiom,
% 2.92/1.58 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_174_transitions_OComm2,axiom,
% 2.92/1.58 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( X != A )
% 2.92/1.58 => ( ( X != B )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P3 )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_175_transitions_OComm1,axiom,
% 2.92/1.58 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( X != A )
% 2.92/1.58 => ( ( X != B )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q2 )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_176_Late__Semantics_OComm2,axiom,
% 2.92/1.58 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_177_Late__Semantics_OComm1,axiom,
% 2.92/1.58 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_178_alphaBoundResidual,axiom,
% 2.92/1.58 ! [X5: name,P: pi,A: late_subject,X: name] :
% 2.92/1.58 ( ( fresh_name_pi @ X5 @ P )
% 2.92/1.58 => ( ( late_BoundR @ A @ X @ P )
% 2.92/1.58 = ( late_BoundR @ A @ X5 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X5 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_179_freeRes__perm__empty,axiom,
% 2.92/1.58 ! [FreeRes_Rep: late_freeRes_Rep] :
% 2.92/1.58 ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 2.92/1.58 = FreeRes_Rep ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_180_subject__perm__empty,axiom,
% 2.92/1.58 ! [Subject_Rep: late_subject_Rep] :
% 2.92/1.58 ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 2.92/1.58 = Subject_Rep ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_181_residual__perm__empty,axiom,
% 2.92/1.58 ! [Residual_Rep: late_residual_Rep] :
% 2.92/1.58 ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 2.92/1.58 = Residual_Rep ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_182_freeRes_Ofresh_I1_J,axiom,
% 2.92/1.58 ! [A: name,X2: name,X1: name] :
% 2.92/1.58 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X2 )
% 2.92/1.58 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_183_Late__Semantics_OfreeRes_Oinject,axiom,
% 2.92/1.58 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 2.92/1.58 ( ( ( late_OutputR @ X2 @ X1 )
% 2.92/1.58 = ( late_OutputR @ Y2 @ Y1 ) )
% 2.92/1.58 = ( ( X2 = Y2 )
% 2.92/1.58 & ( X1 = Y1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_184_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 2.92/1.58 ! [X1: name,Y1: name] :
% 2.92/1.58 ( ( ( late_BoundOutputS @ X1 )
% 2.92/1.58 = ( late_BoundOutputS @ Y1 ) )
% 2.92/1.58 = ( X1 = Y1 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_185_freeRes_Ofresh_I2_J,axiom,
% 2.92/1.58 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_186_freeRes_Operm_I2_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ late_TauR )
% 2.92/1.58 = late_TauR ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_187_cComm1_Ohyps_I8_J,axiom,
% 2.92/1.58 fresh_1143631827t_unit @ ya @ product_Unity ).
% 2.92/1.58
% 2.92/1.58 thf(fact_188_residual_Ofresh_I2_J,axiom,
% 2.92/1.58 ! [A: name,X2: late_freeRes,X1: pi] :
% 2.92/1.58 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 2.92/1.58 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 2.92/1.58 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_189_substTrans,axiom,
% 2.92/1.58 ! [B: name,P: pi,A: name,C: name] :
% 2.92/1.58 ( ( fresh_name_pi @ B @ P )
% 2.92/1.58 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 2.92/1.58 = ( subs @ P @ A @ C ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_190_residual_Operm_I2_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 2.92/1.58 ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 2.92/1.58 = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_191_freeRes_Operm_I1_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 2.92/1.58 ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 2.92/1.58 = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_192_subject_Operm_I1_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X1: name] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 2.92/1.58 = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_193_subject_Operm_I2_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X1: name] :
% 2.92/1.58 ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 2.92/1.58 = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_194_subject_Ofresh_I2_J,axiom,
% 2.92/1.58 ! [A: name,X1: name] :
% 2.92/1.58 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 2.92/1.58 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_195_subject_Ofresh_I1_J,axiom,
% 2.92/1.58 ! [A: name,X1: name] :
% 2.92/1.58 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 2.92/1.58 = ( fresh_name_name @ A @ X1 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_196_residual_Operm_I1_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 2.92/1.58 ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 2.92/1.58 = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_197_name__bij,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 2.92/1.58 ( ( ( perm_name_name @ Pi @ X )
% 2.92/1.58 = ( perm_name_name @ Pi @ Y ) )
% 2.92/1.58 = ( X = Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_198_freshResidual,axiom,
% 2.92/1.58 ! [P: pi,Rs: late_residual,X: name] :
% 2.92/1.58 ( ( late_transitions @ P @ Rs )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_199_resCasesF,axiom,
% 2.92/1.58 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 2.92/1.58 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 2.92/1.58 => ( ! [P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 2.92/1.58 => ( F2 @ ( res @ X @ P4 ) ) ) )
% 2.92/1.58 => ( F2 @ XP ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_200_resCasesF_H,axiom,
% 2.92/1.58 ! [X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.92/1.58 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 2.92/1.58 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.92/1.58 ( ( ( res @ X @ P )
% 2.92/1.58 = ( res @ Y3 @ P5 ) )
% 2.92/1.58 => ( ( ( late_FreeR @ Alpha @ P3 )
% 2.92/1.58 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.92/1.58 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_201_ResF,axiom,
% 2.92/1.58 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 2.92/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P3 ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_202_Late__Semantics_OResB,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Y @ A )
% 2.92/1.58 => ( ( Y != X )
% 2.92/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_203_freshFreeDerivative_I1_J,axiom,
% 2.92/1.58 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_204_freshBoundDerivative_I1_J,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_205_transitions_OResB,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Y @ A )
% 2.92/1.58 => ( ( Y != X )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A )
% 2.92/1.58 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_206_parCasesB_H,axiom,
% 2.92/1.58 ! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
% 2.92/1.58 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 2.92/1.58 => ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Q3: pi] :
% 2.92/1.58 ( ( ( par @ P @ Q )
% 2.92/1.58 = ( par @ P5 @ Q3 ) )
% 2.92/1.58 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 2.92/1.58 = ( late_BoundR @ A3 @ X6 @ ( par @ P4 @ Q3 ) ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P5 )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q3 )
% 2.92/1.58 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) )
% 2.92/1.58 => ~ ! [Q3: pi,A3: late_subject,X6: name,Q4: pi,P5: pi] :
% 2.92/1.58 ( ( ( par @ P @ Q )
% 2.92/1.58 = ( par @ P5 @ Q3 ) )
% 2.92/1.58 => ( ( ( late_BoundR @ B @ Y @ P3 )
% 2.92/1.58 = ( late_BoundR @ A3 @ X6 @ ( par @ P5 @ Q4 ) ) )
% 2.92/1.58 => ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P5 )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q3 )
% 2.92/1.58 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_207_transitions_OPar1B,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_208_transitions_OPar2B,axiom,
% 2.92/1.58 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_209_resCases_H,axiom,
% 2.92/1.58 ! [X: name,P: pi,Rs: late_residual] :
% 2.92/1.58 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 2.92/1.58 => ( ! [P5: pi,A3: name,B2: name] :
% 2.92/1.58 ( ( ( res @ X @ P )
% 2.92/1.58 = ( res @ B2 @ P5 ) )
% 2.92/1.58 => ! [P4: pi] :
% 2.92/1.58 ( ( Rs
% 2.92/1.58 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
% 2.92/1.58 => ( A3 = B2 ) ) ) )
% 2.92/1.58 => ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
% 2.92/1.58 ( ( ( res @ X @ P )
% 2.92/1.58 = ( res @ Y3 @ P5 ) )
% 2.92/1.58 => ( ( Rs
% 2.92/1.58 = ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 2.92/1.58 => ( ( Y3 != X6 )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P5 )
% 2.92/1.58 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) )
% 2.92/1.58 => ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
% 2.92/1.58 ( ( ( res @ X @ P )
% 2.92/1.58 = ( res @ Y3 @ P5 ) )
% 2.92/1.58 => ( ( Rs
% 2.92/1.58 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
% 2.92/1.58 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_210_residual_Oinject_I2_J,axiom,
% 2.92/1.58 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 2.92/1.58 ( ( ( late_FreeR @ X2 @ X1 )
% 2.92/1.58 = ( late_FreeR @ Y2 @ Y1 ) )
% 2.92/1.58 = ( ( X2 = Y2 )
% 2.92/1.58 & ( X1 = Y1 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_211_resCasesB_H,axiom,
% 2.92/1.58 ! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
% 2.92/1.58 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
% 2.92/1.58 => ( ! [P5: pi,A3: name,B2: name] :
% 2.92/1.58 ( ( ( res @ X5 @ P )
% 2.92/1.58 = ( res @ B2 @ P5 ) )
% 2.92/1.58 => ! [P4: pi] :
% 2.92/1.58 ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 2.92/1.58 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
% 2.92/1.58 => ( A3 = B2 ) ) ) )
% 2.92/1.58 => ~ ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
% 2.92/1.58 ( ( ( res @ X5 @ P )
% 2.92/1.58 = ( res @ Y3 @ P5 ) )
% 2.92/1.58 => ( ( ( late_BoundR @ A @ Y4 @ P3 )
% 2.92/1.58 = ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
% 2.92/1.58 => ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 2.92/1.58 => ( ( Y3 != X6 )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P5 )
% 2.92/1.58 => ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_212_residual_Odistinct_I1_J,axiom,
% 2.92/1.58 ! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
% 2.92/1.58 ( ( late_BoundR @ Subject @ Name2 @ Pi )
% 2.92/1.58 != ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_213_residual_Oinducts,axiom,
% 2.92/1.58 ! [P: late_residual > $o,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_214_eqvt,axiom,
% 2.92/1.58 ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( late_transitions @ X1 @ X2 )
% 2.92/1.58 => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_215_freeRes_Oinducts,axiom,
% 2.92/1.58 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 2.92/1.58 ( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
% 2.92/1.58 => ( ( P @ late_TauR )
% 2.92/1.58 => ( P @ FreeRes3 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_216_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 2.92/1.58 ! [Name12: name,Name23: name] :
% 2.92/1.58 ( ( late_OutputR @ Name12 @ Name23 )
% 2.92/1.58 != late_TauR ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_217_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 2.92/1.58 ! [Name2: name,Name: name] :
% 2.92/1.58 ( ( late_InputS @ Name2 )
% 2.92/1.58 != ( late_BoundOutputS @ Name ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_218_subject_Oinducts,axiom,
% 2.92/1.58 ! [P: late_subject > $o,Subject: late_subject] :
% 2.92/1.58 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 2.92/1.58 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 2.92/1.58 => ( P @ Subject ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_219_resCasesB,axiom,
% 2.92/1.58 ! [Y: name,P: pi,A: late_subject,X: name,YP: pi,F2: late_subject > pi > $o] :
% 2.92/1.58 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ YP ) )
% 2.92/1.58 => ( ( X != Y )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ! [B2: name,P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P4 ) )
% 2.92/1.58 => ( ( B2 != Y )
% 2.92/1.58 => ( ( A
% 2.92/1.58 = ( late_BoundOutputS @ B2 ) )
% 2.92/1.58 => ( F2 @ ( late_BoundOutputS @ B2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P4 ) ) ) ) )
% 2.92/1.58 => ( ! [P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Y @ A )
% 2.92/1.58 => ( F2 @ A @ ( res @ Y @ P4 ) ) ) )
% 2.92/1.58 => ( F2 @ A @ YP ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_220_Par1F,axiom,
% 2.92/1.58 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_221_Par2F,axiom,
% 2.92/1.58 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_222_freshBoundDerivative_I2_J,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( ( Y != X )
% 2.92/1.58 => ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_223_residual_Ostrong__inducts,axiom,
% 2.92/1.58 ! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
% 2.92/1.58 ( ( fresh_1143631827t_unit @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_224_residual_Ostrong__inducts,axiom,
% 2.92/1.58 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_225_residual_Ostrong__inducts,axiom,
% 2.92/1.58 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 2.92/1.58 ( ( fresh_name_name @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_226_residual_Ostrong__inducts,axiom,
% 2.92/1.58 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_227_residual_Ostrong__induct,axiom,
% 2.92/1.58 ! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
% 2.92/1.58 ( ( fresh_1143631827t_unit @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_228_residual_Ostrong__induct,axiom,
% 2.92/1.58 ! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_229_residual_Ostrong__induct,axiom,
% 2.92/1.58 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 2.92/1.58 ( ( fresh_name_name @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_230_residual_Ostrong__induct,axiom,
% 2.92/1.58 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 2.92/1.58 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ Name3 @ Z2 )
% 2.92/1.58 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 2.92/1.58 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 2.92/1.58 => ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
% 2.92/1.58 => ( P @ Z @ Residual ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_231_freshFreeDerivative_I2_J,axiom,
% 2.92/1.58 ! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( fresh_name_pi @ Y @ P3 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_232_Late__Semantics_OPar1B,axiom,
% 2.92/1.58 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_233_Late__Semantics_OPar2B,axiom,
% 2.92/1.58 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_234_parCasesB,axiom,
% 2.92/1.58 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 2.92/1.58 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ Q )
% 2.92/1.58 => ( ! [P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 2.92/1.58 => ( Prop @ ( par @ P4 @ Q ) ) )
% 2.92/1.58 => ( ! [Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
% 2.92/1.58 => ( Prop @ ( par @ P @ Q4 ) ) )
% 2.92/1.58 => ( Prop @ PQ ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_235_Open,axiom,
% 2.92/1.58 ! [P: pi,A: name,B: name,P3: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 2.92/1.58 => ( ( A != B )
% 2.92/1.58 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_236_derivativeEqvtI2,axiom,
% 2.92/1.58 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 2.92/1.58 => ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_237_derivativeEqvtI,axiom,
% 2.92/1.58 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 2.92/1.58 => ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_238_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,Y: product_unit] :
% 2.92/1.58 ( ( fresh_994967853t_unit @ A @ ( produc1076565719t_unit @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_239_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,Y: name] :
% 2.92/1.58 ( ( fresh_1826856600t_name @ A @ ( produc421428802t_name @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_240_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,Y: pi] :
% 2.92/1.58 ( ( fresh_707692390nit_pi @ A @ ( produc1806354576nit_pi @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_241_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: product_unit] :
% 2.92/1.58 ( ( fresh_90540034t_unit @ A @ ( produc1785453612t_unit @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X )
% 2.92/1.58 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_242_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: pi] :
% 2.92/1.58 ( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X )
% 2.92/1.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_243_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: pi,Y: product_unit] :
% 2.92/1.58 ( ( fresh_997779380t_unit @ A @ ( produc1831798878t_unit @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 & ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_244_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: pi,Y: name] :
% 2.92/1.58 ( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_245_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: name] :
% 2.92/1.58 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X )
% 2.92/1.58 & ( fresh_name_name @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_246_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: pi,Y: pi] :
% 2.92/1.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_247_fresh__prod,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X )
% 2.92/1.58 & ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_248_Res,axiom,
% 2.92/1.58 ! [Y: name,R: pi,S: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ Y @ R )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_249_ScopeExt,axiom,
% 2.92/1.58 ! [Y: name,R: pi,Z: name,S: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ Y @ R )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_250_fresh__list__cons,axiom,
% 2.92/1.58 ! [A: name,X: product_unit,Xs: list_Product_unit] :
% 2.92/1.58 ( ( fresh_1732817625t_unit @ A @ ( cons_Product_unit @ X @ Xs ) )
% 2.92/1.58 = ( ( fresh_1143631827t_unit @ A @ X )
% 2.92/1.58 & ( fresh_1732817625t_unit @ A @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_251_fresh__list__cons,axiom,
% 2.92/1.58 ! [A: name,X: produc1141751126_pi_pi,Xs: list_P431515740_pi_pi] :
% 2.92/1.58 ( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs ) )
% 2.92/1.58 = ( ( fresh_1376661020_pi_pi @ A @ X )
% 2.92/1.58 & ( fresh_1958133282_pi_pi @ A @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_252_fresh__list__cons,axiom,
% 2.92/1.58 ! [A: name,X: name,Xs: list_name] :
% 2.92/1.58 ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs ) )
% 2.92/1.58 = ( ( fresh_name_name @ A @ X )
% 2.92/1.58 & ( fresh_name_list_name @ A @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_253_fresh__list__cons,axiom,
% 2.92/1.58 ! [A: name,X: pi,Xs: list_pi] :
% 2.92/1.58 ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs ) )
% 2.92/1.58 = ( ( fresh_name_pi @ A @ X )
% 2.92/1.58 & ( fresh_name_list_pi @ A @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_254_fresh__list__cons,axiom,
% 2.92/1.58 ! [A: name,X: name > noption_pi,Xs: list_name_noption_pi] :
% 2.92/1.58 ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ X @ Xs ) )
% 2.92/1.58 = ( ( fresh_543891186ion_pi @ A @ X )
% 2.92/1.58 & ( fresh_1135477378ion_pi @ A @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_255_Bound_Ohyps_I5_J,axiom,
% 2.92/1.58 fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_256_name__fresh,axiom,
% 2.92/1.58 ( fresh_name_name
% 2.92/1.58 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_257_fresh__unit,axiom,
% 2.92/1.58 ! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_258_freshUnit,axiom,
% 2.92/1.58 ! [Y: name] : ( fresh_1143631827t_unit @ Y @ product_Unity ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_259_allE__Nil,axiom,
% 2.92/1.58 ! [P: list_P227219501e_name > $o] :
% 2.92/1.58 ( ! [X_1: list_P227219501e_name] : ( P @ X_1 )
% 2.92/1.58 => ( P @ nil_Pr743626285e_name ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_260_abs__fun__if,axiom,
% 2.92/1.58 ! [C: $o,Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( C
% 2.92/1.58 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 2.92/1.58 & ( ~ C
% 2.92/1.58 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_261_abs__fun__if,axiom,
% 2.92/1.58 ! [C: $o,Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( C
% 2.92/1.58 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 2.92/1.58 & ( ~ C
% 2.92/1.58 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_262_abs__fun__if,axiom,
% 2.92/1.58 ! [C: $o,Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 2.92/1.58 ( ( C
% 2.92/1.58 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 2.92/1.58 & ( ~ C
% 2.92/1.58 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_263_abs__fun__if,axiom,
% 2.92/1.58 ! [C: $o,Pi: list_P227219501e_name,X: name,Y: name] :
% 2.92/1.58 ( ( C
% 2.92/1.58 => ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_name @ Pi @ X ) ) )
% 2.92/1.58 & ( ~ C
% 2.92/1.58 => ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_name @ Pi @ Y ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_264_abs__fun__if,axiom,
% 2.92/1.58 ! [C: $o,Pi: list_P227219501e_name,X: pi,Y: pi] :
% 2.92/1.58 ( ( C
% 2.92/1.58 => ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_pi @ Pi @ X ) ) )
% 2.92/1.58 & ( ~ C
% 2.92/1.58 => ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
% 2.92/1.58 = ( perm_name_pi @ Pi @ Y ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_265_pt__bij3,axiom,
% 2.92/1.58 ! [X: late_subject,Y: late_subject,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( X = Y )
% 2.92/1.58 => ( ( perm_n1559866809ubject @ Pi @ X )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_266_pt__bij3,axiom,
% 2.92/1.58 ! [X: late_freeRes,Y: late_freeRes,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( X = Y )
% 2.92/1.58 => ( ( perm_n336613537reeRes @ Pi @ X )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_267_pt__bij3,axiom,
% 2.92/1.58 ! [X: pi_Rep,Y: pi_Rep,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( X = Y )
% 2.92/1.58 => ( ( perm_name_pi_Rep @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_268_pt__bij3,axiom,
% 2.92/1.58 ! [X: name,Y: name,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( X = Y )
% 2.92/1.58 => ( ( perm_name_name @ Pi @ X )
% 2.92/1.58 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_269_pt__bij3,axiom,
% 2.92/1.58 ! [X: pi,Y: pi,Pi: list_P227219501e_name] :
% 2.92/1.58 ( ( X = Y )
% 2.92/1.58 => ( ( perm_name_pi @ Pi @ X )
% 2.92/1.58 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_270_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y ) )
% 2.92/1.58 = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_271_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_freeRes] :
% 2.92/1.58 ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y ) )
% 2.92/1.58 = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_272_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi_Rep] :
% 2.92/1.58 ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y ) )
% 2.92/1.58 = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_273_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: name] :
% 2.92/1.58 ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y ) )
% 2.92/1.58 = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_274_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi] :
% 2.92/1.58 ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y ) )
% 2.92/1.58 = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_275_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_subject] :
% 2.92/1.58 ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y ) )
% 2.92/1.58 = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_276_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y ) )
% 2.92/1.58 = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_277_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi_Rep] :
% 2.92/1.58 ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y ) )
% 2.92/1.58 = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_278_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: name] :
% 2.92/1.58 ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y ) )
% 2.92/1.58 = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_279_perm__prod_Osimps,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi] :
% 2.92/1.58 ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y ) )
% 2.92/1.58 = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_280_fresh__prodD_I2_J,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: name] :
% 2.92/1.58 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 2.92/1.58 => ( fresh_name_name @ A @ Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_281_fresh__prodD_I2_J,axiom,
% 2.92/1.58 ! [A: name,X: pi,Y: pi] :
% 2.92/1.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.92/1.58 => ( fresh_name_pi @ A @ Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_282_fresh__prodD_I2_J,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.92/1.58 => ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_283_fresh__prodD_I1_J,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: name] :
% 2.92/1.58 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 2.92/1.58 => ( fresh_name_name @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_284_fresh__prodD_I1_J,axiom,
% 2.92/1.58 ! [A: name,X: pi,Y: pi] :
% 2.92/1.58 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 2.92/1.58 => ( fresh_name_pi @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_285_fresh__prodD_I1_J,axiom,
% 2.92/1.58 ! [A: name,X: name,Y: product_prod_pi_pi] :
% 2.92/1.58 ( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
% 2.92/1.58 => ( fresh_name_name @ A @ X ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_286_if__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 2.92/1.58 ( ( ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 2.92/1.58 & ( ~ ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_287_if__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 2.92/1.58 ( ( ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 2.92/1.58 & ( ~ ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_288_if__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 2.92/1.58 ( ( ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 2.92/1.58 & ( ~ ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_289_if__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 2.92/1.58 ( ( ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_name @ Pi @ C1 ) ) )
% 2.92/1.58 & ( ~ ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_290_if__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 2.92/1.58 ( ( ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_pi @ Pi @ C1 ) ) )
% 2.92/1.58 & ( ~ ( perm_name_o @ Pi @ B )
% 2.92/1.58 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 2.92/1.58 = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_291_cons__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_subject,Xs: list_Late_subject] :
% 2.92/1.58 ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs ) )
% 2.92/1.58 = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_292_cons__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: late_freeRes,Xs: list_Late_freeRes] :
% 2.92/1.58 ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs ) )
% 2.92/1.58 = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_293_cons__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi_Rep,Xs: list_pi_Rep] :
% 2.92/1.58 ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs ) )
% 2.92/1.58 = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_294_cons__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: name,Xs: list_name] :
% 2.92/1.58 ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs ) )
% 2.92/1.58 = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_295_cons__eqvt,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X: pi,Xs: list_pi] :
% 2.92/1.58 ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs ) )
% 2.92/1.58 = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_296_resSimCases,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: product_unit] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [Q4: pi,A3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.92/1.58 => ( ( A3 != X )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.92/1.58 => ( ( X != Y3 )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ Y3 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_297_resSimCases,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [Q4: pi,A3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.92/1.58 => ( ( A3 != X )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.92/1.58 => ( ( X != Y3 )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_298_resSimCases,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [Q4: pi,A3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.92/1.58 => ( ( A3 != X )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.92/1.58 => ( ( X != Y3 )
% 2.92/1.58 => ( ( fresh_name_name @ Y3 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_299_resSimCases,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [Q4: pi,A3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
% 2.92/1.58 => ( ( A3 != X )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,A3: late_subject,Y3: name] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X @ A3 )
% 2.92/1.58 => ( ( X != Y3 )
% 2.92/1.58 => ( ( fresh_name_pi @ Y3 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
% 2.92/1.58 => ( ! [Q4: pi,Alpha2: late_freeRes] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_300_simCasesCont,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: product_unit] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 2.92/1.58 => ( ( fresh_1143631827t_unit @ X6 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 2.92/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_301_simCasesCont,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 2.92/1.58 => ( ( fresh_1376661020_pi_pi @ X6 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 2.92/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_302_simCasesCont,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 2.92/1.58 => ( ( fresh_name_name @ X6 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 2.92/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_303_simCasesCont,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ! [A3: late_subject,X6: name,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ P )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ Q )
% 2.92/1.58 => ( ( fresh_717452603ubject @ X6 @ A3 )
% 2.92/1.58 => ( ( fresh_name_pi @ X6 @ C3 )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
% 2.92/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_304_eqvtRelI,axiom,
% 2.92/1.58 ! [Rel: set_Pr806375235ubject,P: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( eqvt_Late_subject @ Rel )
% 2.92/1.58 => ( ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel )
% 2.92/1.58 => ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_305_eqvtRelI,axiom,
% 2.92/1.58 ! [Rel: set_Pr1780909331reeRes,P: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( eqvt_Late_freeRes @ Rel )
% 2.92/1.58 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel )
% 2.92/1.58 => ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_306_eqvtRelI,axiom,
% 2.92/1.58 ! [Rel: set_Pr1131282415pi_Rep,P: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( eqvt_pi_Rep @ Rel )
% 2.92/1.58 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel )
% 2.92/1.58 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_307_eqvtRelI,axiom,
% 2.92/1.58 ! [Rel: set_Pr443758855e_name,P: name,Q: name,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( eqvt_name @ Rel )
% 2.92/1.58 => ( ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel )
% 2.92/1.58 => ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_308_eqvtRelI,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,Perm: list_P227219501e_name] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_309_eqvtRelE,axiom,
% 2.92/1.58 ! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P: late_subject,Q: late_subject] :
% 2.92/1.58 ( ( eqvt_Late_subject @ Rel )
% 2.92/1.58 => ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
% 2.92/1.58 => ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_310_eqvtRelE,axiom,
% 2.92/1.58 ! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P: late_freeRes,Q: late_freeRes] :
% 2.92/1.58 ( ( eqvt_Late_freeRes @ Rel )
% 2.92/1.58 => ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
% 2.92/1.58 => ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_311_eqvtRelE,axiom,
% 2.92/1.58 ! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P: pi_Rep,Q: pi_Rep] :
% 2.92/1.58 ( ( eqvt_pi_Rep @ Rel )
% 2.92/1.58 => ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
% 2.92/1.58 => ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_312_eqvtRelE,axiom,
% 2.92/1.58 ! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P: name,Q: name] :
% 2.92/1.58 ( ( eqvt_name @ Rel )
% 2.92/1.58 => ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
% 2.92/1.58 => ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_313_eqvtRelE,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P: pi,Q: pi] :
% 2.92/1.58 ( ( eqvt_pi @ Rel )
% 2.92/1.58 => ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_314_parSym,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 2.92/1.58 ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 2.92/1.58 => ( ! [R2: pi,S2: pi,X6: name] :
% 2.92/1.58 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ R2 ) @ ( res @ X6 @ S2 ) ) @ Rel ) )
% 2.92/1.58 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_315_simE_I2_J,axiom,
% 2.92/1.58 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 2.92/1.58 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 2.92/1.58 => ? [P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q2 ) @ Rel ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_316_eqvt__def,axiom,
% 2.92/1.58 ( eqvt_pi
% 2.92/1.58 = ( ^ [Rel2: set_Pr1834926343_pi_pi] :
% 2.92/1.58 ! [X3: product_prod_pi_pi,Perm2: list_P227219501e_name] :
% 2.92/1.58 ( ( member558706512_pi_pi @ X3 @ Rel2 )
% 2.92/1.58 => ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X3 ) @ Rel2 ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_317_parAssocLeft,axiom,
% 2.92/1.58 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 2.92/1.58 ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 2.92/1.58 => ( ! [S2: pi,T: pi,X6: name] :
% 2.92/1.58 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ S2 ) @ ( res @ X6 @ T ) ) @ Rel ) )
% 2.92/1.58 => ( ! [S2: pi,T: pi,U: pi,X6: name] :
% 2.92/1.58 ( ( fresh_name_pi @ X6 @ S2 )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X6 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 2.92/1.58 => ( ! [S2: pi,T: pi,U: pi,X6: name] :
% 2.92/1.58 ( ( fresh_name_pi @ X6 @ U )
% 2.92/1.58 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X6 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X6 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 2.92/1.58 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_318_simE_I1_J,axiom,
% 2.92/1.58 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 2.92/1.58 ( ( strong743114133lation @ P @ Rel @ Q )
% 2.92/1.58 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ X @ P )
% 2.92/1.58 => ? [P4: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
% 2.92/1.58 & ( strong2129052853vative @ P4 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_319_simCases,axiom,
% 2.92/1.58 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 2.92/1.58 ( ! [A3: late_subject,Y3: name,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
% 2.92/1.58 => ( ( fresh_name_pi @ Y3 @ P )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
% 2.92/1.58 => ( ! [Alpha2: late_freeRes,Q4: pi] :
% 2.92/1.58 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
% 2.92/1.58 => ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
% 2.92/1.58 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_320_simulation__def,axiom,
% 2.92/1.58 ( strong743114133lation
% 2.92/1.58 = ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 2.92/1.58 ( ! [A4: late_subject,X3: name,Q6: pi] :
% 2.92/1.58 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A4 @ X3 @ Q6 ) )
% 2.92/1.58 & ( fresh_name_pi @ X3 @ P7 ) )
% 2.92/1.58 => ? [P8: pi] :
% 2.92/1.58 ( ( late_transitions @ P7 @ ( late_BoundR @ A4 @ X3 @ P8 ) )
% 2.92/1.58 & ( strong2129052853vative @ P8 @ Q6 @ A4 @ X3 @ Rel2 ) ) )
% 2.92/1.58 & ! [Alpha3: late_freeRes,Q6: pi] :
% 2.92/1.58 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 2.92/1.58 => ? [P8: pi] :
% 2.92/1.58 ( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
% 2.92/1.58 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_321_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 2.92/1.58 ! [X2: name,Y2: name] :
% 2.92/1.58 ( ( ( late_BoundOutputS @ X2 )
% 2.92/1.58 = ( late_BoundOutputS @ Y2 ) )
% 2.92/1.58 = ( X2 = Y2 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_322_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 2.92/1.58 ! [X1: name,Y1: name] :
% 2.92/1.58 ( ( ( late_InputS @ X1 )
% 2.92/1.58 = ( late_InputS @ Y1 ) )
% 2.92/1.58 = ( X1 = Y1 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_323_Late__Semantics1_OfreeRes_Oinject,axiom,
% 2.92/1.58 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 2.92/1.58 ( ( ( late_OutputR @ X11 @ X12 )
% 2.92/1.58 = ( late_OutputR @ Y11 @ Y12 ) )
% 2.92/1.58 = ( ( X11 = Y11 )
% 2.92/1.58 & ( X12 = Y12 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 2.92/1.58 ! [X11: name,X12: name] :
% 2.92/1.58 ( ( late_OutputR @ X11 @ X12 )
% 2.92/1.58 != late_TauR ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_325_freeRes_Oexhaust,axiom,
% 2.92/1.58 ! [Y: late_freeRes] :
% 2.92/1.58 ( ! [X112: name,X122: name] :
% 2.92/1.58 ( Y
% 2.92/1.58 != ( late_OutputR @ X112 @ X122 ) )
% 2.92/1.58 => ( Y = late_TauR ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_326_subject_Oexhaust,axiom,
% 2.92/1.58 ! [Y: late_subject] :
% 2.92/1.58 ( ! [X13: name] :
% 2.92/1.58 ( Y
% 2.92/1.58 != ( late_InputS @ X13 ) )
% 2.92/1.58 => ~ ! [X22: name] :
% 2.92/1.58 ( Y
% 2.92/1.58 != ( late_BoundOutputS @ X22 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_327_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 2.92/1.58 ! [X1: name,X2: name] :
% 2.92/1.58 ( ( late_InputS @ X1 )
% 2.92/1.58 != ( late_BoundOutputS @ X2 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_328_inputCases,axiom,
% 2.92/1.58 ! [A: name,X: name,P: pi,B: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 2.92/1.58 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ YP ) )
% 2.92/1.58 => ( ( Y != A )
% 2.92/1.58 => ( ( Y != X )
% 2.92/1.58 => ( ( fresh_name_pi @ Y @ P )
% 2.92/1.58 => ( ( ( B
% 2.92/1.58 = ( late_InputS @ A ) )
% 2.92/1.58 => ( ( YP
% 2.92/1.58 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) )
% 2.92/1.58 => ( Prop @ ( late_InputS @ A ) @ Y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) ) ) )
% 2.92/1.58 => ( Prop @ B @ Y @ YP ) ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_329_list_Oinject,axiom,
% 2.92/1.58 ! [X21: produc367475239e_name,X222: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 2.92/1.58 ( ( ( cons_P1213805021e_name @ X21 @ X222 )
% 2.92/1.58 = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 2.92/1.58 = ( ( X21 = Y21 )
% 2.92/1.58 & ( X222 = Y22 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_330_pi_Operm_I4_J,axiom,
% 2.92/1.58 ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 2.92/1.58 ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 2.92/1.58 = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_331_pi_Odistinct_I57_J,axiom,
% 2.92/1.58 ! [Name12: name,Name23: name,Pi: pi,Name: name,Pi3: pi] :
% 2.92/1.58 ( ( input @ Name12 @ Name23 @ Pi )
% 2.92/1.58 != ( res @ Name @ Pi3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_332_pi_Odistinct_I55_J,axiom,
% 2.92/1.58 ! [Name12: name,Name23: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 2.92/1.58 ( ( input @ Name12 @ Name23 @ Pi )
% 2.92/1.58 != ( par @ Pi12 @ Pi22 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_333_resTrans_I2_J,axiom,
% 2.92/1.58 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 2.92/1.58 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_334_inputFreeTrans,axiom,
% 2.92/1.58 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.92/1.58 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_335_resInputFreeTrans,axiom,
% 2.92/1.58 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 2.92/1.58 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_336_old_Ounit_Oinducts,axiom,
% 2.92/1.58 ! [P: product_unit > $o,Unit: product_unit] :
% 2.92/1.58 ( ( P @ product_Unity )
% 2.92/1.58 => ( P @ Unit ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_337_old_Ounit_Oexhaust,axiom,
% 2.92/1.58 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_338_inputBoundOutputTrans,axiom,
% 2.92/1.58 ! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
% 2.92/1.58 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_339_Late__Semantics_OInput,axiom,
% 2.92/1.58 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_340_transitions_OInput,axiom,
% 2.92/1.58 ! [X: name,A: name,P: pi] :
% 2.92/1.58 ( ( X != A )
% 2.92/1.58 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_341_inputIneqTrans,axiom,
% 2.92/1.58 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
% 2.92/1.58 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
% 2.92/1.58 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_342_resInputBoundOutputTrans,axiom,
% 2.92/1.58 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
% 2.92/1.58 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_343_alphaInput,axiom,
% 2.92/1.58 ! [C: name,P: pi,A: name,X: name] :
% 2.92/1.58 ( ( fresh_name_pi @ C @ P )
% 2.92/1.58 => ( ( input @ A @ X @ P )
% 2.92/1.58 = ( input @ A @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_344_default__unit__def,axiom,
% 2.92/1.58 defaul1399868459t_unit = product_Unity ).
% 2.92/1.58
% 2.92/1.58 thf(fact_345_residual__Rep_Oinject_I2_J,axiom,
% 2.92/1.58 ! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
% 2.92/1.58 ( ( ( late_r347633188eR_Rep @ X21 @ X222 )
% 2.92/1.58 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 2.92/1.58 = ( ( X21 = Y21 )
% 2.92/1.58 & ( X222 = Y22 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_346_name__calc_I1_J,axiom,
% 2.92/1.58 ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 2.92/1.58 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 2.92/1.58 = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_347_name__calc_I3_J,axiom,
% 2.92/1.58 ! [A: name,C: name,B: name] :
% 2.92/1.58 ( ( ( A = C )
% 2.92/1.58 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 2.92/1.58 = B ) )
% 2.92/1.58 & ( ( A != C )
% 2.92/1.58 => ( ( ( B = C )
% 2.92/1.58 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 2.92/1.58 = A ) )
% 2.92/1.58 & ( ( B != C )
% 2.92/1.58 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
% 2.92/1.58 = C ) ) ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(fact_348_Agent_Oswap__name__def,axiom,
% 2.92/1.58 swap_name2 = swap_name ).
% 2.92/1.58
% 2.92/1.58 thf(fact_349_pi_Ofresh_I9_J,axiom,
% 2.92/1.58 ! [A: name,X1: name,X2: pi] :
% 2.92/1.58 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 2.92/1.58 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 2.92/1.58 ! [X: pi,Y: pi] :
% 2.92/1.58 ( ( if_pi @ $false @ X @ Y )
% 2.92/1.58 = Y ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 2.92/1.58 ! [X: pi,Y: pi] :
% 2.92/1.58 ( ( if_pi @ $true @ X @ Y )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 2.92/1.58 ! [X: name,Y: name] :
% 2.92/1.58 ( ( if_name @ $false @ X @ Y )
% 2.92/1.58 = Y ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 2.92/1.58 ! [X: name,Y: name] :
% 2.92/1.58 ( ( if_name @ $true @ X @ Y )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 2.92/1.58 ! [X: pi_Rep,Y: pi_Rep] :
% 2.92/1.58 ( ( if_pi_Rep @ $false @ X @ Y )
% 2.92/1.58 = Y ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 2.92/1.58 ! [X: pi_Rep,Y: pi_Rep] :
% 2.92/1.58 ( ( if_pi_Rep @ $true @ X @ Y )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 2.92/1.58 ! [X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( if_Late_freeRes @ $false @ X @ Y )
% 2.92/1.58 = Y ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 2.92/1.58 ! [X: late_freeRes,Y: late_freeRes] :
% 2.92/1.58 ( ( if_Late_freeRes @ $true @ X @ Y )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 2.92/1.58 ! [P: $o] :
% 2.92/1.58 ( ( P = $true )
% 2.92/1.58 | ( P = $false ) ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 2.92/1.58 ! [X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( if_Late_subject @ $false @ X @ Y )
% 2.92/1.58 = Y ) ).
% 2.92/1.58
% 2.92/1.58 thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 2.92/1.58 ! [X: late_subject,Y: late_subject] :
% 2.92/1.58 ( ( if_Late_subject @ $true @ X @ Y )
% 2.92/1.58 = X ) ).
% 2.92/1.58
% 2.92/1.58 thf(conj_0,conjecture,
% 2.92/1.58 ? [P6: pi] :
% 2.92/1.58 ( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ P6 ) )
% 2.92/1.58 & ( strong2129052853vative @ P6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ) ).
% 2.92/1.58 ------------------------
% 3.07/1.63 % (8622)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_8414 for (2999ds/4Mi)
% 3.07/1.63 % (8625)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_8414 for (2999ds/2Mi)
% 3.07/1.63 % (8623)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_8414 for (2999ds/27Mi)
% 3.07/1.63 % (8625)Instruction limit reached!
% 3.07/1.63 % (8625)------------------------------
% 3.07/1.63 % (8625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (8625)Termination reason: Unknown
% 3.07/1.63 % (8625)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (8625)Memory used [KB]: 1663
% 3.07/1.63 % (8625)Time elapsed: 0.003 s
% 3.07/1.63 % (8625)Instructions burned: 3 (million)
% 3.07/1.63 % (8625)------------------------------
% 3.07/1.63 % (8625)------------------------------
% 3.07/1.63 % (8622)Instruction limit reached!
% 3.07/1.63 % (8622)------------------------------
% 3.07/1.63 % (8622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.63 % (8622)Termination reason: Unknown
% 3.07/1.63 % (8622)Termination phase: shuffling
% 3.07/1.63
% 3.07/1.63 % (8622)Memory used [KB]: 1791
% 3.07/1.63 % (8622)Time elapsed: 0.004 s
% 3.07/1.63 % (8622)Instructions burned: 7 (million)
% 3.07/1.63 % (8622)------------------------------
% 3.07/1.63 % (8622)------------------------------
% 3.07/1.63 % (8621)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/183Mi)
% 3.07/1.63 % (8624)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/2Mi)
% 3.07/1.63 % (8626)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_8414 for (2999ds/275Mi)
% 3.07/1.63 % (8627)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/18Mi)
% 3.07/1.64 % (8623)Instruction limit reached!
% 3.07/1.64 % (8623)------------------------------
% 3.07/1.64 % (8623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (8623)Termination reason: Unknown
% 3.07/1.64 % (8623)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (8623)Memory used [KB]: 2046
% 3.07/1.64 % (8623)Time elapsed: 0.010 s
% 3.07/1.64 % (8623)Instructions burned: 27 (million)
% 3.07/1.64 % (8623)------------------------------
% 3.07/1.64 % (8623)------------------------------
% 3.07/1.64 % (8624)Instruction limit reached!
% 3.07/1.64 % (8624)------------------------------
% 3.07/1.64 % (8624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (8624)Termination reason: Unknown
% 3.07/1.64 % (8624)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (8624)Memory used [KB]: 1663
% 3.07/1.64 % (8624)Time elapsed: 0.003 s
% 3.07/1.64 % (8624)Instructions burned: 2 (million)
% 3.07/1.64 % (8624)------------------------------
% 3.07/1.64 % (8624)------------------------------
% 3.07/1.64 % (8628)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/3Mi)
% 3.07/1.64 % (8629)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_8414 for (2999ds/37Mi)
% 3.07/1.64 % (8628)Instruction limit reached!
% 3.07/1.64 % (8628)------------------------------
% 3.07/1.64 % (8628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.64 % (8628)Termination reason: Unknown
% 3.07/1.64 % (8628)Termination phase: shuffling
% 3.07/1.64
% 3.07/1.64 % (8628)Memory used [KB]: 1663
% 3.07/1.64 % (8628)Time elapsed: 0.003 s
% 3.07/1.64 % (8628)Instructions burned: 5 (million)
% 3.07/1.64 % (8628)------------------------------
% 3.07/1.64 % (8628)------------------------------
% 3.07/1.65 % (8630)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_8414 for (2999ds/15Mi)
% 3.07/1.65 % (8627)Instruction limit reached!
% 3.07/1.65 % (8627)------------------------------
% 3.07/1.65 % (8627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (8627)Termination reason: Unknown
% 3.07/1.65 % (8627)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (8627)Memory used [KB]: 1918
% 3.07/1.65 % (8627)Time elapsed: 0.014 s
% 3.07/1.65 % (8627)Instructions burned: 18 (million)
% 3.07/1.65 % (8627)------------------------------
% 3.07/1.65 % (8627)------------------------------
% 3.07/1.65 % (8632)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_8414 for (2999ds/1041Mi)
% 3.07/1.65 % (8629)Instruction limit reached!
% 3.07/1.65 % (8629)------------------------------
% 3.07/1.65 % (8629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (8629)Termination reason: Unknown
% 3.07/1.65 % (8629)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (8629)Memory used [KB]: 2302
% 3.07/1.65 % (8629)Time elapsed: 0.012 s
% 3.07/1.65 % (8629)Instructions burned: 40 (million)
% 3.07/1.65 % (8629)------------------------------
% 3.07/1.65 % (8629)------------------------------
% 3.07/1.65 % (8630)Instruction limit reached!
% 3.07/1.65 % (8630)------------------------------
% 3.07/1.65 % (8630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.65 % (8630)Termination reason: Unknown
% 3.07/1.65 % (8630)Termination phase: shuffling
% 3.07/1.65
% 3.07/1.65 % (8630)Memory used [KB]: 1918
% 3.07/1.65 % (8630)Time elapsed: 0.006 s
% 3.07/1.65 % (8630)Instructions burned: 15 (million)
% 3.07/1.65 % (8630)------------------------------
% 3.07/1.65 % (8630)------------------------------
% 3.07/1.65 % (8631)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_8414 for (2999ds/3Mi)
% 3.07/1.66 % (8631)Instruction limit reached!
% 3.07/1.66 % (8631)------------------------------
% 3.07/1.66 % (8631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (8631)Termination reason: Unknown
% 3.07/1.66 % (8631)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (8631)Memory used [KB]: 1663
% 3.07/1.66 % (8631)Time elapsed: 0.004 s
% 3.07/1.66 % (8631)Instructions burned: 3 (million)
% 3.07/1.66 % (8631)------------------------------
% 3.07/1.66 % (8631)------------------------------
% 3.07/1.66 % (8634)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/16Mi)
% 3.07/1.66 % (8635)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_8414 for (2999ds/3Mi)
% 3.07/1.66 % (8635)Instruction limit reached!
% 3.07/1.66 % (8635)------------------------------
% 3.07/1.66 % (8635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (8635)Termination reason: Unknown
% 3.07/1.66 % (8635)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (8635)Memory used [KB]: 1663
% 3.07/1.66 % (8635)Time elapsed: 0.003 s
% 3.07/1.66 % (8635)Instructions burned: 6 (million)
% 3.07/1.66 % (8635)------------------------------
% 3.07/1.66 % (8635)------------------------------
% 3.07/1.66 % (8633)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/7Mi)
% 3.07/1.66 % (8634)Instruction limit reached!
% 3.07/1.66 % (8634)------------------------------
% 3.07/1.66 % (8634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (8634)Termination reason: Unknown
% 3.07/1.66 % (8634)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (8634)Memory used [KB]: 1918
% 3.07/1.66 % (8634)Time elapsed: 0.007 s
% 3.07/1.66 % (8634)Instructions burned: 19 (million)
% 3.07/1.66 % (8634)------------------------------
% 3.07/1.66 % (8634)------------------------------
% 3.07/1.67 % (8633)Instruction limit reached!
% 3.07/1.67 % (8633)------------------------------
% 3.07/1.67 % (8633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (8633)Termination reason: Unknown
% 3.07/1.67 % (8633)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (8633)Memory used [KB]: 1791
% 3.07/1.67 % (8633)Time elapsed: 0.007 s
% 3.07/1.67 % (8633)Instructions burned: 8 (million)
% 3.07/1.67 % (8633)------------------------------
% 3.07/1.67 % (8633)------------------------------
% 3.07/1.67 % (8637)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/7Mi)
% 3.07/1.67 % (8636)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_8414 for (2999ds/3Mi)
% 3.07/1.67 % (8637)Instruction limit reached!
% 3.07/1.67 % (8637)------------------------------
% 3.07/1.67 % (8637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (8637)Termination reason: Unknown
% 3.07/1.67 % (8637)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (8637)Memory used [KB]: 1791
% 3.07/1.67 % (8637)Time elapsed: 0.004 s
% 3.07/1.67 % (8637)Instructions burned: 9 (million)
% 3.07/1.67 % (8637)------------------------------
% 3.07/1.67 % (8637)------------------------------
% 3.07/1.67 % (8636)Instruction limit reached!
% 3.07/1.67 % (8636)------------------------------
% 3.07/1.67 % (8636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (8636)Termination reason: Unknown
% 3.07/1.67 % (8636)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (8636)Memory used [KB]: 1663
% 3.07/1.67 % (8636)Time elapsed: 0.003 s
% 3.07/1.67 % (8636)Instructions burned: 3 (million)
% 3.07/1.67 % (8636)------------------------------
% 3.07/1.67 % (8636)------------------------------
% 3.07/1.67 % (8638)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/3Mi)
% 3.07/1.67 % (8638)Instruction limit reached!
% 3.07/1.67 % (8638)------------------------------
% 3.07/1.67 % (8638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (8638)Termination reason: Unknown
% 3.07/1.67 % (8638)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (8638)Memory used [KB]: 1663
% 3.07/1.67 % (8638)Time elapsed: 0.002 s
% 3.07/1.67 % (8638)Instructions burned: 3 (million)
% 3.07/1.67 % (8638)------------------------------
% 3.07/1.67 % (8638)------------------------------
% 3.07/1.68 % (8640)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/18Mi)
% 3.07/1.68 % (8639)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/4Mi)
% 3.07/1.68 % (8642)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/6Mi)
% 3.07/1.69 % (8641)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/710Mi)
% 3.07/1.69 % (8642)Instruction limit reached!
% 3.07/1.69 % (8642)------------------------------
% 3.07/1.69 % (8642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (8642)Termination reason: Unknown
% 3.07/1.69 % (8642)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (8642)Memory used [KB]: 1791
% 3.07/1.69 % (8642)Time elapsed: 0.004 s
% 3.07/1.69 % (8642)Instructions burned: 8 (million)
% 3.07/1.69 % (8642)------------------------------
% 3.07/1.69 % (8642)------------------------------
% 3.07/1.69 % (8639)Instruction limit reached!
% 3.07/1.69 % (8639)------------------------------
% 3.07/1.69 % (8639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (8639)Termination reason: Unknown
% 3.07/1.69 % (8639)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (8639)Memory used [KB]: 1663
% 3.07/1.69 % (8639)Time elapsed: 0.005 s
% 3.07/1.69 % (8639)Instructions burned: 5 (million)
% 3.07/1.69 % (8639)------------------------------
% 3.07/1.69 % (8639)------------------------------
% 3.07/1.69 % (8640)Instruction limit reached!
% 3.07/1.69 % (8640)------------------------------
% 3.07/1.69 % (8640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (8640)Termination reason: Unknown
% 3.07/1.69 % (8640)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (8640)Memory used [KB]: 1918
% 3.07/1.69 % (8640)Time elapsed: 0.008 s
% 3.07/1.69 % (8640)Instructions burned: 20 (million)
% 3.07/1.69 % (8640)------------------------------
% 3.07/1.69 % (8640)------------------------------
% 3.07/1.70 % (8643)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_8414 for (2999ds/902Mi)
% 3.07/1.70 % (8645)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8414 for (2999ds/5Mi)
% 3.07/1.70 % (8644)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_8414 for (2999ds/21Mi)
% 3.07/1.70 % (8645)Instruction limit reached!
% 3.07/1.70 % (8645)------------------------------
% 3.07/1.70 % (8645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (8645)Termination reason: Unknown
% 3.07/1.70 % (8645)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (8645)Memory used [KB]: 1791
% 3.07/1.70 % (8645)Time elapsed: 0.003 s
% 3.07/1.70 % (8645)Instructions burned: 6 (million)
% 3.07/1.70 % (8645)------------------------------
% 3.07/1.70 % (8645)------------------------------
% 3.07/1.71 % (8644)Instruction limit reached!
% 3.07/1.71 % (8644)------------------------------
% 3.07/1.71 % (8644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (8644)Termination reason: Unknown
% 3.07/1.71 % (8644)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (8644)Memory used [KB]: 1918
% 3.07/1.71 % (8644)Time elapsed: 0.009 s
% 3.07/1.71 % (8644)Instructions burned: 22 (million)
% 3.07/1.71 % (8644)------------------------------
% 3.07/1.71 % (8644)------------------------------
% 3.07/1.71 % (8646)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_8414 for (2998ds/6Mi)
% 3.07/1.71 % (8646)Instruction limit reached!
% 3.07/1.71 % (8646)------------------------------
% 3.07/1.71 % (8646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (8646)Termination reason: Unknown
% 3.07/1.71 % (8646)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (8646)Memory used [KB]: 1791
% 3.07/1.71 % (8646)Time elapsed: 0.004 s
% 3.07/1.71 % (8646)Instructions burned: 9 (million)
% 3.07/1.71 % (8646)------------------------------
% 3.07/1.71 % (8646)------------------------------
% 3.07/1.72 % (8647)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8414 for (2998ds/377Mi)
% 3.07/1.72 % (8648)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_8414 for (2998ds/779Mi)
% 3.07/1.73 % (8621)Instruction limit reached!
% 3.07/1.73 % (8621)------------------------------
% 3.07/1.73 % (8621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.73 % (8621)Termination reason: Unknown
% 3.07/1.73 % (8621)Termination phase: Saturation
% 3.07/1.73
% 3.07/1.73 % (8621)Memory used [KB]: 7547
% 3.07/1.73 % (8621)Time elapsed: 0.097 s
% 3.07/1.73 % (8621)Instructions burned: 184 (million)
% 3.07/1.73 % (8621)------------------------------
% 3.07/1.73 % (8621)------------------------------
% 3.07/1.74 % (8626)Refutation not found, incomplete strategy
% 3.07/1.74 % (8626)------------------------------
% 3.07/1.74 % (8626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.74 % (8626)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.74
% 3.07/1.74
% 3.07/1.74 % (8626)Memory used [KB]: 8699
% 3.07/1.74 % (8626)Time elapsed: 0.103 s
% 3.07/1.74 % (8626)Instructions burned: 224 (million)
% 3.07/1.74 % (8626)------------------------------
% 3.07/1.74 % (8626)------------------------------
% 3.07/1.75 % (8649)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_8414 for (2998ds/19Mi)
% 3.07/1.75 % (8650)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8414 for (2998ds/879Mi)
% 3.07/1.75 % (8649)Instruction limit reached!
% 3.07/1.75 % (8649)------------------------------
% 3.07/1.75 % (8649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.75 % (8649)Termination reason: Unknown
% 3.07/1.75 % (8649)Termination phase: shuffling
% 3.07/1.75
% 3.07/1.75 % (8649)Memory used [KB]: 2046
% 3.07/1.75 % (8649)Time elapsed: 0.010 s
% 3.07/1.75 % (8649)Instructions burned: 20 (million)
% 3.07/1.75 % (8649)------------------------------
% 3.07/1.75 % (8649)------------------------------
% 3.07/1.76 % (8651)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8414 for (2998ds/17Mi)
% 3.07/1.77 % (8632)First to succeed.
% 3.07/1.77 % (8632)Refutation found. Thanks to Tanya!
% 3.07/1.77 % SZS status ContradictoryAxioms for DTF2THF_8414
% 3.07/1.77 % SZS output start Proof for DTF2THF_8414
% 3.07/1.77 thf(type_def_5, type, name: $tType).
% 3.07/1.77 thf(type_def_6, type, pi: $tType).
% 3.07/1.77 thf(type_def_8, type, produc367475239e_name: $tType).
% 3.07/1.77 thf(type_def_9, type, product_unit: $tType).
% 3.07/1.77 thf(type_def_10, type, pi_Rep: $tType).
% 3.07/1.77 thf(type_def_11, type, late_freeRes: $tType).
% 3.07/1.77 thf(type_def_12, type, late_subject: $tType).
% 3.07/1.77 thf(type_def_13, type, late_residual: $tType).
% 3.07/1.77 thf(type_def_14, type, late_residual_Rep: $tType).
% 3.07/1.77 thf(type_def_15, type, noption_pi: $tType).
% 3.07/1.77 thf(type_def_16, type, list_name_noption_pi: $tType).
% 3.07/1.77 thf(type_def_17, type, list_name: $tType).
% 3.07/1.77 thf(type_def_18, type, list_pi: $tType).
% 3.07/1.77 thf(type_def_19, type, list_pi_Rep: $tType).
% 3.07/1.77 thf(type_def_20, type, list_Late_freeRes: $tType).
% 3.07/1.77 thf(type_def_21, type, list_Late_subject: $tType).
% 3.07/1.77 thf(type_def_22, type, list_P227219501e_name: $tType).
% 3.07/1.77 thf(type_def_23, type, produc1141751126_pi_pi: $tType).
% 3.07/1.77 thf(type_def_24, type, list_P431515740_pi_pi: $tType).
% 3.07/1.77 thf(type_def_25, type, list_Product_unit: $tType).
% 3.07/1.77 thf(type_def_26, type, product_prod_name_pi: $tType).
% 3.07/1.77 thf(type_def_27, type, produc546891580t_unit: $tType).
% 3.07/1.77 thf(type_def_28, type, product_prod_pi_name: $tType).
% 3.07/1.77 thf(type_def_29, type, product_prod_pi_pi: $tType).
% 3.07/1.77 thf(type_def_30, type, produc1028309998t_unit: $tType).
% 3.07/1.77 thf(type_def_31, type, produc135724498t_name: $tType).
% 3.07/1.77 thf(type_def_32, type, produc738223008nit_pi: $tType).
% 3.07/1.77 thf(type_def_33, type, produc971140967t_unit: $tType).
% 3.07/1.77 thf(type_def_34, type, late_freeRes_Rep: $tType).
% 3.07/1.77 thf(type_def_35, type, late_subject_Rep: $tType).
% 3.07/1.77 thf(type_def_36, type, produc2052722628s_name: $tType).
% 3.07/1.77 thf(type_def_37, type, produc992857746Res_pi: $tType).
% 3.07/1.77 thf(type_def_38, type, produc1777919905pi_Rep: $tType).
% 3.07/1.77 thf(type_def_39, type, produc1357834675reeRes: $tType).
% 3.07/1.77 thf(type_def_40, type, produc214645451ubject: $tType).
% 3.07/1.77 thf(type_def_41, type, produc1998742700t_name: $tType).
% 3.07/1.77 thf(type_def_42, type, produc140253050ect_pi: $tType).
% 3.07/1.77 thf(type_def_43, type, produc257012921pi_Rep: $tType).
% 3.07/1.77 thf(type_def_44, type, produc355105483reeRes: $tType).
% 3.07/1.77 thf(type_def_45, type, produc1359399907ubject: $tType).
% 3.07/1.77 thf(type_def_46, type, set_name: $tType).
% 3.07/1.77 thf(type_def_47, type, set_pi: $tType).
% 3.07/1.77 thf(type_def_48, type, set_pi_Rep: $tType).
% 3.07/1.77 thf(type_def_49, type, set_Late_freeRes: $tType).
% 3.07/1.77 thf(type_def_50, type, set_Late_subject: $tType).
% 3.07/1.77 thf(type_def_51, type, set_Pr1834926343_pi_pi: $tType).
% 3.07/1.77 thf(type_def_52, type, produc1212344719pi_Rep: $tType).
% 3.07/1.77 thf(type_def_53, type, set_Pr443758855e_name: $tType).
% 3.07/1.77 thf(type_def_54, type, set_Pr1131282415pi_Rep: $tType).
% 3.07/1.77 thf(type_def_55, type, set_Pr1780909331reeRes: $tType).
% 3.07/1.77 thf(type_def_56, type, set_Pr806375235ubject: $tType).
% 3.07/1.77 thf(func_def_0, type, list_P431515740_pi_pi: $tType).
% 3.07/1.77 thf(func_def_1, type, set_Pr806375235ubject: $tType).
% 3.07/1.77 thf(func_def_2, type, set_Pr1780909331reeRes: $tType).
% 3.07/1.77 thf(func_def_3, type, produc1141751126_pi_pi: $tType).
% 3.07/1.77 thf(func_def_4, type, produc1359399907ubject: $tType).
% 3.07/1.77 thf(func_def_5, type, produc355105483reeRes: $tType).
% 3.07/1.77 thf(func_def_6, type, produc214645451ubject: $tType).
% 3.07/1.77 thf(func_def_7, type, produc1357834675reeRes: $tType).
% 3.07/1.77 thf(func_def_8, type, set_Pr1131282415pi_Rep: $tType).
% 3.07/1.77 thf(func_def_9, type, produc971140967t_unit: $tType).
% 3.07/1.77 thf(func_def_10, type, produc257012921pi_Rep: $tType).
% 3.07/1.77 thf(func_def_11, type, produc1777919905pi_Rep: $tType).
% 3.07/1.77 thf(func_def_12, type, list_name_noption_pi: $tType).
% 3.07/1.77 thf(func_def_13, type, list_P227219501e_name: $tType).
% 3.07/1.77 thf(func_def_14, type, set_Pr443758855e_name: $tType).
% 3.07/1.77 thf(func_def_15, type, produc1998742700t_name: $tType).
% 3.07/1.77 thf(func_def_16, type, produc2052722628s_name: $tType).
% 3.07/1.77 thf(func_def_17, type, produc140253050ect_pi: $tType).
% 3.07/1.77 thf(func_def_18, type, produc992857746Res_pi: $tType).
% 3.07/1.77 thf(func_def_19, type, set_Pr1834926343_pi_pi: $tType).
% 3.07/1.77 thf(func_def_20, type, produc135724498t_name: $tType).
% 3.07/1.77 thf(func_def_21, type, produc1212344719pi_Rep: $tType).
% 3.07/1.77 thf(func_def_22, type, produc546891580t_unit: $tType).
% 3.07/1.77 thf(func_def_23, type, produc738223008nit_pi: $tType).
% 3.07/1.77 thf(func_def_24, type, produc1028309998t_unit: $tType).
% 3.07/1.77 thf(func_def_25, type, produc367475239e_name: $tType).
% 3.07/1.77 thf(func_def_26, type, product_prod_pi_name: $tType).
% 3.07/1.77 thf(func_def_27, type, product_prod_name_pi: $tType).
% 3.07/1.77 thf(func_def_28, type, product_prod_pi_pi: $tType).
% 3.07/1.77 thf(func_def_29, type, list_Late_subject: $tType).
% 3.07/1.77 thf(func_def_30, type, list_Late_freeRes: $tType).
% 3.07/1.77 thf(func_def_31, type, set_Late_subject: $tType).
% 3.07/1.77 thf(func_def_32, type, set_Late_freeRes: $tType).
% 3.07/1.77 thf(func_def_33, type, list_Product_unit: $tType).
% 3.07/1.77 thf(func_def_34, type, list_pi_Rep: $tType).
% 3.07/1.77 thf(func_def_35, type, late_residual_Rep: $tType).
% 3.07/1.77 thf(func_def_36, type, noption_pi: $tType).
% 3.07/1.77 thf(func_def_37, type, late_subject_Rep: $tType).
% 3.07/1.77 thf(func_def_38, type, late_freeRes_Rep: $tType).
% 3.07/1.77 thf(func_def_39, type, set_pi_Rep: $tType).
% 3.07/1.77 thf(func_def_40, type, list_name: $tType).
% 3.07/1.77 thf(func_def_41, type, set_name: $tType).
% 3.07/1.77 thf(func_def_42, type, list_pi: $tType).
% 3.07/1.77 thf(func_def_43, type, late_residual: $tType).
% 3.07/1.77 thf(func_def_44, type, late_subject: $tType).
% 3.07/1.77 thf(func_def_45, type, late_freeRes: $tType).
% 3.07/1.77 thf(func_def_46, type, set_pi: $tType).
% 3.07/1.77 thf(func_def_47, type, product_unit: $tType).
% 3.07/1.77 thf(func_def_48, type, pi_Rep: $tType).
% 3.07/1.77 thf(func_def_49, type, name: $tType).
% 3.07/1.77 thf(func_def_50, type, pi: $tType).
% 3.07/1.77 thf(func_def_51, type, input: name > name > pi > pi).
% 3.07/1.77 thf(func_def_52, type, par: pi > pi > pi).
% 3.07/1.77 thf(func_def_53, type, res: name > pi > pi).
% 3.07/1.77 thf(func_def_54, type, swap_name: produc367475239e_name > name > name).
% 3.07/1.77 thf(func_def_55, type, subs: pi > name > name > pi).
% 3.07/1.77 thf(func_def_56, type, defaul1399868459t_unit: product_unit).
% 3.07/1.77 thf(func_def_57, type, if_name: $o > name > name > name).
% 3.07/1.77 thf(func_def_58, type, if_pi: $o > pi > pi > pi).
% 3.07/1.77 thf(func_def_59, type, if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep).
% 3.07/1.77 thf(func_def_60, type, if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes).
% 3.07/1.77 thf(func_def_61, type, if_Late_subject: $o > late_subject > late_subject > late_subject).
% 3.07/1.77 thf(func_def_62, type, late_OutputR: name > name > late_freeRes).
% 3.07/1.77 thf(func_def_63, type, late_TauR: late_freeRes).
% 3.07/1.77 thf(func_def_64, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.07/1.77 thf(func_def_65, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.07/1.77 thf(func_def_66, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 3.07/1.77 thf(func_def_67, type, late_BoundOutputS: name > late_subject).
% 3.07/1.77 thf(func_def_68, type, late_InputS: name > late_subject).
% 3.07/1.77 thf(func_def_69, type, late_transitions: pi > late_residual > $o).
% 3.07/1.77 thf(func_def_70, type, cons_name_noption_pi: (name > noption_pi) > list_name_noption_pi > list_name_noption_pi).
% 3.07/1.77 thf(func_def_71, type, cons_name: name > list_name > list_name).
% 3.07/1.77 thf(func_def_72, type, cons_pi: pi > list_pi > list_pi).
% 3.07/1.77 thf(func_def_73, type, cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep).
% 3.07/1.77 thf(func_def_74, type, cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes).
% 3.07/1.77 thf(func_def_75, type, cons_Late_subject: late_subject > list_Late_subject > list_Late_subject).
% 3.07/1.77 thf(func_def_76, type, cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name).
% 3.07/1.77 thf(func_def_77, type, cons_P749510156_pi_pi: produc1141751126_pi_pi > list_P431515740_pi_pi > list_P431515740_pi_pi).
% 3.07/1.77 thf(func_def_78, type, cons_Product_unit: product_unit > list_Product_unit > list_Product_unit).
% 3.07/1.77 thf(func_def_79, type, nil_Pr743626285e_name: list_P227219501e_name).
% 3.07/1.77 thf(func_def_80, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 3.07/1.77 thf(func_def_81, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 3.07/1.77 thf(func_def_82, type, fresh_name_name: name > name > $o).
% 3.07/1.77 thf(func_def_83, type, fresh_name_pi: name > pi > $o).
% 3.07/1.77 thf(func_def_84, type, fresh_name_pi_Rep: name > pi_Rep > $o).
% 3.07/1.77 thf(func_def_85, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.07/1.77 thf(func_def_86, type, fresh_81631222sidual: name > late_residual > $o).
% 3.07/1.77 thf(func_def_87, type, fresh_717452603ubject: name > late_subject > $o).
% 3.07/1.77 thf(func_def_88, type, fresh_1135477378ion_pi: name > list_name_noption_pi > $o).
% 3.07/1.77 thf(func_def_89, type, fresh_name_list_name: name > list_name > $o).
% 3.07/1.77 thf(func_def_90, type, fresh_name_list_pi: name > list_pi > $o).
% 3.07/1.77 thf(func_def_91, type, fresh_922791155e_name: name > list_P227219501e_name > $o).
% 3.07/1.77 thf(func_def_92, type, fresh_1958133282_pi_pi: name > list_P431515740_pi_pi > $o).
% 3.07/1.77 thf(func_def_93, type, fresh_1732817625t_unit: name > list_Product_unit > $o).
% 3.07/1.77 thf(func_def_94, type, fresh_441084397e_name: name > produc367475239e_name > $o).
% 3.07/1.77 thf(func_def_95, type, fresh_93646139ame_pi: name > product_prod_name_pi > $o).
% 3.07/1.77 thf(func_def_96, type, fresh_1376661020_pi_pi: name > produc1141751126_pi_pi > $o).
% 3.07/1.77 thf(func_def_97, type, fresh_90540034t_unit: name > produc546891580t_unit > $o).
% 3.07/1.77 thf(func_def_98, type, fresh_261416607i_name: name > product_prod_pi_name > $o).
% 3.07/1.77 thf(func_def_99, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 3.07/1.77 thf(func_def_100, type, fresh_997779380t_unit: name > produc1028309998t_unit > $o).
% 3.07/1.77 thf(func_def_101, type, fresh_1826856600t_name: name > produc135724498t_name > $o).
% 3.07/1.77 thf(func_def_102, type, fresh_707692390nit_pi: name > produc738223008nit_pi > $o).
% 3.07/1.77 thf(func_def_103, type, fresh_994967853t_unit: name > produc971140967t_unit > $o).
% 3.07/1.77 thf(func_def_104, type, fresh_1143631827t_unit: name > product_unit > $o).
% 3.07/1.77 thf(func_def_105, type, perm_n382765978reeRes: list_P227219501e_name > (name > late_freeRes) > name > late_freeRes).
% 3.07/1.77 thf(func_def_106, type, perm_n1387060402ubject: list_P227219501e_name > (name > late_subject) > name > late_subject).
% 3.07/1.77 thf(func_def_107, type, perm_n1667196784ion_pi: list_P227219501e_name > (name > noption_pi) > name > noption_pi).
% 3.07/1.77 thf(func_def_108, type, perm_n1333244520reeRes: list_P227219501e_name > (pi > late_freeRes) > pi > late_freeRes).
% 3.07/1.77 thf(func_def_109, type, perm_n190055296ubject: list_P227219501e_name > (pi > late_subject) > pi > late_subject).
% 3.07/1.77 thf(func_def_110, type, perm_n1841560599reeRes: list_P227219501e_name > (pi_Rep > late_freeRes) > pi_Rep > late_freeRes).
% 3.07/1.77 thf(func_def_111, type, perm_n698371375ubject: list_P227219501e_name > (pi_Rep > late_subject) > pi_Rep > late_subject).
% 3.07/1.77 thf(func_def_112, type, perm_n1446290985reeRes: list_P227219501e_name > (late_freeRes > late_freeRes) > late_freeRes > late_freeRes).
% 3.07/1.77 thf(func_def_113, type, perm_n303101761ubject: list_P227219501e_name > (late_freeRes > late_subject) > late_freeRes > late_subject).
% 3.07/1.77 thf(func_def_114, type, perm_n443561793reeRes: list_P227219501e_name > (late_subject > late_freeRes) > late_subject > late_freeRes).
% 3.07/1.77 thf(func_def_115, type, perm_n1447856217ubject: list_P227219501e_name > (late_subject > late_subject) > late_subject > late_subject).
% 3.07/1.77 thf(func_def_116, type, perm_name_o: list_P227219501e_name > $o > $o).
% 3.07/1.77 thf(func_def_117, type, perm_name_name: list_P227219501e_name > name > name).
% 3.07/1.77 thf(func_def_118, type, perm_name_pi: list_P227219501e_name > pi > pi).
% 3.07/1.77 thf(func_def_119, type, perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep).
% 3.07/1.77 thf(func_def_120, type, perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes).
% 3.07/1.77 thf(func_def_121, type, perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep).
% 3.07/1.77 thf(func_def_122, type, perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual).
% 3.07/1.77 thf(func_def_123, type, perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep).
% 3.07/1.77 thf(func_def_124, type, perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject).
% 3.07/1.77 thf(func_def_125, type, perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep).
% 3.07/1.77 thf(func_def_126, type, perm_name_list_name: list_P227219501e_name > list_name > list_name).
% 3.07/1.77 thf(func_def_127, type, perm_name_list_pi: list_P227219501e_name > list_pi > list_pi).
% 3.07/1.77 thf(func_def_128, type, perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep).
% 3.07/1.77 thf(func_def_129, type, perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes).
% 3.07/1.77 thf(func_def_130, type, perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject).
% 3.07/1.77 thf(func_def_131, type, perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name).
% 3.07/1.77 thf(func_def_132, type, perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi).
% 3.07/1.77 thf(func_def_133, type, perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi).
% 3.07/1.77 thf(func_def_134, type, perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name).
% 3.07/1.77 thf(func_def_135, type, perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi).
% 3.07/1.77 thf(func_def_136, type, perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep).
% 3.07/1.77 thf(func_def_137, type, perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes).
% 3.07/1.77 thf(func_def_138, type, perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject).
% 3.07/1.77 thf(func_def_139, type, perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name).
% 3.07/1.77 thf(func_def_140, type, perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi).
% 3.07/1.77 thf(func_def_141, type, perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep).
% 3.07/1.77 thf(func_def_142, type, perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes).
% 3.07/1.77 thf(func_def_143, type, perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject).
% 3.07/1.77 thf(func_def_144, type, perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit).
% 3.07/1.77 thf(func_def_145, type, perm_name_set_name: list_P227219501e_name > set_name > set_name).
% 3.07/1.77 thf(func_def_146, type, perm_name_set_pi: list_P227219501e_name > set_pi > set_pi).
% 3.07/1.77 thf(func_def_147, type, perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep).
% 3.07/1.77 thf(func_def_148, type, perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes).
% 3.07/1.77 thf(func_def_149, type, perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject).
% 3.07/1.77 thf(func_def_150, type, perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi).
% 3.07/1.77 thf(func_def_151, type, swap_name2: produc367475239e_name > name > name).
% 3.07/1.77 thf(func_def_152, type, produc1570949143e_name: name > name > produc367475239e_name).
% 3.07/1.77 thf(func_def_153, type, product_Pair_name_pi: name > pi > product_prod_name_pi).
% 3.07/1.77 thf(func_def_154, type, produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi).
% 3.07/1.77 thf(func_def_155, type, produc1785453612t_unit: name > product_unit > produc546891580t_unit).
% 3.07/1.77 thf(func_def_156, type, product_Pair_pi_name: pi > name > product_prod_pi_name).
% 3.07/1.77 thf(func_def_157, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 3.07/1.77 thf(func_def_158, type, produc1831798878t_unit: pi > product_unit > produc1028309998t_unit).
% 3.07/1.77 thf(func_def_159, type, produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep).
% 3.07/1.77 thf(func_def_160, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 3.07/1.77 thf(func_def_161, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 3.07/1.77 thf(func_def_162, type, produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep).
% 3.07/1.77 thf(func_def_163, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 3.07/1.77 thf(func_def_164, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 3.07/1.77 thf(func_def_165, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 3.07/1.77 thf(func_def_166, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 3.07/1.77 thf(func_def_167, type, produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep).
% 3.07/1.77 thf(func_def_168, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 3.07/1.77 thf(func_def_169, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 3.07/1.77 thf(func_def_170, type, produc421428802t_name: product_unit > name > produc135724498t_name).
% 3.07/1.77 thf(func_def_171, type, produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi).
% 3.07/1.77 thf(func_def_172, type, produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit).
% 3.07/1.77 thf(func_def_173, type, product_Unity: product_unit).
% 3.07/1.77 thf(func_def_174, type, eqvt_name: set_Pr443758855e_name > $o).
% 3.07/1.77 thf(func_def_175, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 3.07/1.77 thf(func_def_176, type, eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o).
% 3.07/1.77 thf(func_def_177, type, eqvt_Late_freeRes: set_Pr1780909331reeRes > $o).
% 3.07/1.77 thf(func_def_178, type, eqvt_Late_subject: set_Pr806375235ubject > $o).
% 3.07/1.77 thf(func_def_179, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 3.07/1.77 thf(func_def_180, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 3.07/1.77 thf(func_def_181, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 3.07/1.77 thf(func_def_182, type, member_name: name > set_name > $o).
% 3.07/1.77 thf(func_def_183, type, member_pi: pi > set_pi > $o).
% 3.07/1.77 thf(func_def_184, type, member_pi_Rep: pi_Rep > set_pi_Rep > $o).
% 3.07/1.77 thf(func_def_185, type, member_Late_freeRes: late_freeRes > set_Late_freeRes > $o).
% 3.07/1.77 thf(func_def_186, type, member_Late_subject: late_subject > set_Late_subject > $o).
% 3.07/1.77 thf(func_def_187, type, member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $o).
% 3.07/1.77 thf(func_def_188, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.07/1.77 thf(func_def_189, type, member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o).
% 3.07/1.77 thf(func_def_190, type, member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o).
% 3.07/1.77 thf(func_def_191, type, member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $o).
% 3.07/1.77 thf(func_def_192, type, p: pi).
% 3.07/1.77 thf(func_def_193, type, pq: pi).
% 3.07/1.77 thf(func_def_194, type, p2: pi).
% 3.07/1.77 thf(func_def_195, type, q: pi).
% 3.07/1.77 thf(func_def_196, type, q2: pi).
% 3.07/1.77 thf(func_def_197, type, rel: set_Pr1834926343_pi_pi).
% 3.07/1.77 thf(func_def_198, type, aa: late_subject).
% 3.07/1.77 thf(func_def_199, type, ab: name).
% 3.07/1.77 thf(func_def_200, type, b: name).
% 3.07/1.77 thf(func_def_201, type, c: name).
% 3.07/1.77 thf(func_def_202, type, x: name).
% 3.07/1.77 thf(func_def_203, type, xPQ: pi).
% 3.07/1.77 thf(func_def_204, type, y: name).
% 3.07/1.77 thf(func_def_205, type, ya: name).
% 3.07/1.77 thf(func_def_229, type, ph1: !>[X0: $tType]:(X0)).
% 3.07/1.77 thf(func_def_230, type, sK2: name > name).
% 3.07/1.77 thf(func_def_231, type, sK3: product_unit > name).
% 3.07/1.77 thf(func_def_232, type, sK4: pi > name).
% 3.07/1.77 thf(func_def_233, type, sK5: produc1141751126_pi_pi > name).
% 3.07/1.77 thf(f1839,plain,(
% 3.07/1.77 $false),
% 3.07/1.77 inference(equality_resolution,[status(thm)],[f1838])).
% 3.07/1.77 thf(f1838,plain,(
% 3.07/1.77 ( ! [X2 : name,X1 : name] : (((late_OutputR @ ab @ x) != (late_OutputR @ X1 @ X2))) )),
% 3.07/1.77 inference(equality_proxy_clausification,[status(thm)],[f1835])).
% 3.07/1.77 thf(f1835,plain,(
% 3.07/1.77 ( ! [X2 : name,X1 : name] : (($false = ((late_OutputR @ ab @ x) = (late_OutputR @ X1 @ X2)))) )),
% 3.07/1.77 inference(not_proxy_clausification,[status(thm)],[f1834])).
% 3.07/1.77 thf(f1834,plain,(
% 3.07/1.77 ( ! [X2 : name,X1 : name] : (($true = (~ ((late_OutputR @ ab @ x) = (late_OutputR @ X1 @ X2))))) )),
% 3.07/1.77 inference(beta_eta_normalization,[status(thm)],[f1833])).
% 3.07/1.77 thf(f1833,plain,(
% 3.07/1.77 ( ! [X2 : name,X1 : name] : (($true = ((^[Y0 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ X1 @ Y0)))) @ X2))) )),
% 3.07/1.77 inference(pi_clausification,[status(thm)],[f1832])).
% 3.07/1.77 thf(f1832,plain,(
% 3.07/1.77 ( ! [X1 : name] : (((!! @ name @ (^[Y0 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ X1 @ Y0))))) = $true)) )),
% 3.07/1.77 inference(beta_eta_normalization,[status(thm)],[f1831])).
% 3.07/1.77 thf(f1831,plain,(
% 3.07/1.77 ( ! [X1 : name] : ((((^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y0 @ Y1)))))) @ X1) = $true)) )),
% 3.07/1.77 inference(pi_clausification,[status(thm)],[f1499])).
% 3.07/1.77 thf(f1499,plain,(
% 3.07/1.77 ($true = (!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ ((late_OutputR @ ab @ x) = (late_OutputR @ Y0 @ Y1))))))))),
% 3.07/1.77 inference(definition_unfolding,[status(thm)],[f1418,f1230])).
% 3.07/1.77 thf(f1230,plain,(
% 3.07/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 3.07/1.77 inference(cnf_transformation,[status(thm)],[f611])).
% 3.07/1.77 thf(f611,plain,(
% 3.07/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 3.07/1.77 inference(fool_elimination,[status(thm)],[f2])).
% 3.07/1.77 thf(f2,axiom,(
% 3.07/1.77 ((late_OutputR @ ab @ x) = late_TauR)),
% 3.07/1.77 file('/export/starexec/sandbox2/tmp/tmp.dCSmdHGfAN/DTF2THF_8414.p',fact_1_cComm1_Ohyps_I9_J)).
% 3.07/1.77 thf(f1418,plain,(
% 3.07/1.77 ($true = (!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ (late_TauR = (late_OutputR @ Y0 @ Y1))))))))),
% 3.07/1.77 inference(cnf_transformation,[status(thm)],[f590])).
% 3.07/1.77 thf(f590,plain,(
% 3.07/1.77 ($true = (!! @ name @ (^[Y0 : name]: (!! @ name @ (^[Y1 : name]: (~ (late_TauR = (late_OutputR @ Y0 @ Y1))))))))),
% 3.07/1.77 inference(fool_elimination,[status(thm)],[f589])).
% 3.07/1.77 thf(f589,plain,(
% 3.07/1.77 ! [X0 : name,X1 : name] : (late_TauR != (late_OutputR @ X1 @ X0))),
% 3.07/1.77 inference(rectify,[status(thm)],[f325])).
% 3.07/1.77 thf(f325,axiom,(
% 3.07/1.77 ! [X87 : name,X86 : name] : (late_TauR != (late_OutputR @ X86 @ X87))),
% 3.07/1.77 file('/export/starexec/sandbox2/tmp/tmp.dCSmdHGfAN/DTF2THF_8414.p',fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J)).
% 3.07/1.77 % SZS output end Proof for DTF2THF_8414
% 3.07/1.77 % (8632)------------------------------
% 3.07/1.77 % (8632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.77 % (8632)Termination reason: Refutation
% 3.07/1.77
% 3.07/1.77 % (8632)Memory used [KB]: 8443
% 3.07/1.77 % (8632)Time elapsed: 0.119 s
% 3.07/1.77 % (8632)Instructions burned: 424 (million)
% 3.07/1.77 % (8632)------------------------------
% 3.07/1.77 % (8632)------------------------------
% 3.07/1.77 % (8620)Success in time 0.195 s
%------------------------------------------------------------------------------