%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP190^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Theorem 3.14s 1.95s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 288 ( 6 ~; 0 |; 0 &; 259 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 41 ( 40 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 159 ( 155 usr; 19 con; 0-5 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 35 ( 15 ^; 20 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
name: $tType ).
thf(type_def_6,type,
pi: $tType ).
thf(type_def_8,type,
list_P227219501e_name: $tType ).
thf(type_def_9,type,
produc367475239e_name: $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_l1406151091e_name: $tType ).
thf(type_def_23,type,
produc2008547984reeRes: $tType ).
thf(type_def_24,type,
produc865358760ubject: $tType ).
thf(type_def_25,type,
product_prod_pi_pi: $tType ).
thf(type_def_26,type,
produc2052722628s_name: $tType ).
thf(type_def_27,type,
produc992857746Res_pi: $tType ).
thf(type_def_28,type,
produc1357834675reeRes: $tType ).
thf(type_def_29,type,
produc214645451ubject: $tType ).
thf(type_def_30,type,
produc1998742700t_name: $tType ).
thf(type_def_31,type,
produc140253050ect_pi: $tType ).
thf(type_def_32,type,
produc355105483reeRes: $tType ).
thf(type_def_33,type,
produc1359399907ubject: $tType ).
thf(type_def_34,type,
late_freeRes_Rep: $tType ).
thf(type_def_35,type,
late_subject_Rep: $tType ).
thf(type_def_36,type,
produc1777919905pi_Rep: $tType ).
thf(type_def_37,type,
produc257012921pi_Rep: $tType ).
thf(type_def_38,type,
set_name: $tType ).
thf(type_def_39,type,
set_pi: $tType ).
thf(type_def_40,type,
set_pi_Rep: $tType ).
thf(type_def_41,type,
set_Late_freeRes: $tType ).
thf(type_def_42,type,
set_Late_subject: $tType ).
thf(type_def_43,type,
set_Pr1834926343_pi_pi: $tType ).
thf(type_def_44,type,
produc1872410278e_name: $tType ).
thf(type_def_45,type,
produc890461031e_name: $tType ).
thf(func_def_0,type,
produc1872410278e_name: $tType ).
thf(func_def_1,type,
produc890461031e_name: $tType ).
thf(func_def_2,type,
list_l1406151091e_name: $tType ).
thf(func_def_3,type,
produc1359399907ubject: $tType ).
thf(func_def_4,type,
produc355105483reeRes: $tType ).
thf(func_def_5,type,
produc214645451ubject: $tType ).
thf(func_def_6,type,
produc1357834675reeRes: $tType ).
thf(func_def_7,type,
produc257012921pi_Rep: $tType ).
thf(func_def_8,type,
produc1777919905pi_Rep: $tType ).
thf(func_def_9,type,
list_name_noption_pi: $tType ).
thf(func_def_10,type,
list_P227219501e_name: $tType ).
thf(func_def_11,type,
produc1998742700t_name: $tType ).
thf(func_def_12,type,
produc2052722628s_name: $tType ).
thf(func_def_13,type,
produc865358760ubject: $tType ).
thf(func_def_14,type,
produc2008547984reeRes: $tType ).
thf(func_def_15,type,
produc140253050ect_pi: $tType ).
thf(func_def_16,type,
produc992857746Res_pi: $tType ).
thf(func_def_17,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_18,type,
produc367475239e_name: $tType ).
thf(func_def_19,type,
product_prod_pi_pi: $tType ).
thf(func_def_20,type,
list_Late_subject: $tType ).
thf(func_def_21,type,
list_Late_freeRes: $tType ).
thf(func_def_22,type,
set_Late_subject: $tType ).
thf(func_def_23,type,
set_Late_freeRes: $tType ).
thf(func_def_24,type,
list_pi_Rep: $tType ).
thf(func_def_25,type,
late_residual_Rep: $tType ).
thf(func_def_26,type,
noption_pi: $tType ).
thf(func_def_27,type,
late_subject_Rep: $tType ).
thf(func_def_28,type,
late_freeRes_Rep: $tType ).
thf(func_def_29,type,
set_pi_Rep: $tType ).
thf(func_def_30,type,
list_name: $tType ).
thf(func_def_31,type,
set_name: $tType ).
thf(func_def_32,type,
list_pi: $tType ).
thf(func_def_33,type,
late_residual: $tType ).
thf(func_def_34,type,
late_subject: $tType ).
thf(func_def_35,type,
late_freeRes: $tType ).
thf(func_def_36,type,
set_pi: $tType ).
thf(func_def_37,type,
pi_Rep: $tType ).
thf(func_def_38,type,
name: $tType ).
thf(func_def_39,type,
pi: $tType ).
thf(func_def_40,type,
input: name > name > pi > pi ).
thf(func_def_41,type,
par: pi > pi > pi ).
thf(func_def_42,type,
res: name > pi > pi ).
thf(func_def_43,type,
name_prm_name: list_P227219501e_name > name > name ).
thf(func_def_44,type,
swap_name: produc367475239e_name > name > name ).
thf(func_def_45,type,
subs: pi > name > name > pi ).
thf(func_def_46,type,
if_name: $o > name > name > name ).
thf(func_def_47,type,
if_pi: $o > pi > pi > pi ).
thf(func_def_48,type,
if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep ).
thf(func_def_49,type,
if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes ).
thf(func_def_50,type,
if_Late_subject: $o > late_subject > late_subject > late_subject ).
thf(func_def_51,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_52,type,
late_TauR: late_freeRes ).
thf(func_def_53,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_54,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_55,type,
late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep ).
thf(func_def_56,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_57,type,
late_InputS: name > late_subject ).
thf(func_def_58,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_59,type,
cons_name_noption_pi: ( name > noption_pi ) > list_name_noption_pi > list_name_noption_pi ).
thf(func_def_60,type,
cons_name: name > list_name > list_name ).
thf(func_def_61,type,
cons_pi: pi > list_pi > list_pi ).
thf(func_def_62,type,
cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep ).
thf(func_def_63,type,
cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes ).
thf(func_def_64,type,
cons_Late_subject: late_subject > list_Late_subject > list_Late_subject ).
thf(func_def_65,type,
cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name ).
thf(func_def_66,type,
cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).
thf(func_def_67,type,
nil_li29751603e_name: list_l1406151091e_name ).
thf(func_def_68,type,
nil_Pr743626285e_name: list_P227219501e_name ).
thf(func_def_69,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_70,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_71,type,
fresh_name_name: name > name > $o ).
thf(func_def_72,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_73,type,
fresh_name_pi_Rep: name > pi_Rep > $o ).
thf(func_def_74,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_75,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_76,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_77,type,
fresh_1135477378ion_pi: name > list_name_noption_pi > $o ).
thf(func_def_78,type,
fresh_name_list_name: name > list_name > $o ).
thf(func_def_79,type,
fresh_name_list_pi: name > list_pi > $o ).
thf(func_def_80,type,
fresh_1981651763reeRes: name > list_Late_freeRes > $o ).
thf(func_def_81,type,
fresh_838462539ubject: name > list_Late_subject > $o ).
thf(func_def_82,type,
fresh_922791155e_name: name > list_P227219501e_name > $o ).
thf(func_def_83,type,
fresh_441084397e_name: name > produc367475239e_name > $o ).
thf(func_def_84,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(func_def_85,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(func_def_86,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(func_def_87,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(func_def_88,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(func_def_89,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(func_def_90,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(func_def_91,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(func_def_92,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(func_def_93,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(func_def_94,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
thf(func_def_95,type,
perm_n382765978reeRes: list_P227219501e_name > ( name > late_freeRes ) > name > late_freeRes ).
thf(func_def_96,type,
perm_n1387060402ubject: list_P227219501e_name > ( name > late_subject ) > name > late_subject ).
thf(func_def_97,type,
perm_n1667196784ion_pi: list_P227219501e_name > ( name > noption_pi ) > name > noption_pi ).
thf(func_def_98,type,
perm_n1333244520reeRes: list_P227219501e_name > ( pi > late_freeRes ) > pi > late_freeRes ).
thf(func_def_99,type,
perm_n190055296ubject: list_P227219501e_name > ( pi > late_subject ) > pi > late_subject ).
thf(func_def_100,type,
perm_n1841560599reeRes: list_P227219501e_name > ( pi_Rep > late_freeRes ) > pi_Rep > late_freeRes ).
thf(func_def_101,type,
perm_n698371375ubject: list_P227219501e_name > ( pi_Rep > late_subject ) > pi_Rep > late_subject ).
thf(func_def_102,type,
perm_n1446290985reeRes: list_P227219501e_name > ( late_freeRes > late_freeRes ) > late_freeRes > late_freeRes ).
thf(func_def_103,type,
perm_n303101761ubject: list_P227219501e_name > ( late_freeRes > late_subject ) > late_freeRes > late_subject ).
thf(func_def_104,type,
perm_n443561793reeRes: list_P227219501e_name > ( late_subject > late_freeRes ) > late_subject > late_freeRes ).
thf(func_def_105,type,
perm_n1447856217ubject: list_P227219501e_name > ( late_subject > late_subject ) > late_subject > late_subject ).
thf(func_def_106,type,
perm_name_o: list_P227219501e_name > $o > $o ).
thf(func_def_107,type,
perm_name_name: list_P227219501e_name > name > name ).
thf(func_def_108,type,
perm_name_pi: list_P227219501e_name > pi > pi ).
thf(func_def_109,type,
perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep ).
thf(func_def_110,type,
perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes ).
thf(func_def_111,type,
perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep ).
thf(func_def_112,type,
perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).
thf(func_def_113,type,
perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep ).
thf(func_def_114,type,
perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject ).
thf(func_def_115,type,
perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep ).
thf(func_def_116,type,
perm_name_list_name: list_P227219501e_name > list_name > list_name ).
thf(func_def_117,type,
perm_name_list_pi: list_P227219501e_name > list_pi > list_pi ).
thf(func_def_118,type,
perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).
thf(func_def_119,type,
perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).
thf(func_def_120,type,
perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).
thf(func_def_121,type,
perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).
thf(func_def_122,type,
perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).
thf(func_def_123,type,
perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).
thf(func_def_124,type,
perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
thf(func_def_125,type,
perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
thf(func_def_126,type,
perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
thf(func_def_127,type,
perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
thf(func_def_128,type,
perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
thf(func_def_129,type,
perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
thf(func_def_130,type,
perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
thf(func_def_131,type,
perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
thf(func_def_132,type,
perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
thf(func_def_133,type,
perm_name_set_name: list_P227219501e_name > set_name > set_name ).
thf(func_def_134,type,
perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
thf(func_def_135,type,
perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
thf(func_def_136,type,
perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
thf(func_def_137,type,
perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
thf(func_def_138,type,
perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
thf(func_def_139,type,
swap_name2: produc367475239e_name > name > name ).
thf(func_def_140,type,
produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
thf(func_def_141,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(func_def_142,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(func_def_143,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(func_def_144,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(func_def_145,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(func_def_146,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(func_def_147,type,
produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
thf(func_def_148,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(func_def_149,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(func_def_150,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(func_def_151,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(func_def_152,type,
produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
thf(func_def_153,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(func_def_154,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(func_def_155,type,
produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
thf(func_def_156,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(func_def_157,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(func_def_158,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(func_def_159,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(func_def_160,type,
member_name: name > set_name > $o ).
thf(func_def_161,type,
member_pi: pi > set_pi > $o ).
thf(func_def_162,type,
member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
thf(func_def_163,type,
member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
thf(func_def_164,type,
member_Late_subject: late_subject > set_Late_subject > $o ).
thf(func_def_165,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_166,type,
p: pi ).
thf(func_def_167,type,
p2: pi ).
thf(func_def_168,type,
pxQ: pi ).
thf(func_def_169,type,
q: pi ).
thf(func_def_170,type,
q2: pi ).
thf(func_def_171,type,
q_a: pi ).
thf(func_def_172,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_173,type,
alpha: late_freeRes ).
thf(func_def_174,type,
aa: name ).
thf(func_def_175,type,
b: name ).
thf(func_def_176,type,
x: name ).
thf(func_def_177,type,
y: name ).
thf(func_def_178,type,
z: name ).
thf(func_def_201,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_202,type,
sK2: name > name ).
thf(func_def_203,type,
sK3: late_subject > name ).
thf(func_def_204,type,
sK4: late_freeRes > name ).
thf(func_def_205,type,
sK5: pi > name ).
thf(func_def_206,type,
sK6: produc367475239e_name > list_P227219501e_name ).
thf(func_def_207,type,
sK7: ( list_P227219501e_name > $o ) > list_P227219501e_name ).
thf(func_def_208,type,
sK8: produc367475239e_name > name ).
thf(func_def_209,type,
sK9: produc367475239e_name > name ).
thf(func_def_210,type,
sK10: product_prod_pi_pi > pi ).
thf(func_def_211,type,
sK11: product_prod_pi_pi > pi ).
thf(func_def_212,type,
sK12: product_prod_pi_pi > pi ).
thf(func_def_213,type,
sK13: product_prod_pi_pi > pi ).
thf(func_def_214,type,
sK14: produc367475239e_name > name ).
thf(func_def_215,type,
sK15: produc367475239e_name > name ).
thf(func_def_216,type,
sK16: name > name ).
thf(f2890,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2889]) ).
thf(f2889,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f2888]) ).
thf(f2888,plain,
( $true = ( ~ $true ) ),
inference(backward_demodulation,[status(thm)],[f1435,f2885]) ).
thf(f2885,plain,
! [X0: list_P227219501e_name] :
( $true
= ( late_transitions @ ( perm_name_pi @ X0 @ q ) @ ( perm_n414416632sidual @ X0 @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ) ) ),
inference(boolean_simplification,[status(thm)],[f2878]) ).
thf(f2878,plain,
! [X0: list_P227219501e_name] :
( $true
= ( $true
=> ( late_transitions @ ( perm_name_pi @ X0 @ q ) @ ( perm_n414416632sidual @ X0 @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ) ) ) ),
inference(superposition,[status(thm)],[f2871,f1339]) ).
thf(f1339,plain,
( ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f524]) ).
thf(f524,plain,
( ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) )
= $true ),
inference(fool_elimination,[status(thm)],[f523]) ).
thf(f523,plain,
late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ),
file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_6_cOpen_Ohyps_I1_J) ).
thf(f2871,plain,
! [X2: list_P227219501e_name,X3: pi,X1: late_residual] :
( $true
= ( ( late_transitions @ X3 @ X1 )
=> ( late_transitions @ ( perm_name_pi @ X2 @ X3 ) @ ( perm_n414416632sidual @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2870]) ).
thf(f2870,plain,
! [X2: list_P227219501e_name,X3: pi,X1: late_residual] :
( $true
= ( ^ [Y0: pi] :
( ( late_transitions @ Y0 @ X1 )
=> ( late_transitions @ ( perm_name_pi @ X2 @ Y0 ) @ ( perm_n414416632sidual @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f2866]) ).
thf(f2866,plain,
! [X2: list_P227219501e_name,X1: late_residual] :
( $true
= ( !! @ pi
@ ^ [Y0: pi] :
( ( late_transitions @ Y0 @ X1 )
=> ( late_transitions @ ( perm_name_pi @ X2 @ Y0 ) @ ( perm_n414416632sidual @ X2 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2858]) ).
thf(f2858,plain,
! [X2: list_P227219501e_name,X1: late_residual] :
( $true
= ( ^ [Y0: list_P227219501e_name] :
( !! @ pi
@ ^ [Y1: pi] :
( ( late_transitions @ Y1 @ X1 )
=> ( late_transitions @ ( perm_name_pi @ Y0 @ Y1 ) @ ( perm_n414416632sidual @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2854]) ).
thf(f2854,plain,
! [X1: late_residual] :
( $true
= ( !! @ list_P227219501e_name
@ ^ [Y0: list_P227219501e_name] :
( !! @ pi
@ ^ [Y1: pi] :
( ( late_transitions @ Y1 @ X1 )
=> ( late_transitions @ ( perm_name_pi @ Y0 @ Y1 ) @ ( perm_n414416632sidual @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2853]) ).
thf(f2853,plain,
! [X1: late_residual] :
( ( ^ [Y0: late_residual] :
( !! @ list_P227219501e_name
@ ^ [Y1: list_P227219501e_name] :
( !! @ pi
@ ^ [Y2: pi] :
( ( late_transitions @ Y2 @ Y0 )
=> ( late_transitions @ ( perm_name_pi @ Y1 @ Y2 ) @ ( perm_n414416632sidual @ Y1 @ Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1388]) ).
thf(f1388,plain,
( $true
= ( !! @ late_residual
@ ^ [Y0: late_residual] :
( !! @ list_P227219501e_name
@ ^ [Y1: list_P227219501e_name] :
( !! @ pi
@ ^ [Y2: pi] :
( ( late_transitions @ Y2 @ Y0 )
=> ( late_transitions @ ( perm_name_pi @ Y1 @ Y2 ) @ ( perm_n414416632sidual @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f578]) ).
thf(f578,plain,
( $true
= ( !! @ late_residual
@ ^ [Y0: late_residual] :
( !! @ list_P227219501e_name
@ ^ [Y1: list_P227219501e_name] :
( !! @ pi
@ ^ [Y2: pi] :
( ( late_transitions @ Y2 @ Y0 )
=> ( late_transitions @ ( perm_name_pi @ Y1 @ Y2 ) @ ( perm_n414416632sidual @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f577]) ).
thf(f577,plain,
! [X0: pi,X1: list_P227219501e_name,X2: late_residual] :
( ( late_transitions @ X0 @ X2 )
=> ( late_transitions @ ( perm_name_pi @ X1 @ X0 ) @ ( perm_n414416632sidual @ X1 @ X2 ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
! [X3: pi,X5: list_P227219501e_name,X4: late_residual] :
( ( late_transitions @ X3 @ X4 )
=> ( late_transitions @ ( perm_name_pi @ X5 @ X3 ) @ ( perm_n414416632sidual @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_41_eqvt) ).
thf(f1435,plain,
( ( ~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1083,f1149]) ).
thf(f1149,plain,
aa = b,
inference(cnf_transformation,[status(thm)],[f778]) ).
thf(f778,plain,
aa = b,
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
aa = b,
file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062) ).
thf(f1083,plain,
( $true
= ( ~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f574,plain,
( $true
= ( ~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f573]) ).
thf(f573,plain,
~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
inference(rectify,[status(thm)],[f362]) ).
thf(f362,negated_conjecture,
~ ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
inference(negated_conjecture,[status(cth)],[f361]) ).
thf(f361,conjecture,
late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ),
file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP190^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 08:29:51 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP190^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_808__3416684_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : Strong_Late_Sim_SC/prob_808__3416684_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 540 ( 225 unt; 179 typ; 0 def)
% 0.19/0.46 % Number of atoms : 861 ( 411 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 16 ( 2 avg)
% 0.19/0.46 % Number of connectives : 3945 ( 127 ~; 1 |; 51 &;3390 @)
% 0.19/0.46 % ( 0 <=>; 376 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 27 ( 7 avg)
% 0.19/0.46 % Number of types : 41 ( 40 usr)
% 0.19/0.46 % Number of type conns : 359 ( 359 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 142 ( 139 usr; 18 con; 0-5 aty)
% 0.19/0.46 % Number of variables : 1267 ( 6 ^;1249 !; 12 ?;1267 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:25.375
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (40)
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46 produc1872410278e_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46 produc890461031e_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 0.19/0.46 list_l1406151091e_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46 produc1359399907ubject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 produc355105483reeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46 produc214645451ubject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 produc1357834675reeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46 produc257012921pi_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46 produc1777919905pi_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.19/0.46 list_name_noption_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46 list_P227219501e_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.19/0.46 produc1998742700t_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.19/0.46 produc2052722628s_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46 produc865358760ubject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 produc2008547984reeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.19/0.46 produc140253050ect_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.19/0.46 produc992857746Res_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46 set_Pr1834926343_pi_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
% 0.19/0.46 produc367475239e_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46 product_prod_pi_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46 list_Late_subject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 list_Late_freeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46 set_Late_subject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 set_Late_freeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 0.19/0.46 list_pi_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 0.19/0.46 late_residual_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.19/0.46 noption_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 0.19/0.46 late_subject_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 0.19/0.46 late_freeRes_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 0.19/0.46 set_pi_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 0.19/0.46 list_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 0.19/0.46 set_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 0.19/0.46 list_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.19/0.46 late_residual: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.19/0.46 late_subject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 late_freeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
% 0.19/0.46 set_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Agent__Opi____Rep,type,
% 0.19/0.46 pi_Rep: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Agent__Oname,type,
% 0.19/0.46 name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Agent__Opi,type,
% 0.19/0.46 pi: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (139)
% 0.19/0.46 thf(sy_c_Agent_Opi_OInput,type,
% 0.19/0.46 input: name > name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OPar,type,
% 0.19/0.46 par: pi > pi > pi ).
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% 0.19/0.46 perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46 perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.19/0.46 perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.19/0.46 perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
% 0.19/0.46 perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.19/0.46 perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
% 0.19/0.46 perm_name_set_name: list_P227219501e_name > set_name > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
% 0.19/0.46 perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 0.19/0.46 perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46 perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.19/0.46 perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
% 0.19/0.46 swap_name2: produc367475239e_name > name > name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46 produc1069608854e_name: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > produc1872410278e_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.19/0.46 produc1570949143e_name: name > name > produc367475239e_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.19/0.46 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.19/0.46 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.19/0.46 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.19/0.46 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi____Rep,type,
% 0.19/0.46 produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 0.19/0.46 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.19/0.46 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.19/0.46 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi____Rep,type,
% 0.19/0.46 produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.19/0.46 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
% 0.19/0.46 produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.19/0.46 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.19/0.46 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.19/0.46 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Agent__Oname,type,
% 0.19/0.46 member_name: name > set_name > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Agent__Opi,type,
% 0.19/0.46 member_pi: pi > set_pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Agent__Opi____Rep,type,
% 0.19/0.46 member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Late____Semantics__Osubject,type,
% 0.19/0.46 member_Late_subject: late_subject > set_Late_subject > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.19/0.46 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_P,type,
% 0.19/0.46 p: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_P_H____,type,
% 0.19/0.46 p2: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_PxQ____,type,
% 0.19/0.46 pxQ: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Q,type,
% 0.19/0.46 q: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Q_H____,type,
% 0.19/0.46 q2: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Q_Ha____,type,
% 0.19/0.46 q_a: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Rel,type,
% 0.19/0.46 rel: set_Pr1834926343_pi_pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060alpha_062____,type,
% 0.19/0.46 alpha: late_freeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_aa____,type,
% 0.19/0.46 aa: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_b____,type,
% 0.19/0.46 b: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_x,type,
% 0.19/0.46 x: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_y____,type,
% 0.19/0.46 y: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_z____,type,
% 0.19/0.46 z: name ).
% 0.19/0.46
% 0.19/0.46 % Relevant facts (349)
% 0.19/0.46 thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062,axiom,
% 0.19/0.46 aa = b ).
% 0.19/0.46
% 0.19/0.46 % \<open>a = b\<close>
% 0.19/0.46 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 0.19/0.46 b != x ).
% 0.19/0.46
% 0.19/0.46 % cOpen.hyps(2)
% 0.19/0.46 thf(fact_2_cClose1_Ohyps_I10_J,axiom,
% 0.19/0.46 z != aa ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(10)
% 0.19/0.46 thf(fact_3_cClose1_Ohyps_I6_J,axiom,
% 0.19/0.46 y != z ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(6)
% 0.19/0.46 thf(fact_4_cClose1_Ohyps_I5_J,axiom,
% 0.19/0.46 y != aa ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(5)
% 0.19/0.46 thf(fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.19/0.46 z != x ).
% 0.19/0.46
% 0.19/0.46 % \<open>z \<noteq> x\<close>
% 0.19/0.46 thf(fact_6_cOpen_Ohyps_I1_J,axiom,
% 0.19/0.46 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ).
% 0.19/0.46
% 0.19/0.46 % cOpen.hyps(1)
% 0.19/0.46 thf(fact_7_cOpen_Ohyps_I3_J,axiom,
% 0.19/0.46 ( ( late_BoundOutputS @ aa )
% 0.19/0.46 = ( late_BoundOutputS @ b ) ) ).
% 0.19/0.46
% 0.19/0.46 % cOpen.hyps(3)
% 0.19/0.46 thf(fact_8_cClose1_Ohyps_I14_J,axiom,
% 0.19/0.46 alpha = late_TauR ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(14)
% 0.19/0.46 thf(fact_9_cClose1_Ohyps_I13_J,axiom,
% 0.19/0.46 fresh_name_name @ z @ x ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(13)
% 0.19/0.46 thf(fact_10_perm__swap_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_subject] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(1)
% 0.19/0.46 thf(fact_11_perm__swap_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(1)
% 0.19/0.46 thf(fact_12_perm__swap_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(1)
% 0.19/0.46 thf(fact_13_perm__swap_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: name] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(1)
% 0.19/0.46 thf(fact_14_perm__swap_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(1)
% 0.19/0.46 thf(fact_15_name__id,axiom,
% 0.19/0.46 ! [A: name,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_id
% 0.19/0.46 thf(fact_16_name__id,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_id
% 0.19/0.46 thf(fact_17_name__id,axiom,
% 0.19/0.46 ! [A: name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_id
% 0.19/0.46 thf(fact_18_name__id,axiom,
% 0.19/0.46 ! [A: name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_id
% 0.19/0.46 thf(fact_19_name__id,axiom,
% 0.19/0.46 ! [A: name,X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_id
% 0.19/0.46 thf(fact_20_name__swap,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap
% 0.19/0.46 thf(fact_21_name__swap,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap
% 0.19/0.46 thf(fact_22_name__swap,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap
% 0.19/0.46 thf(fact_23_name__swap,axiom,
% 0.19/0.46 ! [A: name,B: name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap
% 0.19/0.46 thf(fact_24_name__swap,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap
% 0.19/0.46 thf(fact_25_name__swap__bij,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_subject] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap_bij
% 0.19/0.46 thf(fact_26_name__swap__bij,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap_bij
% 0.19/0.46 thf(fact_27_name__swap__bij,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap_bij
% 0.19/0.46 thf(fact_28_name__swap__bij,axiom,
% 0.19/0.46 ! [A: name,B: name,X: name] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap_bij
% 0.19/0.46 thf(fact_29_name__swap__bij,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_swap_bij
% 0.19/0.46 thf(fact_30_pt__name1,axiom,
% 0.19/0.46 ! [X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % pt_name1
% 0.19/0.46 thf(fact_31_pt__name1,axiom,
% 0.19/0.46 ! [X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % pt_name1
% 0.19/0.46 thf(fact_32_pt__name1,axiom,
% 0.19/0.46 ! [X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % pt_name1
% 0.19/0.46 thf(fact_33_pt__name1,axiom,
% 0.19/0.46 ! [X: name] :
% 0.19/0.46 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % pt_name1
% 0.19/0.46 thf(fact_34_pt__name1,axiom,
% 0.19/0.46 ! [X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % pt_name1
% 0.19/0.46 thf(fact_35__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 0.19/0.46 y != x ).
% 0.19/0.46
% 0.19/0.46 % \<open>y \<noteq> x\<close>
% 0.19/0.46 thf(fact_36_perm__swap_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_subject] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(2)
% 0.19/0.46 thf(fact_37_perm__swap_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: late_freeRes] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(2)
% 0.19/0.46 thf(fact_38_perm__swap_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi_Rep] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(2)
% 0.19/0.46 thf(fact_39_perm__swap_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: name] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(2)
% 0.19/0.46 thf(fact_40_perm__swap_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name,X: pi] :
% 0.19/0.46 ( ( 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 ) )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % perm_swap(2)
% 0.19/0.46 thf(fact_41_eqvt,axiom,
% 0.19/0.46 ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( late_transitions @ X1 @ X2 )
% 0.19/0.46 => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eqvt
% 0.19/0.46 thf(fact_42__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 0.19/0.46 fresh_name_pi @ z @ q ).
% 0.19/0.46
% 0.19/0.46 % \<open>z \<sharp> Q\<close>
% 0.19/0.46 thf(fact_43_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.19/0.46 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.19/0.46 ( ( ( late_OutputR @ X2 @ X1 )
% 0.19/0.46 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.19/0.46 = ( ( X2 = Y2 )
% 0.19/0.46 & ( X1 = Y1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.freeRes.inject
% 0.19/0.46 thf(fact_44_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.19/0.46 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.19/0.46 ( ( ( late_OutputR @ X11 @ X12 )
% 0.19/0.46 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.19/0.46 = ( ( X11 = Y11 )
% 0.19/0.46 & ( X12 = Y12 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics1.freeRes.inject
% 0.19/0.46 thf(fact_45_cClose1_Ohyps_I11_J,axiom,
% 0.19/0.46 fresh_name_pi @ z @ p2 ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(11)
% 0.19/0.46 thf(fact_46_cClose1_Ohyps_I7_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ q2 ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(7)
% 0.19/0.46 thf(fact_47_cClose1_Ohyps_I12_J,axiom,
% 0.19/0.46 fresh_name_name @ y @ x ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(12)
% 0.19/0.46 thf(fact_48_assms_I1_J,axiom,
% 0.19/0.46 fresh_name_pi @ x @ p ).
% 0.19/0.46
% 0.19/0.46 % assms(1)
% 0.19/0.46 thf(fact_49_cClose1_Ohyps_I8_J,axiom,
% 0.19/0.46 fresh_name_pi @ z @ p ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(8)
% 0.19/0.46 thf(fact_50_cClose1_Ohyps_I3_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ p ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(3)
% 0.19/0.46 thf(fact_51_residual__perm__empty,axiom,
% 0.19/0.46 ! [Residual_Rep: late_residual_Rep] :
% 0.19/0.46 ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 0.19/0.46 = Residual_Rep ) ).
% 0.19/0.46
% 0.19/0.46 % residual_perm_empty
% 0.19/0.46 thf(fact_52_subject__perm__empty,axiom,
% 0.19/0.46 ! [Subject_Rep: late_subject_Rep] :
% 0.19/0.46 ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 0.19/0.46 = Subject_Rep ) ).
% 0.19/0.46
% 0.19/0.46 % subject_perm_empty
% 0.19/0.46 thf(fact_53_freeRes__perm__empty,axiom,
% 0.19/0.46 ! [FreeRes_Rep: late_freeRes_Rep] :
% 0.19/0.46 ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 0.19/0.46 = FreeRes_Rep ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes_perm_empty
% 0.19/0.46 thf(fact_54_pi__perm__empty,axiom,
% 0.19/0.46 ! [Pi_Rep: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 0.19/0.46 = Pi_Rep ) ).
% 0.19/0.46
% 0.19/0.46 % pi_perm_empty
% 0.19/0.46 thf(fact_55_freeRes_Operm_I1_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.46 = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.perm(1)
% 0.19/0.46 thf(fact_56_subject_Operm_I2_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X1: name] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.46 = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.perm(2)
% 0.19/0.46 thf(fact_57_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.19/0.46 ! [X1: name,Y1: name] :
% 0.19/0.46 ( ( ( late_BoundOutputS @ X1 )
% 0.19/0.46 = ( late_BoundOutputS @ Y1 ) )
% 0.19/0.46 = ( X1 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.subject.inject(2)
% 0.19/0.46 thf(fact_58_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.19/0.46 ! [X2: name,Y2: name] :
% 0.19/0.46 ( ( ( late_BoundOutputS @ X2 )
% 0.19/0.46 = ( late_BoundOutputS @ Y2 ) )
% 0.19/0.46 = ( X2 = Y2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics1.subject.inject(2)
% 0.19/0.46 thf(fact_59_freeRes_Operm_I2_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ late_TauR )
% 0.19/0.46 = late_TauR ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.perm(2)
% 0.19/0.46 thf(fact_60_name__fresh,axiom,
% 0.19/0.46 ( fresh_name_name
% 0.19/0.46 = ( ^ [A2: name,B2: name] : ( A2 != B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh
% 0.19/0.46 thf(fact_61_residual_Operm_I2_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 0.19/0.46 ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.46 = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.perm(2)
% 0.19/0.46 thf(fact_62_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: pi_Rep,B: name] :
% 0.19/0.46 ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.19/0.46 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_63_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,B: name] :
% 0.19/0.46 ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 => ( ( fresh_717452603ubject @ B @ X )
% 0.19/0.46 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_64_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,B: name] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.19/0.46 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_65_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: name,B: name] :
% 0.19/0.46 ( ( fresh_name_name @ A @ X )
% 0.19/0.46 => ( ( fresh_name_name @ B @ X )
% 0.19/0.46 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_66_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: pi,B: name] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi @ B @ X )
% 0.19/0.46 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_67_perm__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: name > noption_pi,B: name] :
% 0.19/0.46 ( ( fresh_543891186ion_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_543891186ion_pi @ B @ X )
% 0.19/0.46 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_fresh_fresh
% 0.19/0.46 thf(fact_68_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: pi_Rep,B: name] :
% 0.19/0.46 ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi_Rep @ B @ X )
% 0.19/0.46 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_69_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,B: name] :
% 0.19/0.46 ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 => ( ( fresh_717452603ubject @ B @ X )
% 0.19/0.46 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_70_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,B: name] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ B @ X )
% 0.19/0.46 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_71_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: name,B: name] :
% 0.19/0.46 ( ( fresh_name_name @ A @ X )
% 0.19/0.46 => ( ( fresh_name_name @ B @ X )
% 0.19/0.46 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_72_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: pi,B: name] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi @ B @ X )
% 0.19/0.46 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_73_name__fresh__fresh,axiom,
% 0.19/0.46 ! [A: name,X: name > noption_pi,B: name] :
% 0.19/0.46 ( ( fresh_543891186ion_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_543891186ion_pi @ B @ X )
% 0.19/0.46 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 0.19/0.46 = X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_fresh_fresh
% 0.19/0.46 thf(fact_74_cClose1_Ohyps_I9_J,axiom,
% 0.19/0.46 fresh_name_pi @ z @ ( res @ x @ q ) ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(9)
% 0.19/0.46 thf(fact_75_cClose1_Ohyps_I4_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ ( res @ x @ q ) ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(4)
% 0.19/0.46 thf(fact_76_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.46 => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_77_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_78_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_79_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: name] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_name_name @ A @ X )
% 0.19/0.46 => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_80_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_name_pi @ A @ X )
% 0.19/0.46 => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_81_fresh__perm__app,axiom,
% 0.19/0.46 ! [A: name,Pi: list_P227219501e_name,X: name > noption_pi] :
% 0.19/0.46 ( ( fresh_922791155e_name @ A @ Pi )
% 0.19/0.46 => ( ( fresh_543891186ion_pi @ A @ X )
% 0.19/0.46 => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_perm_app
% 0.19/0.46 thf(fact_82_name__exists__fresh,axiom,
% 0.19/0.46 ! [X: late_subject] :
% 0.19/0.46 ~ ! [C: name] :
% 0.19/0.46 ~ ( fresh_717452603ubject @ C @ X ) ).
% 0.19/0.46
% 0.19/0.46 % name_exists_fresh
% 0.19/0.46 thf(fact_83_name__exists__fresh,axiom,
% 0.19/0.46 ! [X: late_freeRes] :
% 0.19/0.46 ~ ! [C: name] :
% 0.19/0.46 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 0.19/0.46
% 0.19/0.46 % name_exists_fresh
% 0.19/0.46 thf(fact_84_name__exists__fresh,axiom,
% 0.19/0.46 ! [X: name] :
% 0.19/0.46 ~ ! [C: name] :
% 0.19/0.46 ~ ( fresh_name_name @ C @ X ) ).
% 0.19/0.46
% 0.19/0.46 % name_exists_fresh
% 0.19/0.46 thf(fact_85_name__exists__fresh,axiom,
% 0.19/0.46 ! [X: pi] :
% 0.19/0.46 ~ ! [C: name] :
% 0.19/0.46 ~ ( fresh_name_pi @ C @ X ) ).
% 0.19/0.46
% 0.19/0.46 % name_exists_fresh
% 0.19/0.46 thf(fact_86_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 0.19/0.46 = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_87_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 0.19/0.46 = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_88_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 0.19/0.46 = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_89_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 0.19/0.46 = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_90_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 0.19/0.46 = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_91_fresh__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( fresh_543891186ion_pi @ A @ X ) )
% 0.19/0.46 = ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_eqvt
% 0.19/0.46 thf(fact_92_mem__Collect__eq,axiom,
% 0.19/0.46 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.19/0.46 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.19/0.46 = ( P @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % mem_Collect_eq
% 0.19/0.46 thf(fact_93_Collect__mem__eq,axiom,
% 0.19/0.46 ! [A3: set_Pr1834926343_pi_pi] :
% 0.19/0.46 ( ( collec1051790738_pi_pi
% 0.19/0.46 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A3 ) )
% 0.19/0.46 = A3 ) ).
% 0.19/0.46
% 0.19/0.46 % Collect_mem_eq
% 0.19/0.46 thf(fact_94_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 0.19/0.46 ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 0.19/0.46 = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_95_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 0.19/0.46 ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 0.19/0.46 = ( fresh_717452603ubject @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_96_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 0.19/0.46 = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_97_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 0.19/0.46 ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 0.19/0.46 = ( fresh_name_name @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_98_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 0.19/0.46 = ( fresh_name_pi @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_99_fresh__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 0.19/0.46 ( ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) )
% 0.19/0.46 = ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_bij
% 0.19/0.46 thf(fact_100_name__calc_I2_J,axiom,
% 0.19/0.46 ! [X: name] :
% 0.19/0.46 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % name_calc(2)
% 0.19/0.46 thf(fact_101_freeRes_Oexhaust,axiom,
% 0.19/0.46 ! [Y: late_freeRes] :
% 0.19/0.46 ( ! [X112: name,X122: name] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( late_OutputR @ X112 @ X122 ) )
% 0.19/0.46 => ( Y = late_TauR ) ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.exhaust
% 0.19/0.46 thf(fact_102_freeRes_Oinducts,axiom,
% 0.19/0.46 ! [P: late_freeRes > $o,FreeRes: late_freeRes] :
% 0.19/0.46 ( ! [Name1: name,Name2: name] : ( P @ ( late_OutputR @ Name1 @ Name2 ) )
% 0.19/0.46 => ( ( P @ late_TauR )
% 0.19/0.46 => ( P @ FreeRes ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.inducts
% 0.19/0.46 thf(fact_103_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X11: name,X12: name] :
% 0.19/0.46 ( ( late_OutputR @ X11 @ X12 )
% 0.19/0.46 != late_TauR ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics1.freeRes.distinct(1)
% 0.19/0.46 thf(fact_104_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Name12: name,Name22: name] :
% 0.19/0.46 ( ( late_OutputR @ Name12 @ Name22 )
% 0.19/0.46 != late_TauR ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.freeRes.distinct(1)
% 0.19/0.46 thf(fact_105_freshFreeDerivative_I2_J,axiom,
% 0.19/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshFreeDerivative(2)
% 0.19/0.46 thf(fact_106_swap__simps_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name] :
% 0.19/0.46 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 0.19/0.46 = B ) ).
% 0.19/0.46
% 0.19/0.46 % swap_simps(1)
% 0.19/0.46 thf(fact_107_swap__simps_I2_J,axiom,
% 0.19/0.46 ! [A: name,B: name] :
% 0.19/0.46 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 0.19/0.46 = A ) ).
% 0.19/0.46
% 0.19/0.46 % swap_simps(2)
% 0.19/0.46 thf(fact_108_swap__simps_I3_J,axiom,
% 0.19/0.46 ! [A: name,C2: name,B: name] :
% 0.19/0.46 ( ( A != C2 )
% 0.19/0.46 => ( ( B != C2 )
% 0.19/0.46 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
% 0.19/0.46 = C2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % swap_simps(3)
% 0.19/0.46 thf(fact_109_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: pi_Rep,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_name_pi_Rep @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi_Rep @ C2 @ X )
% 0.19/0.46 => ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_110_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: late_subject,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 => ( ( fresh_717452603ubject @ C2 @ X )
% 0.19/0.46 => ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_111_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: late_freeRes,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ C2 @ X )
% 0.19/0.46 => ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_112_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: name,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_name_name @ A @ X )
% 0.19/0.46 => ( ( fresh_name_name @ C2 @ X )
% 0.19/0.46 => ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_113_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: pi,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_name_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_name_pi @ C2 @ X )
% 0.19/0.46 => ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_114_fresh__aux,axiom,
% 0.19/0.46 ! [C2: name,A: name,X: name > noption_pi,B: name] :
% 0.19/0.46 ( ( C2 != A )
% 0.19/0.46 => ( ( fresh_543891186ion_pi @ A @ X )
% 0.19/0.46 => ( ( fresh_543891186ion_pi @ C2 @ X )
% 0.19/0.46 => ( fresh_543891186ion_pi @ C2 @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_aux
% 0.19/0.46 thf(fact_115_cp__name__name1,axiom,
% 0.19/0.46 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cp_name_name1
% 0.19/0.46 thf(fact_116_cp__name__name1,axiom,
% 0.19/0.46 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cp_name_name1
% 0.19/0.46 thf(fact_117_cp__name__name1,axiom,
% 0.19/0.46 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cp_name_name1
% 0.19/0.46 thf(fact_118_cp__name__name1,axiom,
% 0.19/0.46 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 0.19/0.46 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cp_name_name1
% 0.19/0.46 thf(fact_119_cp__name__name1,axiom,
% 0.19/0.46 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 0.19/0.46 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cp_name_name1
% 0.19/0.46 thf(fact_120_name__perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_perm_compose
% 0.19/0.46 thf(fact_121_name__perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_perm_compose
% 0.19/0.46 thf(fact_122_name__perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_perm_compose
% 0.19/0.46 thf(fact_123_name__perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_perm_compose
% 0.19/0.46 thf(fact_124_name__perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_perm_compose
% 0.19/0.46 thf(fact_125_perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_compose
% 0.19/0.46 thf(fact_126_perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_compose
% 0.19/0.46 thf(fact_127_perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 0.19/0.46 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_compose
% 0.19/0.46 thf(fact_128_perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_compose
% 0.19/0.46 thf(fact_129_perm__compose,axiom,
% 0.19/0.46 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 0.19/0.46 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_compose
% 0.19/0.46 thf(fact_130_perm__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_bij
% 0.19/0.46 thf(fact_131_perm__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_bij
% 0.19/0.46 thf(fact_132_perm__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.19/0.46 ( ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_bij
% 0.19/0.46 thf(fact_133_perm__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.19/0.46 ( ( ( perm_name_name @ Pi @ X )
% 0.19/0.46 = ( perm_name_name @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_bij
% 0.19/0.46 thf(fact_134_perm__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.19/0.46 ( ( ( perm_name_pi @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_bij
% 0.19/0.46 thf(fact_135_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_136_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_137_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_138_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_139_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_140_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_141_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_142_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_143_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_144_perm__app,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 0.19/0.46 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 0.19/0.46 = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_app
% 0.19/0.46 thf(fact_145_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X4: set_Pr1834926343_pi_pi] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X4 ) )
% 0.19/0.46 = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_146_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,X4: set_Late_subject] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X4 ) )
% 0.19/0.46 = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_147_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,X4: set_Late_freeRes] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X4 ) )
% 0.19/0.46 = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_148_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi_Rep,X4: set_pi_Rep] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X4 ) )
% 0.19/0.46 = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_149_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: name,X4: set_name] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member_name @ X @ X4 ) )
% 0.19/0.46 = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_150_in__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi,X4: set_pi] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( member_pi @ X @ X4 ) )
% 0.19/0.46 = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % in_eqvt
% 0.19/0.46 thf(fact_151_eq__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.19/0.46 = ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_eqvt
% 0.19/0.46 thf(fact_152_eq__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.19/0.46 = ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_eqvt
% 0.19/0.46 thf(fact_153_eq__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.19/0.46 = ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_eqvt
% 0.19/0.46 thf(fact_154_eq__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.19/0.46 = ( ( perm_name_name @ Pi @ X )
% 0.19/0.46 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_eqvt
% 0.19/0.46 thf(fact_155_eq__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.19/0.46 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 0.19/0.46 = ( ( perm_name_pi @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_eqvt
% 0.19/0.46 thf(fact_156_residual_Oinject_I2_J,axiom,
% 0.19/0.46 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.19/0.46 ( ( ( late_FreeR @ X2 @ X1 )
% 0.19/0.46 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.19/0.46 = ( ( X2 = Y2 )
% 0.19/0.46 & ( X1 = Y1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.inject(2)
% 0.19/0.46 thf(fact_157_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_158_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,Y: late_freeRes] :
% 0.19/0.46 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_159_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,Y: name] :
% 0.19/0.46 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_160_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,Y: pi] :
% 0.19/0.46 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_161_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,Y: late_subject] :
% 0.19/0.46 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_162_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_163_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,Y: name] :
% 0.19/0.46 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 & ( fresh_name_name @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_164_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,Y: pi] :
% 0.19/0.46 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_165_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: name,Y: late_subject] :
% 0.19/0.46 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_name_name @ A @ X )
% 0.19/0.46 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_166_fresh__prod,axiom,
% 0.19/0.46 ! [A: name,X: name,Y: late_freeRes] :
% 0.19/0.46 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 0.19/0.46 = ( ( fresh_name_name @ A @ X )
% 0.19/0.46 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prod
% 0.19/0.46 thf(fact_167_list_Oinject,axiom,
% 0.19/0.46 ! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 0.19/0.46 ( ( ( cons_P1213805021e_name @ X21 @ X22 )
% 0.19/0.46 = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_168_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: name,B: name,A4: name,B3: name] :
% 0.19/0.46 ( ( ( produc1570949143e_name @ A @ B )
% 0.19/0.46 = ( produc1570949143e_name @ A4 @ B3 ) )
% 0.19/0.46 = ( ( A = A4 )
% 0.19/0.46 & ( B = B3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_169_old_Oprod_Oinject,axiom,
% 0.19/0.46 ! [A: pi,B: pi,A4: pi,B3: pi] :
% 0.19/0.46 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.46 = ( product_Pair_pi_pi @ A4 @ B3 ) )
% 0.19/0.46 = ( ( A = A4 )
% 0.19/0.46 & ( B = B3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inject
% 0.19/0.46 thf(fact_170_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: name,X2: name,Y1: name,Y2: name] :
% 0.19/0.46 ( ( ( produc1570949143e_name @ X1 @ X2 )
% 0.19/0.46 = ( produc1570949143e_name @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_171_prod_Oinject,axiom,
% 0.19/0.46 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 0.19/0.46 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.19/0.46 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 0.19/0.46 = ( ( X1 = Y1 )
% 0.19/0.46 & ( X2 = Y2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod.inject
% 0.19/0.46 thf(fact_172_cClose1_Ohyps_I2_J,axiom,
% 0.19/0.46 late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(2)
% 0.19/0.46 thf(fact_173_fresh__list__cons,axiom,
% 0.19/0.46 ! [A: name,X: late_subject,Xs: list_Late_subject] :
% 0.19/0.46 ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs ) )
% 0.19/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.19/0.46 & ( fresh_838462539ubject @ A @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_list_cons
% 0.19/0.46 thf(fact_174_fresh__list__cons,axiom,
% 0.19/0.46 ! [A: name,X: late_freeRes,Xs: list_Late_freeRes] :
% 0.19/0.46 ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.19/0.46 & ( fresh_1981651763reeRes @ A @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_list_cons
% 0.19/0.46 thf(fact_175_fresh__list__cons,axiom,
% 0.19/0.46 ! [A: name,X: name,Xs: list_name] :
% 0.19/0.46 ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs ) )
% 0.19/0.46 = ( ( fresh_name_name @ A @ X )
% 0.19/0.46 & ( fresh_name_list_name @ A @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_list_cons
% 0.19/0.46 thf(fact_176_fresh__list__cons,axiom,
% 0.19/0.46 ! [A: name,X: pi,Xs: list_pi] :
% 0.19/0.46 ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs ) )
% 0.19/0.46 = ( ( fresh_name_pi @ A @ X )
% 0.19/0.46 & ( fresh_name_list_pi @ A @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_list_cons
% 0.19/0.46 thf(fact_177_fresh__list__cons,axiom,
% 0.19/0.46 ! [A: name,X: name > noption_pi,Xs: list_name_noption_pi] :
% 0.19/0.46 ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ X @ Xs ) )
% 0.19/0.46 = ( ( fresh_543891186ion_pi @ A @ X )
% 0.19/0.46 & ( fresh_1135477378ion_pi @ A @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_list_cons
% 0.19/0.46 thf(fact_178_fresh__prodD_I2_J,axiom,
% 0.19/0.46 ! [A: name,X: name,Y: name] :
% 0.19/0.46 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.19/0.46 => ( fresh_name_name @ A @ Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prodD(2)
% 0.19/0.46 thf(fact_179_fresh__prodD_I2_J,axiom,
% 0.19/0.46 ! [A: name,X: pi,Y: pi] :
% 0.19/0.46 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.19/0.46 => ( fresh_name_pi @ A @ Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prodD(2)
% 0.19/0.46 thf(fact_180_fresh__prodD_I1_J,axiom,
% 0.19/0.46 ! [A: name,X: name,Y: name] :
% 0.19/0.46 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 0.19/0.46 => ( fresh_name_name @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prodD(1)
% 0.19/0.46 thf(fact_181_fresh__prodD_I1_J,axiom,
% 0.19/0.46 ! [A: name,X: pi,Y: pi] :
% 0.19/0.46 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 0.19/0.46 => ( fresh_name_pi @ A @ X ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_prodD(1)
% 0.19/0.46 thf(fact_182_cons__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Xs: list_Late_subject] :
% 0.19/0.46 ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs ) )
% 0.19/0.46 = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cons_eqvt
% 0.19/0.46 thf(fact_183_cons__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Xs: list_Late_freeRes] :
% 0.19/0.46 ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs ) )
% 0.19/0.46 = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cons_eqvt
% 0.19/0.46 thf(fact_184_cons__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi_Rep,Xs: list_pi_Rep] :
% 0.19/0.46 ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs ) )
% 0.19/0.46 = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cons_eqvt
% 0.19/0.46 thf(fact_185_cons__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: name,Xs: list_name] :
% 0.19/0.46 ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs ) )
% 0.19/0.46 = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cons_eqvt
% 0.19/0.46 thf(fact_186_cons__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: pi,Xs: list_pi] :
% 0.19/0.46 ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs ) )
% 0.19/0.46 = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cons_eqvt
% 0.19/0.46 thf(fact_187_freeRes_Ofresh_I2_J,axiom,
% 0.19/0.46 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.fresh(2)
% 0.19/0.46 thf(fact_188_residual_Ofresh_I2_J,axiom,
% 0.19/0.46 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.19/0.46 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.46 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.19/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.fresh(2)
% 0.19/0.46 thf(fact_189_freeRes_Ofresh_I1_J,axiom,
% 0.19/0.46 ! [A: name,X2: name,X1: name] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.46 = ( ( fresh_name_name @ A @ X2 )
% 0.19/0.46 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freeRes.fresh(1)
% 0.19/0.46 thf(fact_190_subject_Ofresh_I2_J,axiom,
% 0.19/0.46 ! [A: name,X1: name] :
% 0.19/0.46 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.46 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.fresh(2)
% 0.19/0.46 thf(fact_191_pi_Operm_I9_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 0.19/0.46 = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.perm(9)
% 0.19/0.46 thf(fact_192_cClose1_Ohyps_I1_J,axiom,
% 0.19/0.46 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 0.19/0.46
% 0.19/0.46 % cClose1.hyps(1)
% 0.19/0.46 thf(fact_193_residual_Operm_I1_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 0.19/0.46 ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.19/0.46 = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.perm(1)
% 0.19/0.46 thf(fact_194_name__bij,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 0.19/0.46 ( ( ( perm_name_name @ Pi @ X )
% 0.19/0.46 = ( perm_name_name @ Pi @ Y ) )
% 0.19/0.46 = ( X = Y ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_bij
% 0.19/0.46 thf(fact_195_Late__Semantics_OResB,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.46 => ( ( Y != X )
% 0.19/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.ResB
% 0.19/0.46 thf(fact_196_transitions_OResB,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.46 => ( ( Y != X )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.ResB
% 0.19/0.46 thf(fact_197_resCasesF,axiom,
% 0.19/0.46 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 0.19/0.46 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.19/0.46 => ( ! [P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.19/0.46 => ( F2 @ ( res @ X @ P3 ) ) ) )
% 0.19/0.46 => ( F2 @ XP ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % resCasesF
% 0.19/0.46 thf(fact_198_resCasesF_H,axiom,
% 0.19/0.46 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.46 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.46 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.19/0.46 ( ( ( res @ X @ P )
% 0.19/0.46 = ( res @ Y3 @ P4 ) )
% 0.19/0.46 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.19/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.46 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % resCasesF'
% 0.19/0.46 thf(fact_199_ResF,axiom,
% 0.19/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.46 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 0.19/0.46 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ResF
% 0.19/0.46 thf(fact_200_freshBoundDerivative_I1_J,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshBoundDerivative(1)
% 0.19/0.46 thf(fact_201_freshRes,axiom,
% 0.19/0.46 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshRes
% 0.19/0.46 thf(fact_202_residual_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Subject: late_subject,Name: name,Pi: pi,FreeRes2: late_freeRes,Pi3: pi] :
% 0.19/0.46 ( ( late_BoundR @ Subject @ Name @ Pi )
% 0.19/0.46 != ( late_FreeR @ FreeRes2 @ Pi3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.distinct(1)
% 0.19/0.46 thf(fact_203_residual_Oinducts,axiom,
% 0.19/0.46 ! [P: late_residual > $o,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.inducts
% 0.19/0.46 thf(fact_204_resCases_H,axiom,
% 0.19/0.46 ! [X: name,P: pi,Rs: late_residual] :
% 0.19/0.46 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.19/0.46 => ( ! [P4: pi,A5: name,B4: name] :
% 0.19/0.46 ( ( ( res @ X @ P )
% 0.19/0.46 = ( res @ B4 @ P4 ) )
% 0.19/0.46 => ! [P3: pi] :
% 0.19/0.46 ( ( Rs
% 0.19/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.19/0.46 => ( A5 = B4 ) ) ) )
% 0.19/0.46 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y3: name] :
% 0.19/0.46 ( ( ( res @ X @ P )
% 0.19/0.46 = ( res @ Y3 @ P4 ) )
% 0.19/0.46 => ( ( Rs
% 0.19/0.46 = ( late_BoundR @ A5 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Y3 @ A5 )
% 0.19/0.46 => ( ( Y3 != X5 )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.46 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) )
% 0.19/0.46 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.19/0.46 ( ( ( res @ X @ P )
% 0.19/0.46 = ( res @ Y3 @ P4 ) )
% 0.19/0.46 => ( ( Rs
% 0.19/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.46 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % resCases'
% 0.19/0.46 thf(fact_205_sorted__wrt_Ocases,axiom,
% 0.19/0.46 ! [X: produc1872410278e_name] :
% 0.19/0.46 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1069608854e_name @ P4 @ nil_Pr743626285e_name ) )
% 0.19/0.46 => ~ ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ Ys ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % sorted_wrt.cases
% 0.19/0.46 thf(fact_206_successively_Ocases,axiom,
% 0.19/0.46 ! [X: produc1872410278e_name] :
% 0.19/0.46 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1069608854e_name @ P4 @ nil_Pr743626285e_name ) )
% 0.19/0.46 => ( ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) ) )
% 0.19/0.46 => ~ ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Y3: produc367475239e_name,Xs2: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % successively.cases
% 0.19/0.46 thf(fact_207_splice_Ocases,axiom,
% 0.19/0.46 ! [X: produc890461031e_name] :
% 0.19/0.46 ( ! [Ys: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.19/0.46 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % splice.cases
% 0.19/0.46 thf(fact_208_shuffles_Ocases,axiom,
% 0.19/0.46 ! [X: produc890461031e_name] :
% 0.19/0.46 ( ! [Ys: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 0.19/0.46 => ( ! [Xs2: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc208131031e_name @ Xs2 @ nil_Pr743626285e_name ) )
% 0.19/0.46 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % shuffles.cases
% 0.19/0.46 thf(fact_209_resCasesB_H,axiom,
% 0.19/0.46 ! [X6: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 0.19/0.46 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 0.19/0.46 => ( ! [P4: pi,A5: name,B4: name] :
% 0.19/0.46 ( ( ( res @ X6 @ P )
% 0.19/0.46 = ( res @ B4 @ P4 ) )
% 0.19/0.46 => ! [P3: pi] :
% 0.19/0.46 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.19/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 0.19/0.46 => ( A5 = B4 ) ) ) )
% 0.19/0.46 => ~ ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y3: name] :
% 0.19/0.46 ( ( ( res @ X6 @ P )
% 0.19/0.46 = ( res @ Y3 @ P4 ) )
% 0.19/0.46 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.19/0.46 = ( late_BoundR @ A5 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Y3 @ A5 )
% 0.19/0.46 => ( ( Y3 != X5 )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.46 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % resCasesB'
% 0.19/0.46 thf(fact_210_Open,axiom,
% 0.19/0.46 ! [P: pi,A: name,B: name,P2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.46 => ( ( A != B )
% 0.19/0.46 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Open
% 0.19/0.46 thf(fact_211_freshResidual,axiom,
% 0.19/0.46 ! [P: pi,Rs: late_residual,X: name] :
% 0.19/0.46 ( ( late_transitions @ P @ Rs )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshResidual
% 0.19/0.46 thf(fact_212_freshBoundDerivative_I2_J,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( ( Y != X )
% 0.19/0.46 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshBoundDerivative(2)
% 0.19/0.46 thf(fact_213_residual_Ostrong__inducts,axiom,
% 0.19/0.46 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.19/0.46 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_inducts
% 0.19/0.46 thf(fact_214_residual_Ostrong__inducts,axiom,
% 0.19/0.46 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_inducts
% 0.19/0.46 thf(fact_215_residual_Ostrong__inducts,axiom,
% 0.19/0.46 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.19/0.46 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_inducts
% 0.19/0.46 thf(fact_216_residual_Ostrong__inducts,axiom,
% 0.19/0.46 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_inducts
% 0.19/0.46 thf(fact_217_residual_Ostrong__induct,axiom,
% 0.19/0.46 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.19/0.46 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_induct
% 0.19/0.46 thf(fact_218_residual_Ostrong__induct,axiom,
% 0.19/0.46 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.19/0.46 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_induct
% 0.19/0.46 thf(fact_219_residual_Ostrong__induct,axiom,
% 0.19/0.46 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.19/0.46 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_induct
% 0.19/0.46 thf(fact_220_residual_Ostrong__induct,axiom,
% 0.19/0.46 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.46 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 0.19/0.46 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual.strong_induct
% 0.19/0.46 thf(fact_221_resCasesB,axiom,
% 0.19/0.46 ! [Y: name,P: pi,A: late_subject,X: name,YP: pi,F2: late_subject > pi > $o] :
% 0.19/0.46 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ YP ) )
% 0.19/0.46 => ( ( X != Y )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ! [B4: name,P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B4 @ Y ) @ P3 ) )
% 0.19/0.46 => ( ( B4 != Y )
% 0.19/0.46 => ( ( A
% 0.19/0.46 = ( late_BoundOutputS @ B4 ) )
% 0.19/0.46 => ( F2 @ ( late_BoundOutputS @ B4 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P3 ) ) ) ) )
% 0.19/0.46 => ( ! [P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.46 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.46 => ( F2 @ A @ ( res @ Y @ P3 ) ) ) )
% 0.19/0.46 => ( F2 @ A @ YP ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % resCasesB
% 0.19/0.46 thf(fact_222_freshFreeDerivative_I1_J,axiom,
% 0.19/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % freshFreeDerivative(1)
% 0.19/0.46 thf(fact_223_surj__pair,axiom,
% 0.19/0.46 ! [P5: produc367475239e_name] :
% 0.19/0.46 ? [X5: name,Y3: name] :
% 0.19/0.46 ( P5
% 0.19/0.46 = ( produc1570949143e_name @ X5 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_224_surj__pair,axiom,
% 0.19/0.46 ! [P5: product_prod_pi_pi] :
% 0.19/0.46 ? [X5: pi,Y3: pi] :
% 0.19/0.46 ( P5
% 0.19/0.46 = ( product_Pair_pi_pi @ X5 @ Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % surj_pair
% 0.19/0.46 thf(fact_225_prod__cases,axiom,
% 0.19/0.46 ! [P: produc367475239e_name > $o,P5: produc367475239e_name] :
% 0.19/0.46 ( ! [A5: name,B4: name] : ( P @ ( produc1570949143e_name @ A5 @ B4 ) )
% 0.19/0.46 => ( P @ P5 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_226_prod__cases,axiom,
% 0.19/0.46 ! [P: product_prod_pi_pi > $o,P5: product_prod_pi_pi] :
% 0.19/0.46 ( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
% 0.19/0.46 => ( P @ P5 ) ) ).
% 0.19/0.46
% 0.19/0.46 % prod_cases
% 0.19/0.46 thf(fact_227_Pair__inject,axiom,
% 0.19/0.46 ! [A: name,B: name,A4: name,B3: name] :
% 0.19/0.46 ( ( ( produc1570949143e_name @ A @ B )
% 0.19/0.46 = ( produc1570949143e_name @ A4 @ B3 ) )
% 0.19/0.46 => ~ ( ( A = A4 )
% 0.19/0.46 => ( B != B3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_228_Pair__inject,axiom,
% 0.19/0.46 ! [A: pi,B: pi,A4: pi,B3: pi] :
% 0.19/0.46 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.19/0.46 = ( product_Pair_pi_pi @ A4 @ B3 ) )
% 0.19/0.46 => ~ ( ( A = A4 )
% 0.19/0.46 => ( B != B3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Pair_inject
% 0.19/0.46 thf(fact_229_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: produc367475239e_name] :
% 0.19/0.46 ~ ! [A5: name,B4: name] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( produc1570949143e_name @ A5 @ B4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_230_old_Oprod_Oexhaust,axiom,
% 0.19/0.46 ! [Y: product_prod_pi_pi] :
% 0.19/0.46 ~ ! [A5: pi,B4: pi] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( product_Pair_pi_pi @ A5 @ B4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.exhaust
% 0.19/0.46 thf(fact_231_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: produc367475239e_name > $o,Prod: produc367475239e_name] :
% 0.19/0.46 ( ! [A5: name,B4: name] : ( P @ ( produc1570949143e_name @ A5 @ B4 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_232_old_Oprod_Oinducts,axiom,
% 0.19/0.46 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.19/0.46 ( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
% 0.19/0.46 => ( P @ Prod ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.prod.inducts
% 0.19/0.46 thf(fact_233_not__Cons__self2,axiom,
% 0.19/0.46 ! [X: produc367475239e_name,Xs: list_P227219501e_name] :
% 0.19/0.46 ( ( cons_P1213805021e_name @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_234_allE__Nil,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > $o] :
% 0.19/0.46 ( ! [X_1: list_P227219501e_name] : ( P @ X_1 )
% 0.19/0.46 => ( P @ nil_Pr743626285e_name ) ) ).
% 0.19/0.46
% 0.19/0.46 % allE_Nil
% 0.19/0.46 thf(fact_235_if__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 0.19/0.46 ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 0.19/0.46 & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % if_eqvt
% 0.19/0.46 thf(fact_236_if__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 0.19/0.46 ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 0.19/0.46 & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % if_eqvt
% 0.19/0.46 thf(fact_237_if__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 0.19/0.46 ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 0.19/0.46 & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % if_eqvt
% 0.19/0.46 thf(fact_238_if__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 0.19/0.46 ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_name @ Pi @ C1 ) ) )
% 0.19/0.46 & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % if_eqvt
% 0.19/0.46 thf(fact_239_if__eqvt,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 0.19/0.46 ( ( ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_pi @ Pi @ C1 ) ) )
% 0.19/0.46 & ( ~ ( perm_name_o @ Pi @ B )
% 0.19/0.46 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 0.19/0.46 = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % if_eqvt
% 0.19/0.46 thf(fact_240_pt__bij3,axiom,
% 0.19/0.46 ! [X: late_subject,Y: late_subject,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 => ( ( perm_n1559866809ubject @ Pi @ X )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pt_bij3
% 0.19/0.46 thf(fact_241_pt__bij3,axiom,
% 0.19/0.46 ! [X: late_freeRes,Y: late_freeRes,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 => ( ( perm_n336613537reeRes @ Pi @ X )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pt_bij3
% 0.19/0.46 thf(fact_242_pt__bij3,axiom,
% 0.19/0.46 ! [X: pi_Rep,Y: pi_Rep,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 => ( ( perm_name_pi_Rep @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pt_bij3
% 0.19/0.46 thf(fact_243_pt__bij3,axiom,
% 0.19/0.46 ! [X: name,Y: name,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 => ( ( perm_name_name @ Pi @ X )
% 0.19/0.46 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pt_bij3
% 0.19/0.46 thf(fact_244_pt__bij3,axiom,
% 0.19/0.46 ! [X: pi,Y: pi,Pi: list_P227219501e_name] :
% 0.19/0.46 ( ( X = Y )
% 0.19/0.46 => ( ( perm_name_pi @ Pi @ X )
% 0.19/0.46 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pt_bij3
% 0.19/0.46 thf(fact_245_abs__fun__if,axiom,
% 0.19/0.46 ! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( C2
% 0.19/0.46 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 0.19/0.46 & ( ~ C2
% 0.19/0.46 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % abs_fun_if
% 0.19/0.46 thf(fact_246_abs__fun__if,axiom,
% 0.19/0.46 ! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( C2
% 0.19/0.46 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 0.19/0.46 & ( ~ C2
% 0.19/0.46 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % abs_fun_if
% 0.19/0.46 thf(fact_247_abs__fun__if,axiom,
% 0.19/0.46 ! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 0.19/0.46 ( ( C2
% 0.19/0.46 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 0.19/0.46 & ( ~ C2
% 0.19/0.46 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % abs_fun_if
% 0.19/0.46 thf(fact_248_abs__fun__if,axiom,
% 0.19/0.46 ! [C2: $o,Pi: list_P227219501e_name,X: name,Y: name] :
% 0.19/0.46 ( ( C2
% 0.19/0.46 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_name @ Pi @ X ) ) )
% 0.19/0.46 & ( ~ C2
% 0.19/0.46 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_name @ Pi @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % abs_fun_if
% 0.19/0.46 thf(fact_249_abs__fun__if,axiom,
% 0.19/0.46 ! [C2: $o,Pi: list_P227219501e_name,X: pi,Y: pi] :
% 0.19/0.46 ( ( C2
% 0.19/0.46 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_pi @ Pi @ X ) ) )
% 0.19/0.46 & ( ~ C2
% 0.19/0.46 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y ) )
% 0.19/0.46 = ( perm_name_pi @ Pi @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % abs_fun_if
% 0.19/0.46 thf(fact_250_alphaRes,axiom,
% 0.19/0.46 ! [C2: name,P: pi,A: name] :
% 0.19/0.46 ( ( fresh_name_pi @ C2 @ P )
% 0.19/0.46 => ( ( res @ A @ P )
% 0.19/0.46 = ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % alphaRes
% 0.19/0.46 thf(fact_251_alphaBoundResidual,axiom,
% 0.19/0.46 ! [X6: name,P: pi,A: late_subject,X: name] :
% 0.19/0.46 ( ( fresh_name_pi @ X6 @ P )
% 0.19/0.46 => ( ( late_BoundR @ A @ X @ P )
% 0.19/0.46 = ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % alphaBoundResidual
% 0.19/0.46 thf(fact_252_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y ) )
% 0.19/0.46 = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_253_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_freeRes] :
% 0.19/0.46 ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y ) )
% 0.19/0.46 = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_254_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi_Rep] :
% 0.19/0.46 ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y ) )
% 0.19/0.46 = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_255_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: name] :
% 0.19/0.46 ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y ) )
% 0.19/0.46 = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_256_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi] :
% 0.19/0.46 ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y ) )
% 0.19/0.46 = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_257_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_subject] :
% 0.19/0.46 ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y ) )
% 0.19/0.46 = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_258_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y ) )
% 0.19/0.46 = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_259_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi_Rep] :
% 0.19/0.46 ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y ) )
% 0.19/0.46 = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_260_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: name] :
% 0.19/0.46 ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y ) )
% 0.19/0.46 = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_261_perm__prod_Osimps,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi] :
% 0.19/0.46 ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y ) )
% 0.19/0.46 = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % perm_prod.simps
% 0.19/0.46 thf(fact_262_list_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.19/0.46 ( nil_Pr743626285e_name
% 0.19/0.46 != ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.distinct(1)
% 0.19/0.46 thf(fact_263_list_OdiscI,axiom,
% 0.19/0.46 ! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
% 0.19/0.46 ( ( List
% 0.19/0.46 = ( cons_P1213805021e_name @ X21 @ X22 ) )
% 0.19/0.46 => ( List != nil_Pr743626285e_name ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.discI
% 0.19/0.46 thf(fact_264_list_Oexhaust,axiom,
% 0.19/0.46 ! [Y: list_P227219501e_name] :
% 0.19/0.46 ( ( Y != nil_Pr743626285e_name )
% 0.19/0.46 => ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.exhaust
% 0.19/0.46 thf(fact_265_list_Oinducts,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > $o,List: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [X13: produc367475239e_name,X23: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ X23 )
% 0.19/0.46 => ( P @ ( cons_P1213805021e_name @ X13 @ X23 ) ) )
% 0.19/0.46 => ( P @ List ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inducts
% 0.19/0.46 thf(fact_266_neq__Nil__conv,axiom,
% 0.19/0.46 ! [Xs: list_P227219501e_name] :
% 0.19/0.46 ( ( Xs != nil_Pr743626285e_name )
% 0.19/0.46 = ( ? [Y5: produc367475239e_name,Ys2: list_P227219501e_name] :
% 0.19/0.46 ( Xs
% 0.19/0.46 = ( cons_P1213805021e_name @ Y5 @ Ys2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % neq_Nil_conv
% 0.19/0.46 thf(fact_267_list__induct2_H,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > list_P227219501e_name > $o,Xs: list_P227219501e_name,Ys3: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name] : ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.19/0.46 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ Xs2 @ Ys )
% 0.19/0.46 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
% 0.19/0.46 => ( P @ Xs @ Ys3 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_induct2'
% 0.19/0.46 thf(fact_268_splice_Oinduct,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.19/0.46 ( ! [X_1: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ X_1 )
% 0.19/0.46 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ Ys @ Xs2 )
% 0.19/0.46 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % splice.induct
% 0.19/0.46 thf(fact_269_induct__list012,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > $o,Xs: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [X5: produc367475239e_name] : ( P @ ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) )
% 0.19/0.46 => ( ! [X5: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ Zs )
% 0.19/0.46 => ( ( P @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
% 0.19/0.46 => ( P @ ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % induct_list012
% 0.19/0.46 thf(fact_270_shuffles_Oinduct,axiom,
% 0.19/0.46 ! [P: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 0.19/0.46 ( ! [X_1: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ X_1 )
% 0.19/0.46 => ( ! [Xs2: list_P227219501e_name] : ( P @ Xs2 @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ Xs2 @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 0.19/0.46 => ( ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys )
% 0.19/0.46 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % shuffles.induct
% 0.19/0.46 thf(fact_271_transpose_Ocases,axiom,
% 0.19/0.46 ! [X: list_l1406151091e_name] :
% 0.19/0.46 ( ( X != nil_li29751603e_name )
% 0.19/0.46 => ( ! [Xss: list_l1406151091e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
% 0.19/0.46 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Xss: list_l1406151091e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transpose.cases
% 0.19/0.46 thf(fact_272_remdups__adj_Ocases,axiom,
% 0.19/0.46 ! [X: list_P227219501e_name] :
% 0.19/0.46 ( ( X != nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [X5: produc367475239e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) )
% 0.19/0.46 => ~ ! [X5: produc367475239e_name,Y3: produc367475239e_name,Xs2: list_P227219501e_name] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % remdups_adj.cases
% 0.19/0.46 thf(fact_273_sorted__wrt_Oinduct,axiom,
% 0.19/0.46 ! [P: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 0.19/0.46 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] : ( P @ P4 @ nil_Pr743626285e_name )
% 0.19/0.46 => ( ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Ys: list_P227219501e_name] :
% 0.19/0.46 ( ( P @ P4 @ Ys )
% 0.19/0.46 => ( P @ P4 @ ( cons_P1213805021e_name @ X5 @ Ys ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % sorted_wrt.induct
% 0.19/0.46 thf(fact_274_Free_Ohyps,axiom,
% 0.19/0.46 late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 0.19/0.46
% 0.19/0.46 % Free.hyps
% 0.19/0.46 thf(fact_275_alphaInput,axiom,
% 0.19/0.46 ! [C2: name,P: pi,A: name,X: name] :
% 0.19/0.46 ( ( fresh_name_pi @ C2 @ P )
% 0.19/0.46 => ( ( input @ A @ X @ P )
% 0.19/0.46 = ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % alphaInput
% 0.19/0.46 thf(fact_276_name__calc_I1_J,axiom,
% 0.19/0.46 ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 0.19/0.46 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 0.19/0.46 = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_calc(1)
% 0.19/0.46 thf(fact_277_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.19/0.46 ! [X1: name,Y1: name] :
% 0.19/0.46 ( ( ( late_InputS @ X1 )
% 0.19/0.46 = ( late_InputS @ Y1 ) )
% 0.19/0.46 = ( X1 = Y1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics1.subject.inject(1)
% 0.19/0.46 thf(fact_278_residual__Rep_Oinject_I2_J,axiom,
% 0.19/0.46 ! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
% 0.19/0.46 ( ( ( late_r347633188eR_Rep @ X21 @ X22 )
% 0.19/0.46 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % residual_Rep.inject(2)
% 0.19/0.46 thf(fact_279_pi_Ofresh_I8_J,axiom,
% 0.19/0.46 ! [A: name,X2: pi,X1: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.19/0.46 = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.fresh(8)
% 0.19/0.46 thf(fact_280_pi_Operm_I8_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi @ ( par @ X2 @ X1 ) )
% 0.19/0.46 = ( par @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.perm(8)
% 0.19/0.46 thf(fact_281_pi_Operm_I4_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 0.19/0.46 ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 0.19/0.46 = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.perm(4)
% 0.19/0.46 thf(fact_282_subject_Ofresh_I1_J,axiom,
% 0.19/0.46 ! [A: name,X1: name] :
% 0.19/0.46 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.19/0.46 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.fresh(1)
% 0.19/0.46 thf(fact_283_subject_Operm_I1_J,axiom,
% 0.19/0.46 ! [Pi: list_P227219501e_name,X1: name] :
% 0.19/0.46 ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 0.19/0.46 = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.perm(1)
% 0.19/0.46 thf(fact_284_ScopeExt,axiom,
% 0.19/0.46 ! [Y: name,R: pi,Z: name,S: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ Y @ R )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) ).
% 0.19/0.46
% 0.19/0.46 % ScopeExt
% 0.19/0.46 thf(fact_285_Res,axiom,
% 0.19/0.46 ! [Y: name,R: pi,S: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ Y @ R )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) ).
% 0.19/0.46
% 0.19/0.46 % Res
% 0.19/0.46 thf(fact_286_pi_Odistinct_I55_J,axiom,
% 0.19/0.46 ! [Name12: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.46 ( ( input @ Name12 @ Name22 @ Pi )
% 0.19/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.distinct(55)
% 0.19/0.46 thf(fact_287_pi_Oinject_I7_J,axiom,
% 0.19/0.46 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.46 ( ( ( par @ X2 @ X1 )
% 0.19/0.46 = ( par @ Y2 @ Y1 ) )
% 0.19/0.46 = ( ( X2 = Y2 )
% 0.19/0.46 & ( X1 = Y1 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.inject(7)
% 0.19/0.46 thf(fact_288_pi_Odistinct_I85_J,axiom,
% 0.19/0.46 ! [Pi1: pi,Pi2: pi,Name4: name,Pi3: pi] :
% 0.19/0.46 ( ( par @ Pi1 @ Pi2 )
% 0.19/0.46 != ( res @ Name4 @ Pi3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.distinct(85)
% 0.19/0.46 thf(fact_289_transitions_OInput,axiom,
% 0.19/0.46 ! [X: name,A: name,P: pi] :
% 0.19/0.46 ( ( X != A )
% 0.19/0.46 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Input
% 0.19/0.46 thf(fact_290_Late__Semantics_OInput,axiom,
% 0.19/0.46 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Input
% 0.19/0.46 thf(fact_291_pi_Odistinct_I57_J,axiom,
% 0.19/0.46 ! [Name12: name,Name22: name,Pi: pi,Name4: name,Pi3: pi] :
% 0.19/0.46 ( ( input @ Name12 @ Name22 @ Pi )
% 0.19/0.46 != ( res @ Name4 @ Pi3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.distinct(57)
% 0.19/0.46 thf(fact_292_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Name: name,Name4: name] :
% 0.19/0.46 ( ( late_InputS @ Name )
% 0.19/0.46 != ( late_BoundOutputS @ Name4 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.subject.distinct(1)
% 0.19/0.46 thf(fact_293_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X1: name,X2: name] :
% 0.19/0.46 ( ( late_InputS @ X1 )
% 0.19/0.46 != ( late_BoundOutputS @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics1.subject.distinct(1)
% 0.19/0.46 thf(fact_294_subject_Oinducts,axiom,
% 0.19/0.46 ! [P: late_subject > $o,Subject: late_subject] :
% 0.19/0.46 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.19/0.46 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.19/0.46 => ( P @ Subject ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.inducts
% 0.19/0.46 thf(fact_295_subject_Oexhaust,axiom,
% 0.19/0.46 ! [Y: late_subject] :
% 0.19/0.46 ( ! [X13: name] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( late_InputS @ X13 ) )
% 0.19/0.46 => ~ ! [X23: name] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( late_BoundOutputS @ X23 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % subject.exhaust
% 0.19/0.46 thf(fact_296_Par2F,axiom,
% 0.19/0.46 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Par2F
% 0.19/0.46 thf(fact_297_Par1F,axiom,
% 0.19/0.46 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Par1F
% 0.19/0.46 thf(fact_298_name__calc_I3_J,axiom,
% 0.19/0.46 ! [A: name,C2: name,B: name] :
% 0.19/0.46 ( ( ( A = C2 )
% 0.19/0.46 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = B ) )
% 0.19/0.46 & ( ( A != C2 )
% 0.19/0.46 => ( ( ( B = C2 )
% 0.19/0.46 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = A ) )
% 0.19/0.46 & ( ( B != C2 )
% 0.19/0.46 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = C2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_calc(3)
% 0.19/0.46 thf(fact_299_resTrans_I2_J,axiom,
% 0.19/0.46 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.19/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.19/0.46
% 0.19/0.46 % resTrans(2)
% 0.19/0.46 thf(fact_300_inputIneqTrans,axiom,
% 0.19/0.46 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.46 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.46 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % inputIneqTrans
% 0.19/0.46 thf(fact_301_inputFreeTrans,axiom,
% 0.19/0.46 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.46 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % inputFreeTrans
% 0.19/0.46 thf(fact_302_Late__Semantics_OPar1B,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Par1B
% 0.19/0.46 thf(fact_303_Late__Semantics_OPar2B,axiom,
% 0.19/0.46 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Par2B
% 0.19/0.46 thf(fact_304_parCasesB,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.19/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ! [P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.46 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.19/0.46 => ( ! [Q3: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.19/0.46 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.19/0.46 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % parCasesB
% 0.19/0.46 thf(fact_305_parCasesB_H,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.46 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Q4: pi] :
% 0.19/0.46 ( ( ( par @ P @ Q )
% 0.19/0.46 = ( par @ P4 @ Q4 ) )
% 0.19/0.46 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.46 = ( late_BoundR @ A5 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 0.19/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.19/0.46 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) )
% 0.19/0.46 => ~ ! [Q4: pi,A5: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.19/0.46 ( ( ( par @ P @ Q )
% 0.19/0.46 = ( par @ P4 @ Q4 ) )
% 0.19/0.46 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.46 = ( late_BoundR @ A5 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.19/0.46 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.19/0.46 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.19/0.46 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % parCasesB'
% 0.19/0.46 thf(fact_306_transitions_OPar1B,axiom,
% 0.19/0.46 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Par1B
% 0.19/0.46 thf(fact_307_transitions_OPar2B,axiom,
% 0.19/0.46 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Par2B
% 0.19/0.46 thf(fact_308_resInputFreeTrans,axiom,
% 0.19/0.46 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % resInputFreeTrans
% 0.19/0.46 thf(fact_309_inputBoundOutputTrans,axiom,
% 0.19/0.46 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 0.19/0.46 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % inputBoundOutputTrans
% 0.19/0.46 thf(fact_310_inputCases,axiom,
% 0.19/0.46 ! [A: name,X: name,P: pi,B: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 0.19/0.46 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ YP ) )
% 0.19/0.46 => ( ( Y != A )
% 0.19/0.46 => ( ( Y != X )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( ( ( B
% 0.19/0.46 = ( late_InputS @ A ) )
% 0.19/0.46 => ( ( YP
% 0.19/0.46 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) )
% 0.19/0.46 => ( Prop @ ( late_InputS @ A ) @ Y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) ) ) )
% 0.19/0.46 => ( Prop @ B @ Y @ YP ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % inputCases
% 0.19/0.46 thf(fact_311_resInputBoundOutputTrans,axiom,
% 0.19/0.46 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.19/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % resInputBoundOutputTrans
% 0.19/0.46 thf(fact_312_Late__Semantics_OClose1,axiom,
% 0.19/0.46 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Close1
% 0.19/0.46 thf(fact_313_Late__Semantics_OClose2,axiom,
% 0.19/0.46 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Close2
% 0.19/0.46 thf(fact_314_transitions_OClose1,axiom,
% 0.19/0.46 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.46 => ( ( X != A )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.46 => ( ( Y != A )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P2 )
% 0.19/0.46 => ( ( X != Y )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Close1
% 0.19/0.46 thf(fact_315_EqvtRel,axiom,
% 0.19/0.46 eqvt_pi @ rel ).
% 0.19/0.46
% 0.19/0.46 % EqvtRel
% 0.19/0.46 thf(fact_316_subst__identity,axiom,
% 0.19/0.46 ! [P: pi,A: name] :
% 0.19/0.46 ( ( subs @ P @ A @ A )
% 0.19/0.46 = P ) ).
% 0.19/0.46
% 0.19/0.46 % subst_identity
% 0.19/0.46 thf(fact_317_simps_I9_J,axiom,
% 0.19/0.46 ! [X: name,C2: name,D: name,P: pi] :
% 0.19/0.46 ( ( X != C2 )
% 0.19/0.46 => ( ( X != D )
% 0.19/0.46 => ( ( subs @ ( res @ X @ P ) @ C2 @ D )
% 0.19/0.46 = ( res @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simps(9)
% 0.19/0.46 thf(fact_318_simps_I8_J,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.19/0.46 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 0.19/0.46 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simps(8)
% 0.19/0.46 thf(fact_319_substTrans,axiom,
% 0.19/0.46 ! [B: name,P: pi,A: name,C2: name] :
% 0.19/0.46 ( ( fresh_name_pi @ B @ P )
% 0.19/0.46 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 0.19/0.46 = ( subs @ P @ A @ C2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substTrans
% 0.19/0.46 thf(fact_320_forget,axiom,
% 0.19/0.46 ! [A: name,P: pi,B: name] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ P )
% 0.19/0.46 => ( ( subs @ P @ A @ B )
% 0.19/0.46 = P ) ) ).
% 0.19/0.46
% 0.19/0.46 % forget
% 0.19/0.46 thf(fact_321_fresh__fact1,axiom,
% 0.19/0.46 ! [A: name,P: pi,C2: name,B: name] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ P )
% 0.19/0.46 => ( ( A != C2 )
% 0.19/0.46 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_fact1
% 0.19/0.46 thf(fact_322_fresh__fact2,axiom,
% 0.19/0.46 ! [A: name,B: name,P: pi] :
% 0.19/0.46 ( ( A != B )
% 0.19/0.46 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % fresh_fact2
% 0.19/0.46 thf(fact_323_Agent_OsubstRes3,axiom,
% 0.19/0.46 ! [B: name,P: pi,A: name] :
% 0.19/0.46 ( ( fresh_name_pi @ B @ P )
% 0.19/0.46 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.19/0.46 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Agent.substRes3
% 0.19/0.46 thf(fact_324_substRes2,axiom,
% 0.19/0.46 ! [B: name,P: pi,A: name] :
% 0.19/0.46 ( ( fresh_name_pi @ B @ P )
% 0.19/0.46 => ( ( res @ A @ P )
% 0.19/0.46 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % substRes2
% 0.19/0.46 thf(fact_325_eqvt__subs,axiom,
% 0.19/0.46 ! [P5: list_P227219501e_name,P: pi,A: name,B: name] :
% 0.19/0.46 ( ( perm_name_pi @ P5 @ ( subs @ P @ A @ B ) )
% 0.19/0.46 = ( subs @ ( perm_name_pi @ P5 @ P ) @ ( perm_name_name @ P5 @ A ) @ ( perm_name_name @ P5 @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eqvt_subs
% 0.19/0.46 thf(fact_326_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3,axiom,
% 0.19/0.46 ! [A: name,P: pi,X: name] :
% 0.19/0.46 ( ( subs @ ( res @ A @ P ) @ X @ A )
% 0.19/0.46 = ( res @ X @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ A ) @ nil_Pr743626285e_name ) @ P ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Strong_Late_Sim_SC_Mirabelle_ygjvazaixl.substRes3
% 0.19/0.46 thf(fact_327_renaming,axiom,
% 0.19/0.46 ! [C2: name,P: pi,A: name,B: name] :
% 0.19/0.46 ( ( fresh_name_pi @ C2 @ P )
% 0.19/0.46 => ( ( subs @ P @ A @ B )
% 0.19/0.46 = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C2 @ A ) @ nil_Pr743626285e_name ) @ P ) @ C2 @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % renaming
% 0.19/0.46 thf(fact_328_injPermSubst,axiom,
% 0.19/0.46 ! [B: name,P: pi,A: name] :
% 0.19/0.46 ( ( fresh_name_pi @ B @ P )
% 0.19/0.46 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ P )
% 0.19/0.46 = ( subs @ P @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % injPermSubst
% 0.19/0.46 thf(fact_329_Late__Semantics_OComm1,axiom,
% 0.19/0.46 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Comm1
% 0.19/0.46 thf(fact_330_Late__Semantics_OComm2,axiom,
% 0.19/0.46 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Late_Semantics.Comm2
% 0.19/0.46 thf(fact_331_transitions_OComm2,axiom,
% 0.19/0.46 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( X != A )
% 0.19/0.46 => ( ( X != B )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Comm2
% 0.19/0.46 thf(fact_332_transitions_OComm1,axiom,
% 0.19/0.46 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( X != A )
% 0.19/0.46 => ( ( X != B )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Comm1
% 0.19/0.46 thf(fact_333_transitions_OClose2,axiom,
% 0.19/0.46 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.46 => ( ( X != A )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.46 => ( ( Y != A )
% 0.19/0.46 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.19/0.46 => ( ( X != Y )
% 0.19/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transitions.Close2
% 0.19/0.46 thf(fact_334_Agent_Oswap__name__def,axiom,
% 0.19/0.46 swap_name2 = swap_name ).
% 0.19/0.46
% 0.19/0.46 % Agent.swap_name_def
% 0.19/0.46 thf(fact_335_swap__name_Osimps,axiom,
% 0.19/0.46 ! [A: name,C2: name,B: name] :
% 0.19/0.46 ( ( ( A = C2 )
% 0.19/0.46 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = B ) )
% 0.19/0.46 & ( ( A != C2 )
% 0.19/0.46 => ( ( ( B = C2 )
% 0.19/0.46 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = A ) )
% 0.19/0.46 & ( ( B != C2 )
% 0.19/0.46 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 0.19/0.46 = C2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % swap_name.simps
% 0.19/0.46 thf(fact_336_name__prm__name_Osimps_I2_J,axiom,
% 0.19/0.46 ! [X: produc367475239e_name,Xs: list_P227219501e_name,A: name] :
% 0.19/0.46 ( ( name_prm_name @ ( cons_P1213805021e_name @ X @ Xs ) @ A )
% 0.19/0.46 = ( swap_name @ X @ ( name_prm_name @ Xs @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % name_prm_name.simps(2)
% 0.19/0.46 thf(fact_337_simE_I2_J,axiom,
% 0.19/0.46 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.19/0.46 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.46 => ? [P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simE(2)
% 0.19/0.46 thf(fact_338_simE_I1_J,axiom,
% 0.19/0.46 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.19/0.46 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.19/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.46 => ? [P3: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.46 & ( strong2129052853vative @ P3 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simE(1)
% 0.19/0.46 thf(fact_339_simulation__def,axiom,
% 0.19/0.46 ( strong743114133lation
% 0.19/0.46 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.19/0.46 ( ! [A2: late_subject,X3: name,Q6: pi] :
% 0.19/0.46 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A2 @ X3 @ Q6 ) )
% 0.19/0.46 & ( fresh_name_pi @ X3 @ P6 ) )
% 0.19/0.46 => ? [P7: pi] :
% 0.19/0.46 ( ( late_transitions @ P6 @ ( late_BoundR @ A2 @ X3 @ P7 ) )
% 0.19/0.46 & ( strong2129052853vative @ P7 @ Q6 @ A2 @ X3 @ Rel2 ) ) )
% 0.19/0.46 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.19/0.46 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.19/0.46 => ? [P7: pi] :
% 0.19/0.46 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.19/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simulation_def
% 0.19/0.46 thf(fact_340_simCases,axiom,
% 0.19/0.46 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.19/0.46 ( ! [A5: late_subject,Y3: name,Q3: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y3 @ Q3 ) )
% 0.19/0.46 => ( ( fresh_name_pi @ Y3 @ P )
% 0.19/0.46 => ? [P8: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y3 @ P8 ) )
% 0.19/0.46 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ Y3 @ Rel ) ) ) )
% 0.19/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.19/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.19/0.46 => ? [P8: pi] :
% 0.19/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 0.19/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 0.19/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simCases
% 0.19/0.46 thf(fact_341_name__prm__name_Osimps_I1_J,axiom,
% 0.19/0.46 ! [A: name] :
% 0.19/0.46 ( ( name_prm_name @ nil_Pr743626285e_name @ A )
% 0.19/0.46 = A ) ).
% 0.19/0.46
% 0.19/0.46 % name_prm_name.simps(1)
% 0.19/0.46 thf(fact_342_derivativeEqvtI2,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.19/0.46 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 0.19/0.46 => ( ( eqvt_pi @ Rel )
% 0.19/0.46 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % derivativeEqvtI2
% 0.19/0.46 thf(fact_343_Agent_Oname__prm__name__def,axiom,
% 0.19/0.46 perm_name_name = name_prm_name ).
% 0.19/0.46
% 0.19/0.46 % Agent.name_prm_name_def
% 0.19/0.46 thf(fact_344_parSym,axiom,
% 0.19/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.19/0.46 ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 0.19/0.46 => ( ! [R2: pi,S2: pi,X5: name] :
% 0.19/0.46 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 0.19/0.46 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % parSym
% 0.19/0.46 thf(fact_345_parAssocLeft,axiom,
% 0.19/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.19/0.46 ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 0.19/0.46 => ( ! [S2: pi,T: pi,X5: name] :
% 0.19/0.46 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T ) ) @ Rel ) )
% 0.19/0.46 => ( ! [S2: pi,T: pi,U: pi,X5: name] :
% 0.19/0.46 ( ( fresh_name_pi @ X5 @ S2 )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.19/0.46 => ( ! [S2: pi,T: pi,U: pi,X5: name] :
% 0.19/0.46 ( ( fresh_name_pi @ X5 @ U )
% 0.19/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 0.19/0.46 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % parAssocLeft
% 0.19/0.46 thf(fact_346_derivativeEqvtI,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 0.19/0.46 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 0.19/0.46 => ( ( eqvt_pi @ Rel )
% 0.19/0.46 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % derivativeEqvtI
% 0.19/0.46 thf(fact_347_pi_Ofresh_I9_J,axiom,
% 0.19/0.46 ! [A: name,X1: name,X2: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.19/0.46 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.fresh(9)
% 0.19/0.46 thf(fact_348_pi_Ofresh_I4_J,axiom,
% 0.19/0.46 ! [A: name,X32: name,X1: name,X2: pi] :
% 0.19/0.46 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.19/0.46 = ( ( fresh_name_name @ A @ X32 )
% 0.19/0.46 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % pi.fresh(4)
% 0.19/0.46
% 0.19/0.46 % Helper facts (11)
% 0.19/0.46 thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 0.19/0.46 ! [X: pi,Y: pi] :
% 0.19/0.46 ( ( if_pi @ $false @ X @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 0.19/0.46 ! [X: pi,Y: pi] :
% 0.19/0.46 ( ( if_pi @ $true @ X @ Y )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.46 ! [X: name,Y: name] :
% 0.19/0.46 ( ( if_name @ $false @ X @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.46 ! [X: name,Y: name] :
% 0.19/0.46 ( ( if_name @ $true @ X @ Y )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.19/0.46 ! [X: pi_Rep,Y: pi_Rep] :
% 0.19/0.46 ( ( if_pi_Rep @ $false @ X @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 0.19/0.46 ! [X: pi_Rep,Y: pi_Rep] :
% 0.19/0.46 ( ( if_pi_Rep @ $true @ X @ Y )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.19/0.46 ! [X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( if_Late_freeRes @ $false @ X @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 0.19/0.46 ! [X: late_freeRes,Y: late_freeRes] :
% 0.19/0.46 ( ( if_Late_freeRes @ $true @ X @ Y )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.46 ! [P: $o] :
% 0.19/0.46 ( ( P = $true )
% 0.19/0.46 | ( P = $false ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.46 ! [X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( if_Late_subject @ $false @ X @ Y )
% 0.19/0.46 = Y ) ).
% 0.19/0.46
% 0.19/0.46 thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 0.19/0.46 ! [X: late_subject,Y: late_subject] :
% 0.19/0.46 ( ( if_Late_subject @ $true @ X @ Y )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % Conjectures (1)
% 0.19/0.46 thf(conj_0,conjecture,
% 0.19/0.46 late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 2.88/1.58 ---- Embedded in THF ---
% 2.88/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.88/1.58 %%% Generated on Tue Feb 24 08:29:52 EST 2026
% 2.88/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.88/1.58 %%% Logic specification used:
% 2.88/1.58 %%% thf(spec, logic, $$dhol).
% 2.88/1.58
% 2.88/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2DTF18628.p
% See solution above
% 2.88/1.58 ------------------------
% 3.07/1.65 ---- Cleaned THF ---
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_062_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_M_Eo_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
% 3.07/1.65 produc890461031e_name: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 3.07/1.65 produc1359399907ubject: $tType ).
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 3.07/1.65 produc355105483reeRes: $tType ).
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
% 3.07/1.65 produc1777919905pi_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
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% 3.07/1.65 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 3.07/1.65 produc2052722628s_name: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 3.07/1.65 produc865358760ubject: $tType ).
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% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 3.07/1.65 produc2008547984reeRes: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 3.07/1.65 produc140253050ect_pi: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 3.07/1.65 produc992857746Res_pi: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__Late____Semantics__Osubject_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
% 3.07/1.65 list_Late_freeRes: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Late____Semantics__Osubject_J,type,
% 3.07/1.65 set_Late_subject: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
% 3.07/1.65 set_Late_freeRes: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__Agent__Opi____Rep_J,type,
% 3.07/1.65 list_pi_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__Oresidual____Rep,type,
% 3.07/1.65 late_residual_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__Osubject____Rep,type,
% 3.07/1.65 late_subject_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__OfreeRes____Rep,type,
% 3.07/1.65 late_freeRes_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Agent__Opi____Rep_J,type,
% 3.07/1.65 set_pi_Rep: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__Agent__Oname_J,type,
% 3.07/1.65 list_name: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 3.07/1.65 set_name: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__List__Olist_It__Agent__Opi_J,type,
% 3.07/1.65 list_pi: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 3.07/1.65 late_residual: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__Osubject,type,
% 3.07/1.65 late_subject: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Late____Semantics__OfreeRes,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Set__Oset_It__Agent__Opi_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Agent__Opi____Rep,type,
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% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Agent__Oname,type,
% 3.07/1.65 name: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(ty_n_t__Agent__Opi,type,
% 3.07/1.65 pi: $tType ).
% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Opi_OInput,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Opi_OPar,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Opi_ORes,type,
% 3.07/1.65 res: name > pi > pi ).
% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Orec_Oname__prm__name,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Orec_Oswap__name,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Agent_Osubs,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_If_001t__Agent__Oname,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_If_001t__Agent__Opi,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_If_001t__Agent__Opi____Rep,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_If_001t__Late____Semantics__OfreeRes,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_If_001t__Late____Semantics__Osubject,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_Late__Semantics_Otransitions,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Agent__Oname,type,
% 3.07/1.65 cons_name: name > list_name > list_name ).
% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Agent__Opi,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Agent__Opi____Rep,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Late____Semantics__OfreeRes,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Late____Semantics__Osubject,type,
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% 3.07/1.65
% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
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% 3.07/1.65 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
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% 3.07/1.65 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
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% 3.07/1.65
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% 3.07/1.65 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
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% 3.07/1.65 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi____Rep,type,
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% 3.07/1.65 thf(sy_v_z____,type,
% 3.07/1.65 z: name ).
% 3.07/1.65
% 3.07/1.65 thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062,axiom,
% 3.07/1.65 aa = b ).
% 3.07/1.65
% 3.07/1.65 thf(fact_1_cOpen_Ohyps_I2_J,axiom,
% 3.07/1.65 b != x ).
% 3.07/1.65
% 3.07/1.65 thf(fact_2_cClose1_Ohyps_I10_J,axiom,
% 3.07/1.65 z != aa ).
% 3.07/1.65
% 3.07/1.65 thf(fact_3_cClose1_Ohyps_I6_J,axiom,
% 3.07/1.65 y != z ).
% 3.07/1.65
% 3.07/1.65 thf(fact_4_cClose1_Ohyps_I5_J,axiom,
% 3.07/1.65 y != aa ).
% 3.07/1.65
% 3.07/1.65 thf(fact_5__092_060open_062z_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 3.07/1.65 z != x ).
% 3.07/1.65
% 3.07/1.65 thf(fact_6_cOpen_Ohyps_I1_J,axiom,
% 3.07/1.65 late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_7_cOpen_Ohyps_I3_J,axiom,
% 3.07/1.65 ( ( late_BoundOutputS @ aa )
% 3.07/1.65 = ( late_BoundOutputS @ b ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_8_cClose1_Ohyps_I14_J,axiom,
% 3.07/1.65 alpha = late_TauR ).
% 3.07/1.65
% 3.07/1.65 thf(fact_9_cClose1_Ohyps_I13_J,axiom,
% 3.07/1.65 fresh_name_name @ z @ x ).
% 3.07/1.65
% 3.07/1.65 thf(fact_10_perm__swap_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_subject] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_11_perm__swap_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_freeRes] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_12_perm__swap_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi_Rep] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_13_perm__swap_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: name] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_14_perm__swap_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_15_name__id,axiom,
% 3.07/1.65 ! [A: name,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_16_name__id,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_17_name__id,axiom,
% 3.07/1.65 ! [A: name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_18_name__id,axiom,
% 3.07/1.65 ! [A: name,X: name] :
% 3.07/1.65 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_19_name__id,axiom,
% 3.07/1.65 ! [A: name,X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_20_name__swap,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_21_name__swap,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_22_name__swap,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_23_name__swap,axiom,
% 3.07/1.65 ! [A: name,B: name,X: name] :
% 3.07/1.65 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_24_name__swap,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_25_name__swap__bij,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_subject] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_26_name__swap__bij,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_freeRes] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_27_name__swap__bij,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi_Rep] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_28_name__swap__bij,axiom,
% 3.07/1.65 ! [A: name,B: name,X: name] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_29_name__swap__bij,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_30_pt__name1,axiom,
% 3.07/1.65 ! [X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_31_pt__name1,axiom,
% 3.07/1.65 ! [X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_32_pt__name1,axiom,
% 3.07/1.65 ! [X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_33_pt__name1,axiom,
% 3.07/1.65 ! [X: name] :
% 3.07/1.65 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_34_pt__name1,axiom,
% 3.07/1.65 ! [X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_35__092_060open_062y_A_092_060noteq_062_Ax_092_060close_062,axiom,
% 3.07/1.65 y != x ).
% 3.07/1.65
% 3.07/1.65 thf(fact_36_perm__swap_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_subject] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_37_perm__swap_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: late_freeRes] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_38_perm__swap_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi_Rep] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_39_perm__swap_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: name] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_40_perm__swap_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name,X: pi] :
% 3.07/1.65 ( ( 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 ) )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_41_eqvt,axiom,
% 3.07/1.65 ! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( late_transitions @ X1 @ X2 )
% 3.07/1.65 => ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_42__092_060open_062z_A_092_060sharp_062_AQ_092_060close_062,axiom,
% 3.07/1.65 fresh_name_pi @ z @ q ).
% 3.07/1.65
% 3.07/1.65 thf(fact_43_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.07/1.65 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 3.07/1.65 ( ( ( late_OutputR @ X2 @ X1 )
% 3.07/1.65 = ( late_OutputR @ Y2 @ Y1 ) )
% 3.07/1.65 = ( ( X2 = Y2 )
% 3.07/1.65 & ( X1 = Y1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_44_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.07/1.65 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 3.07/1.65 ( ( ( late_OutputR @ X11 @ X12 )
% 3.07/1.65 = ( late_OutputR @ Y11 @ Y12 ) )
% 3.07/1.65 = ( ( X11 = Y11 )
% 3.07/1.65 & ( X12 = Y12 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_45_cClose1_Ohyps_I11_J,axiom,
% 3.07/1.65 fresh_name_pi @ z @ p2 ).
% 3.07/1.65
% 3.07/1.65 thf(fact_46_cClose1_Ohyps_I7_J,axiom,
% 3.07/1.65 fresh_name_pi @ y @ q2 ).
% 3.07/1.65
% 3.07/1.65 thf(fact_47_cClose1_Ohyps_I12_J,axiom,
% 3.07/1.65 fresh_name_name @ y @ x ).
% 3.07/1.65
% 3.07/1.65 thf(fact_48_assms_I1_J,axiom,
% 3.07/1.65 fresh_name_pi @ x @ p ).
% 3.07/1.65
% 3.07/1.65 thf(fact_49_cClose1_Ohyps_I8_J,axiom,
% 3.07/1.65 fresh_name_pi @ z @ p ).
% 3.07/1.65
% 3.07/1.65 thf(fact_50_cClose1_Ohyps_I3_J,axiom,
% 3.07/1.65 fresh_name_pi @ y @ p ).
% 3.07/1.65
% 3.07/1.65 thf(fact_51_residual__perm__empty,axiom,
% 3.07/1.65 ! [Residual_Rep: late_residual_Rep] :
% 3.07/1.65 ( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
% 3.07/1.65 = Residual_Rep ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_52_subject__perm__empty,axiom,
% 3.07/1.65 ! [Subject_Rep: late_subject_Rep] :
% 3.07/1.65 ( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
% 3.07/1.65 = Subject_Rep ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_53_freeRes__perm__empty,axiom,
% 3.07/1.65 ! [FreeRes_Rep: late_freeRes_Rep] :
% 3.07/1.65 ( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
% 3.07/1.65 = FreeRes_Rep ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_54_pi__perm__empty,axiom,
% 3.07/1.65 ! [Pi_Rep: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
% 3.07/1.65 = Pi_Rep ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_55_freeRes_Operm_I1_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X2: name,X1: name] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
% 3.07/1.65 = ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_56_subject_Operm_I2_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X1: name] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
% 3.07/1.65 = ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_57_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.07/1.65 ! [X1: name,Y1: name] :
% 3.07/1.65 ( ( ( late_BoundOutputS @ X1 )
% 3.07/1.65 = ( late_BoundOutputS @ Y1 ) )
% 3.07/1.65 = ( X1 = Y1 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_58_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.07/1.65 ! [X2: name,Y2: name] :
% 3.07/1.65 ( ( ( late_BoundOutputS @ X2 )
% 3.07/1.65 = ( late_BoundOutputS @ Y2 ) )
% 3.07/1.65 = ( X2 = Y2 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_59_freeRes_Operm_I2_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ late_TauR )
% 3.07/1.65 = late_TauR ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_60_name__fresh,axiom,
% 3.07/1.65 ( fresh_name_name
% 3.07/1.65 = ( ^ [A2: name,B2: name] : ( A2 != B2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_61_residual_Operm_I2_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
% 3.07/1.65 ( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
% 3.07/1.65 = ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_62_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: pi_Rep,B: name] :
% 3.07/1.65 ( ( fresh_name_pi_Rep @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi_Rep @ B @ X )
% 3.07/1.65 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_63_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,B: name] :
% 3.07/1.65 ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 => ( ( fresh_717452603ubject @ B @ X )
% 3.07/1.65 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_64_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,B: name] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ B @ X )
% 3.07/1.65 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_65_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: name,B: name] :
% 3.07/1.65 ( ( fresh_name_name @ A @ X )
% 3.07/1.65 => ( ( fresh_name_name @ B @ X )
% 3.07/1.65 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_66_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: pi,B: name] :
% 3.07/1.65 ( ( fresh_name_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi @ B @ X )
% 3.07/1.65 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_67_perm__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: name > noption_pi,B: name] :
% 3.07/1.65 ( ( fresh_543891186ion_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_543891186ion_pi @ B @ X )
% 3.07/1.65 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_68_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: pi_Rep,B: name] :
% 3.07/1.65 ( ( fresh_name_pi_Rep @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi_Rep @ B @ X )
% 3.07/1.65 => ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_69_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,B: name] :
% 3.07/1.65 ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 => ( ( fresh_717452603ubject @ B @ X )
% 3.07/1.65 => ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_70_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,B: name] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ B @ X )
% 3.07/1.65 => ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_71_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: name,B: name] :
% 3.07/1.65 ( ( fresh_name_name @ A @ X )
% 3.07/1.65 => ( ( fresh_name_name @ B @ X )
% 3.07/1.65 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_72_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: pi,B: name] :
% 3.07/1.65 ( ( fresh_name_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi @ B @ X )
% 3.07/1.65 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_73_name__fresh__fresh,axiom,
% 3.07/1.65 ! [A: name,X: name > noption_pi,B: name] :
% 3.07/1.65 ( ( fresh_543891186ion_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_543891186ion_pi @ B @ X )
% 3.07/1.65 => ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
% 3.07/1.65 = X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_74_cClose1_Ohyps_I9_J,axiom,
% 3.07/1.65 fresh_name_pi @ z @ ( res @ x @ q ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_75_cClose1_Ohyps_I4_J,axiom,
% 3.07/1.65 fresh_name_pi @ y @ ( res @ x @ q ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_76_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_name_pi_Rep @ A @ X )
% 3.07/1.65 => ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_77_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: late_subject] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 => ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_78_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 => ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_79_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: name] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_name_name @ A @ X )
% 3.07/1.65 => ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_80_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: pi] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_name_pi @ A @ X )
% 3.07/1.65 => ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_81_fresh__perm__app,axiom,
% 3.07/1.65 ! [A: name,Pi: list_P227219501e_name,X: name > noption_pi] :
% 3.07/1.65 ( ( fresh_922791155e_name @ A @ Pi )
% 3.07/1.65 => ( ( fresh_543891186ion_pi @ A @ X )
% 3.07/1.65 => ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_82_name__exists__fresh,axiom,
% 3.07/1.65 ! [X: late_subject] :
% 3.07/1.65 ~ ! [C: name] :
% 3.07/1.65 ~ ( fresh_717452603ubject @ C @ X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_83_name__exists__fresh,axiom,
% 3.07/1.65 ! [X: late_freeRes] :
% 3.07/1.65 ~ ! [C: name] :
% 3.07/1.65 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_84_name__exists__fresh,axiom,
% 3.07/1.65 ! [X: name] :
% 3.07/1.65 ~ ! [C: name] :
% 3.07/1.65 ~ ( fresh_name_name @ C @ X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_85_name__exists__fresh,axiom,
% 3.07/1.65 ! [X: pi] :
% 3.07/1.65 ~ ! [C: name] :
% 3.07/1.65 ~ ( fresh_name_pi @ C @ X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_86_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
% 3.07/1.65 = ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_87_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
% 3.07/1.65 = ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_88_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
% 3.07/1.65 = ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_89_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
% 3.07/1.65 = ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_90_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
% 3.07/1.65 = ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_91_fresh__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( fresh_543891186ion_pi @ A @ X ) )
% 3.07/1.65 = ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_92_mem__Collect__eq,axiom,
% 3.07/1.65 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 3.07/1.65 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 3.07/1.65 = ( P @ A ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_93_Collect__mem__eq,axiom,
% 3.07/1.65 ! [A3: set_Pr1834926343_pi_pi] :
% 3.07/1.65 ( ( collec1051790738_pi_pi
% 3.07/1.65 @ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A3 ) )
% 3.07/1.65 = A3 ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_94_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
% 3.07/1.65 ( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
% 3.07/1.65 = ( fresh_name_pi_Rep @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_95_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: late_subject] :
% 3.07/1.65 ( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
% 3.07/1.65 = ( fresh_717452603ubject @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_96_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
% 3.07/1.65 = ( fresh_1641682979reeRes @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_97_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: name] :
% 3.07/1.65 ( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
% 3.07/1.65 = ( fresh_name_name @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_98_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: pi] :
% 3.07/1.65 ( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
% 3.07/1.65 = ( fresh_name_pi @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_99_fresh__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
% 3.07/1.65 ( ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) )
% 3.07/1.65 = ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_100_name__calc_I2_J,axiom,
% 3.07/1.65 ! [X: name] :
% 3.07/1.65 ( ( perm_name_name @ nil_Pr743626285e_name @ X )
% 3.07/1.65 = X ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_101_freeRes_Oexhaust,axiom,
% 3.07/1.65 ! [Y: late_freeRes] :
% 3.07/1.65 ( ! [X112: name,X122: name] :
% 3.07/1.65 ( Y
% 3.07/1.65 != ( late_OutputR @ X112 @ X122 ) )
% 3.07/1.65 => ( Y = late_TauR ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_102_freeRes_Oinducts,axiom,
% 3.07/1.65 ! [P: late_freeRes > $o,FreeRes: late_freeRes] :
% 3.07/1.65 ( ! [Name1: name,Name2: name] : ( P @ ( late_OutputR @ Name1 @ Name2 ) )
% 3.07/1.65 => ( ( P @ late_TauR )
% 3.07/1.65 => ( P @ FreeRes ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_103_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.07/1.65 ! [X11: name,X12: name] :
% 3.07/1.65 ( ( late_OutputR @ X11 @ X12 )
% 3.07/1.65 != late_TauR ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_104_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.07/1.65 ! [Name12: name,Name22: name] :
% 3.07/1.65 ( ( late_OutputR @ Name12 @ Name22 )
% 3.07/1.65 != late_TauR ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_105_freshFreeDerivative_I2_J,axiom,
% 3.07/1.65 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.07/1.65 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.65 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_106_swap__simps_I1_J,axiom,
% 3.07/1.65 ! [A: name,B: name] :
% 3.07/1.65 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
% 3.07/1.65 = B ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_107_swap__simps_I2_J,axiom,
% 3.07/1.65 ! [A: name,B: name] :
% 3.07/1.65 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
% 3.07/1.65 = A ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_108_swap__simps_I3_J,axiom,
% 3.07/1.65 ! [A: name,C2: name,B: name] :
% 3.07/1.65 ( ( A != C2 )
% 3.07/1.65 => ( ( B != C2 )
% 3.07/1.65 => ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C2 )
% 3.07/1.65 = C2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_109_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: pi_Rep,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_name_pi_Rep @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi_Rep @ C2 @ X )
% 3.07/1.65 => ( fresh_name_pi_Rep @ C2 @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_110_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: late_subject,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 => ( ( fresh_717452603ubject @ C2 @ X )
% 3.07/1.65 => ( fresh_717452603ubject @ C2 @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_111_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: late_freeRes,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ C2 @ X )
% 3.07/1.65 => ( fresh_1641682979reeRes @ C2 @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_112_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: name,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_name_name @ A @ X )
% 3.07/1.65 => ( ( fresh_name_name @ C2 @ X )
% 3.07/1.65 => ( fresh_name_name @ C2 @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_113_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: pi,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_name_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_name_pi @ C2 @ X )
% 3.07/1.65 => ( fresh_name_pi @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_114_fresh__aux,axiom,
% 3.07/1.65 ! [C2: name,A: name,X: name > noption_pi,B: name] :
% 3.07/1.65 ( ( C2 != A )
% 3.07/1.65 => ( ( fresh_543891186ion_pi @ A @ X )
% 3.07/1.65 => ( ( fresh_543891186ion_pi @ C2 @ X )
% 3.07/1.65 => ( fresh_543891186ion_pi @ C2 @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_115_cp__name__name1,axiom,
% 3.07/1.65 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_116_cp__name__name1,axiom,
% 3.07/1.65 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_117_cp__name__name1,axiom,
% 3.07/1.65 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_118_cp__name__name1,axiom,
% 3.07/1.65 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
% 3.07/1.65 ( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
% 3.07/1.65 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_119_cp__name__name1,axiom,
% 3.07/1.65 ! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
% 3.07/1.65 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_120_name__perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_121_name__perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_122_name__perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_123_name__perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 3.07/1.65 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_124_name__perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_125_perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_126_perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_127_perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
% 3.07/1.65 ( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_128_perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
% 3.07/1.65 ( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_129_perm__compose,axiom,
% 3.07/1.65 ! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
% 3.07/1.65 ( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
% 3.07/1.65 = ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_130_perm__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 3.07/1.65 ( ( ( perm_n1559866809ubject @ Pi @ X )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_131_perm__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 3.07/1.65 ( ( ( perm_n336613537reeRes @ Pi @ X )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_132_perm__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 3.07/1.65 ( ( ( perm_name_pi_Rep @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_133_perm__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 3.07/1.65 ( ( ( perm_name_name @ Pi @ X )
% 3.07/1.65 = ( perm_name_name @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_134_perm__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 3.07/1.65 ( ( ( perm_name_pi @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_135_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_136_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_137_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_138_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_139_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
% 3.07/1.65 ( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_140_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_141_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_142_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_143_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_144_perm__app,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
% 3.07/1.65 ( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
% 3.07/1.65 = ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_145_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X4: set_Pr1834926343_pi_pi] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X4 ) )
% 3.07/1.65 = ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_146_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,X4: set_Late_subject] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X4 ) )
% 3.07/1.65 = ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_147_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,X4: set_Late_freeRes] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X4 ) )
% 3.07/1.65 = ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_148_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi_Rep,X4: set_pi_Rep] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X4 ) )
% 3.07/1.65 = ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_149_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: name,X4: set_name] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member_name @ X @ X4 ) )
% 3.07/1.65 = ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_150_in__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi,X4: set_pi] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( member_pi @ X @ X4 ) )
% 3.07/1.65 = ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X4 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_151_eq__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 3.07/1.65 = ( ( perm_n1559866809ubject @ Pi @ X )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_152_eq__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 3.07/1.65 = ( ( perm_n336613537reeRes @ Pi @ X )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_153_eq__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 3.07/1.65 = ( ( perm_name_pi_Rep @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_154_eq__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 3.07/1.65 = ( ( perm_name_name @ Pi @ X )
% 3.07/1.65 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_155_eq__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi,Y: pi] :
% 3.07/1.65 ( ( perm_name_o @ Pi @ ( X = Y ) )
% 3.07/1.65 = ( ( perm_name_pi @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_156_residual_Oinject_I2_J,axiom,
% 3.07/1.65 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 3.07/1.65 ( ( ( late_FreeR @ X2 @ X1 )
% 3.07/1.65 = ( late_FreeR @ Y2 @ Y1 ) )
% 3.07/1.65 = ( ( X2 = Y2 )
% 3.07/1.65 & ( X1 = Y1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_157_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,Y: late_subject] :
% 3.07/1.65 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_158_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,Y: late_freeRes] :
% 3.07/1.65 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_159_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,Y: name] :
% 3.07/1.65 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 & ( fresh_name_name @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_160_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,Y: pi] :
% 3.07/1.65 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_161_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,Y: late_subject] :
% 3.07/1.65 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_162_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 3.07/1.65 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_163_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,Y: name] :
% 3.07/1.65 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 & ( fresh_name_name @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_164_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,Y: pi] :
% 3.07/1.65 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 & ( fresh_name_pi @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_165_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: name,Y: late_subject] :
% 3.07/1.65 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_name_name @ A @ X )
% 3.07/1.65 & ( fresh_717452603ubject @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_166_fresh__prod,axiom,
% 3.07/1.65 ! [A: name,X: name,Y: late_freeRes] :
% 3.07/1.65 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
% 3.07/1.65 = ( ( fresh_name_name @ A @ X )
% 3.07/1.65 & ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_167_list_Oinject,axiom,
% 3.07/1.65 ! [X21: produc367475239e_name,X22: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
% 3.07/1.65 ( ( ( cons_P1213805021e_name @ X21 @ X22 )
% 3.07/1.65 = ( cons_P1213805021e_name @ Y21 @ Y22 ) )
% 3.07/1.65 = ( ( X21 = Y21 )
% 3.07/1.65 & ( X22 = Y22 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_168_old_Oprod_Oinject,axiom,
% 3.07/1.65 ! [A: name,B: name,A4: name,B3: name] :
% 3.07/1.65 ( ( ( produc1570949143e_name @ A @ B )
% 3.07/1.65 = ( produc1570949143e_name @ A4 @ B3 ) )
% 3.07/1.65 = ( ( A = A4 )
% 3.07/1.65 & ( B = B3 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_169_old_Oprod_Oinject,axiom,
% 3.07/1.65 ! [A: pi,B: pi,A4: pi,B3: pi] :
% 3.07/1.65 ( ( ( product_Pair_pi_pi @ A @ B )
% 3.07/1.65 = ( product_Pair_pi_pi @ A4 @ B3 ) )
% 3.07/1.65 = ( ( A = A4 )
% 3.07/1.65 & ( B = B3 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_170_prod_Oinject,axiom,
% 3.07/1.65 ! [X1: name,X2: name,Y1: name,Y2: name] :
% 3.07/1.65 ( ( ( produc1570949143e_name @ X1 @ X2 )
% 3.07/1.65 = ( produc1570949143e_name @ Y1 @ Y2 ) )
% 3.07/1.65 = ( ( X1 = Y1 )
% 3.07/1.65 & ( X2 = Y2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_171_prod_Oinject,axiom,
% 3.07/1.65 ! [X1: pi,X2: pi,Y1: pi,Y2: pi] :
% 3.07/1.65 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 3.07/1.65 = ( product_Pair_pi_pi @ Y1 @ Y2 ) )
% 3.07/1.65 = ( ( X1 = Y1 )
% 3.07/1.65 & ( X2 = Y2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_172_cClose1_Ohyps_I2_J,axiom,
% 3.07/1.65 late_transitions @ ( res @ x @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_173_fresh__list__cons,axiom,
% 3.07/1.65 ! [A: name,X: late_subject,Xs: list_Late_subject] :
% 3.07/1.65 ( ( fresh_838462539ubject @ A @ ( cons_Late_subject @ X @ Xs ) )
% 3.07/1.65 = ( ( fresh_717452603ubject @ A @ X )
% 3.07/1.65 & ( fresh_838462539ubject @ A @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_174_fresh__list__cons,axiom,
% 3.07/1.65 ! [A: name,X: late_freeRes,Xs: list_Late_freeRes] :
% 3.07/1.65 ( ( fresh_1981651763reeRes @ A @ ( cons_Late_freeRes @ X @ Xs ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.07/1.65 & ( fresh_1981651763reeRes @ A @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_175_fresh__list__cons,axiom,
% 3.07/1.65 ! [A: name,X: name,Xs: list_name] :
% 3.07/1.65 ( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs ) )
% 3.07/1.65 = ( ( fresh_name_name @ A @ X )
% 3.07/1.65 & ( fresh_name_list_name @ A @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_176_fresh__list__cons,axiom,
% 3.07/1.65 ! [A: name,X: pi,Xs: list_pi] :
% 3.07/1.65 ( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs ) )
% 3.07/1.65 = ( ( fresh_name_pi @ A @ X )
% 3.07/1.65 & ( fresh_name_list_pi @ A @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_177_fresh__list__cons,axiom,
% 3.07/1.65 ! [A: name,X: name > noption_pi,Xs: list_name_noption_pi] :
% 3.07/1.65 ( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ X @ Xs ) )
% 3.07/1.65 = ( ( fresh_543891186ion_pi @ A @ X )
% 3.07/1.65 & ( fresh_1135477378ion_pi @ A @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_178_fresh__prodD_I2_J,axiom,
% 3.07/1.65 ! [A: name,X: name,Y: name] :
% 3.07/1.65 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 3.07/1.65 => ( fresh_name_name @ A @ Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_179_fresh__prodD_I2_J,axiom,
% 3.07/1.65 ! [A: name,X: pi,Y: pi] :
% 3.07/1.65 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 3.07/1.65 => ( fresh_name_pi @ A @ Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_180_fresh__prodD_I1_J,axiom,
% 3.07/1.65 ! [A: name,X: name,Y: name] :
% 3.07/1.65 ( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
% 3.07/1.65 => ( fresh_name_name @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_181_fresh__prodD_I1_J,axiom,
% 3.07/1.65 ! [A: name,X: pi,Y: pi] :
% 3.07/1.65 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
% 3.07/1.65 => ( fresh_name_pi @ A @ X ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_182_cons__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Xs: list_Late_subject] :
% 3.07/1.65 ( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs ) )
% 3.07/1.65 = ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_183_cons__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Xs: list_Late_freeRes] :
% 3.07/1.65 ( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs ) )
% 3.07/1.65 = ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_184_cons__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi_Rep,Xs: list_pi_Rep] :
% 3.07/1.65 ( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs ) )
% 3.07/1.65 = ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_185_cons__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: name,Xs: list_name] :
% 3.07/1.65 ( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs ) )
% 3.07/1.65 = ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_186_cons__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: pi,Xs: list_pi] :
% 3.07/1.65 ( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs ) )
% 3.07/1.65 = ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_187_freeRes_Ofresh_I2_J,axiom,
% 3.07/1.65 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_188_residual_Ofresh_I2_J,axiom,
% 3.07/1.65 ! [A: name,X2: late_freeRes,X1: pi] :
% 3.07/1.65 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 3.07/1.65 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 3.07/1.65 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_189_freeRes_Ofresh_I1_J,axiom,
% 3.07/1.65 ! [A: name,X2: name,X1: name] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 3.07/1.65 = ( ( fresh_name_name @ A @ X2 )
% 3.07/1.65 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_190_subject_Ofresh_I2_J,axiom,
% 3.07/1.65 ! [A: name,X1: name] :
% 3.07/1.65 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 3.07/1.65 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_191_pi_Operm_I9_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X1: name,X2: pi] :
% 3.07/1.65 ( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
% 3.07/1.65 = ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_192_cClose1_Ohyps_I1_J,axiom,
% 3.07/1.65 late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_193_residual_Operm_I1_J,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
% 3.07/1.65 ( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.07/1.65 = ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_194_name__bij,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: name,Y: name] :
% 3.07/1.65 ( ( ( perm_name_name @ Pi @ X )
% 3.07/1.65 = ( perm_name_name @ Pi @ Y ) )
% 3.07/1.65 = ( X = Y ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_195_Late__Semantics_OResB,axiom,
% 3.07/1.65 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Y @ A )
% 3.07/1.65 => ( ( Y != X )
% 3.07/1.65 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_196_transitions_OResB,axiom,
% 3.07/1.65 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Y @ A )
% 3.07/1.65 => ( ( Y != X )
% 3.07/1.65 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.65 => ( ( fresh_717452603ubject @ X @ A )
% 3.07/1.65 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_197_resCasesF,axiom,
% 3.07/1.65 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
% 3.07/1.65 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.07/1.65 => ( ! [P3: pi] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.07/1.65 => ( F2 @ ( res @ X @ P3 ) ) ) )
% 3.07/1.65 => ( F2 @ XP ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_198_resCasesF_H,axiom,
% 3.07/1.65 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.07/1.65 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.07/1.65 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 3.07/1.65 ( ( ( res @ X @ P )
% 3.07/1.65 = ( res @ Y3 @ P4 ) )
% 3.07/1.65 => ( ( ( late_FreeR @ Alpha @ P2 )
% 3.07/1.65 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.07/1.65 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_199_ResF,axiom,
% 3.07/1.65 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.07/1.65 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 3.07/1.65 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_200_freshBoundDerivative_I1_J,axiom,
% 3.07/1.65 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.65 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.65 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_201_freshRes,axiom,
% 3.07/1.65 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_202_residual_Odistinct_I1_J,axiom,
% 3.07/1.65 ! [Subject: late_subject,Name: name,Pi: pi,FreeRes2: late_freeRes,Pi3: pi] :
% 3.07/1.65 ( ( late_BoundR @ Subject @ Name @ Pi )
% 3.07/1.65 != ( late_FreeR @ FreeRes2 @ Pi3 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_203_residual_Oinducts,axiom,
% 3.07/1.65 ! [P: late_residual > $o,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_204_resCases_H,axiom,
% 3.07/1.65 ! [X: name,P: pi,Rs: late_residual] :
% 3.07/1.65 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 3.07/1.65 => ( ! [P4: pi,A5: name,B4: name] :
% 3.07/1.65 ( ( ( res @ X @ P )
% 3.07/1.65 = ( res @ B4 @ P4 ) )
% 3.07/1.65 => ! [P3: pi] :
% 3.07/1.65 ( ( Rs
% 3.07/1.65 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 3.07/1.65 => ( A5 = B4 ) ) ) )
% 3.07/1.65 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y3: name] :
% 3.07/1.65 ( ( ( res @ X @ P )
% 3.07/1.65 = ( res @ Y3 @ P4 ) )
% 3.07/1.65 => ( ( Rs
% 3.07/1.65 = ( late_BoundR @ A5 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Y3 @ A5 )
% 3.07/1.65 => ( ( Y3 != X5 )
% 3.07/1.65 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.07/1.65 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) )
% 3.07/1.65 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 3.07/1.65 ( ( ( res @ X @ P )
% 3.07/1.65 = ( res @ Y3 @ P4 ) )
% 3.07/1.65 => ( ( Rs
% 3.07/1.65 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.07/1.65 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_205_sorted__wrt_Ocases,axiom,
% 3.07/1.65 ! [X: produc1872410278e_name] :
% 3.07/1.65 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc1069608854e_name @ P4 @ nil_Pr743626285e_name ) )
% 3.07/1.65 => ~ ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ Ys ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_206_successively_Ocases,axiom,
% 3.07/1.65 ! [X: produc1872410278e_name] :
% 3.07/1.65 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc1069608854e_name @ P4 @ nil_Pr743626285e_name ) )
% 3.07/1.65 => ( ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) ) )
% 3.07/1.65 => ~ ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Y3: produc367475239e_name,Xs2: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc1069608854e_name @ P4 @ ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_207_splice_Ocases,axiom,
% 3.07/1.65 ! [X: produc890461031e_name] :
% 3.07/1.65 ( ! [Ys: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 3.07/1.65 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_208_shuffles_Ocases,axiom,
% 3.07/1.65 ! [X: produc890461031e_name] :
% 3.07/1.65 ( ! [Ys: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc208131031e_name @ nil_Pr743626285e_name @ Ys ) )
% 3.07/1.65 => ( ! [Xs2: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc208131031e_name @ Xs2 @ nil_Pr743626285e_name ) )
% 3.07/1.65 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( X
% 3.07/1.65 != ( produc208131031e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_209_resCasesB_H,axiom,
% 3.07/1.65 ! [X6: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 3.07/1.65 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 3.07/1.65 => ( ! [P4: pi,A5: name,B4: name] :
% 3.07/1.65 ( ( ( res @ X6 @ P )
% 3.07/1.65 = ( res @ B4 @ P4 ) )
% 3.07/1.65 => ! [P3: pi] :
% 3.07/1.65 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 3.07/1.65 = ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
% 3.07/1.65 => ( A5 = B4 ) ) ) )
% 3.07/1.65 => ~ ! [P4: pi,A5: late_subject,X5: name,P3: pi,Y3: name] :
% 3.07/1.65 ( ( ( res @ X6 @ P )
% 3.07/1.65 = ( res @ Y3 @ P4 ) )
% 3.07/1.65 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 3.07/1.65 = ( late_BoundR @ A5 @ X5 @ ( res @ Y3 @ P3 ) ) )
% 3.07/1.65 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Y3 @ A5 )
% 3.07/1.65 => ( ( Y3 != X5 )
% 3.07/1.65 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.07/1.65 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_210_Open,axiom,
% 3.07/1.65 ! [P: pi,A: name,B: name,P2: pi] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.07/1.65 => ( ( A != B )
% 3.07/1.65 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_211_freshResidual,axiom,
% 3.07/1.65 ! [P: pi,Rs: late_residual,X: name] :
% 3.07/1.65 ( ( late_transitions @ P @ Rs )
% 3.07/1.65 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.65 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_212_freshBoundDerivative_I2_J,axiom,
% 3.07/1.65 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.65 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.65 => ( ( Y != X )
% 3.07/1.65 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_213_residual_Ostrong__inducts,axiom,
% 3.07/1.65 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 3.07/1.65 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_214_residual_Ostrong__inducts,axiom,
% 3.07/1.65 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_215_residual_Ostrong__inducts,axiom,
% 3.07/1.65 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 3.07/1.65 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_216_residual_Ostrong__inducts,axiom,
% 3.07/1.65 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 3.07/1.65 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_217_residual_Ostrong__induct,axiom,
% 3.07/1.65 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 3.07/1.65 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_218_residual_Ostrong__induct,axiom,
% 3.07/1.65 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 3.07/1.65 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_219_residual_Ostrong__induct,axiom,
% 3.07/1.65 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 3.07/1.65 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_220_residual_Ostrong__induct,axiom,
% 3.07/1.65 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.07/1.65 ( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 3.07/1.65 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.07/1.65 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
% 3.07/1.65 => ( ! [FreeRes3: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.07/1.65 => ( P @ Z @ Residual ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_221_resCasesB,axiom,
% 3.07/1.65 ! [Y: name,P: pi,A: late_subject,X: name,YP: pi,F2: late_subject > pi > $o] :
% 3.07/1.65 ( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ YP ) )
% 3.07/1.65 => ( ( X != Y )
% 3.07/1.65 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.65 => ( ! [B4: name,P3: pi] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B4 @ Y ) @ P3 ) )
% 3.07/1.65 => ( ( B4 != Y )
% 3.07/1.65 => ( ( A
% 3.07/1.65 = ( late_BoundOutputS @ B4 ) )
% 3.07/1.65 => ( F2 @ ( late_BoundOutputS @ B4 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P3 ) ) ) ) )
% 3.07/1.65 => ( ! [P3: pi] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.07/1.65 => ( ( fresh_717452603ubject @ Y @ A )
% 3.07/1.65 => ( F2 @ A @ ( res @ Y @ P3 ) ) ) )
% 3.07/1.65 => ( F2 @ A @ YP ) ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_222_freshFreeDerivative_I1_J,axiom,
% 3.07/1.65 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.07/1.65 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.07/1.65 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.65 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_223_surj__pair,axiom,
% 3.07/1.65 ! [P5: produc367475239e_name] :
% 3.07/1.65 ? [X5: name,Y3: name] :
% 3.07/1.65 ( P5
% 3.07/1.65 = ( produc1570949143e_name @ X5 @ Y3 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_224_surj__pair,axiom,
% 3.07/1.65 ! [P5: product_prod_pi_pi] :
% 3.07/1.65 ? [X5: pi,Y3: pi] :
% 3.07/1.65 ( P5
% 3.07/1.65 = ( product_Pair_pi_pi @ X5 @ Y3 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_225_prod__cases,axiom,
% 3.07/1.65 ! [P: produc367475239e_name > $o,P5: produc367475239e_name] :
% 3.07/1.65 ( ! [A5: name,B4: name] : ( P @ ( produc1570949143e_name @ A5 @ B4 ) )
% 3.07/1.65 => ( P @ P5 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_226_prod__cases,axiom,
% 3.07/1.65 ! [P: product_prod_pi_pi > $o,P5: product_prod_pi_pi] :
% 3.07/1.65 ( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
% 3.07/1.65 => ( P @ P5 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_227_Pair__inject,axiom,
% 3.07/1.65 ! [A: name,B: name,A4: name,B3: name] :
% 3.07/1.65 ( ( ( produc1570949143e_name @ A @ B )
% 3.07/1.65 = ( produc1570949143e_name @ A4 @ B3 ) )
% 3.07/1.65 => ~ ( ( A = A4 )
% 3.07/1.65 => ( B != B3 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_228_Pair__inject,axiom,
% 3.07/1.65 ! [A: pi,B: pi,A4: pi,B3: pi] :
% 3.07/1.65 ( ( ( product_Pair_pi_pi @ A @ B )
% 3.07/1.65 = ( product_Pair_pi_pi @ A4 @ B3 ) )
% 3.07/1.65 => ~ ( ( A = A4 )
% 3.07/1.65 => ( B != B3 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_229_old_Oprod_Oexhaust,axiom,
% 3.07/1.65 ! [Y: produc367475239e_name] :
% 3.07/1.65 ~ ! [A5: name,B4: name] :
% 3.07/1.65 ( Y
% 3.07/1.65 != ( produc1570949143e_name @ A5 @ B4 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_230_old_Oprod_Oexhaust,axiom,
% 3.07/1.65 ! [Y: product_prod_pi_pi] :
% 3.07/1.65 ~ ! [A5: pi,B4: pi] :
% 3.07/1.65 ( Y
% 3.07/1.65 != ( product_Pair_pi_pi @ A5 @ B4 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_231_old_Oprod_Oinducts,axiom,
% 3.07/1.65 ! [P: produc367475239e_name > $o,Prod: produc367475239e_name] :
% 3.07/1.65 ( ! [A5: name,B4: name] : ( P @ ( produc1570949143e_name @ A5 @ B4 ) )
% 3.07/1.65 => ( P @ Prod ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_232_old_Oprod_Oinducts,axiom,
% 3.07/1.65 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 3.07/1.65 ( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
% 3.07/1.65 => ( P @ Prod ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_233_not__Cons__self2,axiom,
% 3.07/1.65 ! [X: produc367475239e_name,Xs: list_P227219501e_name] :
% 3.07/1.65 ( ( cons_P1213805021e_name @ X @ Xs )
% 3.07/1.65 != Xs ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_234_allE__Nil,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > $o] :
% 3.07/1.65 ( ! [X_1: list_P227219501e_name] : ( P @ X_1 )
% 3.07/1.65 => ( P @ nil_Pr743626285e_name ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_235_if__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
% 3.07/1.65 ( ( ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ C1 ) ) )
% 3.07/1.65 & ( ~ ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_236_if__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
% 3.07/1.65 ( ( ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ C1 ) ) )
% 3.07/1.65 & ( ~ ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_237_if__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
% 3.07/1.65 ( ( ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ C1 ) ) )
% 3.07/1.65 & ( ~ ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_238_if__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
% 3.07/1.65 ( ( ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_name @ Pi @ C1 ) ) )
% 3.07/1.65 & ( ~ ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_239_if__eqvt,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
% 3.07/1.65 ( ( ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_pi @ Pi @ C1 ) ) )
% 3.07/1.65 & ( ~ ( perm_name_o @ Pi @ B )
% 3.07/1.65 => ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
% 3.07/1.65 = ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_240_pt__bij3,axiom,
% 3.07/1.65 ! [X: late_subject,Y: late_subject,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( X = Y )
% 3.07/1.65 => ( ( perm_n1559866809ubject @ Pi @ X )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_241_pt__bij3,axiom,
% 3.07/1.65 ! [X: late_freeRes,Y: late_freeRes,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( X = Y )
% 3.07/1.65 => ( ( perm_n336613537reeRes @ Pi @ X )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_242_pt__bij3,axiom,
% 3.07/1.65 ! [X: pi_Rep,Y: pi_Rep,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( X = Y )
% 3.07/1.65 => ( ( perm_name_pi_Rep @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_243_pt__bij3,axiom,
% 3.07/1.65 ! [X: name,Y: name,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( X = Y )
% 3.07/1.65 => ( ( perm_name_name @ Pi @ X )
% 3.07/1.65 = ( perm_name_name @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_244_pt__bij3,axiom,
% 3.07/1.65 ! [X: pi,Y: pi,Pi: list_P227219501e_name] :
% 3.07/1.65 ( ( X = Y )
% 3.07/1.65 => ( ( perm_name_pi @ Pi @ X )
% 3.07/1.65 = ( perm_name_pi @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_245_abs__fun__if,axiom,
% 3.07/1.65 ! [C2: $o,Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 3.07/1.65 ( ( C2
% 3.07/1.65 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ X ) ) )
% 3.07/1.65 & ( ~ C2
% 3.07/1.65 => ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_n1559866809ubject @ Pi @ Y ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_246_abs__fun__if,axiom,
% 3.07/1.65 ! [C2: $o,Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 3.07/1.65 ( ( C2
% 3.07/1.65 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ X ) ) )
% 3.07/1.65 & ( ~ C2
% 3.07/1.65 => ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_n336613537reeRes @ Pi @ Y ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_247_abs__fun__if,axiom,
% 3.07/1.65 ! [C2: $o,Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
% 3.07/1.65 ( ( C2
% 3.07/1.65 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ X ) ) )
% 3.07/1.65 & ( ~ C2
% 3.07/1.65 => ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_pi_Rep @ Pi @ Y ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_248_abs__fun__if,axiom,
% 3.07/1.65 ! [C2: $o,Pi: list_P227219501e_name,X: name,Y: name] :
% 3.07/1.65 ( ( C2
% 3.07/1.65 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_name @ Pi @ X ) ) )
% 3.07/1.65 & ( ~ C2
% 3.07/1.65 => ( ( perm_name_name @ Pi @ ( if_name @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_name @ Pi @ Y ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_249_abs__fun__if,axiom,
% 3.07/1.65 ! [C2: $o,Pi: list_P227219501e_name,X: pi,Y: pi] :
% 3.07/1.65 ( ( C2
% 3.07/1.65 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_pi @ Pi @ X ) ) )
% 3.07/1.65 & ( ~ C2
% 3.07/1.65 => ( ( perm_name_pi @ Pi @ ( if_pi @ C2 @ X @ Y ) )
% 3.07/1.65 = ( perm_name_pi @ Pi @ Y ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_250_alphaRes,axiom,
% 3.07/1.65 ! [C2: name,P: pi,A: name] :
% 3.07/1.65 ( ( fresh_name_pi @ C2 @ P )
% 3.07/1.65 => ( ( res @ A @ P )
% 3.07/1.65 = ( res @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C2 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_251_alphaBoundResidual,axiom,
% 3.07/1.65 ! [X6: name,P: pi,A: late_subject,X: name] :
% 3.07/1.65 ( ( fresh_name_pi @ X6 @ P )
% 3.07/1.65 => ( ( late_BoundR @ A @ X @ P )
% 3.07/1.65 = ( late_BoundR @ A @ X6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X6 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_252_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
% 3.07/1.65 ( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y ) )
% 3.07/1.65 = ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_253_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: late_freeRes] :
% 3.07/1.65 ( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y ) )
% 3.07/1.65 = ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_254_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi_Rep] :
% 3.07/1.65 ( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y ) )
% 3.07/1.65 = ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_255_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: name] :
% 3.07/1.65 ( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y ) )
% 3.07/1.65 = ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_256_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_subject,Y: pi] :
% 3.07/1.65 ( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y ) )
% 3.07/1.65 = ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_257_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_subject] :
% 3.07/1.65 ( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y ) )
% 3.07/1.65 = ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_258_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
% 3.07/1.65 ( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y ) )
% 3.07/1.65 = ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_259_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi_Rep] :
% 3.07/1.65 ( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y ) )
% 3.07/1.65 = ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_260_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: name] :
% 3.07/1.65 ( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y ) )
% 3.07/1.65 = ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_261_perm__prod_Osimps,axiom,
% 3.07/1.65 ! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi] :
% 3.07/1.65 ( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y ) )
% 3.07/1.65 = ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_262_list_Odistinct_I1_J,axiom,
% 3.07/1.65 ! [X21: produc367475239e_name,X22: list_P227219501e_name] :
% 3.07/1.65 ( nil_Pr743626285e_name
% 3.07/1.65 != ( cons_P1213805021e_name @ X21 @ X22 ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_263_list_OdiscI,axiom,
% 3.07/1.65 ! [List: list_P227219501e_name,X21: produc367475239e_name,X22: list_P227219501e_name] :
% 3.07/1.65 ( ( List
% 3.07/1.65 = ( cons_P1213805021e_name @ X21 @ X22 ) )
% 3.07/1.65 => ( List != nil_Pr743626285e_name ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_264_list_Oexhaust,axiom,
% 3.07/1.65 ! [Y: list_P227219501e_name] :
% 3.07/1.65 ( ( Y != nil_Pr743626285e_name )
% 3.07/1.65 => ~ ! [X212: produc367475239e_name,X222: list_P227219501e_name] :
% 3.07/1.65 ( Y
% 3.07/1.65 != ( cons_P1213805021e_name @ X212 @ X222 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_265_list_Oinducts,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > $o,List: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ nil_Pr743626285e_name )
% 3.07/1.65 => ( ! [X13: produc367475239e_name,X23: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ X23 )
% 3.07/1.65 => ( P @ ( cons_P1213805021e_name @ X13 @ X23 ) ) )
% 3.07/1.65 => ( P @ List ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_266_neq__Nil__conv,axiom,
% 3.07/1.65 ! [Xs: list_P227219501e_name] :
% 3.07/1.65 ( ( Xs != nil_Pr743626285e_name )
% 3.07/1.65 = ( ? [Y5: produc367475239e_name,Ys2: list_P227219501e_name] :
% 3.07/1.65 ( Xs
% 3.07/1.65 = ( cons_P1213805021e_name @ Y5 @ Ys2 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_267_list__induct2_H,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > list_P227219501e_name > $o,Xs: list_P227219501e_name,Ys3: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ nil_Pr743626285e_name @ nil_Pr743626285e_name )
% 3.07/1.65 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name] : ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ nil_Pr743626285e_name )
% 3.07/1.65 => ( ! [Y3: produc367475239e_name,Ys: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 3.07/1.65 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ Xs2 @ Ys )
% 3.07/1.65 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) )
% 3.07/1.65 => ( P @ Xs @ Ys3 ) ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_268_splice_Oinduct,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 3.07/1.65 ( ! [X_1: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ X_1 )
% 3.07/1.65 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ Ys @ Xs2 )
% 3.07/1.65 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys ) )
% 3.07/1.65 => ( P @ A0 @ A1 ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_269_induct__list012,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > $o,Xs: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ nil_Pr743626285e_name )
% 3.07/1.65 => ( ! [X5: produc367475239e_name] : ( P @ ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) )
% 3.07/1.65 => ( ! [X5: produc367475239e_name,Y3: produc367475239e_name,Zs: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ Zs )
% 3.07/1.65 => ( ( P @ ( cons_P1213805021e_name @ Y3 @ Zs ) )
% 3.07/1.65 => ( P @ ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Zs ) ) ) ) )
% 3.07/1.65 => ( P @ Xs ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_270_shuffles_Oinduct,axiom,
% 3.07/1.65 ! [P: list_P227219501e_name > list_P227219501e_name > $o,A0: list_P227219501e_name,A1: list_P227219501e_name] :
% 3.07/1.65 ( ! [X_1: list_P227219501e_name] : ( P @ nil_Pr743626285e_name @ X_1 )
% 3.07/1.65 => ( ! [Xs2: list_P227219501e_name] : ( P @ Xs2 @ nil_Pr743626285e_name )
% 3.07/1.65 => ( ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Y3: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.07/1.65 ( ( P @ Xs2 @ ( cons_P1213805021e_name @ Y3 @ Ys ) )
% 3.07/1.65 => ( ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Ys )
% 3.07/1.65 => ( P @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ ( cons_P1213805021e_name @ Y3 @ Ys ) ) ) )
% 3.07/1.65 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.07/1.65
% 3.07/1.65 thf(fact_271_transpose_Ocases,axiom,
% 3.07/1.66 ! [X: list_l1406151091e_name] :
% 3.07/1.66 ( ( X != nil_li29751603e_name )
% 3.07/1.66 => ( ! [Xss: list_l1406151091e_name] :
% 3.07/1.66 ( X
% 3.07/1.66 != ( cons_l798145763e_name @ nil_Pr743626285e_name @ Xss ) )
% 3.07/1.66 => ~ ! [X5: produc367475239e_name,Xs2: list_P227219501e_name,Xss: list_l1406151091e_name] :
% 3.07/1.66 ( X
% 3.07/1.66 != ( cons_l798145763e_name @ ( cons_P1213805021e_name @ X5 @ Xs2 ) @ Xss ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_272_remdups__adj_Ocases,axiom,
% 3.07/1.66 ! [X: list_P227219501e_name] :
% 3.07/1.66 ( ( X != nil_Pr743626285e_name )
% 3.07/1.66 => ( ! [X5: produc367475239e_name] :
% 3.07/1.66 ( X
% 3.07/1.66 != ( cons_P1213805021e_name @ X5 @ nil_Pr743626285e_name ) )
% 3.07/1.66 => ~ ! [X5: produc367475239e_name,Y3: produc367475239e_name,Xs2: list_P227219501e_name] :
% 3.07/1.66 ( X
% 3.07/1.66 != ( cons_P1213805021e_name @ X5 @ ( cons_P1213805021e_name @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_273_sorted__wrt_Oinduct,axiom,
% 3.07/1.66 ! [P: ( produc367475239e_name > produc367475239e_name > $o ) > list_P227219501e_name > $o,A0: produc367475239e_name > produc367475239e_name > $o,A1: list_P227219501e_name] :
% 3.07/1.66 ( ! [P4: produc367475239e_name > produc367475239e_name > $o] : ( P @ P4 @ nil_Pr743626285e_name )
% 3.07/1.66 => ( ! [P4: produc367475239e_name > produc367475239e_name > $o,X5: produc367475239e_name,Ys: list_P227219501e_name] :
% 3.07/1.66 ( ( P @ P4 @ Ys )
% 3.07/1.66 => ( P @ P4 @ ( cons_P1213805021e_name @ X5 @ Ys ) ) )
% 3.07/1.66 => ( P @ A0 @ A1 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_274_Free_Ohyps,axiom,
% 3.07/1.66 late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pxQ ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_275_alphaInput,axiom,
% 3.07/1.66 ! [C2: name,P: pi,A: name,X: name] :
% 3.07/1.66 ( ( fresh_name_pi @ C2 @ P )
% 3.07/1.66 => ( ( input @ A @ X @ P )
% 3.07/1.66 = ( input @ A @ C2 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C2 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_276_name__calc_I1_J,axiom,
% 3.07/1.66 ! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
% 3.07/1.66 ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
% 3.07/1.66 = ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_277_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.07/1.66 ! [X1: name,Y1: name] :
% 3.07/1.66 ( ( ( late_InputS @ X1 )
% 3.07/1.66 = ( late_InputS @ Y1 ) )
% 3.07/1.66 = ( X1 = Y1 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_278_residual__Rep_Oinject_I2_J,axiom,
% 3.07/1.66 ! [X21: late_freeRes,X22: pi,Y21: late_freeRes,Y22: pi] :
% 3.07/1.66 ( ( ( late_r347633188eR_Rep @ X21 @ X22 )
% 3.07/1.66 = ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
% 3.07/1.66 = ( ( X21 = Y21 )
% 3.07/1.66 & ( X22 = Y22 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_279_pi_Ofresh_I8_J,axiom,
% 3.07/1.66 ! [A: name,X2: pi,X1: pi] :
% 3.07/1.66 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 3.07/1.66 = ( ( fresh_name_pi @ A @ X2 )
% 3.07/1.66 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_280_pi_Operm_I8_J,axiom,
% 3.07/1.66 ! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
% 3.07/1.66 ( ( perm_name_pi @ Pi @ ( par @ X2 @ X1 ) )
% 3.07/1.66 = ( par @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_281_pi_Operm_I4_J,axiom,
% 3.07/1.66 ! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
% 3.07/1.66 ( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
% 3.07/1.66 = ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_282_subject_Ofresh_I1_J,axiom,
% 3.07/1.66 ! [A: name,X1: name] :
% 3.07/1.66 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 3.07/1.66 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_283_subject_Operm_I1_J,axiom,
% 3.07/1.66 ! [Pi: list_P227219501e_name,X1: name] :
% 3.07/1.66 ( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
% 3.07/1.66 = ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_284_ScopeExt,axiom,
% 3.07/1.66 ! [Y: name,R: pi,Z: name,S: pi] :
% 3.07/1.66 ( ( fresh_name_pi @ Y @ R )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) ) @ rel ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_285_Res,axiom,
% 3.07/1.66 ! [Y: name,R: pi,S: pi] :
% 3.07/1.66 ( ( fresh_name_pi @ Y @ R )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Y @ ( par @ R @ S ) ) @ ( par @ R @ ( res @ Y @ S ) ) ) @ rel ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_286_pi_Odistinct_I55_J,axiom,
% 3.07/1.66 ! [Name12: name,Name22: name,Pi: pi,Pi12: pi,Pi22: pi] :
% 3.07/1.66 ( ( input @ Name12 @ Name22 @ Pi )
% 3.07/1.66 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_287_pi_Oinject_I7_J,axiom,
% 3.07/1.66 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.07/1.66 ( ( ( par @ X2 @ X1 )
% 3.07/1.66 = ( par @ Y2 @ Y1 ) )
% 3.07/1.66 = ( ( X2 = Y2 )
% 3.07/1.66 & ( X1 = Y1 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_288_pi_Odistinct_I85_J,axiom,
% 3.07/1.66 ! [Pi1: pi,Pi2: pi,Name4: name,Pi3: pi] :
% 3.07/1.66 ( ( par @ Pi1 @ Pi2 )
% 3.07/1.66 != ( res @ Name4 @ Pi3 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_289_transitions_OInput,axiom,
% 3.07/1.66 ! [X: name,A: name,P: pi] :
% 3.07/1.66 ( ( X != A )
% 3.07/1.66 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_290_Late__Semantics_OInput,axiom,
% 3.07/1.66 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_291_pi_Odistinct_I57_J,axiom,
% 3.07/1.66 ! [Name12: name,Name22: name,Pi: pi,Name4: name,Pi3: pi] :
% 3.07/1.66 ( ( input @ Name12 @ Name22 @ Pi )
% 3.07/1.66 != ( res @ Name4 @ Pi3 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_292_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.07/1.66 ! [Name: name,Name4: name] :
% 3.07/1.66 ( ( late_InputS @ Name )
% 3.07/1.66 != ( late_BoundOutputS @ Name4 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_293_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.07/1.66 ! [X1: name,X2: name] :
% 3.07/1.66 ( ( late_InputS @ X1 )
% 3.07/1.66 != ( late_BoundOutputS @ X2 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_294_subject_Oinducts,axiom,
% 3.07/1.66 ! [P: late_subject > $o,Subject: late_subject] :
% 3.07/1.66 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 3.07/1.66 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 3.07/1.66 => ( P @ Subject ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_295_subject_Oexhaust,axiom,
% 3.07/1.66 ! [Y: late_subject] :
% 3.07/1.66 ( ! [X13: name] :
% 3.07/1.66 ( Y
% 3.07/1.66 != ( late_InputS @ X13 ) )
% 3.07/1.66 => ~ ! [X23: name] :
% 3.07/1.66 ( Y
% 3.07/1.66 != ( late_BoundOutputS @ X23 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_296_Par2F,axiom,
% 3.07/1.66 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_297_Par1F,axiom,
% 3.07/1.66 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_298_name__calc_I3_J,axiom,
% 3.07/1.66 ! [A: name,C2: name,B: name] :
% 3.07/1.66 ( ( ( A = C2 )
% 3.07/1.66 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = B ) )
% 3.07/1.66 & ( ( A != C2 )
% 3.07/1.66 => ( ( ( B = C2 )
% 3.07/1.66 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = A ) )
% 3.07/1.66 & ( ( B != C2 )
% 3.07/1.66 => ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = C2 ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_299_resTrans_I2_J,axiom,
% 3.07/1.66 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 3.07/1.66 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_300_inputIneqTrans,axiom,
% 3.07/1.66 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 3.07/1.66 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 3.07/1.66 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_301_inputFreeTrans,axiom,
% 3.07/1.66 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.07/1.66 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_302_Late__Semantics_OPar1B,axiom,
% 3.07/1.66 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_303_Late__Semantics_OPar2B,axiom,
% 3.07/1.66 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_304_parCasesB,axiom,
% 3.07/1.66 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 3.07/1.66 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ! [P3: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.07/1.66 => ( Prop @ ( par @ P3 @ Q ) ) )
% 3.07/1.66 => ( ! [Q3: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.07/1.66 => ( Prop @ ( par @ P @ Q3 ) ) )
% 3.07/1.66 => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_305_parCasesB_H,axiom,
% 3.07/1.66 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 3.07/1.66 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 3.07/1.66 => ( ! [P4: pi,A5: late_subject,X5: name,P3: pi,Q4: pi] :
% 3.07/1.66 ( ( ( par @ P @ Q )
% 3.07/1.66 = ( par @ P4 @ Q4 ) )
% 3.07/1.66 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 3.07/1.66 = ( late_BoundR @ A5 @ X5 @ ( par @ P3 @ Q4 ) ) )
% 3.07/1.66 => ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X5 @ P3 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.07/1.66 => ( ( fresh_name_pi @ X5 @ Q4 )
% 3.07/1.66 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) )
% 3.07/1.66 => ~ ! [Q4: pi,A5: late_subject,X5: name,Q3: pi,P4: pi] :
% 3.07/1.66 ( ( ( par @ P @ Q )
% 3.07/1.66 = ( par @ P4 @ Q4 ) )
% 3.07/1.66 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 3.07/1.66 = ( late_BoundR @ A5 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 3.07/1.66 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A5 @ X5 @ Q3 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.07/1.66 => ( ( fresh_name_pi @ X5 @ Q4 )
% 3.07/1.66 => ~ ( fresh_717452603ubject @ X5 @ A5 ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_306_transitions_OPar1B,axiom,
% 3.07/1.66 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( fresh_717452603ubject @ X @ A )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_307_transitions_OPar2B,axiom,
% 3.07/1.66 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( fresh_717452603ubject @ X @ A )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_308_resInputFreeTrans,axiom,
% 3.07/1.66 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.07/1.66 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_309_inputBoundOutputTrans,axiom,
% 3.07/1.66 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 3.07/1.66 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_310_inputCases,axiom,
% 3.07/1.66 ! [A: name,X: name,P: pi,B: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
% 3.07/1.66 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ YP ) )
% 3.07/1.66 => ( ( Y != A )
% 3.07/1.66 => ( ( Y != X )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.66 => ( ( ( B
% 3.07/1.66 = ( late_InputS @ A ) )
% 3.07/1.66 => ( ( YP
% 3.07/1.66 = ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) )
% 3.07/1.66 => ( Prop @ ( late_InputS @ A ) @ Y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) ) ) )
% 3.07/1.66 => ( Prop @ B @ Y @ YP ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_311_resInputBoundOutputTrans,axiom,
% 3.07/1.66 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 3.07/1.66 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_312_Late__Semantics_OClose1,axiom,
% 3.07/1.66 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_313_Late__Semantics_OClose2,axiom,
% 3.07/1.66 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ Q )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_314_transitions_OClose1,axiom,
% 3.07/1.66 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ Q )
% 3.07/1.66 => ( ( X != A )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q2 )
% 3.07/1.66 => ( ( Y != A )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ P2 )
% 3.07/1.66 => ( ( X != Y )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_315_EqvtRel,axiom,
% 3.07/1.66 eqvt_pi @ rel ).
% 3.07/1.66
% 3.07/1.66 thf(fact_316_subst__identity,axiom,
% 3.07/1.66 ! [P: pi,A: name] :
% 3.07/1.66 ( ( subs @ P @ A @ A )
% 3.07/1.66 = P ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_317_simps_I9_J,axiom,
% 3.07/1.66 ! [X: name,C2: name,D: name,P: pi] :
% 3.07/1.66 ( ( X != C2 )
% 3.07/1.66 => ( ( X != D )
% 3.07/1.66 => ( ( subs @ ( res @ X @ P ) @ C2 @ D )
% 3.07/1.66 = ( res @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_318_simps_I8_J,axiom,
% 3.07/1.66 ! [P: pi,Q: pi,C2: name,D: name] :
% 3.07/1.66 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 3.07/1.66 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_319_substTrans,axiom,
% 3.07/1.66 ! [B: name,P: pi,A: name,C2: name] :
% 3.07/1.66 ( ( fresh_name_pi @ B @ P )
% 3.07/1.66 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 3.07/1.66 = ( subs @ P @ A @ C2 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_320_forget,axiom,
% 3.07/1.66 ! [A: name,P: pi,B: name] :
% 3.07/1.66 ( ( fresh_name_pi @ A @ P )
% 3.07/1.66 => ( ( subs @ P @ A @ B )
% 3.07/1.66 = P ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_321_fresh__fact1,axiom,
% 3.07/1.66 ! [A: name,P: pi,C2: name,B: name] :
% 3.07/1.66 ( ( fresh_name_pi @ A @ P )
% 3.07/1.66 => ( ( A != C2 )
% 3.07/1.66 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_322_fresh__fact2,axiom,
% 3.07/1.66 ! [A: name,B: name,P: pi] :
% 3.07/1.66 ( ( A != B )
% 3.07/1.66 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_323_Agent_OsubstRes3,axiom,
% 3.07/1.66 ! [B: name,P: pi,A: name] :
% 3.07/1.66 ( ( fresh_name_pi @ B @ P )
% 3.07/1.66 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 3.07/1.66 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_324_substRes2,axiom,
% 3.07/1.66 ! [B: name,P: pi,A: name] :
% 3.07/1.66 ( ( fresh_name_pi @ B @ P )
% 3.07/1.66 => ( ( res @ A @ P )
% 3.07/1.66 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_325_eqvt__subs,axiom,
% 3.07/1.66 ! [P5: list_P227219501e_name,P: pi,A: name,B: name] :
% 3.07/1.66 ( ( perm_name_pi @ P5 @ ( subs @ P @ A @ B ) )
% 3.07/1.66 = ( subs @ ( perm_name_pi @ P5 @ P ) @ ( perm_name_name @ P5 @ A ) @ ( perm_name_name @ P5 @ B ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_326_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3,axiom,
% 3.07/1.66 ! [A: name,P: pi,X: name] :
% 3.07/1.66 ( ( subs @ ( res @ A @ P ) @ X @ A )
% 3.07/1.66 = ( res @ X @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ A ) @ nil_Pr743626285e_name ) @ P ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_327_renaming,axiom,
% 3.07/1.66 ! [C2: name,P: pi,A: name,B: name] :
% 3.07/1.66 ( ( fresh_name_pi @ C2 @ P )
% 3.07/1.66 => ( ( subs @ P @ A @ B )
% 3.07/1.66 = ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C2 @ A ) @ nil_Pr743626285e_name ) @ P ) @ C2 @ B ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_328_injPermSubst,axiom,
% 3.07/1.66 ! [B: name,P: pi,A: name] :
% 3.07/1.66 ( ( fresh_name_pi @ B @ P )
% 3.07/1.66 => ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ P )
% 3.07/1.66 = ( subs @ P @ A @ B ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_329_Late__Semantics_OComm1,axiom,
% 3.07/1.66 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_330_Late__Semantics_OComm2,axiom,
% 3.07/1.66 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_331_transitions_OComm2,axiom,
% 3.07/1.66 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( X != A )
% 3.07/1.66 => ( ( X != B )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P2 )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_332_transitions_OComm1,axiom,
% 3.07/1.66 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( X != A )
% 3.07/1.66 => ( ( X != B )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q2 )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_333_transitions_OClose2,axiom,
% 3.07/1.66 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ Q )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ P )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ Q )
% 3.07/1.66 => ( ( X != A )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P2 )
% 3.07/1.66 => ( ( Y != A )
% 3.07/1.66 => ( ( fresh_name_pi @ Y @ Q2 )
% 3.07/1.66 => ( ( X != Y )
% 3.07/1.66 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_334_Agent_Oswap__name__def,axiom,
% 3.07/1.66 swap_name2 = swap_name ).
% 3.07/1.66
% 3.07/1.66 thf(fact_335_swap__name_Osimps,axiom,
% 3.07/1.66 ! [A: name,C2: name,B: name] :
% 3.07/1.66 ( ( ( A = C2 )
% 3.07/1.66 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = B ) )
% 3.07/1.66 & ( ( A != C2 )
% 3.07/1.66 => ( ( ( B = C2 )
% 3.07/1.66 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = A ) )
% 3.07/1.66 & ( ( B != C2 )
% 3.07/1.66 => ( ( swap_name @ ( produc1570949143e_name @ A @ B ) @ C2 )
% 3.07/1.66 = C2 ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_336_name__prm__name_Osimps_I2_J,axiom,
% 3.07/1.66 ! [X: produc367475239e_name,Xs: list_P227219501e_name,A: name] :
% 3.07/1.66 ( ( name_prm_name @ ( cons_P1213805021e_name @ X @ Xs ) @ A )
% 3.07/1.66 = ( swap_name @ X @ ( name_prm_name @ Xs @ A ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_337_simE_I2_J,axiom,
% 3.07/1.66 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 3.07/1.66 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.07/1.66 => ? [P3: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.07/1.66 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_338_simE_I1_J,axiom,
% 3.07/1.66 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 3.07/1.66 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.07/1.66 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ X @ P )
% 3.07/1.66 => ? [P3: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.07/1.66 & ( strong2129052853vative @ P3 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_339_simulation__def,axiom,
% 3.07/1.66 ( strong743114133lation
% 3.07/1.66 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 3.07/1.66 ( ! [A2: late_subject,X3: name,Q6: pi] :
% 3.07/1.66 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A2 @ X3 @ Q6 ) )
% 3.07/1.66 & ( fresh_name_pi @ X3 @ P6 ) )
% 3.07/1.66 => ? [P7: pi] :
% 3.07/1.66 ( ( late_transitions @ P6 @ ( late_BoundR @ A2 @ X3 @ P7 ) )
% 3.07/1.66 & ( strong2129052853vative @ P7 @ Q6 @ A2 @ X3 @ Rel2 ) ) )
% 3.07/1.66 & ! [Alpha3: late_freeRes,Q6: pi] :
% 3.07/1.66 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 3.07/1.66 => ? [P7: pi] :
% 3.07/1.66 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 3.07/1.66 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_340_simCases,axiom,
% 3.07/1.66 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 3.07/1.66 ( ! [A5: late_subject,Y3: name,Q3: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y3 @ Q3 ) )
% 3.07/1.66 => ( ( fresh_name_pi @ Y3 @ P )
% 3.07/1.66 => ? [P8: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y3 @ P8 ) )
% 3.07/1.66 & ( strong2129052853vative @ P8 @ Q3 @ A5 @ Y3 @ Rel ) ) ) )
% 3.07/1.66 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.07/1.66 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.07/1.66 => ? [P8: pi] :
% 3.07/1.66 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P8 ) )
% 3.07/1.66 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q3 ) @ Rel ) ) )
% 3.07/1.66 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_341_name__prm__name_Osimps_I1_J,axiom,
% 3.07/1.66 ! [A: name] :
% 3.07/1.66 ( ( name_prm_name @ nil_Pr743626285e_name @ A )
% 3.07/1.66 = A ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_342_derivativeEqvtI2,axiom,
% 3.07/1.66 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 3.07/1.66 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 3.07/1.66 => ( ( eqvt_pi @ Rel )
% 3.07/1.66 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_343_Agent_Oname__prm__name__def,axiom,
% 3.07/1.66 perm_name_name = name_prm_name ).
% 3.07/1.66
% 3.07/1.66 thf(fact_344_parSym,axiom,
% 3.07/1.66 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 3.07/1.66 ( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
% 3.07/1.66 => ( ! [R2: pi,S2: pi,X5: name] :
% 3.07/1.66 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ R2 ) @ ( res @ X5 @ S2 ) ) @ Rel ) )
% 3.07/1.66 => ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_345_parAssocLeft,axiom,
% 3.07/1.66 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 3.07/1.66 ( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
% 3.07/1.66 => ( ! [S2: pi,T: pi,X5: name] :
% 3.07/1.66 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ S2 ) @ ( res @ X5 @ T ) ) @ Rel ) )
% 3.07/1.66 => ( ! [S2: pi,T: pi,U: pi,X5: name] :
% 3.07/1.66 ( ( fresh_name_pi @ X5 @ S2 )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X5 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X5 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 3.07/1.66 => ( ! [S2: pi,T: pi,U: pi,X5: name] :
% 3.07/1.66 ( ( fresh_name_pi @ X5 @ U )
% 3.07/1.66 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X5 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X5 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
% 3.07/1.66 => ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_346_derivativeEqvtI,axiom,
% 3.07/1.66 ! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
% 3.07/1.66 ( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
% 3.07/1.66 => ( ( eqvt_pi @ Rel )
% 3.07/1.66 => ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_347_pi_Ofresh_I9_J,axiom,
% 3.07/1.66 ! [A: name,X1: name,X2: pi] :
% 3.07/1.66 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 3.07/1.66 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(fact_348_pi_Ofresh_I4_J,axiom,
% 3.07/1.66 ! [A: name,X32: name,X1: name,X2: pi] :
% 3.07/1.66 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 3.07/1.66 = ( ( fresh_name_name @ A @ X32 )
% 3.07/1.66 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
% 3.07/1.66 ! [X: pi,Y: pi] :
% 3.07/1.66 ( ( if_pi @ $false @ X @ Y )
% 3.07/1.66 = Y ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
% 3.07/1.66 ! [X: pi,Y: pi] :
% 3.07/1.66 ( ( if_pi @ $true @ X @ Y )
% 3.07/1.66 = X ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 3.07/1.66 ! [X: name,Y: name] :
% 3.07/1.66 ( ( if_name @ $false @ X @ Y )
% 3.07/1.66 = Y ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 3.07/1.66 ! [X: name,Y: name] :
% 3.07/1.66 ( ( if_name @ $true @ X @ Y )
% 3.07/1.66 = X ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
% 3.07/1.66 ! [X: pi_Rep,Y: pi_Rep] :
% 3.07/1.66 ( ( if_pi_Rep @ $false @ X @ Y )
% 3.07/1.66 = Y ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
% 3.07/1.66 ! [X: pi_Rep,Y: pi_Rep] :
% 3.07/1.66 ( ( if_pi_Rep @ $true @ X @ Y )
% 3.07/1.66 = X ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 3.07/1.66 ! [X: late_freeRes,Y: late_freeRes] :
% 3.07/1.66 ( ( if_Late_freeRes @ $false @ X @ Y )
% 3.07/1.66 = Y ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
% 3.07/1.66 ! [X: late_freeRes,Y: late_freeRes] :
% 3.07/1.66 ( ( if_Late_freeRes @ $true @ X @ Y )
% 3.07/1.66 = X ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.07/1.66 ! [P: $o] :
% 3.07/1.66 ( ( P = $true )
% 3.07/1.66 | ( P = $false ) ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.07/1.66 ! [X: late_subject,Y: late_subject] :
% 3.07/1.66 ( ( if_Late_subject @ $false @ X @ Y )
% 3.07/1.66 = Y ) ).
% 3.07/1.66
% 3.07/1.66 thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
% 3.07/1.66 ! [X: late_subject,Y: late_subject] :
% 3.07/1.66 ( ( if_Late_subject @ $true @ X @ Y )
% 3.07/1.66 = X ) ).
% 3.07/1.66
% 3.07/1.66 thf(conj_0,conjecture,
% 3.07/1.66 late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ).
% 3.07/1.66 ------------------------
% 3.07/1.68 % (18961)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_18628 for (2999ds/2Mi)
% 3.07/1.68 % (18961)Instruction limit reached!
% 3.07/1.68 % (18961)------------------------------
% 3.07/1.68 % (18961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (18961)Termination reason: Unknown
% 3.07/1.68 % (18961)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (18961)Memory used [KB]: 1663
% 3.07/1.68 % (18961)Time elapsed: 0.003 s
% 3.07/1.68 % (18961)Instructions burned: 5 (million)
% 3.07/1.68 % (18961)------------------------------
% 3.07/1.68 % (18961)------------------------------
% 3.07/1.68 % (18963)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/18Mi)
% 3.07/1.69 % (18957)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/183Mi)
% 3.07/1.69 % (18958)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_18628 for (2999ds/4Mi)
% 3.07/1.69 % (18959)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_18628 for (2999ds/27Mi)
% 3.07/1.69 % (18960)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/2Mi)
% 3.07/1.69 % (18962)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_18628 for (2999ds/275Mi)
% 3.07/1.69 % (18960)Instruction limit reached!
% 3.07/1.69 % (18960)------------------------------
% 3.07/1.69 % (18960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (18960)Termination reason: Unknown
% 3.07/1.69 % (18960)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (18960)Memory used [KB]: 1535
% 3.07/1.69 % (18960)Time elapsed: 0.004 s
% 3.07/1.69 % (18960)Instructions burned: 2 (million)
% 3.07/1.69 % (18960)------------------------------
% 3.07/1.69 % (18960)------------------------------
% 3.07/1.69 % (18958)Instruction limit reached!
% 3.07/1.69 % (18958)------------------------------
% 3.07/1.69 % (18958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (18958)Termination reason: Unknown
% 3.07/1.69 % (18958)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (18958)Memory used [KB]: 1663
% 3.07/1.69 % (18958)Time elapsed: 0.005 s
% 3.07/1.69 % (18958)Instructions burned: 4 (million)
% 3.07/1.69 % (18958)------------------------------
% 3.07/1.69 % (18958)------------------------------
% 3.07/1.69 % (18964)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/3Mi)
% 3.07/1.69 % (18964)Instruction limit reached!
% 3.07/1.69 % (18964)------------------------------
% 3.07/1.69 % (18964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (18964)Termination reason: Unknown
% 3.07/1.69 % (18964)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (18964)Memory used [KB]: 1535
% 3.07/1.69 % (18964)Time elapsed: 0.002 s
% 3.07/1.69 % (18964)Instructions burned: 3 (million)
% 3.07/1.69 % (18964)------------------------------
% 3.07/1.69 % (18964)------------------------------
% 3.07/1.69 % (18963)Instruction limit reached!
% 3.07/1.69 % (18963)------------------------------
% 3.07/1.69 % (18963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (18963)Termination reason: Unknown
% 3.07/1.69 % (18963)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (18963)Memory used [KB]: 1918
% 3.07/1.69 % (18963)Time elapsed: 0.013 s
% 3.07/1.69 % (18963)Instructions burned: 18 (million)
% 3.07/1.69 % (18963)------------------------------
% 3.07/1.69 % (18963)------------------------------
% 3.14/1.70 % (18967)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_18628 for (2999ds/3Mi)
% 3.14/1.70 % (18967)Instruction limit reached!
% 3.14/1.70 % (18967)------------------------------
% 3.14/1.70 % (18967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (18967)Termination reason: Unknown
% 3.14/1.70 % (18967)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (18967)Memory used [KB]: 1663
% 3.14/1.70 % (18967)Time elapsed: 0.003 s
% 3.14/1.70 % (18967)Instructions burned: 6 (million)
% 3.14/1.70 % (18967)------------------------------
% 3.14/1.70 % (18967)------------------------------
% 3.14/1.70 % (18959)Instruction limit reached!
% 3.14/1.70 % (18959)------------------------------
% 3.14/1.70 % (18959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (18959)Termination reason: Unknown
% 3.14/1.70 % (18959)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (18959)Memory used [KB]: 2046
% 3.14/1.70 % (18959)Time elapsed: 0.019 s
% 3.14/1.70 % (18959)Instructions burned: 27 (million)
% 3.14/1.70 % (18959)------------------------------
% 3.14/1.70 % (18959)------------------------------
% 3.14/1.70 % (18965)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_18628 for (2999ds/37Mi)
% 3.14/1.71 % (18966)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_18628 for (2999ds/15Mi)
% 3.14/1.71 % (18968)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_18628 for (2999ds/1041Mi)
% 3.14/1.71 % (18969)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/7Mi)
% 3.14/1.71 % (18966)Instruction limit reached!
% 3.14/1.71 % (18966)------------------------------
% 3.14/1.71 % (18966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (18966)Termination reason: Unknown
% 3.14/1.71 % (18966)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (18966)Memory used [KB]: 1918
% 3.14/1.71 % (18966)Time elapsed: 0.009 s
% 3.14/1.71 % (18966)Instructions burned: 17 (million)
% 3.14/1.71 % (18966)------------------------------
% 3.14/1.71 % (18966)------------------------------
% 3.14/1.71 % (18969)Instruction limit reached!
% 3.14/1.71 % (18969)------------------------------
% 3.14/1.71 % (18969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (18969)Termination reason: Unknown
% 3.14/1.71 % (18969)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (18969)Memory used [KB]: 1791
% 3.14/1.71 % (18969)Time elapsed: 0.004 s
% 3.14/1.71 % (18969)Instructions burned: 9 (million)
% 3.14/1.71 % (18969)------------------------------
% 3.14/1.71 % (18969)------------------------------
% 3.14/1.72 % (18970)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/16Mi)
% 3.14/1.72 % (18965)Instruction limit reached!
% 3.14/1.72 % (18965)------------------------------
% 3.14/1.72 % (18965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72 % (18965)Termination reason: Unknown
% 3.14/1.72 % (18965)Termination phase: shuffling
% 3.14/1.72
% 3.14/1.72 % (18965)Memory used [KB]: 2302
% 3.14/1.72 % (18965)Time elapsed: 0.018 s
% 3.14/1.72 % (18965)Instructions burned: 38 (million)
% 3.14/1.72 % (18965)------------------------------
% 3.14/1.72 % (18965)------------------------------
% 3.14/1.72 % (18972)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_18628 for (2999ds/3Mi)
% 3.14/1.72 % (18971)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_18628 for (2999ds/3Mi)
% 3.14/1.72 % (18972)Instruction limit reached!
% 3.14/1.72 % (18972)------------------------------
% 3.14/1.72 % (18972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72 % (18972)Termination reason: Unknown
% 3.14/1.72 % (18972)Termination phase: shuffling
% 3.14/1.72
% 3.14/1.72 % (18972)Memory used [KB]: 1535
% 3.14/1.72 % (18972)Time elapsed: 0.002 s
% 3.14/1.72 % (18972)Instructions burned: 3 (million)
% 3.14/1.72 % (18972)------------------------------
% 3.14/1.72 % (18972)------------------------------
% 3.14/1.72 % (18971)Instruction limit reached!
% 3.14/1.72 % (18971)------------------------------
% 3.14/1.72 % (18971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72 % (18971)Termination reason: Unknown
% 3.14/1.72 % (18971)Termination phase: shuffling
% 3.14/1.72
% 3.14/1.73 % (18971)Memory used [KB]: 1663
% 3.14/1.73 % (18971)Time elapsed: 0.003 s
% 3.14/1.73 % (18971)Instructions burned: 5 (million)
% 3.14/1.73 % (18971)------------------------------
% 3.14/1.73 % (18971)------------------------------
% 3.14/1.73 % (18970)Instruction limit reached!
% 3.14/1.73 % (18970)------------------------------
% 3.14/1.73 % (18970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (18970)Termination reason: Unknown
% 3.14/1.73 % (18970)Termination phase: shuffling
% 3.14/1.73
% 3.14/1.73 % (18970)Memory used [KB]: 1918
% 3.14/1.73 % (18970)Time elapsed: 0.012 s
% 3.14/1.73 % (18970)Instructions burned: 16 (million)
% 3.14/1.73 % (18970)------------------------------
% 3.14/1.73 % (18970)------------------------------
% 3.14/1.73 % (18973)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/7Mi)
% 3.14/1.73 % (18974)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/3Mi)
% 3.14/1.73 % (18974)Instruction limit reached!
% 3.14/1.73 % (18974)------------------------------
% 3.14/1.73 % (18974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (18974)Termination reason: Unknown
% 3.14/1.73 % (18974)Termination phase: shuffling
% 3.14/1.73
% 3.14/1.73 % (18974)Memory used [KB]: 1663
% 3.14/1.73 % (18974)Time elapsed: 0.002 s
% 3.14/1.73 % (18974)Instructions burned: 3 (million)
% 3.14/1.73 % (18974)------------------------------
% 3.14/1.73 % (18974)------------------------------
% 3.14/1.73 % (18973)Instruction limit reached!
% 3.14/1.73 % (18973)------------------------------
% 3.14/1.73 % (18973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (18973)Termination reason: Unknown
% 3.14/1.73 % (18973)Termination phase: shuffling
% 3.14/1.73
% 3.14/1.73 % (18973)Memory used [KB]: 1791
% 3.14/1.73 % (18973)Time elapsed: 0.004 s
% 3.14/1.73 % (18973)Instructions burned: 8 (million)
% 3.14/1.73 % (18973)------------------------------
% 3.14/1.73 % (18973)------------------------------
% 3.14/1.74 % (18975)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/4Mi)
% 3.14/1.74 % (18975)Instruction limit reached!
% 3.14/1.74 % (18975)------------------------------
% 3.14/1.74 % (18975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.74 % (18975)Termination reason: Unknown
% 3.14/1.74 % (18975)Termination phase: shuffling
% 3.14/1.74
% 3.14/1.74 % (18975)Memory used [KB]: 1663
% 3.14/1.74 % (18975)Time elapsed: 0.004 s
% 3.14/1.74 % (18975)Instructions burned: 6 (million)
% 3.14/1.74 % (18975)------------------------------
% 3.14/1.74 % (18975)------------------------------
% 3.14/1.74 % (18977)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/710Mi)
% 3.14/1.74 % (18978)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/6Mi)
% 3.14/1.75 % (18978)Instruction limit reached!
% 3.14/1.75 % (18978)------------------------------
% 3.14/1.75 % (18978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.75 % (18978)Termination reason: Unknown
% 3.14/1.75 % (18978)Termination phase: shuffling
% 3.14/1.75
% 3.14/1.75 % (18978)Memory used [KB]: 1663
% 3.14/1.75 % (18978)Time elapsed: 0.004 s
% 3.14/1.75 % (18978)Instructions burned: 6 (million)
% 3.14/1.75 % (18978)------------------------------
% 3.14/1.75 % (18978)------------------------------
% 3.14/1.75 % (18976)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/18Mi)
% 3.14/1.75 % (18979)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_18628 for (2999ds/902Mi)
% 3.14/1.75 % (18962)Refutation not found, incomplete strategy
% 3.14/1.75 % (18962)------------------------------
% 3.14/1.75 % (18962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.75 % (18962)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.75
% 3.14/1.75
% 3.14/1.75 % (18962)Memory used [KB]: 7547
% 3.14/1.75 % (18962)Time elapsed: 0.064 s
% 3.14/1.75 % (18962)Instructions burned: 116 (million)
% 3.14/1.75 % (18962)------------------------------
% 3.14/1.75 % (18962)------------------------------
% 3.14/1.76 % (18980)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_18628 for (2999ds/21Mi)
% 3.14/1.76 % (18976)Instruction limit reached!
% 3.14/1.76 % (18976)------------------------------
% 3.14/1.76 % (18976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76 % (18976)Termination reason: Unknown
% 3.14/1.76 % (18976)Termination phase: shuffling
% 3.14/1.76
% 3.14/1.76 % (18976)Memory used [KB]: 1918
% 3.14/1.76 % (18976)Time elapsed: 0.013 s
% 3.14/1.76 % (18976)Instructions burned: 18 (million)
% 3.14/1.76 % (18976)------------------------------
% 3.14/1.76 % (18976)------------------------------
% 3.14/1.76 % (18981)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/5Mi)
% 3.14/1.76 % (18981)Instruction limit reached!
% 3.14/1.76 % (18981)------------------------------
% 3.14/1.76 % (18981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76 % (18981)Termination reason: Unknown
% 3.14/1.76 % (18981)Termination phase: shuffling
% 3.14/1.76
% 3.14/1.76 % (18981)Memory used [KB]: 1663
% 3.14/1.76 % (18981)Time elapsed: 0.003 s
% 3.14/1.76 % (18981)Instructions burned: 6 (million)
% 3.14/1.76 % (18981)------------------------------
% 3.14/1.76 % (18981)------------------------------
% 3.14/1.76 % (18980)Instruction limit reached!
% 3.14/1.76 % (18980)------------------------------
% 3.14/1.76 % (18980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76 % (18980)Termination reason: Unknown
% 3.14/1.76 % (18980)Termination phase: shuffling
% 3.14/1.76
% 3.14/1.76 % (18980)Memory used [KB]: 1918
% 3.14/1.76 % (18980)Time elapsed: 0.009 s
% 3.14/1.76 % (18980)Instructions burned: 21 (million)
% 3.14/1.76 % (18980)------------------------------
% 3.14/1.76 % (18980)------------------------------
% 3.14/1.77 % (18957)Instruction limit reached!
% 3.14/1.77 % (18957)------------------------------
% 3.14/1.77 % (18957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.77 % (18957)Termination reason: Unknown
% 3.14/1.77 % (18957)Termination phase: Saturation
% 3.14/1.77
% 3.14/1.77 % (18957)Memory used [KB]: 7547
% 3.14/1.77 % (18957)Time elapsed: 0.087 s
% 3.14/1.77 % (18957)Instructions burned: 184 (million)
% 3.14/1.77 % (18957)------------------------------
% 3.14/1.77 % (18957)------------------------------
% 3.14/1.77 % (18983)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18628 for (2999ds/377Mi)
% 3.14/1.77 % (18984)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_18628 for (2999ds/779Mi)
% 3.14/1.78 % (18982)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_18628 for (2999ds/6Mi)
% 3.14/1.78 % (18982)Instruction limit reached!
% 3.14/1.78 % (18982)------------------------------
% 3.14/1.78 % (18982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.78 % (18982)Termination reason: Unknown
% 3.14/1.78 % (18982)Termination phase: shuffling
% 3.14/1.78
% 3.14/1.78 % (18982)Memory used [KB]: 1791
% 3.14/1.78 % (18982)Time elapsed: 0.006 s
% 3.14/1.78 % (18982)Instructions burned: 7 (million)
% 3.14/1.78 % (18982)------------------------------
% 3.14/1.78 % (18982)------------------------------
% 3.14/1.78 % (18985)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_18628 for (2998ds/19Mi)
% 3.14/1.79 % (18985)Instruction limit reached!
% 3.14/1.79 % (18985)------------------------------
% 3.14/1.79 % (18985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.79 % (18985)Termination reason: Unknown
% 3.14/1.79 % (18985)Termination phase: shuffling
% 3.14/1.79
% 3.14/1.79 % (18985)Memory used [KB]: 2046
% 3.14/1.79 % (18985)Time elapsed: 0.007 s
% 3.14/1.79 % (18985)Instructions burned: 20 (million)
% 3.14/1.79 % (18985)------------------------------
% 3.14/1.79 % (18985)------------------------------
% 3.14/1.80 % (18987)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/17Mi)
% 3.14/1.80 % (18986)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/879Mi)
% 3.14/1.80 % (18987)Instruction limit reached!
% 3.14/1.80 % (18987)------------------------------
% 3.14/1.80 % (18987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.80 % (18987)Termination reason: Unknown
% 3.14/1.80 % (18987)Termination phase: shuffling
% 3.14/1.80
% 3.14/1.80 % (18987)Memory used [KB]: 1918
% 3.14/1.80 % (18987)Time elapsed: 0.008 s
% 3.14/1.80 % (18987)Instructions burned: 17 (million)
% 3.14/1.80 % (18987)------------------------------
% 3.14/1.80 % (18987)------------------------------
% 3.14/1.81 % (18979)Refutation not found, incomplete strategy
% 3.14/1.81 % (18979)------------------------------
% 3.14/1.81 % (18979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.81 % (18979)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.81
% 3.14/1.81
% 3.14/1.81 % (18979)Memory used [KB]: 8187
% 3.14/1.81 % (18979)Time elapsed: 0.060 s
% 3.14/1.81 % (18979)Instructions burned: 187 (million)
% 3.14/1.81 % (18979)------------------------------
% 3.14/1.81 % (18979)------------------------------
% 3.14/1.81 % (18988)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/3Mi)
% 3.14/1.81 % (18988)Instruction limit reached!
% 3.14/1.81 % (18988)------------------------------
% 3.14/1.81 % (18988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.81 % (18988)Termination reason: Unknown
% 3.14/1.81 % (18988)Termination phase: shuffling
% 3.14/1.81
% 3.14/1.81 % (18988)Memory used [KB]: 1663
% 3.14/1.81 % (18988)Time elapsed: 0.003 s
% 3.14/1.81 % (18988)Instructions burned: 3 (million)
% 3.14/1.81 % (18988)------------------------------
% 3.14/1.81 % (18988)------------------------------
% 3.14/1.82 % (18989)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/30Mi)
% 3.14/1.82 % (18990)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/127Mi)
% 3.14/1.83 % (18989)Instruction limit reached!
% 3.14/1.83 % (18989)------------------------------
% 3.14/1.83 % (18989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.83 % (18989)Termination reason: Unknown
% 3.14/1.83 % (18989)Termination phase: shuffling
% 3.14/1.83
% 3.14/1.83 % (18989)Memory used [KB]: 2046
% 3.14/1.83 % (18989)Time elapsed: 0.012 s
% 3.14/1.83 % (18989)Instructions burned: 30 (million)
% 3.14/1.83 % (18989)------------------------------
% 3.14/1.83 % (18989)------------------------------
% 3.14/1.84 % (18991)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/100Mi)
% 3.14/1.86 % (18990)Instruction limit reached!
% 3.14/1.86 % (18990)------------------------------
% 3.14/1.86 % (18990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.86 % (18990)Termination reason: Unknown
% 3.14/1.86 % (18990)Termination phase: Property scanning
% 3.14/1.86
% 3.14/1.86 % (18990)Memory used [KB]: 2814
% 3.14/1.86 % (18990)Time elapsed: 0.040 s
% 3.14/1.86 % (18990)Instructions burned: 128 (million)
% 3.14/1.86 % (18990)------------------------------
% 3.14/1.86 % (18990)------------------------------
% 3.14/1.87 % (18991)Instruction limit reached!
% 3.14/1.87 % (18991)------------------------------
% 3.14/1.87 % (18991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.87 % (18991)Termination reason: Unknown
% 3.14/1.87 % (18991)Termination phase: Property scanning
% 3.14/1.87
% 3.14/1.87 % (18991)Memory used [KB]: 2942
% 3.14/1.87 % (18991)Time elapsed: 0.031 s
% 3.14/1.87 % (18991)Instructions burned: 103 (million)
% 3.14/1.87 % (18991)------------------------------
% 3.14/1.87 % (18991)------------------------------
% 3.14/1.87 % (18992)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/3Mi)
% 3.14/1.87 % (18992)Instruction limit reached!
% 3.14/1.87 % (18992)------------------------------
% 3.14/1.87 % (18992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.87 % (18992)Termination reason: Unknown
% 3.14/1.87 % (18992)Termination phase: shuffling
% 3.14/1.87
% 3.14/1.87 % (18992)Memory used [KB]: 1663
% 3.14/1.87 % (18992)Time elapsed: 0.002 s
% 3.14/1.87 % (18992)Instructions burned: 3 (million)
% 3.14/1.87 % (18992)------------------------------
% 3.14/1.87 % (18992)------------------------------
% 3.14/1.88 % (18993)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_18628 for (2998ds/20Mi)
% 3.14/1.88 % (18993)Instruction limit reached!
% 3.14/1.88 % (18993)------------------------------
% 3.14/1.88 % (18993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.88 % (18993)Termination reason: Unknown
% 3.14/1.88 % (18993)Termination phase: shuffling
% 3.14/1.88
% 3.14/1.88 % (18993)Memory used [KB]: 1918
% 3.14/1.88 % (18993)Time elapsed: 0.008 s
% 3.14/1.88 % (18993)Instructions burned: 20 (million)
% 3.14/1.88 % (18993)------------------------------
% 3.14/1.88 % (18993)------------------------------
% 3.14/1.88 % (18994)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/86Mi)
% 3.14/1.89 % (18983)Instruction limit reached!
% 3.14/1.89 % (18983)------------------------------
% 3.14/1.89 % (18983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.89 % (18983)Termination reason: Unknown
% 3.14/1.89 % (18983)Termination phase: Saturation
% 3.14/1.89
% 3.14/1.89 % (18983)Memory used [KB]: 8827
% 3.14/1.89 % (18983)Time elapsed: 0.120 s
% 3.14/1.89 % (18983)Instructions burned: 377 (million)
% 3.14/1.89 % (18983)------------------------------
% 3.14/1.89 % (18983)------------------------------
% 3.14/1.89 % (18995)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/107Mi)
% 3.14/1.90 % (18996)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/39Mi)
% 3.14/1.91 % (18994)Instruction limit reached!
% 3.14/1.91 % (18994)------------------------------
% 3.14/1.91 % (18994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.91 % (18994)Termination reason: Unknown
% 3.14/1.91 % (18994)Termination phase: Property scanning
% 3.14/1.91
% 3.14/1.91 % (18994)Memory used [KB]: 2686
% 3.14/1.91 % (18994)Time elapsed: 0.029 s
% 3.14/1.91 % (18994)Instructions burned: 88 (million)
% 3.14/1.91 % (18994)------------------------------
% 3.14/1.91 % (18994)------------------------------
% 3.14/1.91 % (18996)Instruction limit reached!
% 3.14/1.91 % (18996)------------------------------
% 3.14/1.91 % (18996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.91 % (18996)Termination reason: Unknown
% 3.14/1.91 % (18996)Termination phase: shuffling
% 3.14/1.91
% 3.14/1.91 % (18996)Memory used [KB]: 2302
% 3.14/1.91 % (18996)Time elapsed: 0.013 s
% 3.14/1.91 % (18996)Instructions burned: 41 (million)
% 3.14/1.91 % (18996)------------------------------
% 3.14/1.91 % (18996)------------------------------
% 3.14/1.92 % (18997)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/448Mi)
% 3.14/1.92 % (18998)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/46Mi)
% 3.14/1.93 % (18995)Instruction limit reached!
% 3.14/1.93 % (18995)------------------------------
% 3.14/1.93 % (18995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.93 % (18995)Termination reason: Unknown
% 3.14/1.93 % (18995)Termination phase: Property scanning
% 3.14/1.93
% 3.14/1.93 % (18995)Memory used [KB]: 2686
% 3.14/1.93 % (18995)Time elapsed: 0.034 s
% 3.14/1.93 % (18995)Instructions burned: 108 (million)
% 3.14/1.93 % (18995)------------------------------
% 3.14/1.93 % (18995)------------------------------
% 3.14/1.94 % (18998)Instruction limit reached!
% 3.14/1.94 % (18998)------------------------------
% 3.14/1.94 % (18998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.94 % (18998)Termination reason: Unknown
% 3.14/1.94 % (18998)Termination phase: Property scanning
% 3.14/1.94
% 3.14/1.94 % (18998)Memory used [KB]: 2046
% 3.14/1.94 % (18998)Time elapsed: 0.016 s
% 3.14/1.94 % (18998)Instructions burned: 49 (million)
% 3.14/1.94 % (18998)------------------------------
% 3.14/1.94 % (18998)------------------------------
% 3.14/1.94 % (18999)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/98Mi)
% 3.14/1.95 % (18968)First to succeed.
% 3.14/1.95 % (19000)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_18628 for (2997ds/507Mi)
% 3.14/1.95 % (18968)Refutation found. Thanks to Tanya!
% 3.14/1.95 % SZS status Theorem for DTF2THF_18628
% 3.14/1.95 % SZS output start Proof for DTF2THF_18628
% 3.14/1.95 thf(type_def_5, type, name: $tType).
% 3.14/1.95 thf(type_def_6, type, pi: $tType).
% 3.14/1.95 thf(type_def_8, type, list_P227219501e_name: $tType).
% 3.14/1.95 thf(type_def_9, type, produc367475239e_name: $tType).
% 3.14/1.95 thf(type_def_10, type, pi_Rep: $tType).
% 3.14/1.95 thf(type_def_11, type, late_freeRes: $tType).
% 3.14/1.95 thf(type_def_12, type, late_subject: $tType).
% 3.14/1.95 thf(type_def_13, type, late_residual: $tType).
% 3.14/1.95 thf(type_def_14, type, late_residual_Rep: $tType).
% 3.14/1.95 thf(type_def_15, type, noption_pi: $tType).
% 3.14/1.95 thf(type_def_16, type, list_name_noption_pi: $tType).
% 3.14/1.95 thf(type_def_17, type, list_name: $tType).
% 3.14/1.95 thf(type_def_18, type, list_pi: $tType).
% 3.14/1.95 thf(type_def_19, type, list_pi_Rep: $tType).
% 3.14/1.95 thf(type_def_20, type, list_Late_freeRes: $tType).
% 3.14/1.95 thf(type_def_21, type, list_Late_subject: $tType).
% 3.14/1.95 thf(type_def_22, type, list_l1406151091e_name: $tType).
% 3.14/1.95 thf(type_def_23, type, produc2008547984reeRes: $tType).
% 3.14/1.95 thf(type_def_24, type, produc865358760ubject: $tType).
% 3.14/1.95 thf(type_def_25, type, product_prod_pi_pi: $tType).
% 3.14/1.95 thf(type_def_26, type, produc2052722628s_name: $tType).
% 3.14/1.95 thf(type_def_27, type, produc992857746Res_pi: $tType).
% 3.14/1.95 thf(type_def_28, type, produc1357834675reeRes: $tType).
% 3.14/1.95 thf(type_def_29, type, produc214645451ubject: $tType).
% 3.14/1.95 thf(type_def_30, type, produc1998742700t_name: $tType).
% 3.14/1.95 thf(type_def_31, type, produc140253050ect_pi: $tType).
% 3.14/1.95 thf(type_def_32, type, produc355105483reeRes: $tType).
% 3.14/1.95 thf(type_def_33, type, produc1359399907ubject: $tType).
% 3.14/1.95 thf(type_def_34, type, late_freeRes_Rep: $tType).
% 3.14/1.95 thf(type_def_35, type, late_subject_Rep: $tType).
% 3.14/1.95 thf(type_def_36, type, produc1777919905pi_Rep: $tType).
% 3.14/1.95 thf(type_def_37, type, produc257012921pi_Rep: $tType).
% 3.14/1.95 thf(type_def_38, type, set_name: $tType).
% 3.14/1.95 thf(type_def_39, type, set_pi: $tType).
% 3.14/1.95 thf(type_def_40, type, set_pi_Rep: $tType).
% 3.14/1.95 thf(type_def_41, type, set_Late_freeRes: $tType).
% 3.14/1.95 thf(type_def_42, type, set_Late_subject: $tType).
% 3.14/1.95 thf(type_def_43, type, set_Pr1834926343_pi_pi: $tType).
% 3.14/1.95 thf(type_def_44, type, produc1872410278e_name: $tType).
% 3.14/1.95 thf(type_def_45, type, produc890461031e_name: $tType).
% 3.14/1.95 thf(func_def_0, type, produc1872410278e_name: $tType).
% 3.14/1.95 thf(func_def_1, type, produc890461031e_name: $tType).
% 3.14/1.95 thf(func_def_2, type, list_l1406151091e_name: $tType).
% 3.14/1.95 thf(func_def_3, type, produc1359399907ubject: $tType).
% 3.14/1.95 thf(func_def_4, type, produc355105483reeRes: $tType).
% 3.14/1.95 thf(func_def_5, type, produc214645451ubject: $tType).
% 3.14/1.95 thf(func_def_6, type, produc1357834675reeRes: $tType).
% 3.14/1.95 thf(func_def_7, type, produc257012921pi_Rep: $tType).
% 3.14/1.95 thf(func_def_8, type, produc1777919905pi_Rep: $tType).
% 3.14/1.95 thf(func_def_9, type, list_name_noption_pi: $tType).
% 3.14/1.95 thf(func_def_10, type, list_P227219501e_name: $tType).
% 3.14/1.95 thf(func_def_11, type, produc1998742700t_name: $tType).
% 3.14/1.95 thf(func_def_12, type, produc2052722628s_name: $tType).
% 3.14/1.95 thf(func_def_13, type, produc865358760ubject: $tType).
% 3.14/1.95 thf(func_def_14, type, produc2008547984reeRes: $tType).
% 3.14/1.95 thf(func_def_15, type, produc140253050ect_pi: $tType).
% 3.14/1.95 thf(func_def_16, type, produc992857746Res_pi: $tType).
% 3.14/1.95 thf(func_def_17, type, set_Pr1834926343_pi_pi: $tType).
% 3.14/1.95 thf(func_def_18, type, produc367475239e_name: $tType).
% 3.14/1.95 thf(func_def_19, type, product_prod_pi_pi: $tType).
% 3.14/1.95 thf(func_def_20, type, list_Late_subject: $tType).
% 3.14/1.95 thf(func_def_21, type, list_Late_freeRes: $tType).
% 3.14/1.95 thf(func_def_22, type, set_Late_subject: $tType).
% 3.14/1.95 thf(func_def_23, type, set_Late_freeRes: $tType).
% 3.14/1.95 thf(func_def_24, type, list_pi_Rep: $tType).
% 3.14/1.95 thf(func_def_25, type, late_residual_Rep: $tType).
% 3.14/1.95 thf(func_def_26, type, noption_pi: $tType).
% 3.14/1.95 thf(func_def_27, type, late_subject_Rep: $tType).
% 3.14/1.95 thf(func_def_28, type, late_freeRes_Rep: $tType).
% 3.14/1.95 thf(func_def_29, type, set_pi_Rep: $tType).
% 3.14/1.95 thf(func_def_30, type, list_name: $tType).
% 3.14/1.95 thf(func_def_31, type, set_name: $tType).
% 3.14/1.95 thf(func_def_32, type, list_pi: $tType).
% 3.14/1.95 thf(func_def_33, type, late_residual: $tType).
% 3.14/1.95 thf(func_def_34, type, late_subject: $tType).
% 3.14/1.95 thf(func_def_35, type, late_freeRes: $tType).
% 3.14/1.95 thf(func_def_36, type, set_pi: $tType).
% 3.14/1.95 thf(func_def_37, type, pi_Rep: $tType).
% 3.14/1.95 thf(func_def_38, type, name: $tType).
% 3.14/1.95 thf(func_def_39, type, pi: $tType).
% 3.14/1.95 thf(func_def_40, type, input: name > name > pi > pi).
% 3.14/1.95 thf(func_def_41, type, par: pi > pi > pi).
% 3.14/1.95 thf(func_def_42, type, res: name > pi > pi).
% 3.14/1.95 thf(func_def_43, type, name_prm_name: list_P227219501e_name > name > name).
% 3.14/1.95 thf(func_def_44, type, swap_name: produc367475239e_name > name > name).
% 3.14/1.95 thf(func_def_45, type, subs: pi > name > name > pi).
% 3.14/1.95 thf(func_def_46, type, if_name: $o > name > name > name).
% 3.14/1.95 thf(func_def_47, type, if_pi: $o > pi > pi > pi).
% 3.14/1.95 thf(func_def_48, type, if_pi_Rep: $o > pi_Rep > pi_Rep > pi_Rep).
% 3.14/1.95 thf(func_def_49, type, if_Late_freeRes: $o > late_freeRes > late_freeRes > late_freeRes).
% 3.14/1.95 thf(func_def_50, type, if_Late_subject: $o > late_subject > late_subject > late_subject).
% 3.14/1.95 thf(func_def_51, type, late_OutputR: name > name > late_freeRes).
% 3.14/1.95 thf(func_def_52, type, late_TauR: late_freeRes).
% 3.14/1.95 thf(func_def_53, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.14/1.95 thf(func_def_54, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.14/1.95 thf(func_def_55, type, late_r347633188eR_Rep: late_freeRes > pi > late_residual_Rep).
% 3.14/1.95 thf(func_def_56, type, late_BoundOutputS: name > late_subject).
% 3.14/1.95 thf(func_def_57, type, late_InputS: name > late_subject).
% 3.14/1.95 thf(func_def_58, type, late_transitions: pi > late_residual > $o).
% 3.14/1.95 thf(func_def_59, type, cons_name_noption_pi: (name > noption_pi) > list_name_noption_pi > list_name_noption_pi).
% 3.14/1.95 thf(func_def_60, type, cons_name: name > list_name > list_name).
% 3.14/1.95 thf(func_def_61, type, cons_pi: pi > list_pi > list_pi).
% 3.14/1.95 thf(func_def_62, type, cons_pi_Rep: pi_Rep > list_pi_Rep > list_pi_Rep).
% 3.14/1.95 thf(func_def_63, type, cons_Late_freeRes: late_freeRes > list_Late_freeRes > list_Late_freeRes).
% 3.14/1.95 thf(func_def_64, type, cons_Late_subject: late_subject > list_Late_subject > list_Late_subject).
% 3.14/1.95 thf(func_def_65, type, cons_l798145763e_name: list_P227219501e_name > list_l1406151091e_name > list_l1406151091e_name).
% 3.14/1.95 thf(func_def_66, type, cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name).
% 3.14/1.95 thf(func_def_67, type, nil_li29751603e_name: list_l1406151091e_name).
% 3.14/1.95 thf(func_def_68, type, nil_Pr743626285e_name: list_P227219501e_name).
% 3.14/1.95 thf(func_def_69, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 3.14/1.95 thf(func_def_70, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 3.14/1.95 thf(func_def_71, type, fresh_name_name: name > name > $o).
% 3.14/1.95 thf(func_def_72, type, fresh_name_pi: name > pi > $o).
% 3.14/1.95 thf(func_def_73, type, fresh_name_pi_Rep: name > pi_Rep > $o).
% 3.14/1.95 thf(func_def_74, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.14/1.95 thf(func_def_75, type, fresh_81631222sidual: name > late_residual > $o).
% 3.14/1.95 thf(func_def_76, type, fresh_717452603ubject: name > late_subject > $o).
% 3.14/1.95 thf(func_def_77, type, fresh_1135477378ion_pi: name > list_name_noption_pi > $o).
% 3.14/1.95 thf(func_def_78, type, fresh_name_list_name: name > list_name > $o).
% 3.14/1.95 thf(func_def_79, type, fresh_name_list_pi: name > list_pi > $o).
% 3.14/1.95 thf(func_def_80, type, fresh_1981651763reeRes: name > list_Late_freeRes > $o).
% 3.14/1.95 thf(func_def_81, type, fresh_838462539ubject: name > list_Late_subject > $o).
% 3.14/1.95 thf(func_def_82, type, fresh_922791155e_name: name > list_P227219501e_name > $o).
% 3.14/1.95 thf(func_def_83, type, fresh_441084397e_name: name > produc367475239e_name > $o).
% 3.14/1.95 thf(func_def_84, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 3.14/1.95 thf(func_def_85, type, fresh_820177506ubject: name > produc865358760ubject > $o).
% 3.14/1.95 thf(func_def_86, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 3.14/1.95 thf(func_def_87, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 3.14/1.95 thf(func_def_88, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 3.14/1.95 thf(func_def_89, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 3.14/1.95 thf(func_def_90, type, fresh_1498103185ubject: name > produc214645451ubject > $o).
% 3.14/1.95 thf(func_def_91, type, fresh_1953561446t_name: name > produc1998742700t_name > $o).
% 3.14/1.95 thf(func_def_92, type, fresh_994896692ect_pi: name > produc140253050ect_pi > $o).
% 3.14/1.95 thf(func_def_93, type, fresh_1638563217reeRes: name > produc355105483reeRes > $o).
% 3.14/1.95 thf(func_def_94, type, fresh_495373993ubject: name > produc1359399907ubject > $o).
% 3.14/1.95 thf(func_def_95, type, perm_n382765978reeRes: list_P227219501e_name > (name > late_freeRes) > name > late_freeRes).
% 3.14/1.95 thf(func_def_96, type, perm_n1387060402ubject: list_P227219501e_name > (name > late_subject) > name > late_subject).
% 3.14/1.95 thf(func_def_97, type, perm_n1667196784ion_pi: list_P227219501e_name > (name > noption_pi) > name > noption_pi).
% 3.14/1.95 thf(func_def_98, type, perm_n1333244520reeRes: list_P227219501e_name > (pi > late_freeRes) > pi > late_freeRes).
% 3.14/1.95 thf(func_def_99, type, perm_n190055296ubject: list_P227219501e_name > (pi > late_subject) > pi > late_subject).
% 3.14/1.95 thf(func_def_100, type, perm_n1841560599reeRes: list_P227219501e_name > (pi_Rep > late_freeRes) > pi_Rep > late_freeRes).
% 3.14/1.95 thf(func_def_101, type, perm_n698371375ubject: list_P227219501e_name > (pi_Rep > late_subject) > pi_Rep > late_subject).
% 3.14/1.95 thf(func_def_102, type, perm_n1446290985reeRes: list_P227219501e_name > (late_freeRes > late_freeRes) > late_freeRes > late_freeRes).
% 3.14/1.95 thf(func_def_103, type, perm_n303101761ubject: list_P227219501e_name > (late_freeRes > late_subject) > late_freeRes > late_subject).
% 3.14/1.95 thf(func_def_104, type, perm_n443561793reeRes: list_P227219501e_name > (late_subject > late_freeRes) > late_subject > late_freeRes).
% 3.14/1.95 thf(func_def_105, type, perm_n1447856217ubject: list_P227219501e_name > (late_subject > late_subject) > late_subject > late_subject).
% 3.14/1.95 thf(func_def_106, type, perm_name_o: list_P227219501e_name > $o > $o).
% 3.14/1.95 thf(func_def_107, type, perm_name_name: list_P227219501e_name > name > name).
% 3.14/1.95 thf(func_def_108, type, perm_name_pi: list_P227219501e_name > pi > pi).
% 3.14/1.95 thf(func_def_109, type, perm_name_pi_Rep: list_P227219501e_name > pi_Rep > pi_Rep).
% 3.14/1.95 thf(func_def_110, type, perm_n336613537reeRes: list_P227219501e_name > late_freeRes > late_freeRes).
% 3.14/1.95 thf(func_def_111, type, perm_n1938283068es_Rep: list_P227219501e_name > late_freeRes_Rep > late_freeRes_Rep).
% 3.14/1.95 thf(func_def_112, type, perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual).
% 3.14/1.95 thf(func_def_113, type, perm_n890803237al_Rep: list_P227219501e_name > late_residual_Rep > late_residual_Rep).
% 3.14/1.95 thf(func_def_114, type, perm_n1559866809ubject: list_P227219501e_name > late_subject > late_subject).
% 3.14/1.95 thf(func_def_115, type, perm_n697952036ct_Rep: list_P227219501e_name > late_subject_Rep > late_subject_Rep).
% 3.14/1.95 thf(func_def_116, type, perm_name_list_name: list_P227219501e_name > list_name > list_name).
% 3.14/1.95 thf(func_def_117, type, perm_name_list_pi: list_P227219501e_name > list_pi > list_pi).
% 3.14/1.95 thf(func_def_118, type, perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep).
% 3.14/1.95 thf(func_def_119, type, perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes).
% 3.14/1.95 thf(func_def_120, type, perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject).
% 3.14/1.95 thf(func_def_121, type, perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name).
% 3.14/1.95 thf(func_def_122, type, perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi).
% 3.14/1.95 thf(func_def_123, type, perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name).
% 3.14/1.95 thf(func_def_124, type, perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi).
% 3.14/1.95 thf(func_def_125, type, perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep).
% 3.14/1.95 thf(func_def_126, type, perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes).
% 3.14/1.95 thf(func_def_127, type, perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject).
% 3.14/1.95 thf(func_def_128, type, perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name).
% 3.14/1.95 thf(func_def_129, type, perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi).
% 3.14/1.95 thf(func_def_130, type, perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep).
% 3.14/1.95 thf(func_def_131, type, perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes).
% 3.14/1.95 thf(func_def_132, type, perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject).
% 3.14/1.95 thf(func_def_133, type, perm_name_set_name: list_P227219501e_name > set_name > set_name).
% 3.14/1.95 thf(func_def_134, type, perm_name_set_pi: list_P227219501e_name > set_pi > set_pi).
% 3.14/1.95 thf(func_def_135, type, perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep).
% 3.14/1.95 thf(func_def_136, type, perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes).
% 3.14/1.95 thf(func_def_137, type, perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject).
% 3.14/1.95 thf(func_def_138, type, perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi).
% 3.14/1.95 thf(func_def_139, type, swap_name2: produc367475239e_name > name > name).
% 3.14/1.95 thf(func_def_140, type, produc1069608854e_name: (produc367475239e_name > produc367475239e_name > $o) > list_P227219501e_name > produc1872410278e_name).
% 3.14/1.95 thf(func_def_141, type, produc1570949143e_name: name > name > produc367475239e_name).
% 3.14/1.95 thf(func_def_142, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 3.14/1.95 thf(func_def_143, type, produc607574050ubject: name > late_subject > produc865358760ubject).
% 3.14/1.95 thf(func_def_144, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 3.14/1.95 thf(func_def_145, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 3.14/1.95 thf(func_def_146, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 3.14/1.95 thf(func_def_147, type, produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep).
% 3.14/1.95 thf(func_def_148, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 3.14/1.95 thf(func_def_149, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 3.14/1.95 thf(func_def_150, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 3.14/1.95 thf(func_def_151, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 3.14/1.95 thf(func_def_152, type, produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep).
% 3.14/1.95 thf(func_def_153, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 3.14/1.95 thf(func_def_154, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 3.14/1.95 thf(func_def_155, type, produc208131031e_name: list_P227219501e_name > list_P227219501e_name > produc890461031e_name).
% 3.14/1.95 thf(func_def_156, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 3.14/1.95 thf(func_def_157, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 3.14/1.95 thf(func_def_158, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 3.14/1.95 thf(func_def_159, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 3.14/1.95 thf(func_def_160, type, member_name: name > set_name > $o).
% 3.14/1.95 thf(func_def_161, type, member_pi: pi > set_pi > $o).
% 3.14/1.95 thf(func_def_162, type, member_pi_Rep: pi_Rep > set_pi_Rep > $o).
% 3.14/1.95 thf(func_def_163, type, member_Late_freeRes: late_freeRes > set_Late_freeRes > $o).
% 3.14/1.95 thf(func_def_164, type, member_Late_subject: late_subject > set_Late_subject > $o).
% 3.14/1.95 thf(func_def_165, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.14/1.95 thf(func_def_166, type, p: pi).
% 3.14/1.95 thf(func_def_167, type, p2: pi).
% 3.14/1.95 thf(func_def_168, type, pxQ: pi).
% 3.14/1.95 thf(func_def_169, type, q: pi).
% 3.14/1.95 thf(func_def_170, type, q2: pi).
% 3.14/1.95 thf(func_def_171, type, q_a: pi).
% 3.14/1.95 thf(func_def_172, type, rel: set_Pr1834926343_pi_pi).
% 3.14/1.95 thf(func_def_173, type, alpha: late_freeRes).
% 3.14/1.95 thf(func_def_174, type, aa: name).
% 3.14/1.95 thf(func_def_175, type, b: name).
% 3.14/1.95 thf(func_def_176, type, x: name).
% 3.14/1.95 thf(func_def_177, type, y: name).
% 3.14/1.95 thf(func_def_178, type, z: name).
% 3.14/1.95 thf(func_def_201, type, ph1: !>[X0: $tType]:(X0)).
% 3.14/1.95 thf(func_def_202, type, sK2: name > name).
% 3.14/1.95 thf(func_def_203, type, sK3: late_subject > name).
% 3.14/1.95 thf(func_def_204, type, sK4: late_freeRes > name).
% 3.14/1.95 thf(func_def_205, type, sK5: pi > name).
% 3.14/1.95 thf(func_def_206, type, sK6: produc367475239e_name > list_P227219501e_name).
% 3.14/1.95 thf(func_def_207, type, sK7: (list_P227219501e_name > $o) > list_P227219501e_name).
% 3.14/1.95 thf(func_def_208, type, sK8: produc367475239e_name > name).
% 3.14/1.95 thf(func_def_209, type, sK9: produc367475239e_name > name).
% 3.14/1.95 thf(func_def_210, type, sK10: product_prod_pi_pi > pi).
% 3.14/1.95 thf(func_def_211, type, sK11: product_prod_pi_pi > pi).
% 3.14/1.95 thf(func_def_212, type, sK12: product_prod_pi_pi > pi).
% 3.14/1.95 thf(func_def_213, type, sK13: product_prod_pi_pi > pi).
% 3.14/1.95 thf(func_def_214, type, sK14: produc367475239e_name > name).
% 3.14/1.95 thf(func_def_215, type, sK15: produc367475239e_name > name).
% 3.14/1.95 thf(func_def_216, type, sK16: name > name).
% 3.14/1.95 thf(f2890,plain,(
% 3.14/1.95 $false),
% 3.14/1.95 inference(trivial_inequality_removal,[status(thm)],[f2889])).
% 3.14/1.95 thf(f2889,plain,(
% 3.14/1.95 ($true = $false)),
% 3.14/1.95 inference(boolean_simplification,[status(thm)],[f2888])).
% 3.14/1.95 thf(f2888,plain,(
% 3.14/1.95 ($true = (~ $true))),
% 3.14/1.95 inference(backward_demodulation,[status(thm)],[f1435,f2885])).
% 3.14/1.95 thf(f2885,plain,(
% 3.14/1.95 ( ! [X0 : list_P227219501e_name] : (($true = (late_transitions @ (perm_name_pi @ X0 @ q) @ (perm_n414416632sidual @ X0 @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))))) )),
% 3.14/1.95 inference(boolean_simplification,[status(thm)],[f2878])).
% 3.14/1.95 thf(f2878,plain,(
% 3.14/1.95 ( ! [X0 : list_P227219501e_name] : (($true = ($true => (late_transitions @ (perm_name_pi @ X0 @ q) @ (perm_n414416632sidual @ X0 @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)))))) )),
% 3.14/1.95 inference(superposition,[status(thm)],[f2871,f1339])).
% 3.14/1.95 thf(f1339,plain,(
% 3.14/1.95 ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) = $true)),
% 3.14/1.95 inference(cnf_transformation,[status(thm)],[f524])).
% 3.14/1.95 thf(f524,plain,(
% 3.14/1.95 ((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)) = $true)),
% 3.14/1.95 inference(fool_elimination,[status(thm)],[f523])).
% 3.14/1.95 thf(f523,plain,(
% 3.14/1.95 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 3.14/1.95 inference(rectify,[status(thm)],[f7])).
% 3.14/1.95 thf(f7,axiom,(
% 3.14/1.95 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 3.14/1.95 file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_6_cOpen_Ohyps_I1_J)).
% 3.14/1.95 thf(f2871,plain,(
% 3.14/1.95 ( ! [X2 : list_P227219501e_name,X3 : pi,X1 : late_residual] : (($true = ((late_transitions @ X3 @ X1) => (late_transitions @ (perm_name_pi @ X2 @ X3) @ (perm_n414416632sidual @ X2 @ X1))))) )),
% 3.14/1.95 inference(beta_eta_normalization,[status(thm)],[f2870])).
% 3.14/1.95 thf(f2870,plain,(
% 3.14/1.95 ( ! [X2 : list_P227219501e_name,X3 : pi,X1 : late_residual] : (($true = ((^[Y0 : pi]: ((late_transitions @ Y0 @ X1) => (late_transitions @ (perm_name_pi @ X2 @ Y0) @ (perm_n414416632sidual @ X2 @ X1)))) @ X3))) )),
% 3.14/1.95 inference(pi_clausification,[status(thm)],[f2866])).
% 3.14/1.95 thf(f2866,plain,(
% 3.14/1.95 ( ! [X2 : list_P227219501e_name,X1 : late_residual] : (($true = (!! @ pi @ (^[Y0 : pi]: ((late_transitions @ Y0 @ X1) => (late_transitions @ (perm_name_pi @ X2 @ Y0) @ (perm_n414416632sidual @ X2 @ X1))))))) )),
% 3.14/1.95 inference(beta_eta_normalization,[status(thm)],[f2858])).
% 3.14/1.95 thf(f2858,plain,(
% 3.14/1.95 ( ! [X2 : list_P227219501e_name,X1 : late_residual] : (($true = ((^[Y0 : list_P227219501e_name]: (!! @ pi @ (^[Y1 : pi]: ((late_transitions @ Y1 @ X1) => (late_transitions @ (perm_name_pi @ Y0 @ Y1) @ (perm_n414416632sidual @ Y0 @ X1)))))) @ X2))) )),
% 3.14/1.95 inference(pi_clausification,[status(thm)],[f2854])).
% 3.14/1.95 thf(f2854,plain,(
% 3.14/1.95 ( ! [X1 : late_residual] : (($true = (!! @ list_P227219501e_name @ (^[Y0 : list_P227219501e_name]: (!! @ pi @ (^[Y1 : pi]: ((late_transitions @ Y1 @ X1) => (late_transitions @ (perm_name_pi @ Y0 @ Y1) @ (perm_n414416632sidual @ Y0 @ X1))))))))) )),
% 3.14/1.95 inference(beta_eta_normalization,[status(thm)],[f2853])).
% 3.14/1.95 thf(f2853,plain,(
% 3.14/1.95 ( ! [X1 : late_residual] : ((((^[Y0 : late_residual]: (!! @ list_P227219501e_name @ (^[Y1 : list_P227219501e_name]: (!! @ pi @ (^[Y2 : pi]: ((late_transitions @ Y2 @ Y0) => (late_transitions @ (perm_name_pi @ Y1 @ Y2) @ (perm_n414416632sidual @ Y1 @ Y0)))))))) @ X1) = $true)) )),
% 3.14/1.95 inference(pi_clausification,[status(thm)],[f1388])).
% 3.14/1.95 thf(f1388,plain,(
% 3.14/1.95 ($true = (!! @ late_residual @ (^[Y0 : late_residual]: (!! @ list_P227219501e_name @ (^[Y1 : list_P227219501e_name]: (!! @ pi @ (^[Y2 : pi]: ((late_transitions @ Y2 @ Y0) => (late_transitions @ (perm_name_pi @ Y1 @ Y2) @ (perm_n414416632sidual @ Y1 @ Y0))))))))))),
% 3.14/1.95 inference(cnf_transformation,[status(thm)],[f578])).
% 3.14/1.95 thf(f578,plain,(
% 3.14/1.95 ($true = (!! @ late_residual @ (^[Y0 : late_residual]: (!! @ list_P227219501e_name @ (^[Y1 : list_P227219501e_name]: (!! @ pi @ (^[Y2 : pi]: ((late_transitions @ Y2 @ Y0) => (late_transitions @ (perm_name_pi @ Y1 @ Y2) @ (perm_n414416632sidual @ Y1 @ Y0))))))))))),
% 3.14/1.95 inference(fool_elimination,[status(thm)],[f577])).
% 3.14/1.95 thf(f577,plain,(
% 3.14/1.95 ! [X0 : pi,X1 : list_P227219501e_name,X2 : late_residual] : ((late_transitions @ X0 @ X2) => (late_transitions @ (perm_name_pi @ X1 @ X0) @ (perm_n414416632sidual @ X1 @ X2)))),
% 3.14/1.95 inference(rectify,[status(thm)],[f42])).
% 3.14/1.95 thf(f42,axiom,(
% 3.14/1.95 ! [X3 : pi,X5 : list_P227219501e_name,X4 : late_residual] : ((late_transitions @ X3 @ X4) => (late_transitions @ (perm_name_pi @ X5 @ X3) @ (perm_n414416632sidual @ X5 @ X4)))),
% 3.14/1.95 file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_41_eqvt)).
% 3.14/1.95 thf(f1435,plain,(
% 3.14/1.95 ((~ (late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)))) = $true)),
% 3.14/1.95 inference(definition_unfolding,[status(thm)],[f1083,f1149])).
% 3.14/1.95 thf(f1149,plain,(
% 3.14/1.95 (aa = b)),
% 3.14/1.95 inference(cnf_transformation,[status(thm)],[f778])).
% 3.14/1.95 thf(f778,plain,(
% 3.14/1.95 (aa = b)),
% 3.14/1.95 inference(fool_elimination,[status(thm)],[f1])).
% 3.14/1.95 thf(f1,axiom,(
% 3.14/1.95 (aa = b)),
% 3.14/1.95 file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062)).
% 3.14/1.95 thf(f1083,plain,(
% 3.14/1.95 ($true = (~ (late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))))),
% 3.14/1.95 inference(cnf_transformation,[status(thm)],[f574])).
% 3.14/1.95 thf(f574,plain,(
% 3.14/1.95 ($true = (~ (late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))))),
% 3.14/1.95 inference(fool_elimination,[status(thm)],[f573])).
% 3.14/1.95 thf(f573,plain,(
% 3.14/1.95 ~(late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.14/1.95 inference(rectify,[status(thm)],[f362])).
% 3.14/1.95 thf(f362,negated_conjecture,(
% 3.14/1.95 ~(late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.14/1.95 inference(negated_conjecture,[status(cth)],[f361])).
% 3.14/1.95 thf(f361,conjecture,(
% 3.14/1.95 (late_transitions @ (perm_name_pi @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ q) @ (perm_n414416632sidual @ (cons_P1213805021e_name @ (produc1570949143e_name @ z @ x) @ nil_Pr743626285e_name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.14/1.95 file('/export/starexec/sandbox/tmp/tmp.71iL0JE252/DTF2THF_18628.p',conj_0)).
% 3.14/1.95 % SZS output end Proof for DTF2THF_18628
% 3.14/1.95 % (18968)------------------------------
% 3.14/1.95 % (18968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.95 % (18968)Termination reason: Refutation
% 3.14/1.95
% 3.14/1.95 % (18968)Memory used [KB]: 9978
% 3.14/1.95 % (18968)Time elapsed: 0.239 s
% 3.14/1.95 % (18968)Instructions burned: 766 (million)
% 3.14/1.95 % (18968)------------------------------
% 3.14/1.95 % (18968)------------------------------
% 3.14/1.95 % (18956)Success in time 0.295 s
%------------------------------------------------------------------------------