%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP183^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 08:56:13 AM UTC 2026
% Result : Theorem 3.03s 1.69s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 226 ( 17 ~; 9 |; 0 &; 194 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 13 con; 0-5 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
name: $tType ).
thf(type_def_6,type,
pi: $tType ).
thf(type_def_8,type,
late_freeRes: $tType ).
thf(type_def_9,type,
late_subject: $tType ).
thf(type_def_10,type,
late_residual: $tType ).
thf(type_def_11,type,
noption_name: $tType ).
thf(type_def_12,type,
noption_pi: $tType ).
thf(type_def_13,type,
noption_Late_freeRes: $tType ).
thf(type_def_14,type,
noption_Late_subject: $tType ).
thf(type_def_15,type,
produc1462499409ion_pi: $tType ).
thf(type_def_16,type,
produc405342261i_name: $tType ).
thf(type_def_17,type,
produc629157763_pi_pi: $tType ).
thf(type_def_18,type,
produc1834551554reeRes: $tType ).
thf(type_def_19,type,
produc691362330ubject: $tType ).
thf(type_def_20,type,
produc2008547984reeRes: $tType ).
thf(type_def_21,type,
produc865358760ubject: $tType ).
thf(type_def_22,type,
product_prod_pi_pi: $tType ).
thf(type_def_23,type,
produc2052722628s_name: $tType ).
thf(type_def_24,type,
produc992857746Res_pi: $tType ).
thf(type_def_25,type,
produc1357834675reeRes: $tType ).
thf(type_def_26,type,
produc214645451ubject: $tType ).
thf(type_def_27,type,
produc1998742700t_name: $tType ).
thf(type_def_28,type,
produc140253050ect_pi: $tType ).
thf(type_def_29,type,
produc355105483reeRes: $tType ).
thf(type_def_30,type,
produc1359399907ubject: $tType ).
thf(type_def_31,type,
set_Pr1569510577ion_pi: $tType ).
thf(type_def_32,type,
set_Pr1294453099i_name: $tType ).
thf(type_def_33,type,
set_Pr1694908217_pi_pi: $tType ).
thf(type_def_34,type,
set_Pr305743074reeRes: $tType ).
thf(type_def_35,type,
set_Pr248416762ubject: $tType ).
thf(type_def_36,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_0,type,
set_Pr1569510577ion_pi: $tType ).
thf(func_def_1,type,
produc1462499409ion_pi: $tType ).
thf(func_def_2,type,
set_Pr248416762ubject: $tType ).
thf(func_def_3,type,
set_Pr305743074reeRes: $tType ).
thf(func_def_4,type,
set_Pr1294453099i_name: $tType ).
thf(func_def_5,type,
produc691362330ubject: $tType ).
thf(func_def_6,type,
produc1834551554reeRes: $tType ).
thf(func_def_7,type,
set_Pr1694908217_pi_pi: $tType ).
thf(func_def_8,type,
produc405342261i_name: $tType ).
thf(func_def_9,type,
produc629157763_pi_pi: $tType ).
thf(func_def_10,type,
produc1359399907ubject: $tType ).
thf(func_def_11,type,
produc355105483reeRes: $tType ).
thf(func_def_12,type,
produc214645451ubject: $tType ).
thf(func_def_13,type,
produc1357834675reeRes: $tType ).
thf(func_def_14,type,
produc1998742700t_name: $tType ).
thf(func_def_15,type,
produc2052722628s_name: $tType ).
thf(func_def_16,type,
produc865358760ubject: $tType ).
thf(func_def_17,type,
produc2008547984reeRes: $tType ).
thf(func_def_18,type,
produc140253050ect_pi: $tType ).
thf(func_def_19,type,
produc992857746Res_pi: $tType ).
thf(func_def_20,type,
set_Pr1834926343_pi_pi: $tType ).
thf(func_def_21,type,
product_prod_pi_pi: $tType ).
thf(func_def_22,type,
noption_Late_subject: $tType ).
thf(func_def_23,type,
noption_Late_freeRes: $tType ).
thf(func_def_24,type,
noption_name: $tType ).
thf(func_def_25,type,
noption_pi: $tType ).
thf(func_def_26,type,
late_residual: $tType ).
thf(func_def_27,type,
late_subject: $tType ).
thf(func_def_28,type,
late_freeRes: $tType ).
thf(func_def_29,type,
name: $tType ).
thf(func_def_30,type,
pi: $tType ).
thf(func_def_31,type,
input: name > name > pi > pi ).
thf(func_def_32,type,
mismatch: name > name > pi > pi ).
thf(func_def_33,type,
output: name > name > pi > pi ).
thf(func_def_34,type,
par: pi > pi > pi ).
thf(func_def_35,type,
piNil: pi ).
thf(func_def_36,type,
res: name > pi > pi ).
thf(func_def_37,type,
sum: pi > pi > pi ).
thf(func_def_38,type,
tau: pi > pi ).
thf(func_def_39,type,
subs: pi > name > name > pi ).
thf(func_def_40,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_41,type,
late_TauR: late_freeRes ).
thf(func_def_42,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_43,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_44,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_45,type,
late_InputS: name > late_subject ).
thf(func_def_46,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_47,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(func_def_48,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_49,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(func_def_50,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(func_def_51,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(func_def_52,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_53,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(func_def_54,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(func_def_55,type,
fresh_name_name: name > name > $o ).
thf(func_def_56,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_57,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_58,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_59,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_60,type,
fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
thf(func_def_61,type,
fresh_453496559i_name: name > produc405342261i_name > $o ).
thf(func_def_62,type,
fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
thf(func_def_63,type,
fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
thf(func_def_64,type,
fresh_567880928ubject: name > produc691362330ubject > $o ).
thf(func_def_65,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(func_def_66,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(func_def_67,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(func_def_68,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(func_def_69,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(func_def_70,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(func_def_71,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(func_def_72,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(func_def_73,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(func_def_74,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(func_def_75,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
thf(func_def_76,type,
ord_le1032043601ion_pi: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > $o ).
thf(func_def_77,type,
ord_le2082425291i_name: set_Pr1294453099i_name > set_Pr1294453099i_name > $o ).
thf(func_def_78,type,
ord_le1854926745_pi_pi: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > $o ).
thf(func_def_79,type,
ord_le1762471042reeRes: set_Pr305743074reeRes > set_Pr305743074reeRes > $o ).
thf(func_def_80,type,
ord_le1705144730ubject: set_Pr248416762ubject > set_Pr248416762ubject > $o ).
thf(func_def_81,type,
ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_82,type,
produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
thf(func_def_83,type,
produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
thf(func_def_84,type,
produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
thf(func_def_85,type,
produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
thf(func_def_86,type,
produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
thf(func_def_87,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(func_def_88,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(func_def_89,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(func_def_90,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(func_def_91,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(func_def_92,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(func_def_93,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(func_def_94,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(func_def_95,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(func_def_96,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(func_def_97,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(func_def_98,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(func_def_99,type,
id_name_noption_pi: set_Pr1569510577ion_pi ).
thf(func_def_100,type,
id_pi: set_Pr1834926343_pi_pi ).
thf(func_def_101,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(func_def_102,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(func_def_103,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(func_def_104,type,
member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
thf(func_def_105,type,
member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
thf(func_def_106,type,
member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
thf(func_def_107,type,
member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
thf(func_def_108,type,
member938018755ubject: produc691362330ubject > set_Pr248416762ubject > $o ).
thf(func_def_109,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(func_def_110,type,
p: pi ).
thf(func_def_111,type,
pq: pi ).
thf(func_def_112,type,
q: pi ).
thf(func_def_113,type,
q2: pi ).
thf(func_def_114,type,
rel: set_Pr1834926343_pi_pi ).
thf(func_def_115,type,
alpha: late_freeRes ).
thf(func_def_116,type,
x: name ).
thf(func_def_134,type,
sP0: pi > pi > late_subject > name > pi > $o ).
thf(func_def_135,type,
sK1: pi > name ).
thf(func_def_136,type,
sK2: pi > pi > late_subject > name > pi > pi ).
thf(func_def_137,type,
sK3: pi > pi > late_subject > name > pi > pi ).
thf(func_def_138,type,
sK4: pi > pi > late_subject > name > pi > pi ).
thf(func_def_139,type,
sK5: pi > pi > late_subject > name > pi > late_subject ).
thf(func_def_140,type,
sK6: pi > pi > late_subject > name > pi > name ).
thf(func_def_141,type,
sK7: late_subject > pi > pi > name > pi > name ).
thf(func_def_142,type,
sK8: late_subject > pi > pi > name > pi > pi ).
thf(func_def_143,type,
sK9: late_subject > pi > pi > name > pi > pi ).
thf(func_def_144,type,
sK10: late_subject > pi > pi > name > pi > late_subject ).
thf(func_def_145,type,
sK11: late_subject > pi > pi > name > pi > pi ).
thf(func_def_146,type,
sK12: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_147,type,
sK13: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_148,type,
sK14: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_149,type,
sK15: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_150,type,
sK16: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_151,type,
sK17: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_152,type,
sK18: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_153,type,
sK19: pi > name > late_freeRes > ( pi > $o ) > pi ).
thf(func_def_154,type,
sK20: ( pi > $o ) > name > late_subject > pi > pi > pi ).
thf(func_def_155,type,
sK21: ( pi > $o ) > name > late_subject > pi > pi > pi ).
thf(func_def_156,type,
sK22: pi > pi > name > late_freeRes > pi ).
thf(func_def_157,type,
sK23: pi > pi > name > late_freeRes > name ).
thf(func_def_158,type,
sK24: pi > pi > name > late_freeRes > late_freeRes ).
thf(func_def_159,type,
sK25: pi > pi > name > late_freeRes > pi ).
thf(func_def_160,type,
sK26: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_161,type,
sK27: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_162,type,
sK28: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_163,type,
sK29: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_164,type,
sK30: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_165,type,
sK31: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_166,type,
sK32: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_167,type,
sK33: late_freeRes > name ).
thf(func_def_169,type,
ph35:
!>[X0: $tType] : X0 ).
thf(f987,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f986,f963]) ).
thf(f963,plain,
( ( fresh_1641682979reeRes @ x @ alpha )
= $true ),
inference(cnf_transformation,[status(thm)],[f522]) ).
thf(f522,plain,
( ( fresh_1641682979reeRes @ x @ alpha )
= $true ),
inference(fool_elimination,[status(thm)],[f521]) ).
thf(f521,plain,
fresh_1641682979reeRes @ x @ alpha,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
fresh_1641682979reeRes @ x @ alpha,
file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_0_cRes_Ohyps_I2_J) ).
thf(f986,plain,
( ( fresh_1641682979reeRes @ x @ alpha )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f985,f973]) ).
thf(f973,plain,
( ( late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f500]) ).
thf(f500,plain,
( ( late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f499]) ).
thf(f499,plain,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ),
file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062) ).
thf(f985,plain,
( ( ( late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) )
!= $true )
| ( ( fresh_1641682979reeRes @ x @ alpha )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f984]) ).
thf(f984,plain,
( ( ( fresh_1641682979reeRes @ x @ alpha )
!= $true )
| ( $true != $true )
| ( ( late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f960,f943]) ).
thf(f943,plain,
! [X2: name,X3: pi,X0: late_freeRes,X1: pi] :
( ( ( late_transitions @ ( res @ X2 @ X3 ) @ ( late_FreeR @ X0 @ ( res @ X2 @ X1 ) ) )
= $true )
| ( ( late_transitions @ X3 @ ( late_FreeR @ X0 @ X1 ) )
!= $true )
| ( $true
!= ( fresh_1641682979reeRes @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f847]) ).
thf(f847,plain,
! [X0: late_freeRes,X1: pi,X2: name,X3: pi] :
( ( $true
!= ( fresh_1641682979reeRes @ X2 @ X0 ) )
| ( ( late_transitions @ ( res @ X2 @ X3 ) @ ( late_FreeR @ X0 @ ( res @ X2 @ X1 ) ) )
= $true )
| ( ( late_transitions @ X3 @ ( late_FreeR @ X0 @ X1 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f846]) ).
thf(f846,plain,
! [X0: late_freeRes,X1: pi,X2: name,X3: pi] :
( ( ( late_transitions @ ( res @ X2 @ X3 ) @ ( late_FreeR @ X0 @ ( res @ X2 @ X1 ) ) )
= $true )
| ( $true
!= ( fresh_1641682979reeRes @ X2 @ X0 ) )
| ( ( late_transitions @ X3 @ ( late_FreeR @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f820]) ).
thf(f820,plain,
! [X0: late_freeRes,X1: pi,X2: name,X3: pi] :
( ( ( late_transitions @ X3 @ ( late_FreeR @ X0 @ X1 ) )
= $true )
=> ( ( $true
= ( fresh_1641682979reeRes @ X2 @ X0 ) )
=> ( ( late_transitions @ ( res @ X2 @ X3 ) @ ( late_FreeR @ X0 @ ( res @ X2 @ X1 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f819]) ).
thf(f819,plain,
! [X0: late_freeRes,X1: pi,X2: name,X3: pi] :
( ( late_transitions @ X3 @ ( late_FreeR @ X0 @ X1 ) )
=> ( ( fresh_1641682979reeRes @ X2 @ X0 )
=> ( late_transitions @ ( res @ X2 @ X3 ) @ ( late_FreeR @ X0 @ ( res @ X2 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X8: late_freeRes,X12: pi,X16: name,X4: pi] :
( ( late_transitions @ X4 @ ( late_FreeR @ X8 @ X12 ) )
=> ( ( fresh_1641682979reeRes @ X16 @ X8 )
=> ( late_transitions @ ( res @ X16 @ X4 ) @ ( late_FreeR @ X8 @ ( res @ X16 @ X12 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_13_ResF) ).
thf(f960,plain,
( ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f823]) ).
thf(f823,plain,
( ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) )
!= $true ),
inference(flattening,[status(thm)],[f748]) ).
thf(f748,plain,
( ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f747]) ).
thf(f747,plain,
~ ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ),
inference(rectify,[status(thm)],[f315]) ).
thf(f315,negated_conjecture,
~ ( late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ),
inference(negated_conjecture,[status(cth)],[f314]) ).
thf(f314,conjecture,
late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP183^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:29:22 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : ITP183^1 : TPTP v9.2.1. Released v7.5.0.
% 0.26/0.46 % Domain : Interactive Theorem Proving
% 0.26/0.46 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_329__3411594_1
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Des21]
% 0.26/0.46 % Names : Strong_Late_Sim_SC/prob_329__3411594_1 [Des21]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.26/0.46 % Syntax : Number of formulae : 431 ( 161 unt; 117 typ; 0 def)
% 0.26/0.46 % Number of atoms : 906 ( 318 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 16 ( 2 avg)
% 0.26/0.46 % Number of connectives : 3454 ( 150 ~; 10 |; 78 &;2776 @)
% 0.26/0.46 % ( 0 <=>; 440 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 27 ( 8 avg)
% 0.26/0.46 % Number of types : 32 ( 31 usr)
% 0.26/0.46 % Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 87 ( 86 usr; 11 con; 0-5 aty)
% 0.26/0.46 % Number of variables : 1290 ( 26 ^;1226 !; 38 ?;1290 :)
% 0.26/0.46 % SPC : TH0_THM_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:50.938
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % Could-be-implicit typings (31)
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 0.26/0.46 set_Pr1569510577ion_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.26/0.46 produc1462499409ion_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J_J,type,
% 0.26/0.46 set_Pr248416762ubject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.26/0.46 set_Pr305743074reeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 0.26/0.46 set_Pr1294453099i_name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 produc691362330ubject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 produc1834551554reeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 0.26/0.46 set_Pr1694908217_pi_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.26/0.46 produc405342261i_name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.26/0.46 produc629157763_pi_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 produc1359399907ubject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 produc355105483reeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 produc214645451ubject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 produc1357834675reeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.26/0.46 produc1998742700t_name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
% 0.26/0.46 produc2052722628s_name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 produc865358760ubject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 produc2008547984reeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.26/0.46 produc140253050ect_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
% 0.26/0.46 produc992857746Res_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.26/0.46 set_Pr1834926343_pi_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.26/0.46 product_prod_pi_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 0.26/0.46 noption_Late_subject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 noption_Late_freeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 0.26/0.46 noption_name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.26/0.46 noption_pi: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.26/0.46 late_residual: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.26/0.46 late_subject: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 late_freeRes: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Agent__Oname,type,
% 0.26/0.46 name: $tType ).
% 0.26/0.46
% 0.26/0.46 thf(ty_n_t__Agent__Opi,type,
% 0.26/0.46 pi: $tType ).
% 0.26/0.46
% 0.26/0.46 % Explicit typings (86)
% 0.26/0.46 thf(sy_c_Agent_Opi_OInput,type,
% 0.26/0.46 input: name > name > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.26/0.46 mismatch: name > name > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OOutput,type,
% 0.26/0.46 output: name > name > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OPar,type,
% 0.26/0.46 par: pi > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.26/0.46 piNil: pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_ORes,type,
% 0.26/0.46 res: name > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OSum,type,
% 0.26/0.46 sum: pi > pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Opi_OTau,type,
% 0.26/0.46 tau: pi > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Agent_Osubs,type,
% 0.26/0.46 subs: pi > name > name > pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.26/0.46 late_OutputR: name > name > late_freeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 0.26/0.46 late_TauR: late_freeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 0.26/0.46 late_BoundR: late_subject > name > pi > late_residual ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 0.26/0.46 late_FreeR: late_freeRes > pi > late_residual ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 0.26/0.46 late_BoundOutputS: name > late_subject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 0.26/0.46 late_InputS: name > late_subject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Late__Semantics_Otransitions,type,
% 0.26/0.46 late_transitions: pi > late_residual > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.26/0.46 abs_fun_name_name: name > name > name > noption_name ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.26/0.46 abs_fun_name_pi: name > pi > name > noption_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 0.26/0.46 fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.26/0.46 fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 0.26/0.46 fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
% 0.26/0.46 fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.26/0.46 fresh_name_name: name > name > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
% 0.26/0.46 fresh_name_pi: name > pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 fresh_1641682979reeRes: name > late_freeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
% 0.26/0.46 fresh_81631222sidual: name > late_residual > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 fresh_717452603ubject: name > late_subject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.26/0.46 fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.26/0.46 fresh_453496559i_name: name > produc405342261i_name > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.26/0.46 fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 fresh_567880928ubject: name > produc691362330ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 fresh_820177506ubject: name > produc865358760ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.26/0.46 fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
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% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
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% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
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% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 fresh_1498103185ubject: name > produc214645451ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
% 0.26/0.46 fresh_1953561446t_name: name > produc1998742700t_name > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
% 0.26/0.46 fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 fresh_495373993ubject: name > produc1359399907ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 0.26/0.46 ord_le1032043601ion_pi: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J_J,type,
% 0.26/0.46 ord_le2082425291i_name: set_Pr1294453099i_name > set_Pr1294453099i_name > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J_J,type,
% 0.26/0.46 ord_le1854926745_pi_pi: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J_J,type,
% 0.26/0.46 ord_le1762471042reeRes: set_Pr305743074reeRes > set_Pr305743074reeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J_J,type,
% 0.26/0.46 ord_le1705144730ubject: set_Pr248416762ubject > set_Pr248416762ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
% 0.26/0.46 ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.26/0.46 produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
% 0.26/0.46 produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
% 0.26/0.46 produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 0.26/0.46 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.26/0.46 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 0.26/0.46 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.26/0.46 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 0.26/0.46 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 0.26/0.46 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 0.26/0.46 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 0.26/0.46 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Relation_OId_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 0.26/0.46 id_name_noption_pi: set_Pr1569510577ion_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 0.26/0.46 id_pi: set_Pr1834926343_pi_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.26/0.46 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 0.26/0.46 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 0.26/0.46 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.26/0.46 member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 0.26/0.46 member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 0.26/0.46 member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 0.26/0.46 member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 0.26/0.46 member938018755ubject: produc691362330ubject > set_Pr248416762ubject > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 0.26/0.46 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_P,type,
% 0.26/0.46 p: pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_PQ____,type,
% 0.26/0.46 pq: pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_Q,type,
% 0.26/0.46 q: pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_Q_H____,type,
% 0.26/0.46 q2: pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_Rel,type,
% 0.26/0.46 rel: set_Pr1834926343_pi_pi ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v__092_060alpha_062____,type,
% 0.26/0.46 alpha: late_freeRes ).
% 0.26/0.46
% 0.26/0.46 thf(sy_v_x,type,
% 0.26/0.46 x: name ).
% 0.26/0.46
% 0.26/0.46 % Relevant facts (313)
% 0.26/0.46 thf(fact_0_cRes_Ohyps_I2_J,axiom,
% 0.26/0.46 fresh_1641682979reeRes @ x @ alpha ).
% 0.26/0.46
% 0.26/0.46 % cRes.hyps(2)
% 0.26/0.46 thf(fact_1_Eqvt,axiom,
% 0.26/0.46 eqvt_pi @ rel ).
% 0.26/0.46
% 0.26/0.46 % Eqvt
% 0.26/0.46 thf(fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062,axiom,
% 0.26/0.46 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) ).
% 0.26/0.46
% 0.26/0.46 % \<open>P \<oplus> Q \<longmapsto> \<alpha> \<prec> Q'\<close>
% 0.26/0.46 thf(fact_3_cRes_Ohyps_I1_J,axiom,
% 0.26/0.46 late_transitions @ q @ ( late_FreeR @ alpha @ q2 ) ).
% 0.26/0.46
% 0.26/0.46 % cRes.hyps(1)
% 0.26/0.46 thf(fact_4_cSum2_Ohyps,axiom,
% 0.26/0.46 late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.26/0.46
% 0.26/0.46 % cSum2.hyps
% 0.26/0.46 thf(fact_5_Free_Ohyps,axiom,
% 0.26/0.46 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ) ).
% 0.26/0.46
% 0.26/0.46 % Free.hyps
% 0.26/0.46 thf(fact_6_pi_Odistinct_I81_J,axiom,
% 0.26/0.46 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( sum @ Pi1 @ Pi2 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(81)
% 0.26/0.46 thf(fact_7_sumCases,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.26/0.46 => ( ~ ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumCases
% 0.26/0.46 thf(fact_8_sumCases_H,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.26/0.46 => ( ~ ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumCases'
% 0.26/0.46 thf(fact_9_Sum1,axiom,
% 0.26/0.46 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.26/0.46
% 0.26/0.46 % Sum1
% 0.26/0.46 thf(fact_10_Sum2,axiom,
% 0.26/0.46 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ Rs )
% 0.26/0.46 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.26/0.46
% 0.26/0.46 % Sum2
% 0.26/0.46 thf(fact_11_resCasesF,axiom,
% 0.26/0.46 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.26/0.46 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.26/0.46 => ( ! [P2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.26/0.46 => ( F @ ( res @ X @ P2 ) ) ) )
% 0.26/0.46 => ( F @ XP ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resCasesF
% 0.26/0.46 thf(fact_12_resCasesF_H,axiom,
% 0.26/0.46 ! [X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.26/0.46 ( ( ( res @ X @ P )
% 0.26/0.46 = ( res @ Y @ P4 ) )
% 0.26/0.46 => ( ( ( late_FreeR @ Alpha @ P3 )
% 0.26/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.26/0.46 => ~ ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resCasesF'
% 0.26/0.46 thf(fact_13_ResF,axiom,
% 0.26/0.46 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ Y2 @ Alpha )
% 0.26/0.46 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ResF
% 0.26/0.46 thf(fact_14_pi_Oinject_I6_J,axiom,
% 0.26/0.46 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.26/0.46 ( ( ( sum @ X2 @ X1 )
% 0.26/0.46 = ( sum @ Y22 @ Y1 ) )
% 0.26/0.46 = ( ( X2 = Y22 )
% 0.26/0.46 & ( X1 = Y1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(6)
% 0.26/0.46 thf(fact_15_residual_Oinject_I2_J,axiom,
% 0.26/0.46 ! [X2: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 0.26/0.46 ( ( ( late_FreeR @ X2 @ X1 )
% 0.26/0.46 = ( late_FreeR @ Y22 @ Y1 ) )
% 0.26/0.46 = ( ( X2 = Y22 )
% 0.26/0.46 & ( X1 = Y1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.inject(2)
% 0.26/0.46 thf(fact_16_resInputFreeTrans,axiom,
% 0.26/0.46 ! [X: name,A: name,Y2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resInputFreeTrans
% 0.26/0.46 thf(fact_17_resZeroTrans,axiom,
% 0.26/0.46 ! [X: name,Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % resZeroTrans
% 0.26/0.46 thf(fact_18_pi_Odistinct_I5_J,axiom,
% 0.26/0.46 ! [Name1: name,Name2: name,Pi: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(5)
% 0.26/0.46 thf(fact_19_name__exists__fresh,axiom,
% 0.26/0.46 ! [X: late_subject] :
% 0.26/0.46 ~ ! [C: name] :
% 0.26/0.46 ~ ( fresh_717452603ubject @ C @ X ) ).
% 0.26/0.46
% 0.26/0.46 % name_exists_fresh
% 0.26/0.46 thf(fact_20_name__exists__fresh,axiom,
% 0.26/0.46 ! [X: late_freeRes] :
% 0.26/0.46 ~ ! [C: name] :
% 0.26/0.46 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 0.26/0.46
% 0.26/0.46 % name_exists_fresh
% 0.26/0.46 thf(fact_21_name__exists__fresh,axiom,
% 0.26/0.46 ! [X: name] :
% 0.26/0.46 ~ ! [C: name] :
% 0.26/0.46 ~ ( fresh_name_name @ C @ X ) ).
% 0.26/0.46
% 0.26/0.46 % name_exists_fresh
% 0.26/0.46 thf(fact_22_name__exists__fresh,axiom,
% 0.26/0.46 ! [X: pi] :
% 0.26/0.46 ~ ! [C: name] :
% 0.26/0.46 ~ ( fresh_name_pi @ C @ X ) ).
% 0.26/0.46
% 0.26/0.46 % name_exists_fresh
% 0.26/0.46 thf(fact_23_pi_Odistinct_I57_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(57)
% 0.26/0.46 thf(fact_24_zeroTrans,axiom,
% 0.26/0.46 ! [Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % zeroTrans
% 0.26/0.46 thf(fact_25_nilCases_H,axiom,
% 0.26/0.46 ! [Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % nilCases'
% 0.26/0.46 thf(fact_26_pi_Odistinct_I53_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(53)
% 0.26/0.46 thf(fact_27_pi_Odistinct_I15_J,axiom,
% 0.26/0.46 ! [Name: name,Pi: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(15)
% 0.26/0.46 thf(fact_28_pi_Odistinct_I11_J,axiom,
% 0.26/0.46 ! [Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(11)
% 0.26/0.46 thf(fact_29_resTrans_I2_J,axiom,
% 0.26/0.46 ! [X: name,Y2: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y2 @ P ) ) @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % resTrans(2)
% 0.26/0.46 thf(fact_30_inputFreeTrans,axiom,
% 0.26/0.46 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % inputFreeTrans
% 0.26/0.46 thf(fact_31_Id,axiom,
% 0.26/0.46 ord_le630093991_pi_pi @ id_pi @ rel ).
% 0.26/0.46
% 0.26/0.46 % Id
% 0.26/0.46 thf(fact_32_outputFreshTrans,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 0.26/0.46 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputFreshTrans
% 0.26/0.46 thf(fact_33_freshFreeDerivative_I1_J,axiom,
% 0.26/0.46 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( fresh_1641682979reeRes @ Y2 @ Alpha ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshFreeDerivative(1)
% 0.26/0.46 thf(fact_34_nilSim_I2_J,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 0.26/0.46 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % nilSim(2)
% 0.26/0.46 thf(fact_35_resTrans_I1_J,axiom,
% 0.26/0.46 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % resTrans(1)
% 0.26/0.46 thf(fact_36_freeRes_Ofresh_I2_J,axiom,
% 0.26/0.46 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.26/0.46
% 0.26/0.46 % freeRes.fresh(2)
% 0.26/0.46 thf(fact_37_freshFreeDerivative_I2_J,axiom,
% 0.26/0.46 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( fresh_name_pi @ Y2 @ P3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshFreeDerivative(2)
% 0.26/0.46 thf(fact_38_residual_Ostrong__induct,axiom,
% 0.26/0.46 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.26/0.46 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_induct
% 0.26/0.46 thf(fact_39_residual_Ostrong__induct,axiom,
% 0.26/0.46 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_induct
% 0.26/0.46 thf(fact_40_residual_Ostrong__induct,axiom,
% 0.26/0.46 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.26/0.46 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_induct
% 0.26/0.46 thf(fact_41_residual_Ostrong__induct,axiom,
% 0.26/0.46 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_induct
% 0.26/0.46 thf(fact_42_residual_Ostrong__inducts,axiom,
% 0.26/0.46 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 0.26/0.46 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_inducts
% 0.26/0.46 thf(fact_43_residual_Ostrong__inducts,axiom,
% 0.26/0.46 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_inducts
% 0.26/0.46 thf(fact_44_residual_Ostrong__inducts,axiom,
% 0.26/0.46 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 0.26/0.46 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_inducts
% 0.26/0.46 thf(fact_45_residual_Ostrong__inducts,axiom,
% 0.26/0.46 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 0.26/0.46 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Z @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.strong_inducts
% 0.26/0.46 thf(fact_46_Par2F,axiom,
% 0.26/0.46 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Par2F
% 0.26/0.46 thf(fact_47_pi_Ofresh_I8_J,axiom,
% 0.26/0.46 ! [A: name,X2: pi,X1: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_name_pi @ A @ X2 )
% 0.26/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(8)
% 0.26/0.46 thf(fact_48_pi_Ofresh_I7_J,axiom,
% 0.26/0.46 ! [A: name,X2: pi,X1: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_name_pi @ A @ X2 )
% 0.26/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(7)
% 0.26/0.46 thf(fact_49_pi_Ofresh_I2_J,axiom,
% 0.26/0.46 ! [A: name,X3: name,X2: name,X1: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( output @ X3 @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X3 )
% 0.26/0.46 & ( fresh_name_name @ A @ X2 )
% 0.26/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(2)
% 0.26/0.46 thf(fact_50_pi_Ofresh_I1_J,axiom,
% 0.26/0.46 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(1)
% 0.26/0.46 thf(fact_51_residual_Ofresh_I2_J,axiom,
% 0.26/0.46 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.26/0.46 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.26/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.fresh(2)
% 0.26/0.46 thf(fact_52_pi_Oinject_I7_J,axiom,
% 0.26/0.46 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 0.26/0.46 ( ( ( par @ X2 @ X1 )
% 0.26/0.46 = ( par @ Y22 @ Y1 ) )
% 0.26/0.46 = ( ( X2 = Y22 )
% 0.26/0.46 & ( X1 = Y1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(7)
% 0.26/0.46 thf(fact_53_pi_Oinject_I1_J,axiom,
% 0.26/0.46 ! [X3: name,X2: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 0.26/0.46 ( ( ( output @ X3 @ X2 @ X1 )
% 0.26/0.46 = ( output @ Y3 @ Y22 @ Y1 ) )
% 0.26/0.46 = ( ( X3 = Y3 )
% 0.26/0.46 & ( X2 = Y22 )
% 0.26/0.46 & ( X1 = Y1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(1)
% 0.26/0.46 thf(fact_54_mem__Collect__eq,axiom,
% 0.26/0.46 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 0.26/0.46 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 0.26/0.46 = ( P @ A ) ) ).
% 0.26/0.46
% 0.26/0.46 % mem_Collect_eq
% 0.26/0.46 thf(fact_55_Collect__mem__eq,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( collec1051790738_pi_pi
% 0.26/0.46 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A2 ) )
% 0.26/0.46 = A2 ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_mem_eq
% 0.26/0.46 thf(fact_56_Collect__cong,axiom,
% 0.26/0.46 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.26/0.46 ( ! [X5: product_prod_pi_pi] :
% 0.26/0.46 ( ( P @ X5 )
% 0.26/0.46 = ( Q @ X5 ) )
% 0.26/0.46 => ( ( collec1051790738_pi_pi @ P )
% 0.26/0.46 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_cong
% 0.26/0.46 thf(fact_57_pi_Odistinct_I29_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(29)
% 0.26/0.46 thf(fact_58_freshBoundDerivative_I2_J,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( ( Y2 != X )
% 0.26/0.46 => ( fresh_name_pi @ Y2 @ P3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshBoundDerivative(2)
% 0.26/0.46 thf(fact_59_freshBoundDerivative_I1_J,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( fresh_717452603ubject @ Y2 @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshBoundDerivative(1)
% 0.26/0.46 thf(fact_60_Late__Semantics_OPar1B,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Par1B
% 0.26/0.46 thf(fact_61_Late__Semantics_OPar2B,axiom,
% 0.26/0.46 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Par2B
% 0.26/0.46 thf(fact_62_parCasesB,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.26/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ! [P2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.26/0.46 => ( Prop @ ( par @ P2 @ Q ) ) )
% 0.26/0.46 => ( ! [Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.26/0.46 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.26/0.46 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % parCasesB
% 0.26/0.46 thf(fact_63_parCasesB_H,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,B: late_subject,Y2: name,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y2 @ P3 ) )
% 0.26/0.46 => ( ! [P4: pi,A3: late_subject,X5: name,P2: pi,Q4: pi] :
% 0.26/0.46 ( ( ( par @ P @ Q )
% 0.26/0.46 = ( par @ P4 @ Q4 ) )
% 0.26/0.46 => ( ( ( late_BoundR @ B @ Y2 @ P3 )
% 0.26/0.46 = ( late_BoundR @ A3 @ X5 @ ( par @ P2 @ Q4 ) ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.26/0.46 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) )
% 0.26/0.46 => ~ ! [Q4: pi,A3: late_subject,X5: name,Q3: pi,P4: pi] :
% 0.26/0.46 ( ( ( par @ P @ Q )
% 0.26/0.46 = ( par @ P4 @ Q4 ) )
% 0.26/0.46 => ( ( ( late_BoundR @ B @ Y2 @ P3 )
% 0.26/0.46 = ( late_BoundR @ A3 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 0.26/0.46 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q4 )
% 0.26/0.46 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % parCasesB'
% 0.26/0.46 thf(fact_64_freshResidual,axiom,
% 0.26/0.46 ! [P: pi,Rs: late_residual,X: name] :
% 0.26/0.46 ( ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshResidual
% 0.26/0.46 thf(fact_65_transitions_OPar1B,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Par1B
% 0.26/0.46 thf(fact_66_transitions_OPar2B,axiom,
% 0.26/0.46 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Par2B
% 0.26/0.46 thf(fact_67_sumIdempRight,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumIdempRight
% 0.26/0.46 thf(fact_68_sumAssocRight,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumAssocRight
% 0.26/0.46 thf(fact_69_sumIdempLeft,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumIdempLeft
% 0.26/0.46 thf(fact_70_sumAssocLeft,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumAssocLeft
% 0.26/0.46 thf(fact_71_sumSym,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumSym
% 0.26/0.46 thf(fact_72_outputBoundTrans,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,C2: late_subject,X: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C2 @ X @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputBoundTrans
% 0.26/0.46 thf(fact_73_transitions_OResB,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Y2 @ A )
% 0.26/0.46 => ( ( Y2 != X )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A )
% 0.26/0.46 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y2 @ P3 ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.ResB
% 0.26/0.46 thf(fact_74_nilSim_I3_J,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.26/0.46 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % nilSim(3)
% 0.26/0.46 thf(fact_75_sumZeroRight,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumZeroRight
% 0.26/0.46 thf(fact_76_sumZeroLeft,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumZeroLeft
% 0.26/0.46 thf(fact_77_Late__Semantics_OResB,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Y2 @ A )
% 0.26/0.46 => ( ( Y2 != X )
% 0.26/0.46 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y2 @ P3 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.ResB
% 0.26/0.46 thf(fact_78_inputIneqTrans,axiom,
% 0.26/0.46 ! [A: name,X: name,P: pi,B: late_subject,Y2: name,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y2 @ P3 ) )
% 0.26/0.46 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.26/0.46
% 0.26/0.46 % inputIneqTrans
% 0.26/0.46 thf(fact_79_pi_Odistinct_I85_J,axiom,
% 0.26/0.46 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( par @ Pi1 @ Pi2 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(85)
% 0.26/0.46 thf(fact_80_freshRes,axiom,
% 0.26/0.46 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % freshRes
% 0.26/0.46 thf(fact_81_residual_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [Subject2: late_subject,Name4: name,Pi3: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.26/0.46 ( ( late_BoundR @ Subject2 @ Name4 @ Pi3 )
% 0.26/0.46 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.distinct(1)
% 0.26/0.46 thf(fact_82_residual_Oinducts,axiom,
% 0.26/0.46 ! [P: late_residual > $o,Residual: late_residual] :
% 0.26/0.46 ( ! [Subject: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) )
% 0.26/0.46 => ( ! [FreeRes: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 0.26/0.46 => ( P @ Residual ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.inducts
% 0.26/0.46 thf(fact_83_pi_Odistinct_I79_J,axiom,
% 0.26/0.46 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( sum @ Pi1 @ Pi2 )
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(79)
% 0.26/0.46 thf(fact_84_pi_Odistinct_I55_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( input @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(55)
% 0.26/0.46 thf(fact_85_sumResLeft,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,X: name,P: pi,Q: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ ( sum @ ( res @ X @ P ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P @ Q ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % sumResLeft
% 0.26/0.46 thf(fact_86_pi_Odistinct_I13_J,axiom,
% 0.26/0.46 ! [Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(13)
% 0.26/0.46 thf(fact_87_outputTauTrans,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputTauTrans
% 0.26/0.46 thf(fact_88_pi_Odistinct_I31_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(31)
% 0.26/0.46 thf(fact_89_pi_Odistinct_I27_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(27)
% 0.26/0.46 thf(fact_90_pi_Odistinct_I21_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.26/0.46 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(21)
% 0.26/0.46 thf(fact_91_pi_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [Name1: name,Name2: name,Pi: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(1)
% 0.26/0.46 thf(fact_92_nilSimRight,axiom,
% 0.26/0.46 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 0.26/0.46
% 0.26/0.46 % nilSimRight
% 0.26/0.46 thf(fact_93_resOutputTauTrans,axiom,
% 0.26/0.46 ! [X: name,A: name,B: name,P: pi,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resOutputTauTrans
% 0.26/0.46 thf(fact_94_Par1F,axiom,
% 0.26/0.46 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Par1F
% 0.26/0.46 thf(fact_95_Strong__Late__Sim_Oreflexive,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % Strong_Late_Sim.reflexive
% 0.26/0.46 thf(fact_96_subset__antisym,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B2 @ A2 )
% 0.26/0.46 => ( A2 = B2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subset_antisym
% 0.26/0.46 thf(fact_97_subsetI,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ! [X5: product_prod_pi_pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ X5 @ A2 )
% 0.26/0.46 => ( member558706512_pi_pi @ X5 @ B2 ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A2 @ B2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % subsetI
% 0.26/0.46 thf(fact_98_monotonic,axiom,
% 0.26/0.46 ! [P: pi,A2: set_Pr1834926343_pi_pi,P3: pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( strong743114133lation @ P @ A2 @ P3 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( strong743114133lation @ P @ B2 @ P3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % monotonic
% 0.26/0.46 thf(fact_99_order__refl,axiom,
% 0.26/0.46 ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 0.26/0.46
% 0.26/0.46 % order_refl
% 0.26/0.46 thf(fact_100_resOutputInputTrans,axiom,
% 0.26/0.46 ! [X: name,A: name,B: name,P: pi,C2: name,Y2: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resOutputInputTrans
% 0.26/0.46 thf(fact_101_resInputBoundOutputTrans,axiom,
% 0.26/0.46 ! [X: name,A: name,Y2: name,P: pi,B: name,Z: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resInputBoundOutputTrans
% 0.26/0.46 thf(fact_102_resOutputOutputTrans,axiom,
% 0.26/0.46 ! [X: name,A: name,P: pi,B: name,Y2: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y2 ) @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resOutputOutputTrans
% 0.26/0.46 thf(fact_103_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.26/0.46 ! [X2: name,X1: name,Y22: name,Y1: name] :
% 0.26/0.46 ( ( ( late_OutputR @ X2 @ X1 )
% 0.26/0.46 = ( late_OutputR @ Y22 @ Y1 ) )
% 0.26/0.46 = ( ( X2 = Y22 )
% 0.26/0.46 & ( X1 = Y1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.freeRes.inject
% 0.26/0.46 thf(fact_104_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.26/0.46 ! [X1: name,Y1: name] :
% 0.26/0.46 ( ( ( late_BoundOutputS @ X1 )
% 0.26/0.46 = ( late_BoundOutputS @ Y1 ) )
% 0.26/0.46 = ( X1 = Y1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.subject.inject(2)
% 0.26/0.46 thf(fact_105_name__fresh,axiom,
% 0.26/0.46 ( fresh_name_name
% 0.26/0.46 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % name_fresh
% 0.26/0.46 thf(fact_106_subject_Ofresh_I1_J,axiom,
% 0.26/0.46 ! [A: name,X1: name] :
% 0.26/0.46 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.26/0.46 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % subject.fresh(1)
% 0.26/0.46 thf(fact_107_subject_Ofresh_I2_J,axiom,
% 0.26/0.46 ! [A: name,X1: name] :
% 0.26/0.46 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.26/0.46 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % subject.fresh(2)
% 0.26/0.46 thf(fact_108_freeRes_Ofresh_I1_J,axiom,
% 0.26/0.46 ! [A: name,X2: name,X1: name] :
% 0.26/0.46 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X2 )
% 0.26/0.46 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freeRes.fresh(1)
% 0.26/0.46 thf(fact_109_subject_Oinducts,axiom,
% 0.26/0.46 ! [P: late_subject > $o,Subject2: late_subject] :
% 0.26/0.46 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.26/0.46 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.26/0.46 => ( P @ Subject2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subject.inducts
% 0.26/0.46 thf(fact_110_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [Name4: name,Name: name] :
% 0.26/0.46 ( ( late_InputS @ Name4 )
% 0.26/0.46 != ( late_BoundOutputS @ Name ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.subject.distinct(1)
% 0.26/0.46 thf(fact_111_freeRes_Oinducts,axiom,
% 0.26/0.46 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.26/0.46 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 0.26/0.46 => ( ( P @ late_TauR )
% 0.26/0.46 => ( P @ FreeRes3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % freeRes.inducts
% 0.26/0.46 thf(fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name] :
% 0.26/0.46 ( ( late_OutputR @ Name12 @ Name22 )
% 0.26/0.46 != late_TauR ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.freeRes.distinct(1)
% 0.26/0.46 thf(fact_113_Open,axiom,
% 0.26/0.46 ! [P: pi,A: name,B: name,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.26/0.46 => ( ( A != B )
% 0.26/0.46 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Open
% 0.26/0.46 thf(fact_114_order__subst1,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ ( F2 @ B ) )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.26/0.46 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_subst1
% 0.26/0.46 thf(fact_115_order__subst2,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ ( F2 @ B ) @ C2 )
% 0.26/0.46 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_subst2
% 0.26/0.46 thf(fact_116_ord__eq__le__subst,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( A
% 0.26/0.46 = ( F2 @ B ) )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.26/0.46 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_le_subst
% 0.26/0.46 thf(fact_117_ord__le__eq__subst,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( ( ( F2 @ B )
% 0.26/0.46 = C2 )
% 0.26/0.46 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_le_eq_subst
% 0.26/0.46 thf(fact_118_eq__iff,axiom,
% 0.26/0.46 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.26/0.46 = ( ^ [X4: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X4 @ Y5 )
% 0.26/0.46 & ( ord_le630093991_pi_pi @ Y5 @ X4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_iff
% 0.26/0.46 thf(fact_119_antisym,axiom,
% 0.26/0.46 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ Y2 @ X )
% 0.26/0.46 => ( X = Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % antisym
% 0.26/0.46 thf(fact_120_eq__refl,axiom,
% 0.26/0.46 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( X = Y2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ X @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % eq_refl
% 0.26/0.46 thf(fact_121_order_Otrans,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order.trans
% 0.26/0.46 thf(fact_122_antisym__conv,axiom,
% 0.26/0.46 ! [Y2: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ Y2 @ X )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 0.26/0.46 = ( X = Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % antisym_conv
% 0.26/0.46 thf(fact_123_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.46 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.26/0.46 = ( ^ [A4: set_Pr1834926343_pi_pi,B3: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A4 @ B3 )
% 0.26/0.46 & ( ord_le630093991_pi_pi @ B3 @ A4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_class.order.eq_iff
% 0.26/0.46 thf(fact_124_ord__eq__le__trans,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( A = B )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_eq_le_trans
% 0.26/0.46 thf(fact_125_ord__le__eq__trans,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( ( B = C2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % ord_le_eq_trans
% 0.26/0.46 thf(fact_126_order__class_Oorder_Oantisym,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B @ A )
% 0.26/0.46 => ( A = B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_class.order.antisym
% 0.26/0.46 thf(fact_127_order__trans,axiom,
% 0.26/0.46 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ Y2 @ Z )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ X @ Z ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % order_trans
% 0.26/0.46 thf(fact_128_dual__order_Orefl,axiom,
% 0.26/0.46 ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.refl
% 0.26/0.46 thf(fact_129_dual__order_Otrans,axiom,
% 0.26/0.46 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ B @ A )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ C2 @ B )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ C2 @ A ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.trans
% 0.26/0.46 thf(fact_130_dual__order_Oeq__iff,axiom,
% 0.26/0.46 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.26/0.46 = ( ^ [A4: set_Pr1834926343_pi_pi,B3: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ B3 @ A4 )
% 0.26/0.46 & ( ord_le630093991_pi_pi @ A4 @ B3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.eq_iff
% 0.26/0.46 thf(fact_131_dual__order_Oantisym,axiom,
% 0.26/0.46 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ B @ A )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ A @ B )
% 0.26/0.46 => ( A = B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % dual_order.antisym
% 0.26/0.46 thf(fact_132_in__mono,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,X: product_prod_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( ( member558706512_pi_pi @ X @ A2 )
% 0.26/0.46 => ( member558706512_pi_pi @ X @ B2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % in_mono
% 0.26/0.46 thf(fact_133_subsetD,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,C2: product_prod_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( ( member558706512_pi_pi @ C2 @ A2 )
% 0.26/0.46 => ( member558706512_pi_pi @ C2 @ B2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subsetD
% 0.26/0.46 thf(fact_134_equalityE,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( A2 = B2 )
% 0.26/0.46 => ~ ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ~ ( ord_le630093991_pi_pi @ B2 @ A2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % equalityE
% 0.26/0.46 thf(fact_135_subset__eq,axiom,
% 0.26/0.46 ( ord_le630093991_pi_pi
% 0.26/0.46 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ! [X4: product_prod_pi_pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ X4 @ A5 )
% 0.26/0.46 => ( member558706512_pi_pi @ X4 @ B4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subset_eq
% 0.26/0.46 thf(fact_136_equalityD1,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( A2 = B2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A2 @ B2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % equalityD1
% 0.26/0.46 thf(fact_137_equalityD2,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( A2 = B2 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ B2 @ A2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % equalityD2
% 0.26/0.46 thf(fact_138_subset__iff,axiom,
% 0.26/0.46 ( ord_le630093991_pi_pi
% 0.26/0.46 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ! [T: product_prod_pi_pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ T @ A5 )
% 0.26/0.46 => ( member558706512_pi_pi @ T @ B4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subset_iff
% 0.26/0.46 thf(fact_139_subset__refl,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A2 @ A2 ) ).
% 0.26/0.46
% 0.26/0.46 % subset_refl
% 0.26/0.46 thf(fact_140_Collect__mono,axiom,
% 0.26/0.46 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.26/0.46 ( ! [X5: product_prod_pi_pi] :
% 0.26/0.46 ( ( P @ X5 )
% 0.26/0.46 => ( Q @ X5 ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_mono
% 0.26/0.46 thf(fact_141_subset__trans,axiom,
% 0.26/0.46 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,C3: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ B2 @ C3 )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ A2 @ C3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subset_trans
% 0.26/0.46 thf(fact_142_set__eq__subset,axiom,
% 0.26/0.46 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 0.26/0.46 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ A5 @ B4 )
% 0.26/0.46 & ( ord_le630093991_pi_pi @ B4 @ A5 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % set_eq_subset
% 0.26/0.46 thf(fact_143_Collect__mono__iff,axiom,
% 0.26/0.46 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) )
% 0.26/0.46 = ( ! [X4: product_prod_pi_pi] :
% 0.26/0.46 ( ( P @ X4 )
% 0.26/0.46 => ( Q @ X4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Collect_mono_iff
% 0.26/0.46 thf(fact_144_resCasesB_H,axiom,
% 0.26/0.46 ! [X6: name,P: pi,A: late_subject,Y6: name,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y6 @ P3 ) )
% 0.26/0.46 => ( ! [P4: pi,A3: name,B5: name] :
% 0.26/0.46 ( ( ( res @ X6 @ P )
% 0.26/0.46 = ( res @ B5 @ P4 ) )
% 0.26/0.46 => ! [P2: pi] :
% 0.26/0.46 ( ( ( late_BoundR @ A @ Y6 @ P3 )
% 0.26/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B5 @ P2 ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P2 ) )
% 0.26/0.46 => ( A3 = B5 ) ) ) )
% 0.26/0.46 => ~ ! [P4: pi,A3: late_subject,X5: name,P2: pi,Y: name] :
% 0.26/0.46 ( ( ( res @ X6 @ P )
% 0.26/0.46 = ( res @ Y @ P4 ) )
% 0.26/0.46 => ( ( ( late_BoundR @ A @ Y6 @ P3 )
% 0.26/0.46 = ( late_BoundR @ A3 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Y @ A3 )
% 0.26/0.46 => ( ( Y != X5 )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.26/0.46 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resCasesB'
% 0.26/0.46 thf(fact_145_Output,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % Output
% 0.26/0.46 thf(fact_146_outputIneqTrans,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,C2: name,D: name,P3: pi] :
% 0.26/0.46 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P3 ) )
% 0.26/0.46 => ~ ( ( A != C2 )
% 0.26/0.46 | ( B != D ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputIneqTrans
% 0.26/0.46 thf(fact_147_outputCases_H,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.26/0.46 => ~ ! [A3: name,B5: name,P4: pi] :
% 0.26/0.46 ( ( ( A = A3 )
% 0.26/0.46 & ( B = B5 )
% 0.26/0.46 & ( P = P4 ) )
% 0.26/0.46 => ( Rs
% 0.26/0.46 != ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputCases'
% 0.26/0.46 thf(fact_148_outputCases,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.26/0.46 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( ( ( Alpha
% 0.26/0.46 = ( late_OutputR @ A @ B ) )
% 0.26/0.46 => ( ( P = P3 )
% 0.26/0.46 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.26/0.46 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % outputCases
% 0.26/0.46 thf(fact_149_Late__Semantics_OInput,axiom,
% 0.26/0.46 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Input
% 0.26/0.46 thf(fact_150_transitions_OInput,axiom,
% 0.26/0.46 ! [X: name,A: name,P: pi] :
% 0.26/0.46 ( ( X != A )
% 0.26/0.46 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Input
% 0.26/0.46 thf(fact_151_inputBoundOutputTrans,axiom,
% 0.26/0.46 ! [A: name,X: name,P: pi,B: name,Y2: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y2 @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % inputBoundOutputTrans
% 0.26/0.46 thf(fact_152_resCases_H,axiom,
% 0.26/0.46 ! [X: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.26/0.46 => ( ! [P4: pi,A3: name,B5: name] :
% 0.26/0.46 ( ( ( res @ X @ P )
% 0.26/0.46 = ( res @ B5 @ P4 ) )
% 0.26/0.46 => ! [P2: pi] :
% 0.26/0.46 ( ( Rs
% 0.26/0.46 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B5 @ P2 ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P2 ) )
% 0.26/0.46 => ( A3 = B5 ) ) ) )
% 0.26/0.46 => ( ! [P4: pi,A3: late_subject,X5: name,P2: pi,Y: name] :
% 0.26/0.46 ( ( ( res @ X @ P )
% 0.26/0.46 = ( res @ Y @ P4 ) )
% 0.26/0.46 => ( ( Rs
% 0.26/0.46 = ( late_BoundR @ A3 @ X5 @ ( res @ Y @ P2 ) ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Y @ A3 )
% 0.26/0.46 => ( ( Y != X5 )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P4 )
% 0.26/0.46 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) )
% 0.26/0.46 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 0.26/0.46 ( ( ( res @ X @ P )
% 0.26/0.46 = ( res @ Y @ P4 ) )
% 0.26/0.46 => ( ( Rs
% 0.26/0.46 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 0.26/0.46 => ~ ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resCases'
% 0.26/0.46 thf(fact_153_transitions_OClose2,axiom,
% 0.26/0.46 ! [P: pi,A: name,Y2: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ Q )
% 0.26/0.46 => ( ( X != A )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P3 )
% 0.26/0.46 => ( ( Y2 != A )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ Q2 )
% 0.26/0.46 => ( ( X != Y2 )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Close2
% 0.26/0.46 thf(fact_154_transitions_OClose1,axiom,
% 0.26/0.46 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ Q )
% 0.26/0.46 => ( ( X != A )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q2 )
% 0.26/0.46 => ( ( Y2 != A )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P3 )
% 0.26/0.46 => ( ( X != Y2 )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Close1
% 0.26/0.46 thf(fact_155_Late__Semantics_OClose2,axiom,
% 0.26/0.46 ! [P: pi,A: name,Y2: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ Q )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Close2
% 0.26/0.46 thf(fact_156_Late__Semantics_OClose1,axiom,
% 0.26/0.46 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y2 @ P )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Close1
% 0.26/0.46 thf(fact_157_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.26/0.46 ! [X2: name,Y22: name] :
% 0.26/0.46 ( ( ( late_BoundOutputS @ X2 )
% 0.26/0.46 = ( late_BoundOutputS @ Y22 ) )
% 0.26/0.46 = ( X2 = Y22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics1.subject.inject(2)
% 0.26/0.46 thf(fact_158_subst__identity,axiom,
% 0.26/0.46 ! [P: pi,A: name] :
% 0.26/0.46 ( ( subs @ P @ A @ A )
% 0.26/0.46 = P ) ).
% 0.26/0.46
% 0.26/0.46 % subst_identity
% 0.26/0.46 thf(fact_159_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.26/0.46 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 0.26/0.46 ( ( ( late_OutputR @ X11 @ X12 )
% 0.26/0.46 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.26/0.46 = ( ( X11 = Y11 )
% 0.26/0.46 & ( X12 = Y12 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics1.freeRes.inject
% 0.26/0.46 thf(fact_160_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.26/0.46 ! [X1: name,Y1: name] :
% 0.26/0.46 ( ( ( late_InputS @ X1 )
% 0.26/0.46 = ( late_InputS @ Y1 ) )
% 0.26/0.46 = ( X1 = Y1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics1.subject.inject(1)
% 0.26/0.46 thf(fact_161_simps_I9_J,axiom,
% 0.26/0.46 ! [X: name,C2: name,D: name,P: pi] :
% 0.26/0.46 ( ( X != C2 )
% 0.26/0.46 => ( ( X != D )
% 0.26/0.46 => ( ( subs @ ( res @ X @ P ) @ C2 @ D )
% 0.26/0.46 = ( res @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simps(9)
% 0.26/0.46 thf(fact_162_simps_I8_J,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.26/0.46 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 0.26/0.46 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simps(8)
% 0.26/0.46 thf(fact_163_substTrans,axiom,
% 0.26/0.46 ! [B: name,P: pi,A: name,C2: name] :
% 0.26/0.46 ( ( fresh_name_pi @ B @ P )
% 0.26/0.46 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 0.26/0.46 = ( subs @ P @ A @ C2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % substTrans
% 0.26/0.46 thf(fact_164_simps_I7_J,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,C2: name,D: name] :
% 0.26/0.46 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 0.26/0.46 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simps(7)
% 0.26/0.46 thf(fact_165_simps_I1_J,axiom,
% 0.26/0.46 ! [C2: name,D: name] :
% 0.26/0.46 ( ( subs @ piNil @ C2 @ D )
% 0.26/0.46 = piNil ) ).
% 0.26/0.46
% 0.26/0.46 % simps(1)
% 0.26/0.46 thf(fact_166_forget,axiom,
% 0.26/0.46 ! [A: name,P: pi,B: name] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ P )
% 0.26/0.46 => ( ( subs @ P @ A @ B )
% 0.26/0.46 = P ) ) ).
% 0.26/0.46
% 0.26/0.46 % forget
% 0.26/0.46 thf(fact_167_fresh__fact1,axiom,
% 0.26/0.46 ! [A: name,P: pi,C2: name,B: name] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ P )
% 0.26/0.46 => ( ( A != C2 )
% 0.26/0.46 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_fact1
% 0.26/0.46 thf(fact_168_fresh__fact2,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi] :
% 0.26/0.46 ( ( A != B )
% 0.26/0.46 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_fact2
% 0.26/0.46 thf(fact_169_substRes3,axiom,
% 0.26/0.46 ! [B: name,P: pi,A: name] :
% 0.26/0.46 ( ( fresh_name_pi @ B @ P )
% 0.26/0.46 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.26/0.46 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % substRes3
% 0.26/0.46 thf(fact_170_substRes2,axiom,
% 0.26/0.46 ! [B: name,P: pi,A: name] :
% 0.26/0.46 ( ( fresh_name_pi @ B @ P )
% 0.26/0.46 => ( ( res @ A @ P )
% 0.26/0.46 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % substRes2
% 0.26/0.46 thf(fact_171_freeRes_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: late_freeRes] :
% 0.26/0.46 ( ! [X112: name,X122: name] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( late_OutputR @ X112 @ X122 ) )
% 0.26/0.46 => ( Y2 = late_TauR ) ) ).
% 0.26/0.46
% 0.26/0.46 % freeRes.exhaust
% 0.26/0.46 thf(fact_172_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [X11: name,X12: name] :
% 0.26/0.46 ( ( late_OutputR @ X11 @ X12 )
% 0.26/0.46 != late_TauR ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics1.freeRes.distinct(1)
% 0.26/0.46 thf(fact_173_subject_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: late_subject] :
% 0.26/0.46 ( ! [X13: name] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( late_InputS @ X13 ) )
% 0.26/0.46 => ~ ! [X22: name] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % subject.exhaust
% 0.26/0.46 thf(fact_174_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.26/0.46 ! [X1: name,X2: name] :
% 0.26/0.46 ( ( late_InputS @ X1 )
% 0.26/0.46 != ( late_BoundOutputS @ X2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics1.subject.distinct(1)
% 0.26/0.46 thf(fact_175_Late__Semantics_OComm1,axiom,
% 0.26/0.46 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Comm1
% 0.26/0.46 thf(fact_176_Late__Semantics_OComm2,axiom,
% 0.26/0.46 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Late_Semantics.Comm2
% 0.26/0.46 thf(fact_177_transitions_OComm1,axiom,
% 0.26/0.46 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( X != A )
% 0.26/0.46 => ( ( X != B )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q2 )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Comm1
% 0.26/0.46 thf(fact_178_transitions_OComm2,axiom,
% 0.26/0.46 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ Q )
% 0.26/0.46 => ( ( X != A )
% 0.26/0.46 => ( ( X != B )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P3 )
% 0.26/0.46 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % transitions.Comm2
% 0.26/0.46 thf(fact_179_resSimCases,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_subject] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [Q3: pi,A3: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 0.26/0.46 => ( ( A3 != X )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.26/0.46 => ( ( X != Y )
% 0.26/0.46 => ( ( fresh_717452603ubject @ Y @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resSimCases
% 0.26/0.46 thf(fact_180_resSimCases,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [Q3: pi,A3: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 0.26/0.46 => ( ( A3 != X )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.26/0.46 => ( ( X != Y )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ Y @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resSimCases
% 0.26/0.46 thf(fact_181_resSimCases,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [Q3: pi,A3: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 0.26/0.46 => ( ( A3 != X )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.26/0.46 => ( ( X != Y )
% 0.26/0.46 => ( ( fresh_name_name @ Y @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resSimCases
% 0.26/0.46 thf(fact_182_resSimCases,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [Q3: pi,A3: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 0.26/0.46 => ( ( A3 != X )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X @ A3 )
% 0.26/0.46 => ( ( X != Y )
% 0.26/0.46 => ( ( fresh_name_pi @ Y @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 0.26/0.46 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % resSimCases
% 0.26/0.46 thf(fact_183_simE_I1_J,axiom,
% 0.26/0.46 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 0.26/0.46 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X @ P )
% 0.26/0.46 => ? [P2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.26/0.46 & ( strong2129052853vative @ P2 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simE(1)
% 0.26/0.46 thf(fact_184_simCasesCont,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_subject] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X5 @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 0.26/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simCasesCont
% 0.26/0.46 thf(fact_185_simCasesCont,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 0.26/0.46 => ( ( fresh_1641682979reeRes @ X5 @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 0.26/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simCasesCont
% 0.26/0.46 thf(fact_186_simCasesCont,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 0.26/0.46 => ( ( fresh_name_name @ X5 @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 0.26/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simCasesCont
% 0.26/0.46 thf(fact_187_simCasesCont,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 0.26/0.46 ( ( eqvt_pi @ Rel )
% 0.26/0.46 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ P )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ Q )
% 0.26/0.46 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 0.26/0.46 => ( ( fresh_name_pi @ X5 @ C3 )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 0.26/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simCasesCont
% 0.26/0.46 thf(fact_188_derivativeMonotonic,axiom,
% 0.26/0.46 ! [P: pi,Q: pi,A: late_subject,X: name,A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ( strong2129052853vative @ P @ Q @ A @ X @ A2 )
% 0.26/0.46 => ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 0.26/0.46 => ( strong2129052853vative @ P @ Q @ A @ X @ B2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % derivativeMonotonic
% 0.26/0.46 thf(fact_189_simulation__def,axiom,
% 0.26/0.46 ( strong743114133lation
% 0.26/0.46 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 0.26/0.46 ( ! [A4: late_subject,X4: name,Q6: pi] :
% 0.26/0.46 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A4 @ X4 @ Q6 ) )
% 0.26/0.46 & ( fresh_name_pi @ X4 @ P6 ) )
% 0.26/0.46 => ? [P7: pi] :
% 0.26/0.46 ( ( late_transitions @ P6 @ ( late_BoundR @ A4 @ X4 @ P7 ) )
% 0.26/0.46 & ( strong2129052853vative @ P7 @ Q6 @ A4 @ X4 @ Rel2 ) ) )
% 0.26/0.46 & ! [Alpha3: late_freeRes,Q6: pi] :
% 0.26/0.46 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 0.26/0.46 => ? [P7: pi] :
% 0.26/0.46 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simulation_def
% 0.26/0.46 thf(fact_190_simCases,axiom,
% 0.26/0.46 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ! [A3: late_subject,Y: name,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 0.26/0.46 => ( ( fresh_name_pi @ Y @ P )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 0.26/0.46 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ Y @ Rel ) ) ) )
% 0.26/0.46 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 0.26/0.46 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 0.26/0.46 => ? [P5: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simCases
% 0.26/0.46 thf(fact_191_simE_I2_J,axiom,
% 0.26/0.46 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 0.26/0.46 ( ( strong743114133lation @ P @ Rel @ Q )
% 0.26/0.46 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.26/0.46 => ? [P2: pi] :
% 0.26/0.46 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.26/0.46 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q2 ) @ Rel ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simE(2)
% 0.26/0.46 thf(fact_192_derivativeReflexive,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi,A: late_subject,X: name] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( strong2129052853vative @ P @ P @ A @ X @ Rel ) ) ).
% 0.26/0.46
% 0.26/0.46 % derivativeReflexive
% 0.26/0.46 thf(fact_193_pair__in__Id__conv,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name > noption_pi] :
% 0.26/0.46 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 0.26/0.46 = ( A = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % pair_in_Id_conv
% 0.26/0.46 thf(fact_194_pair__in__Id__conv,axiom,
% 0.26/0.46 ! [A: pi,B: pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.26/0.46 = ( A = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % pair_in_Id_conv
% 0.26/0.46 thf(fact_195_IdI,axiom,
% 0.26/0.46 ! [A: name > noption_pi] : ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ A ) @ id_name_noption_pi ) ).
% 0.26/0.46
% 0.26/0.46 % IdI
% 0.26/0.46 thf(fact_196_IdI,axiom,
% 0.26/0.46 ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 0.26/0.46
% 0.26/0.46 % IdI
% 0.26/0.46 thf(fact_197_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr248416762ubject,S: set_Pr248416762ubject] :
% 0.26/0.46 ( ! [X5: name > noption_pi,Y: late_subject] :
% 0.26/0.46 ( ( member938018755ubject @ ( produc581368530ubject @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member938018755ubject @ ( produc581368530ubject @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le1705144730ubject @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_198_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr305743074reeRes,S: set_Pr305743074reeRes] :
% 0.26/0.46 ( ! [X5: name > noption_pi,Y: late_freeRes] :
% 0.26/0.46 ( ( member2081207979reeRes @ ( produc1505598906reeRes @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member2081207979reeRes @ ( produc1505598906reeRes @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le1762471042reeRes @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_199_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr1294453099i_name,S: set_Pr1294453099i_name] :
% 0.26/0.46 ( ! [X5: name > noption_pi,Y: name] :
% 0.26/0.46 ( ( member1353687244i_name @ ( produc540578151i_name @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member1353687244i_name @ ( produc540578151i_name @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le2082425291i_name @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_200_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr1694908217_pi_pi,S: set_Pr1694908217_pi_pi] :
% 0.26/0.46 ( ! [X5: name > noption_pi,Y: pi] :
% 0.26/0.46 ( ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le1854926745_pi_pi @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_201_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr1569510577ion_pi,S: set_Pr1569510577ion_pi] :
% 0.26/0.46 ( ! [X5: name > noption_pi,Y: name > noption_pi] :
% 0.26/0.46 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le1032043601ion_pi @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_202_subrelI,axiom,
% 0.26/0.46 ! [R2: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 0.26/0.46 ( ! [X5: pi,Y: pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X5 @ Y ) @ R2 )
% 0.26/0.46 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X5 @ Y ) @ S ) )
% 0.26/0.46 => ( ord_le630093991_pi_pi @ R2 @ S ) ) ).
% 0.26/0.46
% 0.26/0.46 % subrelI
% 0.26/0.46 thf(fact_203_IdE,axiom,
% 0.26/0.46 ! [P8: produc1462499409ion_pi] :
% 0.26/0.46 ( ( member1632198138ion_pi @ P8 @ id_name_noption_pi )
% 0.26/0.46 => ~ ! [X5: name > noption_pi] :
% 0.26/0.46 ( P8
% 0.26/0.46 != ( produc1342893193ion_pi @ X5 @ X5 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % IdE
% 0.26/0.46 thf(fact_204_IdE,axiom,
% 0.26/0.46 ! [P8: product_prod_pi_pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ P8 @ id_pi )
% 0.26/0.46 => ~ ! [X5: pi] :
% 0.26/0.46 ( P8
% 0.26/0.46 != ( product_Pair_pi_pi @ X5 @ X5 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % IdE
% 0.26/0.46 thf(fact_205_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_subject,Y2: late_subject] :
% 0.26/0.46 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.26/0.46 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_206_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_subject,Y2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.26/0.46 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_207_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_subject,Y2: name] :
% 0.26/0.46 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.26/0.46 & ( fresh_name_name @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_208_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_subject,Y2: pi] :
% 0.26/0.46 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_717452603ubject @ A @ X )
% 0.26/0.46 & ( fresh_name_pi @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_209_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_freeRes,Y2: late_subject] :
% 0.26/0.46 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.26/0.46 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_210_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_freeRes,Y2: late_freeRes] :
% 0.26/0.46 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.26/0.46 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_211_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_freeRes,Y2: name] :
% 0.26/0.46 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.26/0.46 & ( fresh_name_name @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_212_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: late_freeRes,Y2: pi] :
% 0.26/0.46 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_1641682979reeRes @ A @ X )
% 0.26/0.46 & ( fresh_name_pi @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_213_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: name,Y2: late_subject] :
% 0.26/0.46 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X )
% 0.26/0.46 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_214_fresh__prod,axiom,
% 0.26/0.46 ! [A: name,X: name,Y2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y2 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X )
% 0.26/0.46 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prod
% 0.26/0.46 thf(fact_215_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: late_subject,A6: name > noption_pi,B6: late_subject] :
% 0.26/0.46 ( ( ( produc581368530ubject @ A @ B )
% 0.26/0.46 = ( produc581368530ubject @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_216_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: late_freeRes,A6: name > noption_pi,B6: late_freeRes] :
% 0.26/0.46 ( ( ( produc1505598906reeRes @ A @ B )
% 0.26/0.46 = ( produc1505598906reeRes @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_217_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name,A6: name > noption_pi,B6: name] :
% 0.26/0.46 ( ( ( produc540578151i_name @ A @ B )
% 0.26/0.46 = ( produc540578151i_name @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_218_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: pi,A6: name > noption_pi,B6: pi] :
% 0.26/0.46 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.26/0.46 = ( produc1820286517_pi_pi @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_219_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name > noption_pi,A6: name > noption_pi,B6: name > noption_pi] :
% 0.26/0.46 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.26/0.46 = ( produc1342893193ion_pi @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_220_old_Oprod_Oinject,axiom,
% 0.26/0.46 ! [A: pi,B: pi,A6: pi,B6: pi] :
% 0.26/0.46 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.26/0.46 = ( product_Pair_pi_pi @ A6 @ B6 ) )
% 0.26/0.46 = ( ( A = A6 )
% 0.26/0.46 & ( B = B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inject
% 0.26/0.46 thf(fact_221_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y22: late_subject] :
% 0.26/0.46 ( ( ( produc581368530ubject @ X1 @ X2 )
% 0.26/0.46 = ( produc581368530ubject @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_222_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y22: late_freeRes] :
% 0.26/0.46 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 0.26/0.46 = ( produc1505598906reeRes @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_223_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y22: name] :
% 0.26/0.46 ( ( ( produc540578151i_name @ X1 @ X2 )
% 0.26/0.46 = ( produc540578151i_name @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_224_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y22: pi] :
% 0.26/0.46 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 0.26/0.46 = ( produc1820286517_pi_pi @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_225_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y22: name > noption_pi] :
% 0.26/0.46 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 0.26/0.46 = ( produc1342893193ion_pi @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_226_prod_Oinject,axiom,
% 0.26/0.46 ! [X1: pi,X2: pi,Y1: pi,Y22: pi] :
% 0.26/0.46 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 0.26/0.46 = ( product_Pair_pi_pi @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X1 = Y1 )
% 0.26/0.46 & ( X2 = Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod.inject
% 0.26/0.46 thf(fact_227_surj__pair,axiom,
% 0.26/0.46 ! [P8: produc691362330ubject] :
% 0.26/0.46 ? [X5: name > noption_pi,Y: late_subject] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( produc581368530ubject @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_228_surj__pair,axiom,
% 0.26/0.46 ! [P8: produc1834551554reeRes] :
% 0.26/0.46 ? [X5: name > noption_pi,Y: late_freeRes] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( produc1505598906reeRes @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_229_surj__pair,axiom,
% 0.26/0.46 ! [P8: produc405342261i_name] :
% 0.26/0.46 ? [X5: name > noption_pi,Y: name] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( produc540578151i_name @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_230_surj__pair,axiom,
% 0.26/0.46 ! [P8: produc629157763_pi_pi] :
% 0.26/0.46 ? [X5: name > noption_pi,Y: pi] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( produc1820286517_pi_pi @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_231_surj__pair,axiom,
% 0.26/0.46 ! [P8: produc1462499409ion_pi] :
% 0.26/0.46 ? [X5: name > noption_pi,Y: name > noption_pi] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( produc1342893193ion_pi @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_232_surj__pair,axiom,
% 0.26/0.46 ! [P8: product_prod_pi_pi] :
% 0.26/0.46 ? [X5: pi,Y: pi] :
% 0.26/0.46 ( P8
% 0.26/0.46 = ( product_Pair_pi_pi @ X5 @ Y ) ) ).
% 0.26/0.46
% 0.26/0.46 % surj_pair
% 0.26/0.46 thf(fact_233_prod__cases,axiom,
% 0.26/0.46 ! [P: produc691362330ubject > $o,P8: produc691362330ubject] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_234_prod__cases,axiom,
% 0.26/0.46 ! [P: produc1834551554reeRes > $o,P8: produc1834551554reeRes] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_235_prod__cases,axiom,
% 0.26/0.46 ! [P: produc405342261i_name > $o,P8: produc405342261i_name] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: name] : ( P @ ( produc540578151i_name @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_236_prod__cases,axiom,
% 0.26/0.46 ! [P: produc629157763_pi_pi > $o,P8: produc629157763_pi_pi] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_237_prod__cases,axiom,
% 0.26/0.46 ! [P: produc1462499409ion_pi > $o,P8: produc1462499409ion_pi] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_238_prod__cases,axiom,
% 0.26/0.46 ! [P: product_prod_pi_pi > $o,P8: product_prod_pi_pi] :
% 0.26/0.46 ( ! [A3: pi,B5: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ P8 ) ) ).
% 0.26/0.46
% 0.26/0.46 % prod_cases
% 0.26/0.46 thf(fact_239_Pair__inject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: late_subject,A6: name > noption_pi,B6: late_subject] :
% 0.26/0.46 ( ( ( produc581368530ubject @ A @ B )
% 0.26/0.46 = ( produc581368530ubject @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_240_Pair__inject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: late_freeRes,A6: name > noption_pi,B6: late_freeRes] :
% 0.26/0.46 ( ( ( produc1505598906reeRes @ A @ B )
% 0.26/0.46 = ( produc1505598906reeRes @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_241_Pair__inject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name,A6: name > noption_pi,B6: name] :
% 0.26/0.46 ( ( ( produc540578151i_name @ A @ B )
% 0.26/0.46 = ( produc540578151i_name @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_242_Pair__inject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: pi,A6: name > noption_pi,B6: pi] :
% 0.26/0.46 ( ( ( produc1820286517_pi_pi @ A @ B )
% 0.26/0.46 = ( produc1820286517_pi_pi @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_243_Pair__inject,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name > noption_pi,A6: name > noption_pi,B6: name > noption_pi] :
% 0.26/0.46 ( ( ( produc1342893193ion_pi @ A @ B )
% 0.26/0.46 = ( produc1342893193ion_pi @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_244_Pair__inject,axiom,
% 0.26/0.46 ! [A: pi,B: pi,A6: pi,B6: pi] :
% 0.26/0.46 ( ( ( product_Pair_pi_pi @ A @ B )
% 0.26/0.46 = ( product_Pair_pi_pi @ A6 @ B6 ) )
% 0.26/0.46 => ~ ( ( A = A6 )
% 0.26/0.46 => ( B != B6 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Pair_inject
% 0.26/0.46 thf(fact_245_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: produc691362330ubject] :
% 0.26/0.46 ~ ! [A3: name > noption_pi,B5: late_subject] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( produc581368530ubject @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_246_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: produc1834551554reeRes] :
% 0.26/0.46 ~ ! [A3: name > noption_pi,B5: late_freeRes] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( produc1505598906reeRes @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_247_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: produc405342261i_name] :
% 0.26/0.46 ~ ! [A3: name > noption_pi,B5: name] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( produc540578151i_name @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_248_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: produc629157763_pi_pi] :
% 0.26/0.46 ~ ! [A3: name > noption_pi,B5: pi] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( produc1820286517_pi_pi @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_249_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: produc1462499409ion_pi] :
% 0.26/0.46 ~ ! [A3: name > noption_pi,B5: name > noption_pi] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( produc1342893193ion_pi @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_250_old_Oprod_Oexhaust,axiom,
% 0.26/0.46 ! [Y2: product_prod_pi_pi] :
% 0.26/0.46 ~ ! [A3: pi,B5: pi] :
% 0.26/0.46 ( Y2
% 0.26/0.46 != ( product_Pair_pi_pi @ A3 @ B5 ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.exhaust
% 0.26/0.46 thf(fact_251_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_252_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_253_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: name] : ( P @ ( produc540578151i_name @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_254_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_255_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 0.26/0.46 ( ! [A3: name > noption_pi,B5: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_256_old_Oprod_Oinducts,axiom,
% 0.26/0.46 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 0.26/0.46 ( ! [A3: pi,B5: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B5 ) )
% 0.26/0.46 => ( P @ Prod ) ) ).
% 0.26/0.46
% 0.26/0.46 % old.prod.inducts
% 0.26/0.46 thf(fact_257_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: late_subject] :
% 0.26/0.46 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_717452603ubject @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_258_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_1641682979reeRes @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_259_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: name] :
% 0.26/0.46 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_name_name @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_260_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: pi] :
% 0.26/0.46 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_name_pi @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_261_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: name > noption_pi] :
% 0.26/0.46 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_262_fresh__prodD_I2_J,axiom,
% 0.26/0.46 ! [A: name,X: pi,Y2: pi] :
% 0.26/0.46 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_name_pi @ A @ Y2 ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(2)
% 0.26/0.46 thf(fact_263_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: late_subject] :
% 0.26/0.46 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_264_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: late_freeRes] :
% 0.26/0.46 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_265_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: name] :
% 0.26/0.46 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_266_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: pi] :
% 0.26/0.46 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_267_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: name > noption_pi,Y2: name > noption_pi] :
% 0.26/0.46 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_268_fresh__prodD_I1_J,axiom,
% 0.26/0.46 ! [A: name,X: pi,Y2: pi] :
% 0.26/0.46 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y2 ) )
% 0.26/0.46 => ( fresh_name_pi @ A @ X ) ) ).
% 0.26/0.46
% 0.26/0.46 % fresh_prodD(1)
% 0.26/0.46 thf(fact_269_IdD,axiom,
% 0.26/0.46 ! [A: name > noption_pi,B: name > noption_pi] :
% 0.26/0.46 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 0.26/0.46 => ( A = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % IdD
% 0.26/0.46 thf(fact_270_IdD,axiom,
% 0.26/0.46 ! [A: pi,B: pi] :
% 0.26/0.46 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 0.26/0.46 => ( A = B ) ) ).
% 0.26/0.46
% 0.26/0.46 % IdD
% 0.26/0.46 thf(fact_271_resTauOutputTrans,axiom,
% 0.26/0.46 ! [X: name,P: pi,A: name,B: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resTauOutputTrans
% 0.26/0.46 thf(fact_272_residual_Ofresh_I1_J,axiom,
% 0.26/0.46 ! [A: name,X3: late_subject,X1: name,X2: pi] :
% 0.26/0.46 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X3 @ X1 @ X2 ) )
% 0.26/0.46 = ( ( fresh_717452603ubject @ A @ X3 )
% 0.26/0.46 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.fresh(1)
% 0.26/0.46 thf(fact_273_pi_Ofresh_I3_J,axiom,
% 0.26/0.46 ! [A: name,X1: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.26/0.46 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(3)
% 0.26/0.46 thf(fact_274_simps_I2_J,axiom,
% 0.26/0.46 ! [P: pi,C2: name,D: name] :
% 0.26/0.46 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 0.26/0.46 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % simps(2)
% 0.26/0.46 thf(fact_275_pi_Ofresh_I9_J,axiom,
% 0.26/0.46 ! [A: name,X1: name,X2: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.26/0.46 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(9)
% 0.26/0.46 thf(fact_276_pi_Ofresh_I4_J,axiom,
% 0.26/0.46 ! [A: name,X3: name,X1: name,X2: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( input @ X3 @ X1 @ X2 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X3 )
% 0.26/0.46 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(4)
% 0.26/0.46 thf(fact_277_name__fresh__abs,axiom,
% 0.26/0.46 ! [B: name,A: name,X: late_subject] :
% 0.26/0.46 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % name_fresh_abs
% 0.26/0.46 thf(fact_278_name__fresh__abs,axiom,
% 0.26/0.46 ! [B: name,A: name,X: late_freeRes] :
% 0.26/0.46 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % name_fresh_abs
% 0.26/0.46 thf(fact_279_name__fresh__abs,axiom,
% 0.26/0.46 ! [B: name,A: name,X: name] :
% 0.26/0.46 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % name_fresh_abs
% 0.26/0.46 thf(fact_280_name__fresh__abs,axiom,
% 0.26/0.46 ! [B: name,A: name,X: pi] :
% 0.26/0.46 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % name_fresh_abs
% 0.26/0.46 thf(fact_281_abs__fresh_I1_J,axiom,
% 0.26/0.46 ! [B: name,A: name,X: late_subject] :
% 0.26/0.46 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_fresh(1)
% 0.26/0.46 thf(fact_282_abs__fresh_I1_J,axiom,
% 0.26/0.46 ! [B: name,A: name,X: late_freeRes] :
% 0.26/0.46 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_fresh(1)
% 0.26/0.46 thf(fact_283_abs__fresh_I1_J,axiom,
% 0.26/0.46 ! [B: name,A: name,X: name] :
% 0.26/0.46 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_fresh(1)
% 0.26/0.46 thf(fact_284_abs__fresh_I1_J,axiom,
% 0.26/0.46 ! [B: name,A: name,X: pi] :
% 0.26/0.46 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.26/0.46 = ( ( B = A )
% 0.26/0.46 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % abs_fresh(1)
% 0.26/0.46 thf(fact_285_pi_Oinject_I2_J,axiom,
% 0.26/0.46 ! [X1: pi,Y1: pi] :
% 0.26/0.46 ( ( ( tau @ X1 )
% 0.26/0.46 = ( tau @ Y1 ) )
% 0.26/0.46 = ( X1 = Y1 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(2)
% 0.26/0.46 thf(fact_286_pi_Odistinct_I3_J,axiom,
% 0.26/0.46 ! [Pi: pi] :
% 0.26/0.46 ( piNil
% 0.26/0.46 != ( tau @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(3)
% 0.26/0.46 thf(fact_287_pi_Odistinct_I19_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 0.26/0.46 ( ( output @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( tau @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(19)
% 0.26/0.46 thf(fact_288_pi_Odistinct_I35_J,axiom,
% 0.26/0.46 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.26/0.46 ( ( tau @ Pi3 )
% 0.26/0.46 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(35)
% 0.26/0.46 thf(fact_289_pi_Odistinct_I41_J,axiom,
% 0.26/0.46 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( tau @ Pi3 )
% 0.26/0.46 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(41)
% 0.26/0.46 thf(fact_290_pi_Odistinct_I43_J,axiom,
% 0.26/0.46 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( tau @ Pi3 )
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(43)
% 0.26/0.46 thf(fact_291_pi_Odistinct_I45_J,axiom,
% 0.26/0.46 ! [Pi3: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( tau @ Pi3 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(45)
% 0.26/0.46 thf(fact_292_pi_Oinject_I3_J,axiom,
% 0.26/0.46 ! [X3: name,X1: name,X2: pi,Y3: name,Y1: name,Y22: pi] :
% 0.26/0.46 ( ( ( input @ X3 @ X1 @ X2 )
% 0.26/0.46 = ( input @ Y3 @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X3 = Y3 )
% 0.26/0.46 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.26/0.46 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(3)
% 0.26/0.46 thf(fact_293_residual_Oinject_I1_J,axiom,
% 0.26/0.46 ! [X3: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 0.26/0.46 ( ( ( late_BoundR @ X3 @ X1 @ X2 )
% 0.26/0.46 = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( X3 = Y3 )
% 0.26/0.46 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.26/0.46 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % residual.inject(1)
% 0.26/0.46 thf(fact_294_pi_Oinject_I8_J,axiom,
% 0.26/0.46 ! [X1: name,X2: pi,Y1: name,Y22: pi] :
% 0.26/0.46 ( ( ( res @ X1 @ X2 )
% 0.26/0.46 = ( res @ Y1 @ Y22 ) )
% 0.26/0.46 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.26/0.46 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.inject(8)
% 0.26/0.46 thf(fact_295_tauBoundTrans,axiom,
% 0.26/0.46 ! [P: pi,A: late_subject,X: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % tauBoundTrans
% 0.26/0.46 thf(fact_296_nilSim_I1_J,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 0.26/0.46 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % nilSim(1)
% 0.26/0.46 thf(fact_297_resTauBoundTrans,axiom,
% 0.26/0.46 ! [X: name,P: pi,A: late_subject,Y2: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y2 @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % resTauBoundTrans
% 0.26/0.46 thf(fact_298_tauOutputTrans,axiom,
% 0.26/0.46 ! [P: pi,A: name,B: name,P3: pi] :
% 0.26/0.46 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 0.26/0.46
% 0.26/0.46 % tauOutputTrans
% 0.26/0.46 thf(fact_299_tauCases,axiom,
% 0.26/0.46 ! [P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 0.26/0.46 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 0.26/0.46 => ( ( ( Alpha = late_TauR )
% 0.26/0.46 => ( ( P = P3 )
% 0.26/0.46 => ( Prop @ late_TauR @ P ) ) )
% 0.26/0.46 => ( Prop @ Alpha @ P3 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % tauCases
% 0.26/0.46 thf(fact_300_tauCases_H,axiom,
% 0.26/0.46 ! [P: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.26/0.46 => ~ ! [P4: pi] :
% 0.26/0.46 ( ( ( tau @ P )
% 0.26/0.46 = ( tau @ P4 ) )
% 0.26/0.46 => ( Rs
% 0.26/0.46 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % tauCases'
% 0.26/0.46 thf(fact_301_Tau,axiom,
% 0.26/0.46 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.26/0.46
% 0.26/0.46 % Tau
% 0.26/0.46 thf(fact_302_inputCases_H,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.26/0.46 => ~ ! [X5: name,A3: name,P4: pi] :
% 0.26/0.46 ( ( ( A = A3 )
% 0.26/0.46 & ( ( abs_fun_name_pi @ B @ P )
% 0.26/0.46 = ( abs_fun_name_pi @ X5 @ P4 ) ) )
% 0.26/0.46 => ( ( Rs
% 0.26/0.46 = ( late_BoundR @ ( late_InputS @ A3 ) @ X5 @ P4 ) )
% 0.26/0.46 => ( X5 = A3 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % inputCases'
% 0.26/0.46 thf(fact_303_mismatchIdRight,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( ( A != B )
% 0.26/0.46 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A @ B @ P ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mismatchIdRight
% 0.26/0.46 thf(fact_304_mismatchIdLeft,axiom,
% 0.26/0.46 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 0.26/0.46 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 0.26/0.46 => ( ( A != B )
% 0.26/0.46 => ( strong743114133lation @ ( mismatch @ A @ B @ P ) @ Rel @ P ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mismatchIdLeft
% 0.26/0.46 thf(fact_305_pi_Ofresh_I6_J,axiom,
% 0.26/0.46 ! [A: name,X3: name,X2: name,X1: pi] :
% 0.26/0.46 ( ( fresh_name_pi @ A @ ( mismatch @ X3 @ X2 @ X1 ) )
% 0.26/0.46 = ( ( fresh_name_name @ A @ X3 )
% 0.26/0.46 & ( fresh_name_name @ A @ X2 )
% 0.26/0.46 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.fresh(6)
% 0.26/0.46 thf(fact_306_pi_Odistinct_I39_J,axiom,
% 0.26/0.46 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 0.26/0.46 ( ( tau @ Pi3 )
% 0.26/0.46 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(39)
% 0.26/0.46 thf(fact_307_mismatchCases,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.26/0.46 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.26/0.46 => ( ( ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( ( A != B )
% 0.26/0.46 => ( F @ A @ B ) ) )
% 0.26/0.46 => ( F @ A @ B ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mismatchCases
% 0.26/0.46 thf(fact_308_mismatchTrans,axiom,
% 0.26/0.46 ! [A: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.26/0.46
% 0.26/0.46 % mismatchTrans
% 0.26/0.46 thf(fact_309_mismatchCases_H,axiom,
% 0.26/0.46 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.26/0.46 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.26/0.46 => ~ ! [P4: pi,A3: name,B5: name] :
% 0.26/0.46 ( ( ( A = A3 )
% 0.26/0.46 & ( B = B5 )
% 0.26/0.46 & ( P = P4 ) )
% 0.26/0.46 => ( ( late_transitions @ P4 @ Rs )
% 0.26/0.46 => ( A3 = B5 ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % mismatchCases'
% 0.26/0.46 thf(fact_310_Mismatch,axiom,
% 0.26/0.46 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.26/0.46 ( ( late_transitions @ P @ Rs )
% 0.26/0.46 => ( ( A != B )
% 0.26/0.46 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.26/0.46
% 0.26/0.46 % Mismatch
% 0.26/0.46 thf(fact_311_pi_Odistinct_I75_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 0.26/0.46 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( res @ Name @ Pi ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(75)
% 0.26/0.46 thf(fact_312_pi_Odistinct_I73_J,axiom,
% 0.26/0.46 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 0.26/0.46 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 0.26/0.46 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.26/0.46
% 0.26/0.46 % pi.distinct(73)
% 0.26/0.46
% 0.26/0.46 % Conjectures (1)
% 0.26/0.46 thf(conj_0,conjecture,
% 0.26/0.46 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 2.87/1.56 ---- Embedded in THF ---
% 2.87/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.87/1.56 %%% Generated on Tue Feb 24 08:29:23 EST 2026
% 2.87/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.87/1.56 %%% Logic specification used:
% 2.87/1.56 %%% thf(spec, logic, $$dhol).
% 2.87/1.56
% 2.87/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2DTF32500.p
% See solution above
% 2.87/1.56 ------------------------
% 3.03/1.62 ---- Cleaned THF ---
% 3.03/1.62 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
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% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
% 3.03/1.62 produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
% 3.03/1.62 produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
% 3.03/1.62 produc607574050ubject: name > late_subject > produc865358760ubject ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
% 3.03/1.62 product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 3.03/1.62 produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
% 3.03/1.62 produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
% 3.03/1.62 produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
% 3.03/1.62 produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 3.03/1.62 produc1647375838t_name: late_subject > name > produc1998742700t_name ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
% 3.03/1.62 produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
% 3.03/1.62 produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
% 3.03/1.62 produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
% 3.03/1.62 eqvt_pi: set_Pr1834926343_pi_pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Relation_OId_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 3.03/1.62 id_name_noption_pi: set_Pr1569510577ion_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Relation_OId_001t__Agent__Opi,type,
% 3.03/1.62 id_pi: set_Pr1834926343_pi_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.03/1.62 collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Strong__Late__Sim_Oderivative,type,
% 3.03/1.62 strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_Strong__Late__Sim_Osimulation,type,
% 3.03/1.62 strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 3.03/1.62 member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Oname_J,type,
% 3.03/1.62 member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Agent__Opi_J,type,
% 3.03/1.62 member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__OfreeRes_J,type,
% 3.03/1.62 member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_Mt__Late____Semantics__Osubject_J,type,
% 3.03/1.62 member938018755ubject: produc691362330ubject > set_Pr248416762ubject > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
% 3.03/1.62 member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_P,type,
% 3.03/1.62 p: pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_PQ____,type,
% 3.03/1.62 pq: pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_Q,type,
% 3.03/1.62 q: pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_Q_H____,type,
% 3.03/1.62 q2: pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_Rel,type,
% 3.03/1.62 rel: set_Pr1834926343_pi_pi ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v__092_060alpha_062____,type,
% 3.03/1.62 alpha: late_freeRes ).
% 3.03/1.62
% 3.03/1.62 thf(sy_v_x,type,
% 3.03/1.62 x: name ).
% 3.03/1.62
% 3.03/1.62 thf(fact_0_cRes_Ohyps_I2_J,axiom,
% 3.03/1.62 fresh_1641682979reeRes @ x @ alpha ).
% 3.03/1.62
% 3.03/1.62 thf(fact_1_Eqvt,axiom,
% 3.03/1.62 eqvt_pi @ rel ).
% 3.03/1.62
% 3.03/1.62 thf(fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062,axiom,
% 3.03/1.62 late_transitions @ ( sum @ p @ q ) @ ( late_FreeR @ alpha @ q2 ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_3_cRes_Ohyps_I1_J,axiom,
% 3.03/1.62 late_transitions @ q @ ( late_FreeR @ alpha @ q2 ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_4_cSum2_Ohyps,axiom,
% 3.03/1.62 late_transitions @ ( res @ x @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_5_Free_Ohyps,axiom,
% 3.03/1.62 late_transitions @ ( sum @ ( res @ x @ p ) @ ( res @ x @ q ) ) @ ( late_FreeR @ alpha @ pq ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_6_pi_Odistinct_I81_J,axiom,
% 3.03/1.62 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( sum @ Pi1 @ Pi2 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_7_sumCases,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.03/1.62 => ( ~ ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_8_sumCases_H,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.03/1.62 => ( ~ ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_9_Sum1,axiom,
% 3.03/1.62 ! [P: pi,Rs: late_residual,Q: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_10_Sum2,axiom,
% 3.03/1.62 ! [Q: pi,Rs: late_residual,P: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ Rs )
% 3.03/1.62 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_11_resCasesF,axiom,
% 3.03/1.62 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 3.03/1.62 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.03/1.62 => ( ! [P2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.03/1.62 => ( F @ ( res @ X @ P2 ) ) ) )
% 3.03/1.62 => ( F @ XP ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_12_resCasesF_H,axiom,
% 3.03/1.62 ! [X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 3.03/1.62 ( ( ( res @ X @ P )
% 3.03/1.62 = ( res @ Y @ P4 ) )
% 3.03/1.62 => ( ( ( late_FreeR @ Alpha @ P3 )
% 3.03/1.62 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 3.03/1.62 => ~ ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_13_ResF,axiom,
% 3.03/1.62 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ Y2 @ Alpha )
% 3.03/1.62 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y2 @ P3 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_14_pi_Oinject_I6_J,axiom,
% 3.03/1.62 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.03/1.62 ( ( ( sum @ X2 @ X1 )
% 3.03/1.62 = ( sum @ Y22 @ Y1 ) )
% 3.03/1.62 = ( ( X2 = Y22 )
% 3.03/1.62 & ( X1 = Y1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_15_residual_Oinject_I2_J,axiom,
% 3.03/1.62 ! [X2: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
% 3.03/1.62 ( ( ( late_FreeR @ X2 @ X1 )
% 3.03/1.62 = ( late_FreeR @ Y22 @ Y1 ) )
% 3.03/1.62 = ( ( X2 = Y22 )
% 3.03/1.62 & ( X1 = Y1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_16_resInputFreeTrans,axiom,
% 3.03/1.62 ! [X: name,A: name,Y2: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y2 @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_17_resZeroTrans,axiom,
% 3.03/1.62 ! [X: name,Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_18_pi_Odistinct_I5_J,axiom,
% 3.03/1.62 ! [Name1: name,Name2: name,Pi: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_19_name__exists__fresh,axiom,
% 3.03/1.62 ! [X: late_subject] :
% 3.03/1.62 ~ ! [C: name] :
% 3.03/1.62 ~ ( fresh_717452603ubject @ C @ X ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_20_name__exists__fresh,axiom,
% 3.03/1.62 ! [X: late_freeRes] :
% 3.03/1.62 ~ ! [C: name] :
% 3.03/1.62 ~ ( fresh_1641682979reeRes @ C @ X ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_21_name__exists__fresh,axiom,
% 3.03/1.62 ! [X: name] :
% 3.03/1.62 ~ ! [C: name] :
% 3.03/1.62 ~ ( fresh_name_name @ C @ X ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_22_name__exists__fresh,axiom,
% 3.03/1.62 ! [X: pi] :
% 3.03/1.62 ~ ! [C: name] :
% 3.03/1.62 ~ ( fresh_name_pi @ C @ X ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_23_pi_Odistinct_I57_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_24_zeroTrans,axiom,
% 3.03/1.62 ! [Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_25_nilCases_H,axiom,
% 3.03/1.62 ! [Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_26_pi_Odistinct_I53_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_27_pi_Odistinct_I15_J,axiom,
% 3.03/1.62 ! [Name: name,Pi: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_28_pi_Odistinct_I11_J,axiom,
% 3.03/1.62 ! [Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_29_resTrans_I2_J,axiom,
% 3.03/1.62 ! [X: name,Y2: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y2 @ P ) ) @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_30_inputFreeTrans,axiom,
% 3.03/1.62 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_31_Id,axiom,
% 3.03/1.62 ord_le630093991_pi_pi @ id_pi @ rel ).
% 3.03/1.62
% 3.03/1.62 thf(fact_32_outputFreshTrans,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 3.03/1.62 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_33_freshFreeDerivative_I1_J,axiom,
% 3.03/1.62 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( fresh_1641682979reeRes @ Y2 @ Alpha ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_34_nilSim_I2_J,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
% 3.03/1.62 ~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_35_resTrans_I1_J,axiom,
% 3.03/1.62 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_36_freeRes_Ofresh_I2_J,axiom,
% 3.03/1.62 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_37_freshFreeDerivative_I2_J,axiom,
% 3.03/1.62 ! [P: pi,Alpha: late_freeRes,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( fresh_name_pi @ Y2 @ P3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_38_residual_Ostrong__induct,axiom,
% 3.03/1.62 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 3.03/1.62 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_39_residual_Ostrong__induct,axiom,
% 3.03/1.62 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_40_residual_Ostrong__induct,axiom,
% 3.03/1.62 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 3.03/1.62 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_41_residual_Ostrong__induct,axiom,
% 3.03/1.62 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_42_residual_Ostrong__inducts,axiom,
% 3.03/1.62 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_subject] :
% 3.03/1.62 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_43_residual_Ostrong__inducts,axiom,
% 3.03/1.62 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_44_residual_Ostrong__inducts,axiom,
% 3.03/1.62 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: name] :
% 3.03/1.62 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_45_residual_Ostrong__inducts,axiom,
% 3.03/1.62 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi,Z2: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Name3 @ Subject )
% 3.03/1.62 => ( P @ Z2 @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) ) ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Z @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_46_Par2F,axiom,
% 3.03/1.62 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_47_pi_Ofresh_I8_J,axiom,
% 3.03/1.62 ! [A: name,X2: pi,X1: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_name_pi @ A @ X2 )
% 3.03/1.62 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_48_pi_Ofresh_I7_J,axiom,
% 3.03/1.62 ! [A: name,X2: pi,X1: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_name_pi @ A @ X2 )
% 3.03/1.62 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_49_pi_Ofresh_I2_J,axiom,
% 3.03/1.62 ! [A: name,X3: name,X2: name,X1: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( output @ X3 @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X3 )
% 3.03/1.62 & ( fresh_name_name @ A @ X2 )
% 3.03/1.62 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_50_pi_Ofresh_I1_J,axiom,
% 3.03/1.62 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_51_residual_Ofresh_I2_J,axiom,
% 3.03/1.62 ! [A: name,X2: late_freeRes,X1: pi] :
% 3.03/1.62 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 3.03/1.62 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_52_pi_Oinject_I7_J,axiom,
% 3.03/1.62 ! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
% 3.03/1.62 ( ( ( par @ X2 @ X1 )
% 3.03/1.62 = ( par @ Y22 @ Y1 ) )
% 3.03/1.62 = ( ( X2 = Y22 )
% 3.03/1.62 & ( X1 = Y1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_53_pi_Oinject_I1_J,axiom,
% 3.03/1.62 ! [X3: name,X2: name,X1: pi,Y3: name,Y22: name,Y1: pi] :
% 3.03/1.62 ( ( ( output @ X3 @ X2 @ X1 )
% 3.03/1.62 = ( output @ Y3 @ Y22 @ Y1 ) )
% 3.03/1.62 = ( ( X3 = Y3 )
% 3.03/1.62 & ( X2 = Y22 )
% 3.03/1.62 & ( X1 = Y1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_54_mem__Collect__eq,axiom,
% 3.03/1.62 ! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
% 3.03/1.62 ( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
% 3.03/1.62 = ( P @ A ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_55_Collect__mem__eq,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( collec1051790738_pi_pi
% 3.03/1.62 @ ^ [X4: product_prod_pi_pi] : ( member558706512_pi_pi @ X4 @ A2 ) )
% 3.03/1.62 = A2 ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_56_Collect__cong,axiom,
% 3.03/1.62 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 3.03/1.62 ( ! [X5: product_prod_pi_pi] :
% 3.03/1.62 ( ( P @ X5 )
% 3.03/1.62 = ( Q @ X5 ) )
% 3.03/1.62 => ( ( collec1051790738_pi_pi @ P )
% 3.03/1.62 = ( collec1051790738_pi_pi @ Q ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_57_pi_Odistinct_I29_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_58_freshBoundDerivative_I2_J,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( ( Y2 != X )
% 3.03/1.62 => ( fresh_name_pi @ Y2 @ P3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_59_freshBoundDerivative_I1_J,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( fresh_717452603ubject @ Y2 @ A ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_60_Late__Semantics_OPar1B,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_61_Late__Semantics_OPar2B,axiom,
% 3.03/1.62 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_62_parCasesB,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 3.03/1.62 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ! [P2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.03/1.62 => ( Prop @ ( par @ P2 @ Q ) ) )
% 3.03/1.62 => ( ! [Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.03/1.62 => ( Prop @ ( par @ P @ Q3 ) ) )
% 3.03/1.62 => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_63_parCasesB_H,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,B: late_subject,Y2: name,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y2 @ P3 ) )
% 3.03/1.62 => ( ! [P4: pi,A3: late_subject,X5: name,P2: pi,Q4: pi] :
% 3.03/1.62 ( ( ( par @ P @ Q )
% 3.03/1.62 = ( par @ P4 @ Q4 ) )
% 3.03/1.62 => ( ( ( late_BoundR @ B @ Y2 @ P3 )
% 3.03/1.62 = ( late_BoundR @ A3 @ X5 @ ( par @ P2 @ Q4 ) ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q4 )
% 3.03/1.62 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) )
% 3.03/1.62 => ~ ! [Q4: pi,A3: late_subject,X5: name,Q3: pi,P4: pi] :
% 3.03/1.62 ( ( ( par @ P @ Q )
% 3.03/1.62 = ( par @ P4 @ Q4 ) )
% 3.03/1.62 => ( ( ( late_BoundR @ B @ Y2 @ P3 )
% 3.03/1.62 = ( late_BoundR @ A3 @ X5 @ ( par @ P4 @ Q3 ) ) )
% 3.03/1.62 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q4 )
% 3.03/1.62 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_64_freshResidual,axiom,
% 3.03/1.62 ! [P: pi,Rs: late_residual,X: name] :
% 3.03/1.62 ( ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_65_transitions_OPar1B,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_66_transitions_OPar2B,axiom,
% 3.03/1.62 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_67_sumIdempRight,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ P @ P ) @ Rel @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_68_sumAssocRight,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ P @ ( sum @ Q @ R ) ) @ Rel @ ( sum @ ( sum @ P @ Q ) @ R ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_69_sumIdempLeft,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ P ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_70_sumAssocLeft,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ ( sum @ P @ Q ) @ R ) @ Rel @ ( sum @ P @ ( sum @ Q @ R ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_71_sumSym,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ P @ Q ) @ Rel @ ( sum @ Q @ P ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_72_outputBoundTrans,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,C2: late_subject,X: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C2 @ X @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_73_transitions_OResB,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Y2 @ A )
% 3.03/1.62 => ( ( Y2 != X )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A )
% 3.03/1.62 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y2 @ P3 ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_74_nilSim_I3_J,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 3.03/1.62 ~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_75_sumZeroRight,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( sum @ P @ piNil ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_76_sumZeroLeft,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ P @ piNil ) @ Rel @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_77_Late__Semantics_OResB,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi,Y2: name] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Y2 @ A )
% 3.03/1.62 => ( ( Y2 != X )
% 3.03/1.62 => ( late_transitions @ ( res @ Y2 @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y2 @ P3 ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_78_inputIneqTrans,axiom,
% 3.03/1.62 ! [A: name,X: name,P: pi,B: late_subject,Y2: name,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y2 @ P3 ) )
% 3.03/1.62 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_79_pi_Odistinct_I85_J,axiom,
% 3.03/1.62 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( par @ Pi1 @ Pi2 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_80_freshRes,axiom,
% 3.03/1.62 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_81_residual_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [Subject2: late_subject,Name4: name,Pi3: pi,FreeRes2: late_freeRes,Pi: pi] :
% 3.03/1.62 ( ( late_BoundR @ Subject2 @ Name4 @ Pi3 )
% 3.03/1.62 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_82_residual_Oinducts,axiom,
% 3.03/1.62 ! [P: late_residual > $o,Residual: late_residual] :
% 3.03/1.62 ( ! [Subject: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject @ Name3 @ Pi4 ) )
% 3.03/1.62 => ( ! [FreeRes: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi4 ) )
% 3.03/1.62 => ( P @ Residual ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_83_pi_Odistinct_I79_J,axiom,
% 3.03/1.62 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( sum @ Pi1 @ Pi2 )
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_84_pi_Odistinct_I55_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( input @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_85_sumResLeft,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,X: name,P: pi,Q: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ ( sum @ ( res @ X @ P ) @ ( res @ X @ Q ) ) @ Rel @ ( res @ X @ ( sum @ P @ Q ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_86_pi_Odistinct_I13_J,axiom,
% 3.03/1.62 ! [Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_87_outputTauTrans,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_88_pi_Odistinct_I31_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_89_pi_Odistinct_I27_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_90_pi_Odistinct_I21_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.03/1.62 ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_91_pi_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [Name1: name,Name2: name,Pi: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( output @ Name1 @ Name2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_92_nilSimRight,axiom,
% 3.03/1.62 ! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_93_resOutputTauTrans,axiom,
% 3.03/1.62 ! [X: name,A: name,B: name,P: pi,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_94_Par1F,axiom,
% 3.03/1.62 ! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_95_Strong__Late__Sim_Oreflexive,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_96_subset__antisym,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B2 @ A2 )
% 3.03/1.62 => ( A2 = B2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_97_subsetI,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ! [X5: product_prod_pi_pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ X5 @ A2 )
% 3.03/1.62 => ( member558706512_pi_pi @ X5 @ B2 ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A2 @ B2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_98_monotonic,axiom,
% 3.03/1.62 ! [P: pi,A2: set_Pr1834926343_pi_pi,P3: pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( strong743114133lation @ P @ A2 @ P3 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( strong743114133lation @ P @ B2 @ P3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_99_order__refl,axiom,
% 3.03/1.62 ! [X: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ X @ X ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_100_resOutputInputTrans,axiom,
% 3.03/1.62 ! [X: name,A: name,B: name,P: pi,C2: name,Y2: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y2 @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_101_resInputBoundOutputTrans,axiom,
% 3.03/1.62 ! [X: name,A: name,Y2: name,P: pi,B: name,Z: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y2 @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_102_resOutputOutputTrans,axiom,
% 3.03/1.62 ! [X: name,A: name,P: pi,B: name,Y2: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y2 ) @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_103_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.03/1.62 ! [X2: name,X1: name,Y22: name,Y1: name] :
% 3.03/1.62 ( ( ( late_OutputR @ X2 @ X1 )
% 3.03/1.62 = ( late_OutputR @ Y22 @ Y1 ) )
% 3.03/1.62 = ( ( X2 = Y22 )
% 3.03/1.62 & ( X1 = Y1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_104_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.03/1.62 ! [X1: name,Y1: name] :
% 3.03/1.62 ( ( ( late_BoundOutputS @ X1 )
% 3.03/1.62 = ( late_BoundOutputS @ Y1 ) )
% 3.03/1.62 = ( X1 = Y1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_105_name__fresh,axiom,
% 3.03/1.62 ( fresh_name_name
% 3.03/1.62 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_106_subject_Ofresh_I1_J,axiom,
% 3.03/1.62 ! [A: name,X1: name] :
% 3.03/1.62 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 3.03/1.62 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_107_subject_Ofresh_I2_J,axiom,
% 3.03/1.62 ! [A: name,X1: name] :
% 3.03/1.62 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 3.03/1.62 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_108_freeRes_Ofresh_I1_J,axiom,
% 3.03/1.62 ! [A: name,X2: name,X1: name] :
% 3.03/1.62 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X2 )
% 3.03/1.62 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_109_subject_Oinducts,axiom,
% 3.03/1.62 ! [P: late_subject > $o,Subject2: late_subject] :
% 3.03/1.62 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 3.03/1.62 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 3.03/1.62 => ( P @ Subject2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_110_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [Name4: name,Name: name] :
% 3.03/1.62 ( ( late_InputS @ Name4 )
% 3.03/1.62 != ( late_BoundOutputS @ Name ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_111_freeRes_Oinducts,axiom,
% 3.03/1.62 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 3.03/1.62 ( ! [Name13: name,Name23: name] : ( P @ ( late_OutputR @ Name13 @ Name23 ) )
% 3.03/1.62 => ( ( P @ late_TauR )
% 3.03/1.62 => ( P @ FreeRes3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_112_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name] :
% 3.03/1.62 ( ( late_OutputR @ Name12 @ Name22 )
% 3.03/1.62 != late_TauR ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_113_Open,axiom,
% 3.03/1.62 ! [P: pi,A: name,B: name,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.03/1.62 => ( ( A != B )
% 3.03/1.62 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_114_order__subst1,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ ( F2 @ B ) )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.03/1.62 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_115_order__subst2,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ ( F2 @ B ) @ C2 )
% 3.03/1.62 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_116_ord__eq__le__subst,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( A
% 3.03/1.62 = ( F2 @ B ) )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.03/1.62 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_117_ord__le__eq__subst,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,F2: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( ( ( F2 @ B )
% 3.03/1.62 = C2 )
% 3.03/1.62 => ( ! [X5: set_Pr1834926343_pi_pi,Y: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X5 @ Y )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ X5 ) @ ( F2 @ Y ) ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_118_eq__iff,axiom,
% 3.03/1.62 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 3.03/1.62 = ( ^ [X4: set_Pr1834926343_pi_pi,Y5: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X4 @ Y5 )
% 3.03/1.62 & ( ord_le630093991_pi_pi @ Y5 @ X4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_119_antisym,axiom,
% 3.03/1.62 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ Y2 @ X )
% 3.03/1.62 => ( X = Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_120_eq__refl,axiom,
% 3.03/1.62 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( X = Y2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ X @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_121_order_Otrans,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_122_antisym__conv,axiom,
% 3.03/1.62 ! [Y2: set_Pr1834926343_pi_pi,X: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ Y2 @ X )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 3.03/1.62 = ( X = Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_123_order__class_Oorder_Oeq__iff,axiom,
% 3.03/1.62 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 3.03/1.62 = ( ^ [A4: set_Pr1834926343_pi_pi,B3: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A4 @ B3 )
% 3.03/1.62 & ( ord_le630093991_pi_pi @ B3 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_124_ord__eq__le__trans,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( A = B )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B @ C2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_125_ord__le__eq__trans,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( ( B = C2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A @ C2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_126_order__class_Oorder_Oantisym,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi,B: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B @ A )
% 3.03/1.62 => ( A = B ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_127_order__trans,axiom,
% 3.03/1.62 ! [X: set_Pr1834926343_pi_pi,Y2: set_Pr1834926343_pi_pi,Z: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ X @ Y2 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ Y2 @ Z )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ X @ Z ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_128_dual__order_Orefl,axiom,
% 3.03/1.62 ! [A: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A @ A ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_129_dual__order_Otrans,axiom,
% 3.03/1.62 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi,C2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ B @ A )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ C2 @ B )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ C2 @ A ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_130_dual__order_Oeq__iff,axiom,
% 3.03/1.62 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 3.03/1.62 = ( ^ [A4: set_Pr1834926343_pi_pi,B3: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ B3 @ A4 )
% 3.03/1.62 & ( ord_le630093991_pi_pi @ A4 @ B3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_131_dual__order_Oantisym,axiom,
% 3.03/1.62 ! [B: set_Pr1834926343_pi_pi,A: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ B @ A )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ A @ B )
% 3.03/1.62 => ( A = B ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_132_in__mono,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,X: product_prod_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( ( member558706512_pi_pi @ X @ A2 )
% 3.03/1.62 => ( member558706512_pi_pi @ X @ B2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_133_subsetD,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,C2: product_prod_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( ( member558706512_pi_pi @ C2 @ A2 )
% 3.03/1.62 => ( member558706512_pi_pi @ C2 @ B2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_134_equalityE,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( A2 = B2 )
% 3.03/1.62 => ~ ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ~ ( ord_le630093991_pi_pi @ B2 @ A2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_135_subset__eq,axiom,
% 3.03/1.62 ( ord_le630093991_pi_pi
% 3.03/1.62 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ! [X4: product_prod_pi_pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ X4 @ A5 )
% 3.03/1.62 => ( member558706512_pi_pi @ X4 @ B4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_136_equalityD1,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( A2 = B2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A2 @ B2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_137_equalityD2,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( A2 = B2 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ B2 @ A2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_138_subset__iff,axiom,
% 3.03/1.62 ( ord_le630093991_pi_pi
% 3.03/1.62 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ! [T: product_prod_pi_pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ T @ A5 )
% 3.03/1.62 => ( member558706512_pi_pi @ T @ B4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_139_subset__refl,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi] : ( ord_le630093991_pi_pi @ A2 @ A2 ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_140_Collect__mono,axiom,
% 3.03/1.62 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 3.03/1.62 ( ! [X5: product_prod_pi_pi] :
% 3.03/1.62 ( ( P @ X5 )
% 3.03/1.62 => ( Q @ X5 ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_141_subset__trans,axiom,
% 3.03/1.62 ! [A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi,C3: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ B2 @ C3 )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ A2 @ C3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_142_set__eq__subset,axiom,
% 3.03/1.62 ( ( ^ [Y4: set_Pr1834926343_pi_pi,Z3: set_Pr1834926343_pi_pi] : ( Y4 = Z3 ) )
% 3.03/1.62 = ( ^ [A5: set_Pr1834926343_pi_pi,B4: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ A5 @ B4 )
% 3.03/1.62 & ( ord_le630093991_pi_pi @ B4 @ A5 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_143_Collect__mono__iff,axiom,
% 3.03/1.62 ! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ ( collec1051790738_pi_pi @ P ) @ ( collec1051790738_pi_pi @ Q ) )
% 3.03/1.62 = ( ! [X4: product_prod_pi_pi] :
% 3.03/1.62 ( ( P @ X4 )
% 3.03/1.62 => ( Q @ X4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_144_resCasesB_H,axiom,
% 3.03/1.62 ! [X6: name,P: pi,A: late_subject,Y6: name,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( res @ X6 @ P ) @ ( late_BoundR @ A @ Y6 @ P3 ) )
% 3.03/1.62 => ( ! [P4: pi,A3: name,B5: name] :
% 3.03/1.62 ( ( ( res @ X6 @ P )
% 3.03/1.62 = ( res @ B5 @ P4 ) )
% 3.03/1.62 => ! [P2: pi] :
% 3.03/1.62 ( ( ( late_BoundR @ A @ Y6 @ P3 )
% 3.03/1.62 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B5 @ P2 ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P2 ) )
% 3.03/1.62 => ( A3 = B5 ) ) ) )
% 3.03/1.62 => ~ ! [P4: pi,A3: late_subject,X5: name,P2: pi,Y: name] :
% 3.03/1.62 ( ( ( res @ X6 @ P )
% 3.03/1.62 = ( res @ Y @ P4 ) )
% 3.03/1.62 => ( ( ( late_BoundR @ A @ Y6 @ P3 )
% 3.03/1.62 = ( late_BoundR @ A3 @ X5 @ ( res @ Y @ P2 ) ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Y @ A3 )
% 3.03/1.62 => ( ( Y != X5 )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.03/1.62 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_145_Output,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_146_outputIneqTrans,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,C2: name,D: name,P3: pi] :
% 3.03/1.62 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P3 ) )
% 3.03/1.62 => ~ ( ( A != C2 )
% 3.03/1.62 | ( B != D ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_147_outputCases_H,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 3.03/1.62 => ~ ! [A3: name,B5: name,P4: pi] :
% 3.03/1.62 ( ( ( A = A3 )
% 3.03/1.62 & ( B = B5 )
% 3.03/1.62 & ( P = P4 ) )
% 3.03/1.62 => ( Rs
% 3.03/1.62 != ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_148_outputCases,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 3.03/1.62 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( ( ( Alpha
% 3.03/1.62 = ( late_OutputR @ A @ B ) )
% 3.03/1.62 => ( ( P = P3 )
% 3.03/1.62 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 3.03/1.62 => ( Prop @ Alpha @ P3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_149_Late__Semantics_OInput,axiom,
% 3.03/1.62 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_150_transitions_OInput,axiom,
% 3.03/1.62 ! [X: name,A: name,P: pi] :
% 3.03/1.62 ( ( X != A )
% 3.03/1.62 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_151_inputBoundOutputTrans,axiom,
% 3.03/1.62 ! [A: name,X: name,P: pi,B: name,Y2: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y2 @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_152_resCases_H,axiom,
% 3.03/1.62 ! [X: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 3.03/1.62 => ( ! [P4: pi,A3: name,B5: name] :
% 3.03/1.62 ( ( ( res @ X @ P )
% 3.03/1.62 = ( res @ B5 @ P4 ) )
% 3.03/1.62 => ! [P2: pi] :
% 3.03/1.62 ( ( Rs
% 3.03/1.62 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B5 @ P2 ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B5 ) @ P2 ) )
% 3.03/1.62 => ( A3 = B5 ) ) ) )
% 3.03/1.62 => ( ! [P4: pi,A3: late_subject,X5: name,P2: pi,Y: name] :
% 3.03/1.62 ( ( ( res @ X @ P )
% 3.03/1.62 = ( res @ Y @ P4 ) )
% 3.03/1.62 => ( ( Rs
% 3.03/1.62 = ( late_BoundR @ A3 @ X5 @ ( res @ Y @ P2 ) ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X5 @ P2 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Y @ A3 )
% 3.03/1.62 => ( ( Y != X5 )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P4 )
% 3.03/1.62 => ~ ( fresh_717452603ubject @ X5 @ A3 ) ) ) ) ) ) )
% 3.03/1.62 => ~ ! [P4: pi,Alpha2: late_freeRes,P2: pi,Y: name] :
% 3.03/1.62 ( ( ( res @ X @ P )
% 3.03/1.62 = ( res @ Y @ P4 ) )
% 3.03/1.62 => ( ( Rs
% 3.03/1.62 = ( late_FreeR @ Alpha2 @ ( res @ Y @ P2 ) ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P2 ) )
% 3.03/1.62 => ~ ( fresh_1641682979reeRes @ Y @ Alpha2 ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_153_transitions_OClose2,axiom,
% 3.03/1.62 ! [P: pi,A: name,Y2: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ Q )
% 3.03/1.62 => ( ( X != A )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P3 )
% 3.03/1.62 => ( ( Y2 != A )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ Q2 )
% 3.03/1.62 => ( ( X != Y2 )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_154_transitions_OClose1,axiom,
% 3.03/1.62 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ Q )
% 3.03/1.62 => ( ( X != A )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q2 )
% 3.03/1.62 => ( ( Y2 != A )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P3 )
% 3.03/1.62 => ( ( X != Y2 )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X @ Y2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_155_Late__Semantics_OClose2,axiom,
% 3.03/1.62 ! [P: pi,A: name,Y2: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ Q )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ P3 @ ( subs @ Q2 @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_156_Late__Semantics_OClose1,axiom,
% 3.03/1.62 ! [P: pi,A: name,X: name,P3: pi,Q: pi,Y2: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y2 @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y2 @ P )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y2 @ ( par @ ( subs @ P3 @ X @ Y2 ) @ Q2 ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_157_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.03/1.62 ! [X2: name,Y22: name] :
% 3.03/1.62 ( ( ( late_BoundOutputS @ X2 )
% 3.03/1.62 = ( late_BoundOutputS @ Y22 ) )
% 3.03/1.62 = ( X2 = Y22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_158_subst__identity,axiom,
% 3.03/1.62 ! [P: pi,A: name] :
% 3.03/1.62 ( ( subs @ P @ A @ A )
% 3.03/1.62 = P ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_159_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.03/1.62 ! [X11: name,X12: name,Y11: name,Y12: name] :
% 3.03/1.62 ( ( ( late_OutputR @ X11 @ X12 )
% 3.03/1.62 = ( late_OutputR @ Y11 @ Y12 ) )
% 3.03/1.62 = ( ( X11 = Y11 )
% 3.03/1.62 & ( X12 = Y12 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_160_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.03/1.62 ! [X1: name,Y1: name] :
% 3.03/1.62 ( ( ( late_InputS @ X1 )
% 3.03/1.62 = ( late_InputS @ Y1 ) )
% 3.03/1.62 = ( X1 = Y1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_161_simps_I9_J,axiom,
% 3.03/1.62 ! [X: name,C2: name,D: name,P: pi] :
% 3.03/1.62 ( ( X != C2 )
% 3.03/1.62 => ( ( X != D )
% 3.03/1.62 => ( ( subs @ ( res @ X @ P ) @ C2 @ D )
% 3.03/1.62 = ( res @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_162_simps_I8_J,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,C2: name,D: name] :
% 3.03/1.62 ( ( subs @ ( par @ P @ Q ) @ C2 @ D )
% 3.03/1.62 = ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_163_substTrans,axiom,
% 3.03/1.62 ! [B: name,P: pi,A: name,C2: name] :
% 3.03/1.62 ( ( fresh_name_pi @ B @ P )
% 3.03/1.62 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C2 )
% 3.03/1.62 = ( subs @ P @ A @ C2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_164_simps_I7_J,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,C2: name,D: name] :
% 3.03/1.62 ( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
% 3.03/1.62 = ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_165_simps_I1_J,axiom,
% 3.03/1.62 ! [C2: name,D: name] :
% 3.03/1.62 ( ( subs @ piNil @ C2 @ D )
% 3.03/1.62 = piNil ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_166_forget,axiom,
% 3.03/1.62 ! [A: name,P: pi,B: name] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ P )
% 3.03/1.62 => ( ( subs @ P @ A @ B )
% 3.03/1.62 = P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_167_fresh__fact1,axiom,
% 3.03/1.62 ! [A: name,P: pi,C2: name,B: name] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ P )
% 3.03/1.62 => ( ( A != C2 )
% 3.03/1.62 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_168_fresh__fact2,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi] :
% 3.03/1.62 ( ( A != B )
% 3.03/1.62 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_169_substRes3,axiom,
% 3.03/1.62 ! [B: name,P: pi,A: name] :
% 3.03/1.62 ( ( fresh_name_pi @ B @ P )
% 3.03/1.62 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 3.03/1.62 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_170_substRes2,axiom,
% 3.03/1.62 ! [B: name,P: pi,A: name] :
% 3.03/1.62 ( ( fresh_name_pi @ B @ P )
% 3.03/1.62 => ( ( res @ A @ P )
% 3.03/1.62 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_171_freeRes_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: late_freeRes] :
% 3.03/1.62 ( ! [X112: name,X122: name] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( late_OutputR @ X112 @ X122 ) )
% 3.03/1.62 => ( Y2 = late_TauR ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_172_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [X11: name,X12: name] :
% 3.03/1.62 ( ( late_OutputR @ X11 @ X12 )
% 3.03/1.62 != late_TauR ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_173_subject_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: late_subject] :
% 3.03/1.62 ( ! [X13: name] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( late_InputS @ X13 ) )
% 3.03/1.62 => ~ ! [X22: name] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( late_BoundOutputS @ X22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_174_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.03/1.62 ! [X1: name,X2: name] :
% 3.03/1.62 ( ( late_InputS @ X1 )
% 3.03/1.62 != ( late_BoundOutputS @ X2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_175_Late__Semantics_OComm1,axiom,
% 3.03/1.62 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_176_Late__Semantics_OComm2,axiom,
% 3.03/1.62 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_177_transitions_OComm1,axiom,
% 3.03/1.62 ! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( X != A )
% 3.03/1.62 => ( ( X != B )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q2 )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_178_transitions_OComm2,axiom,
% 3.03/1.62 ! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ Q )
% 3.03/1.62 => ( ( X != A )
% 3.03/1.62 => ( ( X != B )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P3 )
% 3.03/1.62 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_179_resSimCases,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_subject] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [Q3: pi,A3: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 3.03/1.62 => ( ( A3 != X )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A3 )
% 3.03/1.62 => ( ( X != Y )
% 3.03/1.62 => ( ( fresh_717452603ubject @ Y @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_180_resSimCases,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [Q3: pi,A3: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 3.03/1.62 => ( ( A3 != X )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A3 )
% 3.03/1.62 => ( ( X != Y )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ Y @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_181_resSimCases,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [Q3: pi,A3: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 3.03/1.62 => ( ( A3 != X )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A3 )
% 3.03/1.62 => ( ( X != Y )
% 3.03/1.62 => ( ( fresh_name_name @ Y @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_182_resSimCases,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [Q3: pi,A3: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q3 ) )
% 3.03/1.62 => ( ( A3 != X )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,A3: late_subject,Y: name] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X @ A3 )
% 3.03/1.62 => ( ( X != Y )
% 3.03/1.62 => ( ( fresh_name_pi @ Y @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ ( res @ X @ Q3 ) @ A3 @ Y @ Rel ) ) ) ) ) )
% 3.03/1.62 => ( ! [Q3: pi,Alpha2: late_freeRes] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X @ Alpha2 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_183_simE_I1_J,axiom,
% 3.03/1.62 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
% 3.03/1.62 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X @ P )
% 3.03/1.62 => ? [P2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.03/1.62 & ( strong2129052853vative @ P2 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_184_simCasesCont,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_subject] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X5 @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 3.03/1.62 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_185_simCasesCont,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 3.03/1.62 => ( ( fresh_1641682979reeRes @ X5 @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 3.03/1.62 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_186_simCasesCont,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 3.03/1.62 => ( ( fresh_name_name @ X5 @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 3.03/1.62 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_187_simCasesCont,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
% 3.03/1.62 ( ( eqvt_pi @ Rel )
% 3.03/1.62 => ( ! [A3: late_subject,X5: name,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X5 @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ P )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ Q )
% 3.03/1.62 => ( ( fresh_717452603ubject @ X5 @ A3 )
% 3.03/1.62 => ( ( fresh_name_pi @ X5 @ C3 )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ X5 @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ X5 @ Rel ) ) ) ) ) ) )
% 3.03/1.62 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_188_derivativeMonotonic,axiom,
% 3.03/1.62 ! [P: pi,Q: pi,A: late_subject,X: name,A2: set_Pr1834926343_pi_pi,B2: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ( strong2129052853vative @ P @ Q @ A @ X @ A2 )
% 3.03/1.62 => ( ( ord_le630093991_pi_pi @ A2 @ B2 )
% 3.03/1.62 => ( strong2129052853vative @ P @ Q @ A @ X @ B2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_189_simulation__def,axiom,
% 3.03/1.62 ( strong743114133lation
% 3.03/1.62 = ( ^ [P6: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
% 3.03/1.62 ( ! [A4: late_subject,X4: name,Q6: pi] :
% 3.03/1.62 ( ( ( late_transitions @ Q5 @ ( late_BoundR @ A4 @ X4 @ Q6 ) )
% 3.03/1.62 & ( fresh_name_pi @ X4 @ P6 ) )
% 3.03/1.62 => ? [P7: pi] :
% 3.03/1.62 ( ( late_transitions @ P6 @ ( late_BoundR @ A4 @ X4 @ P7 ) )
% 3.03/1.62 & ( strong2129052853vative @ P7 @ Q6 @ A4 @ X4 @ Rel2 ) ) )
% 3.03/1.62 & ! [Alpha3: late_freeRes,Q6: pi] :
% 3.03/1.62 ( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
% 3.03/1.62 => ? [P7: pi] :
% 3.03/1.62 ( ( late_transitions @ P6 @ ( late_FreeR @ Alpha3 @ P7 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P7 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_190_simCases,axiom,
% 3.03/1.62 ! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ! [A3: late_subject,Y: name,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y @ Q3 ) )
% 3.03/1.62 => ( ( fresh_name_pi @ Y @ P )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y @ P5 ) )
% 3.03/1.62 & ( strong2129052853vative @ P5 @ Q3 @ A3 @ Y @ Rel ) ) ) )
% 3.03/1.62 => ( ! [Alpha2: late_freeRes,Q3: pi] :
% 3.03/1.62 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
% 3.03/1.62 => ? [P5: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P5 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P5 @ Q3 ) @ Rel ) ) )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_191_simE_I2_J,axiom,
% 3.03/1.62 ! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
% 3.03/1.62 ( ( strong743114133lation @ P @ Rel @ Q )
% 3.03/1.62 => ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.03/1.62 => ? [P2: pi] :
% 3.03/1.62 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.03/1.62 & ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P2 @ Q2 ) @ Rel ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_192_derivativeReflexive,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi,A: late_subject,X: name] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( strong2129052853vative @ P @ P @ A @ X @ Rel ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_193_pair__in__Id__conv,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name > noption_pi] :
% 3.03/1.62 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 3.03/1.62 = ( A = B ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_194_pair__in__Id__conv,axiom,
% 3.03/1.62 ! [A: pi,B: pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 3.03/1.62 = ( A = B ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_195_IdI,axiom,
% 3.03/1.62 ! [A: name > noption_pi] : ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ A ) @ id_name_noption_pi ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_196_IdI,axiom,
% 3.03/1.62 ! [A: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ A ) @ id_pi ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_197_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr248416762ubject,S: set_Pr248416762ubject] :
% 3.03/1.62 ( ! [X5: name > noption_pi,Y: late_subject] :
% 3.03/1.62 ( ( member938018755ubject @ ( produc581368530ubject @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member938018755ubject @ ( produc581368530ubject @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le1705144730ubject @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_198_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr305743074reeRes,S: set_Pr305743074reeRes] :
% 3.03/1.62 ( ! [X5: name > noption_pi,Y: late_freeRes] :
% 3.03/1.62 ( ( member2081207979reeRes @ ( produc1505598906reeRes @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member2081207979reeRes @ ( produc1505598906reeRes @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le1762471042reeRes @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_199_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr1294453099i_name,S: set_Pr1294453099i_name] :
% 3.03/1.62 ( ! [X5: name > noption_pi,Y: name] :
% 3.03/1.62 ( ( member1353687244i_name @ ( produc540578151i_name @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member1353687244i_name @ ( produc540578151i_name @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le2082425291i_name @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_200_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr1694908217_pi_pi,S: set_Pr1694908217_pi_pi] :
% 3.03/1.62 ( ! [X5: name > noption_pi,Y: pi] :
% 3.03/1.62 ( ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member772629402_pi_pi @ ( produc1820286517_pi_pi @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le1854926745_pi_pi @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_201_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr1569510577ion_pi,S: set_Pr1569510577ion_pi] :
% 3.03/1.62 ( ! [X5: name > noption_pi,Y: name > noption_pi] :
% 3.03/1.62 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member1632198138ion_pi @ ( produc1342893193ion_pi @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le1032043601ion_pi @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_202_subrelI,axiom,
% 3.03/1.62 ! [R2: set_Pr1834926343_pi_pi,S: set_Pr1834926343_pi_pi] :
% 3.03/1.62 ( ! [X5: pi,Y: pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X5 @ Y ) @ R2 )
% 3.03/1.62 => ( member558706512_pi_pi @ ( product_Pair_pi_pi @ X5 @ Y ) @ S ) )
% 3.03/1.62 => ( ord_le630093991_pi_pi @ R2 @ S ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_203_IdE,axiom,
% 3.03/1.62 ! [P8: produc1462499409ion_pi] :
% 3.03/1.62 ( ( member1632198138ion_pi @ P8 @ id_name_noption_pi )
% 3.03/1.62 => ~ ! [X5: name > noption_pi] :
% 3.03/1.62 ( P8
% 3.03/1.62 != ( produc1342893193ion_pi @ X5 @ X5 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_204_IdE,axiom,
% 3.03/1.62 ! [P8: product_prod_pi_pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ P8 @ id_pi )
% 3.03/1.62 => ~ ! [X5: pi] :
% 3.03/1.62 ( P8
% 3.03/1.62 != ( product_Pair_pi_pi @ X5 @ X5 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_205_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_subject,Y2: late_subject] :
% 3.03/1.62 ( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_717452603ubject @ A @ X )
% 3.03/1.62 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_206_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_subject,Y2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_717452603ubject @ A @ X )
% 3.03/1.62 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_207_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_subject,Y2: name] :
% 3.03/1.62 ( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_717452603ubject @ A @ X )
% 3.03/1.62 & ( fresh_name_name @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_208_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_subject,Y2: pi] :
% 3.03/1.62 ( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_717452603ubject @ A @ X )
% 3.03/1.62 & ( fresh_name_pi @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_209_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_freeRes,Y2: late_subject] :
% 3.03/1.62 ( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.03/1.62 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_210_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_freeRes,Y2: late_freeRes] :
% 3.03/1.62 ( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.03/1.62 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_211_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_freeRes,Y2: name] :
% 3.03/1.62 ( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.03/1.62 & ( fresh_name_name @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_212_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: late_freeRes,Y2: pi] :
% 3.03/1.62 ( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_1641682979reeRes @ A @ X )
% 3.03/1.62 & ( fresh_name_pi @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_213_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: name,Y2: late_subject] :
% 3.03/1.62 ( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X )
% 3.03/1.62 & ( fresh_717452603ubject @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_214_fresh__prod,axiom,
% 3.03/1.62 ! [A: name,X: name,Y2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y2 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X )
% 3.03/1.62 & ( fresh_1641682979reeRes @ A @ Y2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_215_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: late_subject,A6: name > noption_pi,B6: late_subject] :
% 3.03/1.62 ( ( ( produc581368530ubject @ A @ B )
% 3.03/1.62 = ( produc581368530ubject @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_216_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: late_freeRes,A6: name > noption_pi,B6: late_freeRes] :
% 3.03/1.62 ( ( ( produc1505598906reeRes @ A @ B )
% 3.03/1.62 = ( produc1505598906reeRes @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_217_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name,A6: name > noption_pi,B6: name] :
% 3.03/1.62 ( ( ( produc540578151i_name @ A @ B )
% 3.03/1.62 = ( produc540578151i_name @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_218_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: pi,A6: name > noption_pi,B6: pi] :
% 3.03/1.62 ( ( ( produc1820286517_pi_pi @ A @ B )
% 3.03/1.62 = ( produc1820286517_pi_pi @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_219_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name > noption_pi,A6: name > noption_pi,B6: name > noption_pi] :
% 3.03/1.62 ( ( ( produc1342893193ion_pi @ A @ B )
% 3.03/1.62 = ( produc1342893193ion_pi @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_220_old_Oprod_Oinject,axiom,
% 3.03/1.62 ! [A: pi,B: pi,A6: pi,B6: pi] :
% 3.03/1.62 ( ( ( product_Pair_pi_pi @ A @ B )
% 3.03/1.62 = ( product_Pair_pi_pi @ A6 @ B6 ) )
% 3.03/1.62 = ( ( A = A6 )
% 3.03/1.62 & ( B = B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_221_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y22: late_subject] :
% 3.03/1.62 ( ( ( produc581368530ubject @ X1 @ X2 )
% 3.03/1.62 = ( produc581368530ubject @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_222_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y22: late_freeRes] :
% 3.03/1.62 ( ( ( produc1505598906reeRes @ X1 @ X2 )
% 3.03/1.62 = ( produc1505598906reeRes @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_223_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y22: name] :
% 3.03/1.62 ( ( ( produc540578151i_name @ X1 @ X2 )
% 3.03/1.62 = ( produc540578151i_name @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_224_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y22: pi] :
% 3.03/1.62 ( ( ( produc1820286517_pi_pi @ X1 @ X2 )
% 3.03/1.62 = ( produc1820286517_pi_pi @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_225_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y22: name > noption_pi] :
% 3.03/1.62 ( ( ( produc1342893193ion_pi @ X1 @ X2 )
% 3.03/1.62 = ( produc1342893193ion_pi @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_226_prod_Oinject,axiom,
% 3.03/1.62 ! [X1: pi,X2: pi,Y1: pi,Y22: pi] :
% 3.03/1.62 ( ( ( product_Pair_pi_pi @ X1 @ X2 )
% 3.03/1.62 = ( product_Pair_pi_pi @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X1 = Y1 )
% 3.03/1.62 & ( X2 = Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_227_surj__pair,axiom,
% 3.03/1.62 ! [P8: produc691362330ubject] :
% 3.03/1.62 ? [X5: name > noption_pi,Y: late_subject] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( produc581368530ubject @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_228_surj__pair,axiom,
% 3.03/1.62 ! [P8: produc1834551554reeRes] :
% 3.03/1.62 ? [X5: name > noption_pi,Y: late_freeRes] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( produc1505598906reeRes @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_229_surj__pair,axiom,
% 3.03/1.62 ! [P8: produc405342261i_name] :
% 3.03/1.62 ? [X5: name > noption_pi,Y: name] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( produc540578151i_name @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_230_surj__pair,axiom,
% 3.03/1.62 ! [P8: produc629157763_pi_pi] :
% 3.03/1.62 ? [X5: name > noption_pi,Y: pi] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( produc1820286517_pi_pi @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_231_surj__pair,axiom,
% 3.03/1.62 ! [P8: produc1462499409ion_pi] :
% 3.03/1.62 ? [X5: name > noption_pi,Y: name > noption_pi] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( produc1342893193ion_pi @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_232_surj__pair,axiom,
% 3.03/1.62 ! [P8: product_prod_pi_pi] :
% 3.03/1.62 ? [X5: pi,Y: pi] :
% 3.03/1.62 ( P8
% 3.03/1.62 = ( product_Pair_pi_pi @ X5 @ Y ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_233_prod__cases,axiom,
% 3.03/1.62 ! [P: produc691362330ubject > $o,P8: produc691362330ubject] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_234_prod__cases,axiom,
% 3.03/1.62 ! [P: produc1834551554reeRes > $o,P8: produc1834551554reeRes] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_235_prod__cases,axiom,
% 3.03/1.62 ! [P: produc405342261i_name > $o,P8: produc405342261i_name] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: name] : ( P @ ( produc540578151i_name @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_236_prod__cases,axiom,
% 3.03/1.62 ! [P: produc629157763_pi_pi > $o,P8: produc629157763_pi_pi] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_237_prod__cases,axiom,
% 3.03/1.62 ! [P: produc1462499409ion_pi > $o,P8: produc1462499409ion_pi] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_238_prod__cases,axiom,
% 3.03/1.62 ! [P: product_prod_pi_pi > $o,P8: product_prod_pi_pi] :
% 3.03/1.62 ( ! [A3: pi,B5: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ P8 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_239_Pair__inject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: late_subject,A6: name > noption_pi,B6: late_subject] :
% 3.03/1.62 ( ( ( produc581368530ubject @ A @ B )
% 3.03/1.62 = ( produc581368530ubject @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_240_Pair__inject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: late_freeRes,A6: name > noption_pi,B6: late_freeRes] :
% 3.03/1.62 ( ( ( produc1505598906reeRes @ A @ B )
% 3.03/1.62 = ( produc1505598906reeRes @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_241_Pair__inject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name,A6: name > noption_pi,B6: name] :
% 3.03/1.62 ( ( ( produc540578151i_name @ A @ B )
% 3.03/1.62 = ( produc540578151i_name @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_242_Pair__inject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: pi,A6: name > noption_pi,B6: pi] :
% 3.03/1.62 ( ( ( produc1820286517_pi_pi @ A @ B )
% 3.03/1.62 = ( produc1820286517_pi_pi @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_243_Pair__inject,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name > noption_pi,A6: name > noption_pi,B6: name > noption_pi] :
% 3.03/1.62 ( ( ( produc1342893193ion_pi @ A @ B )
% 3.03/1.62 = ( produc1342893193ion_pi @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_244_Pair__inject,axiom,
% 3.03/1.62 ! [A: pi,B: pi,A6: pi,B6: pi] :
% 3.03/1.62 ( ( ( product_Pair_pi_pi @ A @ B )
% 3.03/1.62 = ( product_Pair_pi_pi @ A6 @ B6 ) )
% 3.03/1.62 => ~ ( ( A = A6 )
% 3.03/1.62 => ( B != B6 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_245_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: produc691362330ubject] :
% 3.03/1.62 ~ ! [A3: name > noption_pi,B5: late_subject] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( produc581368530ubject @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_246_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: produc1834551554reeRes] :
% 3.03/1.62 ~ ! [A3: name > noption_pi,B5: late_freeRes] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( produc1505598906reeRes @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_247_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: produc405342261i_name] :
% 3.03/1.62 ~ ! [A3: name > noption_pi,B5: name] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( produc540578151i_name @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_248_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: produc629157763_pi_pi] :
% 3.03/1.62 ~ ! [A3: name > noption_pi,B5: pi] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( produc1820286517_pi_pi @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_249_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: produc1462499409ion_pi] :
% 3.03/1.62 ~ ! [A3: name > noption_pi,B5: name > noption_pi] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( produc1342893193ion_pi @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_250_old_Oprod_Oexhaust,axiom,
% 3.03/1.62 ! [Y2: product_prod_pi_pi] :
% 3.03/1.62 ~ ! [A3: pi,B5: pi] :
% 3.03/1.62 ( Y2
% 3.03/1.62 != ( product_Pair_pi_pi @ A3 @ B5 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_251_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: late_subject] : ( P @ ( produc581368530ubject @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_252_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: late_freeRes] : ( P @ ( produc1505598906reeRes @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_253_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: name] : ( P @ ( produc540578151i_name @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_254_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: pi] : ( P @ ( produc1820286517_pi_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_255_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
% 3.03/1.62 ( ! [A3: name > noption_pi,B5: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_256_old_Oprod_Oinducts,axiom,
% 3.03/1.62 ! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
% 3.03/1.62 ( ! [A3: pi,B5: pi] : ( P @ ( product_Pair_pi_pi @ A3 @ B5 ) )
% 3.03/1.62 => ( P @ Prod ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_257_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: late_subject] :
% 3.03/1.62 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_717452603ubject @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_258_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_1641682979reeRes @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_259_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: name] :
% 3.03/1.62 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_name_name @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_260_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: pi] :
% 3.03/1.62 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_name_pi @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_261_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: name > noption_pi] :
% 3.03/1.62 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_262_fresh__prodD_I2_J,axiom,
% 3.03/1.62 ! [A: name,X: pi,Y2: pi] :
% 3.03/1.62 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_name_pi @ A @ Y2 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_263_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: late_subject] :
% 3.03/1.62 ( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_264_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: late_freeRes] :
% 3.03/1.62 ( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_265_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: name] :
% 3.03/1.62 ( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_266_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: pi] :
% 3.03/1.62 ( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_267_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: name > noption_pi,Y2: name > noption_pi] :
% 3.03/1.62 ( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_543891186ion_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_268_fresh__prodD_I1_J,axiom,
% 3.03/1.62 ! [A: name,X: pi,Y2: pi] :
% 3.03/1.62 ( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y2 ) )
% 3.03/1.62 => ( fresh_name_pi @ A @ X ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_269_IdD,axiom,
% 3.03/1.62 ! [A: name > noption_pi,B: name > noption_pi] :
% 3.03/1.62 ( ( member1632198138ion_pi @ ( produc1342893193ion_pi @ A @ B ) @ id_name_noption_pi )
% 3.03/1.62 => ( A = B ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_270_IdD,axiom,
% 3.03/1.62 ! [A: pi,B: pi] :
% 3.03/1.62 ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ A @ B ) @ id_pi )
% 3.03/1.62 => ( A = B ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_271_resTauOutputTrans,axiom,
% 3.03/1.62 ! [X: name,P: pi,A: name,B: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_272_residual_Ofresh_I1_J,axiom,
% 3.03/1.62 ! [A: name,X3: late_subject,X1: name,X2: pi] :
% 3.03/1.62 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X3 @ X1 @ X2 ) )
% 3.03/1.62 = ( ( fresh_717452603ubject @ A @ X3 )
% 3.03/1.62 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_273_pi_Ofresh_I3_J,axiom,
% 3.03/1.62 ! [A: name,X1: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 3.03/1.62 = ( fresh_name_pi @ A @ X1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_274_simps_I2_J,axiom,
% 3.03/1.62 ! [P: pi,C2: name,D: name] :
% 3.03/1.62 ( ( subs @ ( tau @ P ) @ C2 @ D )
% 3.03/1.62 = ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_275_pi_Ofresh_I9_J,axiom,
% 3.03/1.62 ! [A: name,X1: name,X2: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 3.03/1.62 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_276_pi_Ofresh_I4_J,axiom,
% 3.03/1.62 ! [A: name,X3: name,X1: name,X2: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( input @ X3 @ X1 @ X2 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X3 )
% 3.03/1.62 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_277_name__fresh__abs,axiom,
% 3.03/1.62 ! [B: name,A: name,X: late_subject] :
% 3.03/1.62 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_278_name__fresh__abs,axiom,
% 3.03/1.62 ! [B: name,A: name,X: late_freeRes] :
% 3.03/1.62 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_279_name__fresh__abs,axiom,
% 3.03/1.62 ! [B: name,A: name,X: name] :
% 3.03/1.62 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_name_name @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_280_name__fresh__abs,axiom,
% 3.03/1.62 ! [B: name,A: name,X: pi] :
% 3.03/1.62 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_281_abs__fresh_I1_J,axiom,
% 3.03/1.62 ! [B: name,A: name,X: late_subject] :
% 3.03/1.62 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_282_abs__fresh_I1_J,axiom,
% 3.03/1.62 ! [B: name,A: name,X: late_freeRes] :
% 3.03/1.62 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_283_abs__fresh_I1_J,axiom,
% 3.03/1.62 ! [B: name,A: name,X: name] :
% 3.03/1.62 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_name_name @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_284_abs__fresh_I1_J,axiom,
% 3.03/1.62 ! [B: name,A: name,X: pi] :
% 3.03/1.62 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.03/1.62 = ( ( B = A )
% 3.03/1.62 | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_285_pi_Oinject_I2_J,axiom,
% 3.03/1.62 ! [X1: pi,Y1: pi] :
% 3.03/1.62 ( ( ( tau @ X1 )
% 3.03/1.62 = ( tau @ Y1 ) )
% 3.03/1.62 = ( X1 = Y1 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_286_pi_Odistinct_I3_J,axiom,
% 3.03/1.62 ! [Pi: pi] :
% 3.03/1.62 ( piNil
% 3.03/1.62 != ( tau @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_287_pi_Odistinct_I19_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi: pi] :
% 3.03/1.62 ( ( output @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( tau @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_288_pi_Odistinct_I35_J,axiom,
% 3.03/1.62 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.03/1.62 ( ( tau @ Pi3 )
% 3.03/1.62 != ( input @ Name1 @ Name2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_289_pi_Odistinct_I41_J,axiom,
% 3.03/1.62 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( tau @ Pi3 )
% 3.03/1.62 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_290_pi_Odistinct_I43_J,axiom,
% 3.03/1.62 ! [Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( tau @ Pi3 )
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_291_pi_Odistinct_I45_J,axiom,
% 3.03/1.62 ! [Pi3: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( tau @ Pi3 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_292_pi_Oinject_I3_J,axiom,
% 3.03/1.62 ! [X3: name,X1: name,X2: pi,Y3: name,Y1: name,Y22: pi] :
% 3.03/1.62 ( ( ( input @ X3 @ X1 @ X2 )
% 3.03/1.62 = ( input @ Y3 @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X3 = Y3 )
% 3.03/1.62 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.03/1.62 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_293_residual_Oinject_I1_J,axiom,
% 3.03/1.62 ! [X3: late_subject,X1: name,X2: pi,Y3: late_subject,Y1: name,Y22: pi] :
% 3.03/1.62 ( ( ( late_BoundR @ X3 @ X1 @ X2 )
% 3.03/1.62 = ( late_BoundR @ Y3 @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( X3 = Y3 )
% 3.03/1.62 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.03/1.62 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_294_pi_Oinject_I8_J,axiom,
% 3.03/1.62 ! [X1: name,X2: pi,Y1: name,Y22: pi] :
% 3.03/1.62 ( ( ( res @ X1 @ X2 )
% 3.03/1.62 = ( res @ Y1 @ Y22 ) )
% 3.03/1.62 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.03/1.62 = ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_295_tauBoundTrans,axiom,
% 3.03/1.62 ! [P: pi,A: late_subject,X: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_296_nilSim_I1_J,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,P: pi] :
% 3.03/1.62 ~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_297_resTauBoundTrans,axiom,
% 3.03/1.62 ! [X: name,P: pi,A: late_subject,Y2: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y2 @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_298_tauOutputTrans,axiom,
% 3.03/1.62 ! [P: pi,A: name,B: name,P3: pi] :
% 3.03/1.62 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_299_tauCases,axiom,
% 3.03/1.62 ! [P: pi,Alpha: late_freeRes,P3: pi,Prop: late_freeRes > pi > $o] :
% 3.03/1.62 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
% 3.03/1.62 => ( ( ( Alpha = late_TauR )
% 3.03/1.62 => ( ( P = P3 )
% 3.03/1.62 => ( Prop @ late_TauR @ P ) ) )
% 3.03/1.62 => ( Prop @ Alpha @ P3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_300_tauCases_H,axiom,
% 3.03/1.62 ! [P: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 3.03/1.62 => ~ ! [P4: pi] :
% 3.03/1.62 ( ( ( tau @ P )
% 3.03/1.62 = ( tau @ P4 ) )
% 3.03/1.62 => ( Rs
% 3.03/1.62 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_301_Tau,axiom,
% 3.03/1.62 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_302_inputCases_H,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 3.03/1.62 => ~ ! [X5: name,A3: name,P4: pi] :
% 3.03/1.62 ( ( ( A = A3 )
% 3.03/1.62 & ( ( abs_fun_name_pi @ B @ P )
% 3.03/1.62 = ( abs_fun_name_pi @ X5 @ P4 ) ) )
% 3.03/1.62 => ( ( Rs
% 3.03/1.62 = ( late_BoundR @ ( late_InputS @ A3 ) @ X5 @ P4 ) )
% 3.03/1.62 => ( X5 = A3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_303_mismatchIdRight,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( ( A != B )
% 3.03/1.62 => ( strong743114133lation @ P @ Rel @ ( mismatch @ A @ B @ P ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_304_mismatchIdLeft,axiom,
% 3.03/1.62 ! [Rel: set_Pr1834926343_pi_pi,A: name,B: name,P: pi] :
% 3.03/1.62 ( ( ord_le630093991_pi_pi @ id_pi @ Rel )
% 3.03/1.62 => ( ( A != B )
% 3.03/1.62 => ( strong743114133lation @ ( mismatch @ A @ B @ P ) @ Rel @ P ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_305_pi_Ofresh_I6_J,axiom,
% 3.03/1.62 ! [A: name,X3: name,X2: name,X1: pi] :
% 3.03/1.62 ( ( fresh_name_pi @ A @ ( mismatch @ X3 @ X2 @ X1 ) )
% 3.03/1.62 = ( ( fresh_name_name @ A @ X3 )
% 3.03/1.62 & ( fresh_name_name @ A @ X2 )
% 3.03/1.62 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_306_pi_Odistinct_I39_J,axiom,
% 3.03/1.62 ! [Pi3: pi,Name1: name,Name2: name,Pi: pi] :
% 3.03/1.62 ( ( tau @ Pi3 )
% 3.03/1.62 != ( mismatch @ Name1 @ Name2 @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_307_mismatchCases,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.03/1.62 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.03/1.62 => ( ( ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( ( A != B )
% 3.03/1.62 => ( F @ A @ B ) ) )
% 3.03/1.62 => ( F @ A @ B ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_308_mismatchTrans,axiom,
% 3.03/1.62 ! [A: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_309_mismatchCases_H,axiom,
% 3.03/1.62 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.03/1.62 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.03/1.62 => ~ ! [P4: pi,A3: name,B5: name] :
% 3.03/1.62 ( ( ( A = A3 )
% 3.03/1.62 & ( B = B5 )
% 3.03/1.62 & ( P = P4 ) )
% 3.03/1.62 => ( ( late_transitions @ P4 @ Rs )
% 3.03/1.62 => ( A3 = B5 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_310_Mismatch,axiom,
% 3.03/1.62 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 3.03/1.62 ( ( late_transitions @ P @ Rs )
% 3.03/1.62 => ( ( A != B )
% 3.03/1.62 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_311_pi_Odistinct_I75_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Name: name,Pi: pi] :
% 3.03/1.62 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( res @ Name @ Pi ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_312_pi_Odistinct_I73_J,axiom,
% 3.03/1.62 ! [Name12: name,Name22: name,Pi3: pi,Pi12: pi,Pi22: pi] :
% 3.03/1.62 ( ( mismatch @ Name12 @ Name22 @ Pi3 )
% 3.03/1.62 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(conj_0,conjecture,
% 3.03/1.62 late_transitions @ ( res @ x @ ( sum @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ q2 ) ) ).
% 3.03/1.62 ------------------------
% 3.03/1.66 % (300)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_32500 for (2999ds/275Mi)
% 3.03/1.66 % (32766)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32500 for (2999ds/2Mi)
% 3.03/1.66 % (32766)Instruction limit reached!
% 3.03/1.66 % (32766)------------------------------
% 3.03/1.66 % (32766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.66 % (32766)Termination reason: Unknown
% 3.03/1.66 % (32766)Termination phase: shuffling
% 3.03/1.66
% 3.03/1.66 % (32766)Memory used [KB]: 1535
% 3.03/1.66 % (32766)Time elapsed: 0.003 s
% 3.03/1.66 % (32766)Instructions burned: 3 (million)
% 3.03/1.66 % (32766)------------------------------
% 3.03/1.66 % (32766)------------------------------
% 3.03/1.67 % (32763)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32500 for (2999ds/183Mi)
% 3.03/1.67 % (32764)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_32500 for (2999ds/4Mi)
% 3.03/1.67 % (32765)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_32500 for (2999ds/27Mi)
% 3.03/1.67 % (32767)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_32500 for (2999ds/2Mi)
% 3.03/1.67 % (301)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32500 for (2999ds/18Mi)
% 3.03/1.67 % (32767)Instruction limit reached!
% 3.03/1.67 % (32767)------------------------------
% 3.03/1.67 % (32767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (32767)Termination reason: Unknown
% 3.03/1.67 % (32767)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (32767)Memory used [KB]: 1407
% 3.03/1.67 % (32767)Time elapsed: 0.004 s
% 3.03/1.67 % (32767)Instructions burned: 3 (million)
% 3.03/1.67 % (32767)------------------------------
% 3.03/1.67 % (32767)------------------------------
% 3.03/1.67 % (32764)Instruction limit reached!
% 3.03/1.67 % (32764)------------------------------
% 3.03/1.67 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (32764)Termination reason: Unknown
% 3.03/1.67 % (32764)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (32764)Memory used [KB]: 1535
% 3.03/1.67 % (32764)Time elapsed: 0.005 s
% 3.03/1.67 % (32764)Instructions burned: 5 (million)
% 3.03/1.67 % (32764)------------------------------
% 3.03/1.67 % (32764)------------------------------
% 3.03/1.68 % (301)Instruction limit reached!
% 3.03/1.68 % (301)------------------------------
% 3.03/1.68 % (301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (301)Termination reason: Unknown
% 3.03/1.68 % (301)Termination phase: shuffling
% 3.03/1.68
% 3.03/1.68 % (301)Memory used [KB]: 1791
% 3.03/1.68 % (301)Time elapsed: 0.013 s
% 3.03/1.68 % (301)Instructions burned: 18 (million)
% 3.03/1.68 % (301)------------------------------
% 3.03/1.68 % (301)------------------------------
% 3.03/1.68 % (302)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32500 for (2999ds/3Mi)
% 3.03/1.68 % (302)Instruction limit reached!
% 3.03/1.68 % (302)------------------------------
% 3.03/1.68 % (302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (302)Termination reason: Unknown
% 3.03/1.68 % (302)Termination phase: shuffling
% 3.03/1.68
% 3.03/1.68 % (302)Memory used [KB]: 1535
% 3.03/1.68 % (302)Time elapsed: 0.003 s
% 3.03/1.68 % (302)Instructions burned: 3 (million)
% 3.03/1.68 % (302)------------------------------
% 3.03/1.68 % (302)------------------------------
% 3.03/1.68 % (32765)Instruction limit reached!
% 3.03/1.68 % (32765)------------------------------
% 3.03/1.68 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (32765)Termination reason: Unknown
% 3.03/1.68 % (32765)Termination phase: shuffling
% 3.03/1.68
% 3.03/1.68 % (32765)Memory used [KB]: 1918
% 3.03/1.68 % (32765)Time elapsed: 0.019 s
% 3.03/1.68 % (32765)Instructions burned: 28 (million)
% 3.03/1.68 % (32765)------------------------------
% 3.03/1.68 % (32765)------------------------------
% 3.03/1.69 % (300)First to succeed.
% 3.03/1.69 % (303)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_32500 for (2999ds/37Mi)
% 3.03/1.69 % (304)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_32500 for (2999ds/15Mi)
% 3.03/1.69 % (300)Refutation found. Thanks to Tanya!
% 3.03/1.69 % SZS status Theorem for DTF2THF_32500
% 3.03/1.69 % SZS output start Proof for DTF2THF_32500
% 3.03/1.69 thf(type_def_5, type, name: $tType).
% 3.03/1.69 thf(type_def_6, type, pi: $tType).
% 3.03/1.69 thf(type_def_8, type, late_freeRes: $tType).
% 3.03/1.69 thf(type_def_9, type, late_subject: $tType).
% 3.03/1.69 thf(type_def_10, type, late_residual: $tType).
% 3.03/1.69 thf(type_def_11, type, noption_name: $tType).
% 3.03/1.69 thf(type_def_12, type, noption_pi: $tType).
% 3.03/1.69 thf(type_def_13, type, noption_Late_freeRes: $tType).
% 3.03/1.69 thf(type_def_14, type, noption_Late_subject: $tType).
% 3.03/1.69 thf(type_def_15, type, produc1462499409ion_pi: $tType).
% 3.03/1.69 thf(type_def_16, type, produc405342261i_name: $tType).
% 3.03/1.69 thf(type_def_17, type, produc629157763_pi_pi: $tType).
% 3.03/1.69 thf(type_def_18, type, produc1834551554reeRes: $tType).
% 3.03/1.69 thf(type_def_19, type, produc691362330ubject: $tType).
% 3.03/1.69 thf(type_def_20, type, produc2008547984reeRes: $tType).
% 3.03/1.69 thf(type_def_21, type, produc865358760ubject: $tType).
% 3.03/1.69 thf(type_def_22, type, product_prod_pi_pi: $tType).
% 3.03/1.69 thf(type_def_23, type, produc2052722628s_name: $tType).
% 3.03/1.69 thf(type_def_24, type, produc992857746Res_pi: $tType).
% 3.03/1.69 thf(type_def_25, type, produc1357834675reeRes: $tType).
% 3.03/1.69 thf(type_def_26, type, produc214645451ubject: $tType).
% 3.03/1.69 thf(type_def_27, type, produc1998742700t_name: $tType).
% 3.03/1.69 thf(type_def_28, type, produc140253050ect_pi: $tType).
% 3.03/1.69 thf(type_def_29, type, produc355105483reeRes: $tType).
% 3.03/1.69 thf(type_def_30, type, produc1359399907ubject: $tType).
% 3.03/1.69 thf(type_def_31, type, set_Pr1569510577ion_pi: $tType).
% 3.03/1.69 thf(type_def_32, type, set_Pr1294453099i_name: $tType).
% 3.03/1.69 thf(type_def_33, type, set_Pr1694908217_pi_pi: $tType).
% 3.03/1.69 thf(type_def_34, type, set_Pr305743074reeRes: $tType).
% 3.03/1.69 thf(type_def_35, type, set_Pr248416762ubject: $tType).
% 3.03/1.69 thf(type_def_36, type, set_Pr1834926343_pi_pi: $tType).
% 3.03/1.69 thf(func_def_0, type, set_Pr1569510577ion_pi: $tType).
% 3.03/1.69 thf(func_def_1, type, produc1462499409ion_pi: $tType).
% 3.03/1.69 thf(func_def_2, type, set_Pr248416762ubject: $tType).
% 3.03/1.69 thf(func_def_3, type, set_Pr305743074reeRes: $tType).
% 3.03/1.69 thf(func_def_4, type, set_Pr1294453099i_name: $tType).
% 3.03/1.69 thf(func_def_5, type, produc691362330ubject: $tType).
% 3.03/1.69 thf(func_def_6, type, produc1834551554reeRes: $tType).
% 3.03/1.69 thf(func_def_7, type, set_Pr1694908217_pi_pi: $tType).
% 3.03/1.69 thf(func_def_8, type, produc405342261i_name: $tType).
% 3.03/1.69 thf(func_def_9, type, produc629157763_pi_pi: $tType).
% 3.03/1.69 thf(func_def_10, type, produc1359399907ubject: $tType).
% 3.03/1.69 thf(func_def_11, type, produc355105483reeRes: $tType).
% 3.03/1.69 thf(func_def_12, type, produc214645451ubject: $tType).
% 3.03/1.69 thf(func_def_13, type, produc1357834675reeRes: $tType).
% 3.03/1.69 thf(func_def_14, type, produc1998742700t_name: $tType).
% 3.03/1.69 thf(func_def_15, type, produc2052722628s_name: $tType).
% 3.03/1.69 thf(func_def_16, type, produc865358760ubject: $tType).
% 3.03/1.69 thf(func_def_17, type, produc2008547984reeRes: $tType).
% 3.03/1.69 thf(func_def_18, type, produc140253050ect_pi: $tType).
% 3.03/1.69 thf(func_def_19, type, produc992857746Res_pi: $tType).
% 3.03/1.69 thf(func_def_20, type, set_Pr1834926343_pi_pi: $tType).
% 3.03/1.69 thf(func_def_21, type, product_prod_pi_pi: $tType).
% 3.03/1.69 thf(func_def_22, type, noption_Late_subject: $tType).
% 3.03/1.69 thf(func_def_23, type, noption_Late_freeRes: $tType).
% 3.03/1.69 thf(func_def_24, type, noption_name: $tType).
% 3.03/1.69 thf(func_def_25, type, noption_pi: $tType).
% 3.03/1.69 thf(func_def_26, type, late_residual: $tType).
% 3.03/1.69 thf(func_def_27, type, late_subject: $tType).
% 3.03/1.69 thf(func_def_28, type, late_freeRes: $tType).
% 3.03/1.69 thf(func_def_29, type, name: $tType).
% 3.03/1.69 thf(func_def_30, type, pi: $tType).
% 3.03/1.69 thf(func_def_31, type, input: name > name > pi > pi).
% 3.03/1.69 thf(func_def_32, type, mismatch: name > name > pi > pi).
% 3.03/1.69 thf(func_def_33, type, output: name > name > pi > pi).
% 3.03/1.69 thf(func_def_34, type, par: pi > pi > pi).
% 3.03/1.69 thf(func_def_35, type, piNil: pi).
% 3.03/1.69 thf(func_def_36, type, res: name > pi > pi).
% 3.03/1.69 thf(func_def_37, type, sum: pi > pi > pi).
% 3.03/1.69 thf(func_def_38, type, tau: pi > pi).
% 3.03/1.69 thf(func_def_39, type, subs: pi > name > name > pi).
% 3.03/1.69 thf(func_def_40, type, late_OutputR: name > name > late_freeRes).
% 3.03/1.69 thf(func_def_41, type, late_TauR: late_freeRes).
% 3.03/1.69 thf(func_def_42, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.03/1.69 thf(func_def_43, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.03/1.69 thf(func_def_44, type, late_BoundOutputS: name > late_subject).
% 3.03/1.69 thf(func_def_45, type, late_InputS: name > late_subject).
% 3.03/1.69 thf(func_def_46, type, late_transitions: pi > late_residual > $o).
% 3.03/1.69 thf(func_def_47, type, abs_fun_name_name: name > name > name > noption_name).
% 3.03/1.69 thf(func_def_48, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 3.03/1.69 thf(func_def_49, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 3.03/1.69 thf(func_def_50, type, abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject).
% 3.03/1.69 thf(func_def_51, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 3.03/1.69 thf(func_def_52, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 3.03/1.69 thf(func_def_53, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 3.03/1.69 thf(func_def_54, type, fresh_728038529ubject: name > (name > noption_Late_subject) > $o).
% 3.03/1.69 thf(func_def_55, type, fresh_name_name: name > name > $o).
% 3.03/1.69 thf(func_def_56, type, fresh_name_pi: name > pi > $o).
% 3.03/1.69 thf(func_def_57, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.03/1.69 thf(func_def_58, type, fresh_81631222sidual: name > late_residual > $o).
% 3.03/1.69 thf(func_def_59, type, fresh_717452603ubject: name > late_subject > $o).
% 3.03/1.69 thf(func_def_60, type, fresh_225680151ion_pi: name > produc1462499409ion_pi > $o).
% 3.03/1.69 thf(func_def_61, type, fresh_453496559i_name: name > produc405342261i_name > $o).
% 3.03/1.69 thf(func_def_62, type, fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o).
% 3.03/1.69 thf(func_def_63, type, fresh_1711070152reeRes: name > produc1834551554reeRes > $o).
% 3.03/1.69 thf(func_def_64, type, fresh_567880928ubject: name > produc691362330ubject > $o).
% 3.03/1.69 thf(func_def_65, type, fresh_1963366730reeRes: name > produc2008547984reeRes > $o).
% 3.03/1.69 thf(func_def_66, type, fresh_820177506ubject: name > produc865358760ubject > $o).
% 3.03/1.69 thf(func_def_67, type, fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o).
% 3.03/1.69 thf(func_def_68, type, fresh_2007541374s_name: name > produc2052722628s_name > $o).
% 3.03/1.69 thf(func_def_69, type, fresh_1847501388Res_pi: name > produc992857746Res_pi > $o).
% 3.03/1.69 thf(func_def_70, type, fresh_493808761reeRes: name > produc1357834675reeRes > $o).
% 3.03/1.69 thf(func_def_71, type, fresh_1498103185ubject: name > produc214645451ubject > $o).
% 3.03/1.69 thf(func_def_72, type, fresh_1953561446t_name: name > produc1998742700t_name > $o).
% 3.03/1.69 thf(func_def_73, type, fresh_994896692ect_pi: name > produc140253050ect_pi > $o).
% 3.03/1.69 thf(func_def_74, type, fresh_1638563217reeRes: name > produc355105483reeRes > $o).
% 3.03/1.69 thf(func_def_75, type, fresh_495373993ubject: name > produc1359399907ubject > $o).
% 3.03/1.69 thf(func_def_76, type, ord_le1032043601ion_pi: set_Pr1569510577ion_pi > set_Pr1569510577ion_pi > $o).
% 3.03/1.69 thf(func_def_77, type, ord_le2082425291i_name: set_Pr1294453099i_name > set_Pr1294453099i_name > $o).
% 3.03/1.69 thf(func_def_78, type, ord_le1854926745_pi_pi: set_Pr1694908217_pi_pi > set_Pr1694908217_pi_pi > $o).
% 3.03/1.69 thf(func_def_79, type, ord_le1762471042reeRes: set_Pr305743074reeRes > set_Pr305743074reeRes > $o).
% 3.03/1.69 thf(func_def_80, type, ord_le1705144730ubject: set_Pr248416762ubject > set_Pr248416762ubject > $o).
% 3.03/1.69 thf(func_def_81, type, ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.03/1.69 thf(func_def_82, type, produc1342893193ion_pi: (name > noption_pi) > (name > noption_pi) > produc1462499409ion_pi).
% 3.03/1.69 thf(func_def_83, type, produc540578151i_name: (name > noption_pi) > name > produc405342261i_name).
% 3.03/1.69 thf(func_def_84, type, produc1820286517_pi_pi: (name > noption_pi) > pi > produc629157763_pi_pi).
% 3.03/1.69 thf(func_def_85, type, produc1505598906reeRes: (name > noption_pi) > late_freeRes > produc1834551554reeRes).
% 3.03/1.69 thf(func_def_86, type, produc581368530ubject: (name > noption_pi) > late_subject > produc691362330ubject).
% 3.03/1.69 thf(func_def_87, type, produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes).
% 3.03/1.69 thf(func_def_88, type, produc607574050ubject: name > late_subject > produc865358760ubject).
% 3.03/1.69 thf(func_def_89, type, product_Pair_pi_pi: pi > pi > product_prod_pi_pi).
% 3.03/1.69 thf(func_def_90, type, produc1701355766s_name: late_freeRes > name > produc2052722628s_name).
% 3.03/1.69 thf(func_def_91, type, produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi).
% 3.03/1.69 thf(func_def_92, type, produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes).
% 3.03/1.69 thf(func_def_93, type, produc320590723ubject: late_freeRes > late_subject > produc214645451ubject).
% 3.03/1.69 thf(func_def_94, type, produc1647375838t_name: late_subject > name > produc1998742700t_name).
% 3.03/1.69 thf(func_def_95, type, produc324947500ect_pi: late_subject > pi > produc140253050ect_pi).
% 3.03/1.69 thf(func_def_96, type, produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes).
% 3.03/1.69 thf(func_def_97, type, produc1465345179ubject: late_subject > late_subject > produc1359399907ubject).
% 3.03/1.69 thf(func_def_98, type, eqvt_pi: set_Pr1834926343_pi_pi > $o).
% 3.03/1.69 thf(func_def_99, type, id_name_noption_pi: set_Pr1569510577ion_pi).
% 3.03/1.69 thf(func_def_100, type, id_pi: set_Pr1834926343_pi_pi).
% 3.03/1.69 thf(func_def_101, type, collec1051790738_pi_pi: (product_prod_pi_pi > $o) > set_Pr1834926343_pi_pi).
% 3.03/1.69 thf(func_def_102, type, strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o).
% 3.03/1.69 thf(func_def_103, type, strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o).
% 3.03/1.69 thf(func_def_104, type, member1632198138ion_pi: produc1462499409ion_pi > set_Pr1569510577ion_pi > $o).
% 3.03/1.69 thf(func_def_105, type, member1353687244i_name: produc405342261i_name > set_Pr1294453099i_name > $o).
% 3.03/1.69 thf(func_def_106, type, member772629402_pi_pi: produc629157763_pi_pi > set_Pr1694908217_pi_pi > $o).
% 3.03/1.69 thf(func_def_107, type, member2081207979reeRes: produc1834551554reeRes > set_Pr305743074reeRes > $o).
% 3.03/1.69 thf(func_def_108, type, member938018755ubject: produc691362330ubject > set_Pr248416762ubject > $o).
% 3.03/1.69 thf(func_def_109, type, member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o).
% 3.03/1.69 thf(func_def_110, type, p: pi).
% 3.03/1.69 thf(func_def_111, type, pq: pi).
% 3.03/1.69 thf(func_def_112, type, q: pi).
% 3.03/1.69 thf(func_def_113, type, q2: pi).
% 3.03/1.69 thf(func_def_114, type, rel: set_Pr1834926343_pi_pi).
% 3.03/1.69 thf(func_def_115, type, alpha: late_freeRes).
% 3.03/1.69 thf(func_def_116, type, x: name).
% 3.03/1.69 thf(func_def_134, type, sP0: pi > pi > late_subject > name > pi > $o).
% 3.03/1.69 thf(func_def_135, type, sK1: pi > name).
% 3.03/1.69 thf(func_def_136, type, sK2: pi > pi > late_subject > name > pi > pi).
% 3.03/1.69 thf(func_def_137, type, sK3: pi > pi > late_subject > name > pi > pi).
% 3.03/1.69 thf(func_def_138, type, sK4: pi > pi > late_subject > name > pi > pi).
% 3.03/1.69 thf(func_def_139, type, sK5: pi > pi > late_subject > name > pi > late_subject).
% 3.03/1.69 thf(func_def_140, type, sK6: pi > pi > late_subject > name > pi > name).
% 3.03/1.69 thf(func_def_141, type, sK7: late_subject > pi > pi > name > pi > name).
% 3.03/1.69 thf(func_def_142, type, sK8: late_subject > pi > pi > name > pi > pi).
% 3.03/1.69 thf(func_def_143, type, sK9: late_subject > pi > pi > name > pi > pi).
% 3.03/1.69 thf(func_def_144, type, sK10: late_subject > pi > pi > name > pi > late_subject).
% 3.03/1.69 thf(func_def_145, type, sK11: late_subject > pi > pi > name > pi > pi).
% 3.03/1.69 thf(func_def_146, type, sK12: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_147, type, sK13: (late_freeRes > late_residual > $o) > pi).
% 3.03/1.69 thf(func_def_148, type, sK14: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_149, type, sK15: (late_freeRes > late_residual > $o) > name).
% 3.03/1.69 thf(func_def_150, type, sK16: (late_freeRes > late_residual > $o) > pi).
% 3.03/1.69 thf(func_def_151, type, sK17: (late_freeRes > late_residual > $o) > late_subject).
% 3.03/1.69 thf(func_def_152, type, sK18: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_153, type, sK19: pi > name > late_freeRes > (pi > $o) > pi).
% 3.03/1.69 thf(func_def_154, type, sK20: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.03/1.69 thf(func_def_155, type, sK21: (pi > $o) > name > late_subject > pi > pi > pi).
% 3.03/1.69 thf(func_def_156, type, sK22: pi > pi > name > late_freeRes > pi).
% 3.03/1.69 thf(func_def_157, type, sK23: pi > pi > name > late_freeRes > name).
% 3.03/1.69 thf(func_def_158, type, sK24: pi > pi > name > late_freeRes > late_freeRes).
% 3.03/1.69 thf(func_def_159, type, sK25: pi > pi > name > late_freeRes > pi).
% 3.03/1.69 thf(func_def_160, type, sK26: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_161, type, sK27: (late_freeRes > late_residual > $o) > pi).
% 3.03/1.69 thf(func_def_162, type, sK28: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_163, type, sK29: (late_freeRes > late_residual > $o) > pi).
% 3.03/1.69 thf(func_def_164, type, sK30: (late_freeRes > late_residual > $o) > late_subject).
% 3.03/1.69 thf(func_def_165, type, sK31: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.03/1.69 thf(func_def_166, type, sK32: (late_freeRes > late_residual > $o) > name).
% 3.03/1.69 thf(func_def_167, type, sK33: late_freeRes > name).
% 3.03/1.69 thf(func_def_169, type, ph35: !>[X0: $tType]:(X0)).
% 3.03/1.69 thf(f987,plain,(
% 3.03/1.69 $false),
% 3.03/1.69 inference(subsumption_resolution,[status(thm)],[f986,f963])).
% 3.03/1.69 thf(f963,plain,(
% 3.03/1.69 ((fresh_1641682979reeRes @ x @ alpha) = $true)),
% 3.03/1.69 inference(cnf_transformation,[status(thm)],[f522])).
% 3.03/1.69 thf(f522,plain,(
% 3.03/1.69 ((fresh_1641682979reeRes @ x @ alpha) = $true)),
% 3.03/1.69 inference(fool_elimination,[status(thm)],[f521])).
% 3.03/1.69 thf(f521,plain,(
% 3.03/1.69 (fresh_1641682979reeRes @ x @ alpha)),
% 3.03/1.69 inference(rectify,[status(thm)],[f1])).
% 3.03/1.69 thf(f1,axiom,(
% 3.03/1.69 (fresh_1641682979reeRes @ x @ alpha)),
% 3.03/1.69 file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_0_cRes_Ohyps_I2_J)).
% 3.03/1.69 thf(f986,plain,(
% 3.03/1.69 ((fresh_1641682979reeRes @ x @ alpha) != $true)),
% 3.03/1.69 inference(subsumption_resolution,[status(thm)],[f985,f973])).
% 3.03/1.69 thf(f973,plain,(
% 3.03/1.69 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) = $true)),
% 3.03/1.69 inference(cnf_transformation,[status(thm)],[f500])).
% 3.03/1.69 thf(f500,plain,(
% 3.03/1.69 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) = $true)),
% 3.03/1.69 inference(fool_elimination,[status(thm)],[f499])).
% 3.03/1.69 thf(f499,plain,(
% 3.03/1.69 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 3.03/1.69 inference(rectify,[status(thm)],[f3])).
% 3.03/1.69 thf(f3,axiom,(
% 3.03/1.69 (late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2))),
% 3.03/1.69 file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_2__092_060open_062P_A_092_060oplus_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AQ_H_092_060close_062)).
% 3.03/1.69 thf(f985,plain,(
% 3.03/1.69 ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) != $true) | ((fresh_1641682979reeRes @ x @ alpha) != $true)),
% 3.03/1.69 inference(trivial_inequality_removal,[status(thm)],[f984])).
% 3.03/1.69 thf(f984,plain,(
% 3.03/1.69 ((fresh_1641682979reeRes @ x @ alpha) != $true) | ($true != $true) | ((late_transitions @ (sum @ p @ q) @ (late_FreeR @ alpha @ q2)) != $true)),
% 3.03/1.69 inference(superposition,[status(thm)],[f960,f943])).
% 3.03/1.69 thf(f943,plain,(
% 3.03/1.69 ( ! [X2 : name,X3 : pi,X0 : late_freeRes,X1 : pi] : (((late_transitions @ (res @ X2 @ X3) @ (late_FreeR @ X0 @ (res @ X2 @ X1))) = $true) | ((late_transitions @ X3 @ (late_FreeR @ X0 @ X1)) != $true) | ($true != (fresh_1641682979reeRes @ X2 @ X0))) )),
% 3.03/1.69 inference(cnf_transformation,[status(thm)],[f847])).
% 3.03/1.69 thf(f847,plain,(
% 3.03/1.69 ! [X0 : late_freeRes,X1 : pi,X2 : name,X3 : pi] : (($true != (fresh_1641682979reeRes @ X2 @ X0)) | ((late_transitions @ (res @ X2 @ X3) @ (late_FreeR @ X0 @ (res @ X2 @ X1))) = $true) | ((late_transitions @ X3 @ (late_FreeR @ X0 @ X1)) != $true))),
% 3.03/1.69 inference(flattening,[status(thm)],[f846])).
% 3.03/1.69 thf(f846,plain,(
% 3.03/1.69 ! [X0 : late_freeRes,X1 : pi,X2 : name,X3 : pi] : ((((late_transitions @ (res @ X2 @ X3) @ (late_FreeR @ X0 @ (res @ X2 @ X1))) = $true) | ($true != (fresh_1641682979reeRes @ X2 @ X0))) | ((late_transitions @ X3 @ (late_FreeR @ X0 @ X1)) != $true))),
% 3.03/1.69 inference(ennf_transformation,[status(thm)],[f820])).
% 3.03/1.69 thf(f820,plain,(
% 3.03/1.69 ! [X0 : late_freeRes,X1 : pi,X2 : name,X3 : pi] : (((late_transitions @ X3 @ (late_FreeR @ X0 @ X1)) = $true) => (($true = (fresh_1641682979reeRes @ X2 @ X0)) => ((late_transitions @ (res @ X2 @ X3) @ (late_FreeR @ X0 @ (res @ X2 @ X1))) = $true)))),
% 3.03/1.69 inference(fool_elimination,[status(thm)],[f819])).
% 3.03/1.69 thf(f819,plain,(
% 3.03/1.69 ! [X0 : late_freeRes,X1 : pi,X2 : name,X3 : pi] : ((late_transitions @ X3 @ (late_FreeR @ X0 @ X1)) => ((fresh_1641682979reeRes @ X2 @ X0) => (late_transitions @ (res @ X2 @ X3) @ (late_FreeR @ X0 @ (res @ X2 @ X1)))))),
% 3.03/1.69 inference(rectify,[status(thm)],[f14])).
% 3.03/1.69 thf(f14,axiom,(
% 3.03/1.69 ! [X8 : late_freeRes,X12 : pi,X16 : name,X4 : pi] : ((late_transitions @ X4 @ (late_FreeR @ X8 @ X12)) => ((fresh_1641682979reeRes @ X16 @ X8) => (late_transitions @ (res @ X16 @ X4) @ (late_FreeR @ X8 @ (res @ X16 @ X12)))))),
% 3.03/1.69 file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',fact_13_ResF)).
% 3.03/1.69 thf(f960,plain,(
% 3.03/1.69 ((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) != $true)),
% 3.03/1.69 inference(cnf_transformation,[status(thm)],[f823])).
% 3.03/1.69 thf(f823,plain,(
% 3.03/1.69 ((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) != $true)),
% 3.03/1.69 inference(flattening,[status(thm)],[f748])).
% 3.03/1.69 thf(f748,plain,(
% 3.03/1.69 ~((late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2))) = $true)),
% 3.03/1.69 inference(fool_elimination,[status(thm)],[f747])).
% 3.03/1.69 thf(f747,plain,(
% 3.03/1.69 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 3.03/1.69 inference(rectify,[status(thm)],[f315])).
% 3.03/1.69 thf(f315,negated_conjecture,(
% 3.03/1.69 ~(late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 3.03/1.69 inference(negated_conjecture,[status(cth)],[f314])).
% 3.03/1.69 thf(f314,conjecture,(
% 3.03/1.69 (late_transitions @ (res @ x @ (sum @ p @ q)) @ (late_FreeR @ alpha @ (res @ x @ q2)))),
% 3.03/1.69 file('/export/starexec/sandbox2/tmp/tmp.UlTV8PhTY9/DTF2THF_32500.p',conj_0)).
% 3.03/1.69 % SZS output end Proof for DTF2THF_32500
% 3.03/1.69 % (300)------------------------------
% 3.03/1.69 % (300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.69 % (300)Termination reason: Refutation
% 3.03/1.69
% 3.03/1.69 % (300)Memory used [KB]: 6908
% 3.03/1.69 % (300)Time elapsed: 0.027 s
% 3.03/1.69 % (300)Instructions burned: 77 (million)
% 3.03/1.69 % (300)------------------------------
% 3.03/1.69 % (300)------------------------------
% 3.03/1.69 % (32762)Success in time 0.06 s
%------------------------------------------------------------------------------