TPTP Problem File: ITP192^1.p
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%------------------------------------------------------------------------------
% File : ITP192^1 : TPTP v9.0.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Strong_Late_Sim_SC problem prob_997__3418970_1
% Version : Especial.
% English :
% Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source : [Des21]
% Names : Strong_Late_Sim_SC/prob_997__3418970_1 [Des21]
% Status : Theorem
% Rating : 0.38 v9.0.0, 0.50 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% Syntax : Number of formulae : 430 ( 191 unt; 108 typ; 0 def)
% Number of atoms : 882 ( 354 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 4221 ( 172 ~; 11 |; 81 &;3382 @)
% ( 0 <=>; 575 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 289 ( 289 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 82 usr; 16 con; 0-5 aty)
% Number of variables : 1667 ( 9 ^;1620 !; 38 ?;1667 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:33:03.231
%------------------------------------------------------------------------------
% Could-be-implicit typings (26)
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,
produc1462499409ion_pi: $tType ).
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,
produc691362330ubject: $tType ).
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,
produc1834551554reeRes: $tType ).
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,
produc405342261i_name: $tType ).
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,
produc629157763_pi_pi: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
produc1359399907ubject: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
produc355105483reeRes: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
produc214645451ubject: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
produc1357834675reeRes: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
produc1998742700t_name: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
produc2052722628s_name: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
produc865358760ubject: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
produc2008547984reeRes: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
produc140253050ect_pi: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
produc992857746Res_pi: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
set_Pr1834926343_pi_pi: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
product_prod_pi_pi: $tType ).
thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
noption_Late_subject: $tType ).
thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
noption_Late_freeRes: $tType ).
thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
noption_name: $tType ).
thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
noption_pi: $tType ).
thf(ty_n_t__Late____Semantics__Oresidual,type,
late_residual: $tType ).
thf(ty_n_t__Late____Semantics__Osubject,type,
late_subject: $tType ).
thf(ty_n_t__Late____Semantics__OfreeRes,type,
late_freeRes: $tType ).
thf(ty_n_t__Agent__Oname,type,
name: $tType ).
thf(ty_n_t__Agent__Opi,type,
pi: $tType ).
% Explicit typings (82)
thf(sy_c_Agent_Opi_OBang,type,
bang: pi > pi ).
thf(sy_c_Agent_Opi_OInput,type,
input: name > name > pi > pi ).
thf(sy_c_Agent_Opi_OMatch,type,
match: name > name > pi > pi ).
thf(sy_c_Agent_Opi_OMismatch,type,
mismatch: name > name > pi > pi ).
thf(sy_c_Agent_Opi_OOutput,type,
output: name > name > pi > pi ).
thf(sy_c_Agent_Opi_OPar,type,
par: pi > pi > pi ).
thf(sy_c_Agent_Opi_OPiNil,type,
piNil: pi ).
thf(sy_c_Agent_Opi_ORes,type,
res: name > pi > pi ).
thf(sy_c_Agent_Opi_OSum,type,
sum: pi > pi > pi ).
thf(sy_c_Agent_Opi_OTau,type,
tau: pi > pi ).
thf(sy_c_Agent_Osubs,type,
subs: pi > name > name > pi ).
thf(sy_c_Agent_Osubst__name,type,
subst_name: name > name > name > name ).
thf(sy_c_If_001t__Agent__Oname,type,
if_name: $o > name > name > name ).
thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
late_OutputR: name > name > late_freeRes ).
thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
late_TauR: late_freeRes ).
thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
late_BoundOutputS: name > late_subject ).
thf(sy_c_Late__Semantics_Osubject_OInputS,type,
late_InputS: name > late_subject ).
thf(sy_c_Late__Semantics_Otransitions,type,
late_transitions: pi > late_residual > $o ).
thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Oname,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Agent__Opi,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Oname,type,
fresh_name_name: name > name > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Agent__Opi,type,
fresh_name_pi: name > pi > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Oresidual,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
fresh_717452603ubject: name > late_subject > $o ).
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,
fresh_225680151ion_pi: name > produc1462499409ion_pi > $o ).
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,
fresh_453496559i_name: name > produc405342261i_name > $o ).
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,
fresh_253309757_pi_pi: name > produc629157763_pi_pi > $o ).
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,
fresh_1711070152reeRes: name > produc1834551554reeRes > $o ).
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,
fresh_567880928ubject: name > produc691362330ubject > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__OfreeRes_J,type,
fresh_1963366730reeRes: name > produc2008547984reeRes > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Late____Semantics__Osubject_J,type,
fresh_820177506ubject: name > produc865358760ubject > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
fresh_1627595501_pi_pi: name > product_prod_pi_pi > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
fresh_2007541374s_name: name > produc2052722628s_name > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
fresh_1847501388Res_pi: name > produc992857746Res_pi > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
fresh_493808761reeRes: name > produc1357834675reeRes > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
fresh_1498103185ubject: name > produc214645451ubject > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
fresh_1953561446t_name: name > produc1998742700t_name > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
fresh_994896692ect_pi: name > produc140253050ect_pi > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
fresh_1638563217reeRes: name > produc355105483reeRes > $o ).
thf(sy_c_Nominal_Ofresh_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
fresh_495373993ubject: name > produc1359399907ubject > $o ).
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,
produc1342893193ion_pi: ( name > noption_pi ) > ( name > noption_pi ) > produc1462499409ion_pi ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Oname,type,
produc540578151i_name: ( name > noption_pi ) > name > produc405342261i_name ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Agent__Opi,type,
produc1820286517_pi_pi: ( name > noption_pi ) > pi > produc629157763_pi_pi ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__OfreeRes,type,
produc1505598906reeRes: ( name > noption_pi ) > late_freeRes > produc1834551554reeRes ).
thf(sy_c_Product__Type_OPair_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_001t__Late____Semantics__Osubject,type,
produc581368530ubject: ( name > noption_pi ) > late_subject > produc691362330ubject ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__OfreeRes,type,
produc1531804426reeRes: name > late_freeRes > produc2008547984reeRes ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Late____Semantics__Osubject,type,
produc607574050ubject: name > late_subject > produc865358760ubject ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Opi,type,
product_Pair_pi_pi: pi > pi > product_prod_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
produc1701355766s_name: late_freeRes > name > produc2052722628s_name ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Agent__Opi,type,
produc1177552196Res_pi: late_freeRes > pi > produc992857746Res_pi ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__OfreeRes,type,
produc1244821099reeRes: late_freeRes > late_freeRes > produc1357834675reeRes ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__OfreeRes_001t__Late____Semantics__Osubject,type,
produc320590723ubject: late_freeRes > late_subject > produc214645451ubject ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
produc1647375838t_name: late_subject > name > produc1998742700t_name ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Agent__Opi,type,
produc324947500ect_pi: late_subject > pi > produc140253050ect_pi ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__OfreeRes,type,
produc242091907reeRes: late_subject > late_freeRes > produc355105483reeRes ).
thf(sy_c_Product__Type_OPair_001t__Late____Semantics__Osubject_001t__Late____Semantics__Osubject,type,
produc1465345179ubject: late_subject > late_subject > produc1359399907ubject ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
collec1051790738_pi_pi: ( product_prod_pi_pi > $o ) > set_Pr1834926343_pi_pi ).
thf(sy_c_Strong__Late__Sim_Oderivative,type,
strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Strong__Late__Sim_Osimulation,type,
strong743114133lation: pi > set_Pr1834926343_pi_pi > pi > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
member558706512_pi_pi: product_prod_pi_pi > set_Pr1834926343_pi_pi > $o ).
thf(sy_v_P,type,
p: pi ).
thf(sy_v_PQ____,type,
pq: pi ).
thf(sy_v_P_H____,type,
p2: pi ).
thf(sy_v_Q,type,
q: pi ).
thf(sy_v_Q_H____,type,
q2: pi ).
thf(sy_v_Rel,type,
rel: set_Pr1834926343_pi_pi ).
thf(sy_v__092_060alpha_062____,type,
alpha: late_freeRes ).
thf(sy_v_aa____,type,
aa: name ).
thf(sy_v_x,type,
x: name ).
thf(sy_v_xPQ____,type,
xPQ: pi ).
thf(sy_v_y____,type,
y: name ).
thf(sy_v_z____,type,
z: name ).
% Relevant facts (318)
thf(fact_0_cClose1_Ohyps_I3_J,axiom,
fresh_name_pi @ y @ p ).
% cClose1.hyps(3)
thf(fact_1_cClose1_Ohyps_I7_J,axiom,
fresh_name_pi @ y @ q2 ).
% cClose1.hyps(7)
thf(fact_2_cClose1_Ohyps_I6_J,axiom,
y != z ).
% cClose1.hyps(6)
thf(fact_3_assms_I1_J,axiom,
fresh_name_pi @ x @ p ).
% assms(1)
thf(fact_4_cClose1_Ohyps_I12_J,axiom,
fresh_name_name @ y @ x ).
% cClose1.hyps(12)
thf(fact_5_cClose1_Ohyps_I5_J,axiom,
y != aa ).
% cClose1.hyps(5)
thf(fact_6_cClose1_Ohyps_I4_J,axiom,
fresh_name_pi @ y @ q ).
% cClose1.hyps(4)
thf(fact_7_cClose1_Ohyps_I11_J,axiom,
fresh_name_pi @ z @ p2 ).
% cClose1.hyps(11)
thf(fact_8_cClose1_Ohyps_I1_J,axiom,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ aa ) @ y @ p2 ) ).
% cClose1.hyps(1)
thf(fact_9_cClose1_Ohyps_I10_J,axiom,
z != aa ).
% cClose1.hyps(10)
thf(fact_10_cClose1_Ohyps_I13_J,axiom,
fresh_name_name @ z @ x ).
% cClose1.hyps(13)
thf(fact_11_cClose1_Ohyps_I8_J,axiom,
fresh_name_pi @ z @ p ).
% cClose1.hyps(8)
thf(fact_12_cRes_Ohyps_I2_J,axiom,
fresh_1641682979reeRes @ x @ alpha ).
% cRes.hyps(2)
thf(fact_13_assms_I3_J,axiom,
eqvt_pi @ rel ).
% assms(3)
thf(fact_14_cClose1_Ohyps_I14_J,axiom,
alpha = late_TauR ).
% cClose1.hyps(14)
thf(fact_15_cClose1_Ohyps_I2_J,axiom,
late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ aa ) @ z @ q2 ) ).
% cClose1.hyps(2)
thf(fact_16_cClose1_Ohyps_I9_J,axiom,
fresh_name_pi @ z @ q ).
% cClose1.hyps(9)
thf(fact_17_Free_Ohyps,axiom,
late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ xPQ ) ).
% Free.hyps
thf(fact_18_cRes_Ohyps_I1_J,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ pq ) ).
% cRes.hyps(1)
thf(fact_19_freeRes_Ofresh_I2_J,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% freeRes.fresh(2)
thf(fact_20_pi_Ofresh_I8_J,axiom,
! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(8)
thf(fact_21_freshFreeDerivative_I1_J,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% freshFreeDerivative(1)
thf(fact_22_resCasesF,axiom,
! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
=> ( ! [P3: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha )
=> ( F @ ( res @ X @ P3 ) ) ) )
=> ( F @ XP ) ) ) ).
% resCasesF
thf(fact_23_resCasesF_H,axiom,
! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
( ( ( res @ X @ P )
= ( res @ Y2 @ P4 ) )
=> ( ( ( late_FreeR @ Alpha @ P2 )
= ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
=> ~ ( fresh_1641682979reeRes @ Y2 @ Alpha2 ) ) ) ) ) ).
% resCasesF'
thf(fact_24_ResF,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_1641682979reeRes @ Y @ Alpha )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% ResF
thf(fact_25_Res,axiom,
! [Y: name,R: pi,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R @ ( res @ Y @ S ) ) @ ( res @ Y @ ( par @ R @ S ) ) ) @ rel ) ) ).
% Res
thf(fact_26_ScopeExt,axiom,
! [Y: name,R: pi,Z: name,S: pi] :
( ( fresh_name_pi @ Y @ R )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ Z @ ( par @ R @ ( res @ Y @ S ) ) ) @ ( res @ Y @ ( res @ Z @ ( par @ R @ S ) ) ) ) @ rel ) ) ).
% ScopeExt
thf(fact_27_Late__Semantics_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ X @ Q )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% Late_Semantics.Par1B
thf(fact_28_Late__Semantics_OPar2B,axiom,
! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% Late_Semantics.Par2B
thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
! [X1: name,Y1: name] :
( ( ( late_BoundOutputS @ X1 )
= ( late_BoundOutputS @ Y1 ) )
= ( X1 = Y1 ) ) ).
% Late_Semantics.subject.inject(2)
thf(fact_30_name__fresh,axiom,
( fresh_name_name
= ( ^ [A2: name,B: name] : ( A2 != B ) ) ) ).
% name_fresh
thf(fact_31_name__exists__fresh,axiom,
! [X: late_subject] :
~ ! [C: name] :
~ ( fresh_717452603ubject @ C @ X ) ).
% name_exists_fresh
thf(fact_32_name__exists__fresh,axiom,
! [X: late_freeRes] :
~ ! [C: name] :
~ ( fresh_1641682979reeRes @ C @ X ) ).
% name_exists_fresh
thf(fact_33_name__exists__fresh,axiom,
! [X: name] :
~ ! [C: name] :
~ ( fresh_name_name @ C @ X ) ).
% name_exists_fresh
thf(fact_34_name__exists__fresh,axiom,
! [X: pi] :
~ ! [C: name] :
~ ( fresh_name_pi @ C @ X ) ).
% name_exists_fresh
thf(fact_35_pi_Oinject_I7_J,axiom,
! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y22 @ Y1 ) )
= ( ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(7)
thf(fact_36_residual_Oinject_I2_J,axiom,
! [X2: late_freeRes,X1: pi,Y22: late_freeRes,Y1: pi] :
( ( ( late_FreeR @ X2 @ X1 )
= ( late_FreeR @ Y22 @ Y1 ) )
= ( ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% residual.inject(2)
thf(fact_37_pi_Odistinct_I85_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(85)
thf(fact_38_freshRes,axiom,
! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% freshRes
thf(fact_39_residual_Oinducts,axiom,
! [P: late_residual > $o,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Residual ) ) ) ).
% residual.inducts
thf(fact_40_residual_Odistinct_I1_J,axiom,
! [Subject2: late_subject,Name3: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
( ( late_BoundR @ Subject2 @ Name3 @ Pi4 )
!= ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% residual.distinct(1)
thf(fact_41_subject_Oinducts,axiom,
! [P: late_subject > $o,Subject2: late_subject] :
( ! [Name2: name] : ( P @ ( late_InputS @ Name2 ) )
=> ( ! [Name2: name] : ( P @ ( late_BoundOutputS @ Name2 ) )
=> ( P @ Subject2 ) ) ) ).
% subject.inducts
thf(fact_42_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
! [Name3: name,Name: name] :
( ( late_InputS @ Name3 )
!= ( late_BoundOutputS @ Name ) ) ).
% Late_Semantics.subject.distinct(1)
thf(fact_43_Par2F,axiom,
! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% Par2F
thf(fact_44_Par1F,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% Par1F
thf(fact_45_freshBoundDerivative_I2_J,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( Y != X )
=> ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% freshBoundDerivative(2)
thf(fact_46_mem__Collect__eq,axiom,
! [A: product_prod_pi_pi,P: product_prod_pi_pi > $o] :
( ( member558706512_pi_pi @ A @ ( collec1051790738_pi_pi @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_47_Collect__mem__eq,axiom,
! [A3: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_48_Collect__cong,axiom,
! [P: product_prod_pi_pi > $o,Q: product_prod_pi_pi > $o] :
( ! [X4: product_prod_pi_pi] :
( ( P @ X4 )
= ( Q @ X4 ) )
=> ( ( collec1051790738_pi_pi @ P )
= ( collec1051790738_pi_pi @ Q ) ) ) ).
% Collect_cong
thf(fact_49_residual_Ostrong__inducts,axiom,
! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_50_residual_Ostrong__inducts,axiom,
! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_51_residual_Ostrong__inducts,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_52_residual_Ostrong__inducts,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_53_residual_Ostrong__induct,axiom,
! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_54_residual_Ostrong__induct,axiom,
! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_55_residual_Ostrong__induct,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_56_residual_Ostrong__induct,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject: late_subject,Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ( fresh_717452603ubject @ Name2 @ Subject )
=> ( P @ Z2 @ ( late_BoundR @ Subject @ Name2 @ Pi3 ) ) ) )
=> ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_57_freshFreeDerivative_I2_J,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_name_pi @ Y @ P2 ) ) ) ).
% freshFreeDerivative(2)
thf(fact_58_parCasesB,axiom,
! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ! [P3: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( Prop @ ( par @ P3 @ Q ) ) )
=> ( ! [Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
=> ( Prop @ ( par @ P @ Q3 ) ) )
=> ( Prop @ PQ ) ) ) ) ) ) ).
% parCasesB
thf(fact_59_fresh__prod,axiom,
! [A: name,X: late_subject,Y: late_subject] :
( ( fresh_495373993ubject @ A @ ( produc1465345179ubject @ X @ Y ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_717452603ubject @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_60_fresh__prod,axiom,
! [A: name,X: late_subject,Y: late_freeRes] :
( ( fresh_1638563217reeRes @ A @ ( produc242091907reeRes @ X @ Y ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_61_fresh__prod,axiom,
! [A: name,X: late_subject,Y: name] :
( ( fresh_1953561446t_name @ A @ ( produc1647375838t_name @ X @ Y ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_62_fresh__prod,axiom,
! [A: name,X: late_subject,Y: pi] :
( ( fresh_994896692ect_pi @ A @ ( produc324947500ect_pi @ X @ Y ) )
= ( ( fresh_717452603ubject @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_63_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: late_subject] :
( ( fresh_1498103185ubject @ A @ ( produc320590723ubject @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_717452603ubject @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_64_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: late_freeRes] :
( ( fresh_493808761reeRes @ A @ ( produc1244821099reeRes @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_65_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: name] :
( ( fresh_2007541374s_name @ A @ ( produc1701355766s_name @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_66_fresh__prod,axiom,
! [A: name,X: late_freeRes,Y: pi] :
( ( fresh_1847501388Res_pi @ A @ ( produc1177552196Res_pi @ X @ Y ) )
= ( ( fresh_1641682979reeRes @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_67_fresh__prod,axiom,
! [A: name,X: name,Y: late_subject] :
( ( fresh_820177506ubject @ A @ ( produc607574050ubject @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_717452603ubject @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_68_fresh__prod,axiom,
! [A: name,X: name,Y: late_freeRes] :
( ( fresh_1963366730reeRes @ A @ ( produc1531804426reeRes @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1641682979reeRes @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_69_transitions_OClose2,axiom,
! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( ( X != A )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( ( Y != A )
=> ( ( fresh_name_pi @ Y @ Q2 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close2
thf(fact_70_transitions_OClose1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( ( X != A )
=> ( ( fresh_name_pi @ X @ Q2 )
=> ( ( Y != A )
=> ( ( fresh_name_pi @ Y @ P2 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close1
thf(fact_71_Late__Semantics_OClose2,axiom,
! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ Y @ Q )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% Late_Semantics.Close2
thf(fact_72_Late__Semantics_OClose1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% Late_Semantics.Close1
thf(fact_73_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
! [X1: name,Y1: name] :
( ( ( late_InputS @ X1 )
= ( late_InputS @ Y1 ) )
= ( X1 = Y1 ) ) ).
% Late_Semantics1.subject.inject(1)
thf(fact_74_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
! [X2: name,Y22: name] :
( ( ( late_BoundOutputS @ X2 )
= ( late_BoundOutputS @ Y22 ) )
= ( X2 = Y22 ) ) ).
% Late_Semantics1.subject.inject(2)
thf(fact_75_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B2: late_subject,A4: name > noption_pi,B3: late_subject] :
( ( ( produc581368530ubject @ A @ B2 )
= ( produc581368530ubject @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_76_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B2: late_freeRes,A4: name > noption_pi,B3: late_freeRes] :
( ( ( produc1505598906reeRes @ A @ B2 )
= ( produc1505598906reeRes @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_77_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B2: name,A4: name > noption_pi,B3: name] :
( ( ( produc540578151i_name @ A @ B2 )
= ( produc540578151i_name @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_78_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B2: pi,A4: name > noption_pi,B3: pi] :
( ( ( produc1820286517_pi_pi @ A @ B2 )
= ( produc1820286517_pi_pi @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_79_old_Oprod_Oinject,axiom,
! [A: name > noption_pi,B2: name > noption_pi,A4: name > noption_pi,B3: name > noption_pi] :
( ( ( produc1342893193ion_pi @ A @ B2 )
= ( produc1342893193ion_pi @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_80_old_Oprod_Oinject,axiom,
! [A: pi,B2: pi,A4: pi,B3: pi] :
( ( ( product_Pair_pi_pi @ A @ B2 )
= ( product_Pair_pi_pi @ A4 @ B3 ) )
= ( ( A = A4 )
& ( B2 = B3 ) ) ) ).
% old.prod.inject
thf(fact_81_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: late_subject,Y1: name > noption_pi,Y22: late_subject] :
( ( ( produc581368530ubject @ X1 @ X2 )
= ( produc581368530ubject @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_82_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: late_freeRes,Y1: name > noption_pi,Y22: late_freeRes] :
( ( ( produc1505598906reeRes @ X1 @ X2 )
= ( produc1505598906reeRes @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_83_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: name,Y1: name > noption_pi,Y22: name] :
( ( ( produc540578151i_name @ X1 @ X2 )
= ( produc540578151i_name @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_84_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: pi,Y1: name > noption_pi,Y22: pi] :
( ( ( produc1820286517_pi_pi @ X1 @ X2 )
= ( produc1820286517_pi_pi @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_85_prod_Oinject,axiom,
! [X1: name > noption_pi,X2: name > noption_pi,Y1: name > noption_pi,Y22: name > noption_pi] :
( ( ( produc1342893193ion_pi @ X1 @ X2 )
= ( produc1342893193ion_pi @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_86_prod_Oinject,axiom,
! [X1: pi,X2: pi,Y1: pi,Y22: pi] :
( ( ( product_Pair_pi_pi @ X1 @ X2 )
= ( product_Pair_pi_pi @ Y1 @ Y22 ) )
= ( ( X1 = Y1 )
& ( X2 = Y22 ) ) ) ).
% prod.inject
thf(fact_87_subst__identity,axiom,
! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ) ).
% subst_identity
thf(fact_88_simps_I9_J,axiom,
! [X: name,C2: name,D: name,P: pi] :
( ( X != C2 )
=> ( ( X != D )
=> ( ( subs @ ( res @ X @ P ) @ C2 @ D )
= ( res @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ).
% simps(9)
thf(fact_89_simps_I8_J,axiom,
! [P: pi,Q: pi,C2: name,D: name] :
( ( subs @ ( par @ P @ Q ) @ C2 @ D )
= ( par @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% simps(8)
thf(fact_90_substTrans,axiom,
! [B2: name,P: pi,A: name,C2: name] :
( ( fresh_name_pi @ B2 @ P )
=> ( ( subs @ ( subs @ P @ A @ B2 ) @ B2 @ C2 )
= ( subs @ P @ A @ C2 ) ) ) ).
% substTrans
thf(fact_91_residual_Ofresh_I2_J,axiom,
! [A: name,X2: late_freeRes,X1: pi] :
( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
= ( ( fresh_1641682979reeRes @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% residual.fresh(2)
thf(fact_92_subject_Ofresh_I2_J,axiom,
! [A: name,X1: name] :
( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
= ( fresh_name_name @ A @ X1 ) ) ).
% subject.fresh(2)
thf(fact_93_subject_Ofresh_I1_J,axiom,
! [A: name,X1: name] :
( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
= ( fresh_name_name @ A @ X1 ) ) ).
% subject.fresh(1)
thf(fact_94_forget,axiom,
! [A: name,P: pi,B2: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B2 )
= P ) ) ).
% forget
thf(fact_95_fresh__fact1,axiom,
! [A: name,P: pi,C2: name,B2: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C2 )
=> ( fresh_name_pi @ A @ ( subs @ P @ B2 @ C2 ) ) ) ) ).
% fresh_fact1
thf(fact_96_fresh__fact2,axiom,
! [A: name,B2: name,P: pi] :
( ( A != B2 )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B2 ) ) ) ).
% fresh_fact2
thf(fact_97_freshResidual,axiom,
! [P: pi,Rs: late_residual,X: name] :
( ( late_transitions @ P @ Rs )
=> ( ( fresh_name_pi @ X @ P )
=> ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% freshResidual
thf(fact_98_substRes2,axiom,
! [B2: name,P: pi,A: name] :
( ( fresh_name_pi @ B2 @ P )
=> ( ( res @ A @ P )
= ( res @ B2 @ ( subs @ P @ A @ B2 ) ) ) ) ).
% substRes2
thf(fact_99_Agent_OsubstRes3,axiom,
! [B2: name,P: pi,A: name] :
( ( fresh_name_pi @ B2 @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B2 )
= ( res @ B2 @ ( subs @ P @ A @ B2 ) ) ) ) ).
% Agent.substRes3
thf(fact_100_Late__Semantics_OResB,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( ( Y != X )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% Late_Semantics.ResB
thf(fact_101_freshBoundDerivative_I1_J,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_717452603ubject @ Y @ A ) ) ) ).
% freshBoundDerivative(1)
thf(fact_102_surj__pair,axiom,
! [P5: produc691362330ubject] :
? [X4: name > noption_pi,Y2: late_subject] :
( P5
= ( produc581368530ubject @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_103_surj__pair,axiom,
! [P5: produc1834551554reeRes] :
? [X4: name > noption_pi,Y2: late_freeRes] :
( P5
= ( produc1505598906reeRes @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_104_surj__pair,axiom,
! [P5: produc405342261i_name] :
? [X4: name > noption_pi,Y2: name] :
( P5
= ( produc540578151i_name @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_105_surj__pair,axiom,
! [P5: produc629157763_pi_pi] :
? [X4: name > noption_pi,Y2: pi] :
( P5
= ( produc1820286517_pi_pi @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_106_surj__pair,axiom,
! [P5: produc1462499409ion_pi] :
? [X4: name > noption_pi,Y2: name > noption_pi] :
( P5
= ( produc1342893193ion_pi @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_107_surj__pair,axiom,
! [P5: product_prod_pi_pi] :
? [X4: pi,Y2: pi] :
( P5
= ( product_Pair_pi_pi @ X4 @ Y2 ) ) ).
% surj_pair
thf(fact_108_prod__cases,axiom,
! [P: produc691362330ubject > $o,P5: produc691362330ubject] :
( ! [A5: name > noption_pi,B4: late_subject] : ( P @ ( produc581368530ubject @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_109_prod__cases,axiom,
! [P: produc1834551554reeRes > $o,P5: produc1834551554reeRes] :
( ! [A5: name > noption_pi,B4: late_freeRes] : ( P @ ( produc1505598906reeRes @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_110_prod__cases,axiom,
! [P: produc405342261i_name > $o,P5: produc405342261i_name] :
( ! [A5: name > noption_pi,B4: name] : ( P @ ( produc540578151i_name @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_111_prod__cases,axiom,
! [P: produc629157763_pi_pi > $o,P5: produc629157763_pi_pi] :
( ! [A5: name > noption_pi,B4: pi] : ( P @ ( produc1820286517_pi_pi @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_112_prod__cases,axiom,
! [P: produc1462499409ion_pi > $o,P5: produc1462499409ion_pi] :
( ! [A5: name > noption_pi,B4: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_113_prod__cases,axiom,
! [P: product_prod_pi_pi > $o,P5: product_prod_pi_pi] :
( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
=> ( P @ P5 ) ) ).
% prod_cases
thf(fact_114_Pair__inject,axiom,
! [A: name > noption_pi,B2: late_subject,A4: name > noption_pi,B3: late_subject] :
( ( ( produc581368530ubject @ A @ B2 )
= ( produc581368530ubject @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_115_Pair__inject,axiom,
! [A: name > noption_pi,B2: late_freeRes,A4: name > noption_pi,B3: late_freeRes] :
( ( ( produc1505598906reeRes @ A @ B2 )
= ( produc1505598906reeRes @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_116_Pair__inject,axiom,
! [A: name > noption_pi,B2: name,A4: name > noption_pi,B3: name] :
( ( ( produc540578151i_name @ A @ B2 )
= ( produc540578151i_name @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_117_Pair__inject,axiom,
! [A: name > noption_pi,B2: pi,A4: name > noption_pi,B3: pi] :
( ( ( produc1820286517_pi_pi @ A @ B2 )
= ( produc1820286517_pi_pi @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_118_Pair__inject,axiom,
! [A: name > noption_pi,B2: name > noption_pi,A4: name > noption_pi,B3: name > noption_pi] :
( ( ( produc1342893193ion_pi @ A @ B2 )
= ( produc1342893193ion_pi @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_119_Pair__inject,axiom,
! [A: pi,B2: pi,A4: pi,B3: pi] :
( ( ( product_Pair_pi_pi @ A @ B2 )
= ( product_Pair_pi_pi @ A4 @ B3 ) )
=> ~ ( ( A = A4 )
=> ( B2 != B3 ) ) ) ).
% Pair_inject
thf(fact_120_old_Oprod_Oexhaust,axiom,
! [Y: produc691362330ubject] :
~ ! [A5: name > noption_pi,B4: late_subject] :
( Y
!= ( produc581368530ubject @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_121_old_Oprod_Oexhaust,axiom,
! [Y: produc1834551554reeRes] :
~ ! [A5: name > noption_pi,B4: late_freeRes] :
( Y
!= ( produc1505598906reeRes @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_122_old_Oprod_Oexhaust,axiom,
! [Y: produc405342261i_name] :
~ ! [A5: name > noption_pi,B4: name] :
( Y
!= ( produc540578151i_name @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_123_old_Oprod_Oexhaust,axiom,
! [Y: produc629157763_pi_pi] :
~ ! [A5: name > noption_pi,B4: pi] :
( Y
!= ( produc1820286517_pi_pi @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_124_old_Oprod_Oexhaust,axiom,
! [Y: produc1462499409ion_pi] :
~ ! [A5: name > noption_pi,B4: name > noption_pi] :
( Y
!= ( produc1342893193ion_pi @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_125_old_Oprod_Oexhaust,axiom,
! [Y: product_prod_pi_pi] :
~ ! [A5: pi,B4: pi] :
( Y
!= ( product_Pair_pi_pi @ A5 @ B4 ) ) ).
% old.prod.exhaust
thf(fact_126_old_Oprod_Oinducts,axiom,
! [P: produc691362330ubject > $o,Prod: produc691362330ubject] :
( ! [A5: name > noption_pi,B4: late_subject] : ( P @ ( produc581368530ubject @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_127_old_Oprod_Oinducts,axiom,
! [P: produc1834551554reeRes > $o,Prod: produc1834551554reeRes] :
( ! [A5: name > noption_pi,B4: late_freeRes] : ( P @ ( produc1505598906reeRes @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_128_old_Oprod_Oinducts,axiom,
! [P: produc405342261i_name > $o,Prod: produc405342261i_name] :
( ! [A5: name > noption_pi,B4: name] : ( P @ ( produc540578151i_name @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_129_old_Oprod_Oinducts,axiom,
! [P: produc629157763_pi_pi > $o,Prod: produc629157763_pi_pi] :
( ! [A5: name > noption_pi,B4: pi] : ( P @ ( produc1820286517_pi_pi @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_130_old_Oprod_Oinducts,axiom,
! [P: produc1462499409ion_pi > $o,Prod: produc1462499409ion_pi] :
( ! [A5: name > noption_pi,B4: name > noption_pi] : ( P @ ( produc1342893193ion_pi @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_131_old_Oprod_Oinducts,axiom,
! [P: product_prod_pi_pi > $o,Prod: product_prod_pi_pi] :
( ! [A5: pi,B4: pi] : ( P @ ( product_Pair_pi_pi @ A5 @ B4 ) )
=> ( P @ Prod ) ) ).
% old.prod.inducts
thf(fact_132_transitions_OResB,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( ( Y != X )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% transitions.ResB
thf(fact_133_parCasesB_H,axiom,
! [P: pi,Q: pi,B2: late_subject,Y: name,P2: pi] :
( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
=> ( ! [P4: pi,A5: late_subject,X4: name,P3: pi,Q4: pi] :
( ( ( par @ P @ Q )
= ( par @ P4 @ Q4 ) )
=> ( ( ( late_BoundR @ B2 @ Y @ P2 )
= ( late_BoundR @ A5 @ X4 @ ( par @ P3 @ Q4 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X4 @ P3 ) )
=> ( ( fresh_name_pi @ X4 @ P4 )
=> ( ( fresh_name_pi @ X4 @ Q4 )
=> ~ ( fresh_717452603ubject @ X4 @ A5 ) ) ) ) ) )
=> ~ ! [Q4: pi,A5: late_subject,X4: name,Q3: pi,P4: pi] :
( ( ( par @ P @ Q )
= ( par @ P4 @ Q4 ) )
=> ( ( ( late_BoundR @ B2 @ Y @ P2 )
= ( late_BoundR @ A5 @ X4 @ ( par @ P4 @ Q3 ) ) )
=> ( ( late_transitions @ Q4 @ ( late_BoundR @ A5 @ X4 @ Q3 ) )
=> ( ( fresh_name_pi @ X4 @ P4 )
=> ( ( fresh_name_pi @ X4 @ Q4 )
=> ~ ( fresh_717452603ubject @ X4 @ A5 ) ) ) ) ) ) ) ) ).
% parCasesB'
thf(fact_134_transitions_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% transitions.Par1B
thf(fact_135_transitions_OPar2B,axiom,
! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% transitions.Par2B
thf(fact_136_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: late_subject] :
( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
=> ( fresh_717452603ubject @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_137_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: late_freeRes] :
( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
=> ( fresh_1641682979reeRes @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_138_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: name] :
( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
=> ( fresh_name_name @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_139_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: pi] :
( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_140_fresh__prodD_I2_J,axiom,
! [A: name,X: name > noption_pi,Y: name > noption_pi] :
( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_141_fresh__prodD_I2_J,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_142_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: late_subject] :
( ( fresh_567880928ubject @ A @ ( produc581368530ubject @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_143_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: late_freeRes] :
( ( fresh_1711070152reeRes @ A @ ( produc1505598906reeRes @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_144_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: name] :
( ( fresh_453496559i_name @ A @ ( produc540578151i_name @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_145_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: pi] :
( ( fresh_253309757_pi_pi @ A @ ( produc1820286517_pi_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_146_fresh__prodD_I1_J,axiom,
! [A: name,X: name > noption_pi,Y: name > noption_pi] :
( ( fresh_225680151ion_pi @ A @ ( produc1342893193ion_pi @ X @ Y ) )
=> ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_147_fresh__prodD_I1_J,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
=> ( fresh_name_pi @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_148_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
! [X1: name,X2: name] :
( ( late_InputS @ X1 )
!= ( late_BoundOutputS @ X2 ) ) ).
% Late_Semantics1.subject.distinct(1)
thf(fact_149_subject_Oexhaust,axiom,
! [Y: late_subject] :
( ! [X12: name] :
( Y
!= ( late_InputS @ X12 ) )
=> ~ ! [X22: name] :
( Y
!= ( late_BoundOutputS @ X22 ) ) ) ).
% subject.exhaust
thf(fact_150_resCases_H,axiom,
! [X: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( res @ X @ P ) @ Rs )
=> ( ! [P4: pi,A5: name,B4: name] :
( ( ( res @ X @ P )
= ( res @ B4 @ P4 ) )
=> ! [P3: pi] :
( ( Rs
= ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
=> ( A5 = B4 ) ) ) )
=> ( ! [P4: pi,A5: late_subject,X4: name,P3: pi,Y2: name] :
( ( ( res @ X @ P )
= ( res @ Y2 @ P4 ) )
=> ( ( Rs
= ( late_BoundR @ A5 @ X4 @ ( res @ Y2 @ P3 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X4 @ P3 ) )
=> ( ( fresh_717452603ubject @ Y2 @ A5 )
=> ( ( Y2 != X4 )
=> ( ( fresh_name_pi @ X4 @ P4 )
=> ~ ( fresh_717452603ubject @ X4 @ A5 ) ) ) ) ) ) )
=> ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y2: name] :
( ( ( res @ X @ P )
= ( res @ Y2 @ P4 ) )
=> ( ( Rs
= ( late_FreeR @ Alpha2 @ ( res @ Y2 @ P3 ) ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
=> ~ ( fresh_1641682979reeRes @ Y2 @ Alpha2 ) ) ) ) ) ) ) ).
% resCases'
thf(fact_151_transitions_OComm1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,B2: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B2 )
=> ( ( fresh_name_pi @ X @ Q2 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B2 ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm1
thf(fact_152_transitions_OComm2,axiom,
! [P: pi,A: name,B2: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B2 )
=> ( ( fresh_name_pi @ X @ P2 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B2 ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm2
thf(fact_153_Late__Semantics_OComm1,axiom,
! [P: pi,A: name,X: name,P2: pi,Q: pi,B2: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B2 ) @ Q2 ) ) ) ) ) ).
% Late_Semantics.Comm1
thf(fact_154_Late__Semantics_OComm2,axiom,
! [P: pi,A: name,B2: name,P2: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P2 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B2 ) ) ) ) ) ) ).
% Late_Semantics.Comm2
thf(fact_155_resCasesB_H,axiom,
! [X5: name,P: pi,A: late_subject,Y3: name,P2: pi] :
( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y3 @ P2 ) )
=> ( ! [P4: pi,A5: name,B4: name] :
( ( ( res @ X5 @ P )
= ( res @ B4 @ P4 ) )
=> ! [P3: pi] :
( ( ( late_BoundR @ A @ Y3 @ P2 )
= ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ B4 @ P3 ) )
=> ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P3 ) )
=> ( A5 = B4 ) ) ) )
=> ~ ! [P4: pi,A5: late_subject,X4: name,P3: pi,Y2: name] :
( ( ( res @ X5 @ P )
= ( res @ Y2 @ P4 ) )
=> ( ( ( late_BoundR @ A @ Y3 @ P2 )
= ( late_BoundR @ A5 @ X4 @ ( res @ Y2 @ P3 ) ) )
=> ( ( late_transitions @ P4 @ ( late_BoundR @ A5 @ X4 @ P3 ) )
=> ( ( fresh_717452603ubject @ Y2 @ A5 )
=> ( ( Y2 != X4 )
=> ( ( fresh_name_pi @ X4 @ P4 )
=> ~ ( fresh_717452603ubject @ X4 @ A5 ) ) ) ) ) ) ) ) ) ).
% resCasesB'
thf(fact_156_Late__Semantics1_OfreeRes_Oinject,axiom,
! [X11: name,X122: name,Y11: name,Y12: name] :
( ( ( late_OutputR @ X11 @ X122 )
= ( late_OutputR @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X122 = Y12 ) ) ) ).
% Late_Semantics1.freeRes.inject
thf(fact_157_Late__Semantics_OfreeRes_Oinject,axiom,
! [X2: name,X1: name,Y22: name,Y1: name] :
( ( ( late_OutputR @ X2 @ X1 )
= ( late_OutputR @ Y22 @ Y1 ) )
= ( ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% Late_Semantics.freeRes.inject
thf(fact_158_freeRes_Ofresh_I1_J,axiom,
! [A: name,X2: name,X1: name] :
( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X2 )
& ( fresh_name_name @ A @ X1 ) ) ) ).
% freeRes.fresh(1)
thf(fact_159_freeRes_Oinducts,axiom,
! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
( ! [Name1: name,Name22: name] : ( P @ ( late_OutputR @ Name1 @ Name22 ) )
=> ( ( P @ late_TauR )
=> ( P @ FreeRes3 ) ) ) ).
% freeRes.inducts
thf(fact_160_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
! [Name12: name,Name23: name] :
( ( late_OutputR @ Name12 @ Name23 )
!= late_TauR ) ).
% Late_Semantics.freeRes.distinct(1)
thf(fact_161_freeRes_Oexhaust,axiom,
! [Y: late_freeRes] :
( ! [X112: name,X123: name] :
( Y
!= ( late_OutputR @ X112 @ X123 ) )
=> ( Y = late_TauR ) ) ).
% freeRes.exhaust
thf(fact_162_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
! [X11: name,X122: name] :
( ( late_OutputR @ X11 @ X122 )
!= late_TauR ) ).
% Late_Semantics1.freeRes.distinct(1)
thf(fact_163_Open,axiom,
! [P: pi,A: name,B2: name,P2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P2 ) )
=> ( ( A != B2 )
=> ( late_transitions @ ( res @ B2 @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B2 @ P2 ) ) ) ) ).
% Open
thf(fact_164_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_subject] :
( ( eqvt_pi @ Rel )
=> ( ! [Q3: pi,A5: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X ) @ Q3 ) )
=> ( ( A5 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) ) )
=> ( ! [Q3: pi,A5: late_subject,Y2: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y2 @ Q3 ) )
=> ( ( fresh_717452603ubject @ X @ A5 )
=> ( ( X != Y2 )
=> ( ( fresh_717452603ubject @ Y2 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y2 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q3 ) @ A5 @ Y2 @ Rel ) ) ) ) ) )
=> ( ! [Q3: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_165_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: late_freeRes] :
( ( eqvt_pi @ Rel )
=> ( ! [Q3: pi,A5: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X ) @ Q3 ) )
=> ( ( A5 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) ) )
=> ( ! [Q3: pi,A5: late_subject,Y2: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y2 @ Q3 ) )
=> ( ( fresh_717452603ubject @ X @ A5 )
=> ( ( X != Y2 )
=> ( ( fresh_1641682979reeRes @ Y2 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y2 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q3 ) @ A5 @ Y2 @ Rel ) ) ) ) ) )
=> ( ! [Q3: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_166_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [Q3: pi,A5: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X ) @ Q3 ) )
=> ( ( A5 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) ) )
=> ( ! [Q3: pi,A5: late_subject,Y2: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y2 @ Q3 ) )
=> ( ( fresh_717452603ubject @ X @ A5 )
=> ( ( X != Y2 )
=> ( ( fresh_name_name @ Y2 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y2 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q3 ) @ A5 @ Y2 @ Rel ) ) ) ) ) )
=> ( ! [Q3: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_167_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [Q3: pi,A5: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A5 @ X ) @ Q3 ) )
=> ( ( A5 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A5 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) ) )
=> ( ! [Q3: pi,A5: late_subject,Y2: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y2 @ Q3 ) )
=> ( ( fresh_717452603ubject @ X @ A5 )
=> ( ( X != Y2 )
=> ( ( fresh_name_pi @ Y2 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y2 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q3 ) @ A5 @ Y2 @ Rel ) ) ) ) ) )
=> ( ! [Q3: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q3 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_168_simE_I1_J,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,A: late_subject,X: name,Q2: pi] :
( ( strong743114133lation @ P @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ? [P3: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
& ( strong2129052853vative @ P3 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% simE(1)
thf(fact_169_simE_I2_J,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi,Q: pi,Alpha: late_freeRes,Q2: pi] :
( ( strong743114133lation @ P @ Rel @ Q )
=> ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
=> ? [P3: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P3 @ Q2 ) @ Rel ) ) ) ) ).
% simE(2)
thf(fact_170_simCases,axiom,
! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
( ! [A5: late_subject,Y2: name,Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ Y2 @ Q3 ) )
=> ( ( fresh_name_pi @ Y2 @ P )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ Y2 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q3 @ A5 @ Y2 @ Rel ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q3: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% simCases
thf(fact_171_simulation__def,axiom,
( strong743114133lation
= ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
( ! [A2: late_subject,X3: name,Q6: pi] :
( ( ( late_transitions @ Q5 @ ( late_BoundR @ A2 @ X3 @ Q6 ) )
& ( fresh_name_pi @ X3 @ P7 ) )
=> ? [P8: pi] :
( ( late_transitions @ P7 @ ( late_BoundR @ A2 @ X3 @ P8 ) )
& ( strong2129052853vative @ P8 @ Q6 @ A2 @ X3 @ Rel2 ) ) )
& ! [Alpha3: late_freeRes,Q6: pi] :
( ( late_transitions @ Q5 @ ( late_FreeR @ Alpha3 @ Q6 ) )
=> ? [P8: pi] :
( ( late_transitions @ P7 @ ( late_FreeR @ Alpha3 @ P8 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P8 @ Q6 ) @ Rel2 ) ) ) ) ) ) ).
% simulation_def
thf(fact_172_parSym,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi] :
( ! [R2: pi,S2: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ R2 @ S2 ) @ ( par @ S2 @ R2 ) ) @ Rel )
=> ( ! [R2: pi,S2: pi,X4: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X4 @ R2 ) @ ( res @ X4 @ S2 ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% parSym
thf(fact_173_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_subject] :
( ( eqvt_pi @ Rel )
=> ( ! [A5: late_subject,X4: name,Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X4 @ Q3 ) )
=> ( ( fresh_name_pi @ X4 @ P )
=> ( ( fresh_name_pi @ X4 @ Q )
=> ( ( fresh_717452603ubject @ X4 @ A5 )
=> ( ( fresh_717452603ubject @ X4 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ X4 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q3 @ A5 @ X4 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q3: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_174_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: late_freeRes] :
( ( eqvt_pi @ Rel )
=> ( ! [A5: late_subject,X4: name,Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X4 @ Q3 ) )
=> ( ( fresh_name_pi @ X4 @ P )
=> ( ( fresh_name_pi @ X4 @ Q )
=> ( ( fresh_717452603ubject @ X4 @ A5 )
=> ( ( fresh_1641682979reeRes @ X4 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ X4 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q3 @ A5 @ X4 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q3: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_175_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [A5: late_subject,X4: name,Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X4 @ Q3 ) )
=> ( ( fresh_name_pi @ X4 @ P )
=> ( ( fresh_name_pi @ X4 @ Q )
=> ( ( fresh_717452603ubject @ X4 @ A5 )
=> ( ( fresh_name_name @ X4 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ X4 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q3 @ A5 @ X4 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q3: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_176_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [A5: late_subject,X4: name,Q3: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A5 @ X4 @ Q3 ) )
=> ( ( fresh_name_pi @ X4 @ P )
=> ( ( fresh_name_pi @ X4 @ Q )
=> ( ( fresh_717452603ubject @ X4 @ A5 )
=> ( ( fresh_name_pi @ X4 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A5 @ X4 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q3 @ A5 @ X4 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q3: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q3 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q3 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_177_parAssocLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,R: pi] :
( ! [S2: pi,T: pi,U: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( par @ S2 @ T ) @ U ) @ ( par @ S2 @ ( par @ T @ U ) ) ) @ Rel )
=> ( ! [S2: pi,T: pi,X4: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X4 @ S2 ) @ ( res @ X4 @ T ) ) @ Rel ) )
=> ( ! [S2: pi,T: pi,U: pi,X4: name] :
( ( fresh_name_pi @ X4 @ S2 )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X4 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X4 @ ( par @ T @ U ) ) ) ) @ Rel ) )
=> ( ! [S2: pi,T: pi,U: pi,X4: name] :
( ( fresh_name_pi @ X4 @ U )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X4 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X4 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% parAssocLeft
thf(fact_178_resTauOutputTrans,axiom,
! [X: name,P: pi,A: name,B2: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P2 ) ) ).
% resTauOutputTrans
thf(fact_179_resOutputTauTrans,axiom,
! [X: name,A: name,B2: name,P: pi,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ B2 @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% resOutputTauTrans
thf(fact_180_resOutputInputTrans,axiom,
! [X: name,A: name,B2: name,P: pi,C2: name,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ B2 @ P ) ) @ ( late_BoundR @ ( late_InputS @ C2 ) @ Y @ P2 ) ) ).
% resOutputInputTrans
thf(fact_181_resOutputOutputTrans,axiom,
! [X: name,A: name,P: pi,B2: name,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P2 ) ) ).
% resOutputOutputTrans
thf(fact_182_pi_Ofresh_I3_J,axiom,
! [A: name,X1: pi] :
( ( fresh_name_pi @ A @ ( tau @ X1 ) )
= ( fresh_name_pi @ A @ X1 ) ) ).
% pi.fresh(3)
thf(fact_183_simps_I2_J,axiom,
! [P: pi,C2: name,D: name] :
( ( subs @ ( tau @ P ) @ C2 @ D )
= ( tau @ ( subs @ P @ C2 @ D ) ) ) ).
% simps(2)
thf(fact_184_pi_Ofresh_I2_J,axiom,
! [A: name,X32: name,X2: name,X1: pi] :
( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_name_name @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(2)
thf(fact_185_pi_Oinject_I2_J,axiom,
! [X1: pi,Y1: pi] :
( ( ( tau @ X1 )
= ( tau @ Y1 ) )
= ( X1 = Y1 ) ) ).
% pi.inject(2)
thf(fact_186_pi_Oinject_I1_J,axiom,
! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
( ( ( output @ X32 @ X2 @ X1 )
= ( output @ Y32 @ Y22 @ Y1 ) )
= ( ( X32 = Y32 )
& ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(1)
thf(fact_187_pi_Odistinct_I19_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( tau @ Pi ) ) ).
% pi.distinct(19)
thf(fact_188_pi_Odistinct_I31_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(31)
thf(fact_189_pi_Odistinct_I29_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(29)
thf(fact_190_pi_Odistinct_I45_J,axiom,
! [Pi4: pi,Name: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(45)
thf(fact_191_pi_Odistinct_I43_J,axiom,
! [Pi4: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(43)
thf(fact_192_resTrans_I1_J,axiom,
! [X: name,B2: name,P: pi,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ ( output @ X @ B2 @ P ) ) @ Rs ) ).
% resTrans(1)
thf(fact_193_outputBoundTrans,axiom,
! [A: name,B2: name,P: pi,C2: late_subject,X: name,P2: pi] :
~ ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_BoundR @ C2 @ X @ P2 ) ) ).
% outputBoundTrans
thf(fact_194_tauBoundTrans,axiom,
! [P: pi,A: late_subject,X: name,P2: pi] :
~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% tauBoundTrans
thf(fact_195_resTauBoundTrans,axiom,
! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% resTauBoundTrans
thf(fact_196_Output,axiom,
! [A: name,B2: name,P: pi] : ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P ) ) ).
% Output
thf(fact_197_outputIneqTrans,axiom,
! [A: name,B2: name,P: pi,C2: name,D: name,P2: pi] :
( ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_FreeR @ ( late_OutputR @ C2 @ D ) @ P2 ) )
=> ~ ( ( A != C2 )
| ( B2 != D ) ) ) ).
% outputIneqTrans
thf(fact_198_outputCases_H,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( output @ A @ B2 @ P ) @ Rs )
=> ~ ! [A5: name,B4: name,P4: pi] :
( ( ( A = A5 )
& ( B2 = B4 )
& ( P = P4 ) )
=> ( Rs
!= ( late_FreeR @ ( late_OutputR @ A5 @ B4 ) @ P4 ) ) ) ) ).
% outputCases'
thf(fact_199_outputCases,axiom,
! [A: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
( ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( ( Alpha
= ( late_OutputR @ A @ B2 ) )
=> ( ( P = P2 )
=> ( Prop @ ( late_OutputR @ A @ B2 ) @ P ) ) )
=> ( Prop @ Alpha @ P2 ) ) ) ).
% outputCases
thf(fact_200_outputTauTrans,axiom,
! [A: name,B2: name,P: pi,P2: pi] :
~ ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% outputTauTrans
thf(fact_201_tauOutputTrans,axiom,
! [P: pi,A: name,B2: name,P2: pi] :
~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B2 ) @ P2 ) ) ).
% tauOutputTrans
thf(fact_202_Tau,axiom,
! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% Tau
thf(fact_203_tauCases_H,axiom,
! [P: pi,Rs: late_residual] :
( ( late_transitions @ ( tau @ P ) @ Rs )
=> ~ ! [P4: pi] :
( ( ( tau @ P )
= ( tau @ P4 ) )
=> ( Rs
!= ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% tauCases'
thf(fact_204_tauCases,axiom,
! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ( ( ( Alpha = late_TauR )
=> ( ( P = P2 )
=> ( Prop @ late_TauR @ P ) ) )
=> ( Prop @ Alpha @ P2 ) ) ) ).
% tauCases
thf(fact_205_outputFreshTrans,axiom,
! [A: name,B2: name,P: pi,Alpha: late_freeRes,P2: pi] :
( ( late_transitions @ ( output @ A @ B2 @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
=> ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
| ( fresh_1641682979reeRes @ B2 @ Alpha ) ) ) ).
% outputFreshTrans
thf(fact_206_resInputBoundOutputTrans,axiom,
! [X: name,A: name,Y: name,P: pi,B2: name,Z: name,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Z @ P2 ) ) ).
% resInputBoundOutputTrans
thf(fact_207_residual_Ofresh_I1_J,axiom,
! [A: name,X32: late_subject,X1: name,X2: pi] :
( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
= ( ( fresh_717452603ubject @ A @ X32 )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% residual.fresh(1)
thf(fact_208_simps_I3_J,axiom,
! [A: name,B2: name,P: pi,C2: name,D: name] :
( ( subs @ ( output @ A @ B2 @ P ) @ C2 @ D )
= ( output @ ( subst_name @ A @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% simps(3)
thf(fact_209_simps_I4_J,axiom,
! [X: name,A: name,C2: name,D: name,P: pi] :
( ( X != A )
=> ( ( X != C2 )
=> ( ( X != D )
=> ( ( subs @ ( input @ A @ X @ P ) @ C2 @ D )
= ( input @ ( subst_name @ A @ C2 @ D ) @ X @ ( subs @ P @ C2 @ D ) ) ) ) ) ) ).
% simps(4)
thf(fact_210_substInput,axiom,
! [X: name,B2: name,C2: name,A: name,P: pi] :
( ( X != B2 )
=> ( ( X != C2 )
=> ( ( subs @ ( input @ A @ X @ P ) @ B2 @ C2 )
= ( input @ ( subst_name @ A @ B2 @ C2 ) @ X @ ( subs @ P @ B2 @ C2 ) ) ) ) ) ).
% substInput
thf(fact_211_pi_Ofresh_I9_J,axiom,
! [A: name,X1: name,X2: pi] :
( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
= ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% pi.fresh(9)
thf(fact_212_pi_Ofresh_I4_J,axiom,
! [A: name,X32: name,X1: name,X2: pi] :
( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% pi.fresh(4)
thf(fact_213_pi_Odistinct_I57_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(57)
thf(fact_214_pi_Odistinct_I55_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(55)
thf(fact_215_pi_Oinject_I8_J,axiom,
! [X1: name,X2: pi,Y1: name,Y22: pi] :
( ( ( res @ X1 @ X2 )
= ( res @ Y1 @ Y22 ) )
= ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ).
% pi.inject(8)
thf(fact_216_subst__name__def,axiom,
( subst_name
= ( ^ [A2: name,B: name,C4: name] : ( if_name @ ( A2 = B ) @ C4 @ A2 ) ) ) ).
% subst_name_def
thf(fact_217_pi_Oinject_I3_J,axiom,
! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y22: pi] :
( ( ( input @ X32 @ X1 @ X2 )
= ( input @ Y32 @ Y1 @ Y22 ) )
= ( ( X32 = Y32 )
& ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% pi.inject(3)
thf(fact_218_abs__fun__eq1,axiom,
! [A: name,X: name,Y: name] :
( ( ( abs_fun_name_name @ A @ X )
= ( abs_fun_name_name @ A @ Y ) )
= ( X = Y ) ) ).
% abs_fun_eq1
thf(fact_219_abs__fun__eq1,axiom,
! [A: name,X: late_freeRes,Y: late_freeRes] :
( ( ( abs_fu681348580reeRes @ A @ X )
= ( abs_fu681348580reeRes @ A @ Y ) )
= ( X = Y ) ) ).
% abs_fun_eq1
thf(fact_220_abs__fun__eq1,axiom,
! [A: name,X: late_subject,Y: late_subject] :
( ( ( abs_fu1904601852ubject @ A @ X )
= ( abs_fu1904601852ubject @ A @ Y ) )
= ( X = Y ) ) ).
% abs_fun_eq1
thf(fact_221_abs__fun__eq1,axiom,
! [A: name,X: pi,Y: pi] :
( ( ( abs_fun_name_pi @ A @ X )
= ( abs_fun_name_pi @ A @ Y ) )
= ( X = Y ) ) ).
% abs_fun_eq1
thf(fact_222_name__fresh__abs,axiom,
! [B2: name,A: name,X: late_subject] :
( ( fresh_728038529ubject @ B2 @ ( abs_fu1904601852ubject @ A @ X ) )
= ( ( B2 = A )
| ( fresh_717452603ubject @ B2 @ X ) ) ) ).
% name_fresh_abs
thf(fact_223_name__fresh__abs,axiom,
! [B2: name,A: name,X: late_freeRes] :
( ( fresh_785364841reeRes @ B2 @ ( abs_fu681348580reeRes @ A @ X ) )
= ( ( B2 = A )
| ( fresh_1641682979reeRes @ B2 @ X ) ) ) ).
% name_fresh_abs
thf(fact_224_name__fresh__abs,axiom,
! [B2: name,A: name,X: name] :
( ( fresh_1093033124n_name @ B2 @ ( abs_fun_name_name @ A @ X ) )
= ( ( B2 = A )
| ( fresh_name_name @ B2 @ X ) ) ) ).
% name_fresh_abs
thf(fact_225_name__fresh__abs,axiom,
! [B2: name,A: name,X: pi] :
( ( fresh_543891186ion_pi @ B2 @ ( abs_fun_name_pi @ A @ X ) )
= ( ( B2 = A )
| ( fresh_name_pi @ B2 @ X ) ) ) ).
% name_fresh_abs
thf(fact_226_abs__fresh_I1_J,axiom,
! [B2: name,A: name,X: late_subject] :
( ( fresh_728038529ubject @ B2 @ ( abs_fu1904601852ubject @ A @ X ) )
= ( ( B2 = A )
| ( fresh_717452603ubject @ B2 @ X ) ) ) ).
% abs_fresh(1)
thf(fact_227_abs__fresh_I1_J,axiom,
! [B2: name,A: name,X: late_freeRes] :
( ( fresh_785364841reeRes @ B2 @ ( abs_fu681348580reeRes @ A @ X ) )
= ( ( B2 = A )
| ( fresh_1641682979reeRes @ B2 @ X ) ) ) ).
% abs_fresh(1)
thf(fact_228_abs__fresh_I1_J,axiom,
! [B2: name,A: name,X: name] :
( ( fresh_1093033124n_name @ B2 @ ( abs_fun_name_name @ A @ X ) )
= ( ( B2 = A )
| ( fresh_name_name @ B2 @ X ) ) ) ).
% abs_fresh(1)
thf(fact_229_abs__fresh_I1_J,axiom,
! [B2: name,A: name,X: pi] :
( ( fresh_543891186ion_pi @ B2 @ ( abs_fun_name_pi @ A @ X ) )
= ( ( B2 = A )
| ( fresh_name_pi @ B2 @ X ) ) ) ).
% abs_fresh(1)
thf(fact_230_residual_Oinject_I1_J,axiom,
! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y22: pi] :
( ( ( late_BoundR @ X32 @ X1 @ X2 )
= ( late_BoundR @ Y32 @ Y1 @ Y22 ) )
= ( ( X32 = Y32 )
& ( ( abs_fun_name_pi @ X1 @ X2 )
= ( abs_fun_name_pi @ Y1 @ Y22 ) ) ) ) ).
% residual.inject(1)
thf(fact_231_pi_Odistinct_I21_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( input @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(21)
thf(fact_232_pi_Odistinct_I35_J,axiom,
! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( input @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(35)
thf(fact_233_inputCases_H,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( input @ A @ B2 @ P ) @ Rs )
=> ~ ! [X4: name,A5: name,P4: pi] :
( ( ( A = A5 )
& ( ( abs_fun_name_pi @ B2 @ P )
= ( abs_fun_name_pi @ X4 @ P4 ) ) )
=> ( ( Rs
= ( late_BoundR @ ( late_InputS @ A5 ) @ X4 @ P4 ) )
=> ( X4 = A5 ) ) ) ) ).
% inputCases'
thf(fact_234_resTrans_I2_J,axiom,
! [X: name,Y: name,P: pi,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% resTrans(2)
thf(fact_235_inputFreeTrans,axiom,
! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% inputFreeTrans
thf(fact_236_resInputFreeTrans,axiom,
! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% resInputFreeTrans
thf(fact_237_Late__Semantics_OInput,axiom,
! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% Late_Semantics.Input
thf(fact_238_transitions_OInput,axiom,
! [X: name,A: name,P: pi] :
( ( X != A )
=> ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% transitions.Input
thf(fact_239_inputBoundOutputTrans,axiom,
! [A: name,X: name,P: pi,B2: name,Y: name,P2: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B2 ) @ Y @ P2 ) ) ).
% inputBoundOutputTrans
thf(fact_240_inputIneqTrans,axiom,
! [A: name,X: name,P: pi,B2: late_subject,Y: name,P2: pi] :
( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B2 @ Y @ P2 ) )
=> ~ ( fresh_717452603ubject @ A @ B2 ) ) ).
% inputIneqTrans
thf(fact_241_parZeroRight,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ Q4 @ ( par @ Q4 @ piNil ) ) @ Rel )
=> ( strong743114133lation @ P @ Rel @ ( par @ P @ piNil ) ) ) ).
% parZeroRight
thf(fact_242_parZeroLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
( ! [Q4: pi] : ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ Q4 @ piNil ) @ Q4 ) @ Rel )
=> ( strong743114133lation @ ( par @ P @ piNil ) @ Rel @ P ) ) ).
% parZeroLeft
thf(fact_243_simps_I6_J,axiom,
! [A: name,B2: name,P: pi,C2: name,D: name] :
( ( subs @ ( mismatch @ A @ B2 @ P ) @ C2 @ D )
= ( mismatch @ ( subst_name @ A @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% simps(6)
thf(fact_244_pi_Ofresh_I1_J,axiom,
! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% pi.fresh(1)
thf(fact_245_simps_I1_J,axiom,
! [C2: name,D: name] :
( ( subs @ piNil @ C2 @ D )
= piNil ) ).
% simps(1)
thf(fact_246_pi_Ofresh_I6_J,axiom,
! [A: name,X32: name,X2: name,X1: pi] :
( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_name_name @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(6)
thf(fact_247_pi_Odistinct_I5_J,axiom,
! [Name13: name,Name24: name,Pi: pi] :
( piNil
!= ( input @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(5)
thf(fact_248_pi_Odistinct_I51_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(51)
thf(fact_249_pi_Odistinct_I75_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( mismatch @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(75)
thf(fact_250_pi_Odistinct_I73_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( mismatch @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(73)
thf(fact_251_pi_Odistinct_I15_J,axiom,
! [Name: name,Pi: pi] :
( piNil
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(15)
thf(fact_252_pi_Odistinct_I13_J,axiom,
! [Pi12: pi,Pi22: pi] :
( piNil
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(13)
thf(fact_253_pi_Odistinct_I25_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(25)
thf(fact_254_nilSimRight,axiom,
! [P: pi,Rel: set_Pr1834926343_pi_pi] : ( strong743114133lation @ P @ Rel @ piNil ) ).
% nilSimRight
thf(fact_255_pi_Odistinct_I1_J,axiom,
! [Name13: name,Name24: name,Pi: pi] :
( piNil
!= ( output @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(1)
thf(fact_256_pi_Odistinct_I39_J,axiom,
! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(39)
thf(fact_257_pi_Odistinct_I3_J,axiom,
! [Pi: pi] :
( piNil
!= ( tau @ Pi ) ) ).
% pi.distinct(3)
thf(fact_258_mismatchNilLeft,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,P: pi] : ( strong743114133lation @ piNil @ Rel @ ( mismatch @ A @ A @ P ) ) ).
% mismatchNilLeft
thf(fact_259_pi_Oinject_I5_J,axiom,
! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
( ( ( mismatch @ X32 @ X2 @ X1 )
= ( mismatch @ Y32 @ Y22 @ Y1 ) )
= ( ( X32 = Y32 )
& ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(5)
thf(fact_260_pi_Odistinct_I9_J,axiom,
! [Name13: name,Name24: name,Pi: pi] :
( piNil
!= ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(9)
thf(fact_261_nilCases_H,axiom,
! [Rs: late_residual] :
~ ( late_transitions @ piNil @ Rs ) ).
% nilCases'
thf(fact_262_zeroTrans,axiom,
! [Rs: late_residual] :
~ ( late_transitions @ piNil @ Rs ) ).
% zeroTrans
thf(fact_263_mismatchCases,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual,F: name > name > $o] :
( ( late_transitions @ ( mismatch @ A @ B2 @ P ) @ Rs )
=> ( ( ( late_transitions @ P @ Rs )
=> ( ( A != B2 )
=> ( F @ A @ B2 ) ) )
=> ( F @ A @ B2 ) ) ) ).
% mismatchCases
thf(fact_264_mismatchTrans,axiom,
! [A: name,P: pi,Rs: late_residual] :
~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% mismatchTrans
thf(fact_265_mismatchCases_H,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( mismatch @ A @ B2 @ P ) @ Rs )
=> ~ ! [P4: pi,A5: name,B4: name] :
( ( ( A = A5 )
& ( B2 = B4 )
& ( P = P4 ) )
=> ( ( late_transitions @ P4 @ Rs )
=> ( A5 = B4 ) ) ) ) ).
% mismatchCases'
thf(fact_266_Mismatch,axiom,
! [P: pi,Rs: late_residual,A: name,B2: name] :
( ( late_transitions @ P @ Rs )
=> ( ( A != B2 )
=> ( late_transitions @ ( mismatch @ A @ B2 @ P ) @ Rs ) ) ) ).
% Mismatch
thf(fact_267_resZeroTrans,axiom,
! [X: name,Rs: late_residual] :
~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% resZeroTrans
thf(fact_268_nilSim_I2_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,X: name,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( input @ A @ X @ P ) ) ).
% nilSim(2)
thf(fact_269_nilSim_I3_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,A: name,B2: name,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( output @ A @ B2 @ P ) ) ).
% nilSim(3)
thf(fact_270_nilSim_I1_J,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi] :
~ ( strong743114133lation @ piNil @ Rel @ ( tau @ P ) ) ).
% nilSim(1)
thf(fact_271_simps_I5_J,axiom,
! [A: name,B2: name,P: pi,C2: name,D: name] :
( ( subs @ ( match @ A @ B2 @ P ) @ C2 @ D )
= ( match @ ( subst_name @ A @ C2 @ D ) @ ( subst_name @ B2 @ C2 @ D ) @ ( subs @ P @ C2 @ D ) ) ) ).
% simps(5)
thf(fact_272_pi_Ofresh_I5_J,axiom,
! [A: name,X32: name,X2: name,X1: pi] :
( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
= ( ( fresh_name_name @ A @ X32 )
& ( fresh_name_name @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(5)
thf(fact_273_pi_Odistinct_I61_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( match @ Name12 @ Name23 @ Pi4 )
!= ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(61)
thf(fact_274_pi_Odistinct_I7_J,axiom,
! [Name13: name,Name24: name,Pi: pi] :
( piNil
!= ( match @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(7)
thf(fact_275_Match,axiom,
! [P: pi,Rs: late_residual,B2: name] :
( ( late_transitions @ P @ Rs )
=> ( late_transitions @ ( match @ B2 @ B2 @ P ) @ Rs ) ) ).
% Match
thf(fact_276_matchCases_H,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( match @ A @ B2 @ P ) @ Rs )
=> ~ ! [P4: pi] :
( ( ( B2 = A )
& ( P = P4 ) )
=> ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% matchCases'
thf(fact_277_matchTrans,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( match @ A @ B2 @ P ) @ Rs )
=> ( A = B2 ) ) ).
% matchTrans
thf(fact_278_matchCases,axiom,
! [A: name,B2: name,P: pi,Rs: late_residual,F: name > name > $o] :
( ( late_transitions @ ( match @ A @ B2 @ P ) @ Rs )
=> ( ( ( late_transitions @ P @ Rs )
=> ( ( A = B2 )
=> ( F @ A @ A ) ) )
=> ( F @ A @ B2 ) ) ) ).
% matchCases
thf(fact_279_pi_Oinject_I4_J,axiom,
! [X32: name,X2: name,X1: pi,Y32: name,Y22: name,Y1: pi] :
( ( ( match @ X32 @ X2 @ X1 )
= ( match @ Y32 @ Y22 @ Y1 ) )
= ( ( X32 = Y32 )
& ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(4)
thf(fact_280_pi_Odistinct_I37_J,axiom,
! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( tau @ Pi4 )
!= ( match @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(37)
thf(fact_281_pi_Odistinct_I23_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( match @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(23)
thf(fact_282_pi_Odistinct_I65_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( match @ Name12 @ Name23 @ Pi4 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(65)
thf(fact_283_pi_Odistinct_I67_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name: name,Pi: pi] :
( ( match @ Name12 @ Name23 @ Pi4 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(67)
thf(fact_284_pi_Odistinct_I49_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( match @ Name13 @ Name24 @ Pi ) ) ).
% pi.distinct(49)
thf(fact_285_matchNilLeft,axiom,
! [A: name,B2: name,Rel: set_Pr1834926343_pi_pi,P: pi] :
( ( A != B2 )
=> ( strong743114133lation @ piNil @ Rel @ ( match @ A @ B2 @ P ) ) ) ).
% matchNilLeft
thf(fact_286_pi_Ostrong__induct,axiom,
! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name2 @ Z2 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_induct
thf(fact_287_pi_Ostrong__induct,axiom,
! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_induct
thf(fact_288_pi_Ostrong__induct,axiom,
! [P: name > pi > $o,Z: name,Pi4: pi] :
( ! [Z2: name] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi13 )
=> ( ! [Za: name] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi13 )
=> ( ! [Za: name] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_induct
thf(fact_289_pi_Ostrong__induct,axiom,
! [P: pi > pi > $o,Z: pi,Pi4: pi] :
( ! [Z2: pi] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi13 )
=> ( ! [Za: pi] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi13 )
=> ( ! [Za: pi] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_induct
thf(fact_290_pi_Ostrong__inducts,axiom,
! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: late_subject] :
( ( fresh_717452603ubject @ Name2 @ Z2 )
=> ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: late_subject] :
( ! [Za: late_subject] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_inducts
thf(fact_291_pi_Ostrong__inducts,axiom,
! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: late_freeRes] :
( ( fresh_1641682979reeRes @ Name2 @ Z2 )
=> ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: late_freeRes] :
( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_inducts
thf(fact_292_pi_Ostrong__inducts,axiom,
! [P: name > pi > $o,Z: name,Pi4: pi] :
( ! [Z2: name] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi13 )
=> ( ! [Za: name] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi13 )
=> ( ! [Za: name] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: name] :
( ( fresh_name_name @ Name2 @ Z2 )
=> ( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: name] :
( ! [Za: name] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_inducts
thf(fact_293_pi_Ostrong__inducts,axiom,
! [P: pi > pi > $o,Z: pi,Pi4: pi] :
( ! [Z2: pi] : ( P @ Z2 @ piNil )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( output @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( tau @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name22 @ Z2 )
=> ( ( fresh_name_name @ Name22 @ Name1 )
=> ( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( input @ Name1 @ Name22 @ Pi3 ) ) ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( match @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Name1: name,Name22: name,Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( mismatch @ Name1 @ Name22 @ Pi3 ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi13 )
=> ( ! [Za: pi] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi13 )
=> ( ! [Za: pi] : ( P @ Za @ Pi23 )
=> ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
=> ( ! [Name2: name,Pi3: pi,Z2: pi] :
( ( fresh_name_pi @ Name2 @ Z2 )
=> ( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( res @ Name2 @ Pi3 ) ) ) )
=> ( ! [Pi3: pi,Z2: pi] :
( ! [Za: pi] : ( P @ Za @ Pi3 )
=> ( P @ Z2 @ ( bang @ Pi3 ) ) )
=> ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% pi.strong_inducts
thf(fact_294_pi_Ofresh_I10_J,axiom,
! [A: name,X1: pi] :
( ( fresh_name_pi @ A @ ( bang @ X1 ) )
= ( fresh_name_pi @ A @ X1 ) ) ).
% pi.fresh(10)
thf(fact_295_pi_Ofresh_I7_J,axiom,
! [A: name,X2: pi,X1: pi] :
( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
= ( ( fresh_name_pi @ A @ X2 )
& ( fresh_name_pi @ A @ X1 ) ) ) ).
% pi.fresh(7)
thf(fact_296_simps_I10_J,axiom,
! [P: pi,C2: name,D: name] :
( ( subs @ ( bang @ P ) @ C2 @ D )
= ( bang @ ( subs @ P @ C2 @ D ) ) ) ).
% simps(10)
thf(fact_297_simps_I7_J,axiom,
! [P: pi,Q: pi,C2: name,D: name] :
( ( subs @ ( sum @ P @ Q ) @ C2 @ D )
= ( sum @ ( subs @ P @ C2 @ D ) @ ( subs @ Q @ C2 @ D ) ) ) ).
% simps(7)
thf(fact_298_pi_Odistinct_I63_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( match @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(63)
thf(fact_299_pi_Odistinct_I69_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
( ( match @ Name12 @ Name23 @ Pi4 )
!= ( bang @ Pi ) ) ).
% pi.distinct(69)
thf(fact_300_bangCases,axiom,
! [P: pi,Rs: late_residual] :
( ( late_transitions @ ( bang @ P ) @ Rs )
=> ~ ! [P4: pi] :
( ( ( bang @ P )
= ( bang @ P4 ) )
=> ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% bangCases
thf(fact_301_Bang,axiom,
! [P: pi,Rs: late_residual] :
( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
=> ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% Bang
thf(fact_302_pi_Odistinct_I53_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(53)
thf(fact_303_pi_Odistinct_I59_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
( ( input @ Name12 @ Name23 @ Pi4 )
!= ( bang @ Pi ) ) ).
% pi.distinct(59)
thf(fact_304_pi_Odistinct_I89_J,axiom,
! [Name3: name,Pi4: pi,Pi: pi] :
( ( res @ Name3 @ Pi4 )
!= ( bang @ Pi ) ) ).
% pi.distinct(89)
thf(fact_305_pi_Odistinct_I87_J,axiom,
! [Pi1: pi,Pi2: pi,Pi: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( bang @ Pi ) ) ).
% pi.distinct(87)
thf(fact_306_sumCases,axiom,
! [P: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases
thf(fact_307_sumCases_H,axiom,
! [P: pi,Q: pi,Rs: late_residual] :
( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
=> ( ~ ( late_transitions @ P @ Rs )
=> ( late_transitions @ Q @ Rs ) ) ) ).
% sumCases'
thf(fact_308_Sum1,axiom,
! [P: pi,Rs: late_residual,Q: pi] :
( ( late_transitions @ P @ Rs )
=> ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% Sum1
thf(fact_309_Sum2,axiom,
! [Q: pi,Rs: late_residual,P: pi] :
( ( late_transitions @ Q @ Rs )
=> ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% Sum2
thf(fact_310_pi_Odistinct_I81_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi ) ) ).
% pi.distinct(81)
thf(fact_311_pi_Odistinct_I79_J,axiom,
! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(79)
thf(fact_312_pi_Oinject_I9_J,axiom,
! [X1: pi,Y1: pi] :
( ( ( bang @ X1 )
= ( bang @ Y1 ) )
= ( X1 = Y1 ) ) ).
% pi.inject(9)
thf(fact_313_pi_Oinject_I6_J,axiom,
! [X2: pi,X1: pi,Y22: pi,Y1: pi] :
( ( ( sum @ X2 @ X1 )
= ( sum @ Y22 @ Y1 ) )
= ( ( X2 = Y22 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(6)
thf(fact_314_pi_Odistinct_I83_J,axiom,
! [Pi1: pi,Pi2: pi,Pi: pi] :
( ( sum @ Pi1 @ Pi2 )
!= ( bang @ Pi ) ) ).
% pi.distinct(83)
thf(fact_315_pi_Odistinct_I27_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi12: pi,Pi22: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(27)
thf(fact_316_pi_Odistinct_I33_J,axiom,
! [Name12: name,Name23: name,Pi4: pi,Pi: pi] :
( ( output @ Name12 @ Name23 @ Pi4 )
!= ( bang @ Pi ) ) ).
% pi.distinct(33)
thf(fact_317_pi_Odistinct_I41_J,axiom,
! [Pi4: pi,Pi12: pi,Pi22: pi] :
( ( tau @ Pi4 )
!= ( sum @ Pi12 @ Pi22 ) ) ).
% pi.distinct(41)
% Helper facts (3)
thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
! [X: name,Y: name] :
( ( if_name @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
! [X: name,Y: name] :
( ( if_name @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
x != aa ).
%------------------------------------------------------------------------------