TPTP Problem File: ITP191^1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP191^1 : TPTP v8.2.0. Released v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : Sledgehammer Strong_Late_Sim_SC problem prob_894__3417700_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_894__3417700_1 [Des21]
% Status : ContradictoryAxioms
% Rating : 0.30 v8.2.0, 0.15 v8.1.0, 0.27 v7.5.0
% Syntax : Number of formulae : 568 ( 217 unt; 206 typ; 0 def)
% Number of atoms : 990 ( 367 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 4476 ( 96 ~; 1 |; 65 &;3860 @)
% ( 0 <=>; 454 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 350 ( 350 >; 0 *; 0 +; 0 <<)
% Number of symbols : 158 ( 155 usr; 20 con; 0-5 aty)
% Number of variables : 1309 ( 7 ^;1275 !; 27 ?;1309 :)
% SPC : TH0_CAX_EQU_NAR
% Comments : This file was generated by Sledgehammer 2021-02-23 15:32:44.830
%------------------------------------------------------------------------------
% Could-be-implicit typings (51)
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% Explicit typings (155)
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thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__List__Olist_It__Agent__Opi____Rep_J,type,
perm_n729617823pi_Rep: list_P227219501e_name > list_pi_Rep > list_pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__List__Olist_It__Late____Semantics__OfreeRes_J,type,
perm_n808352945reeRes: list_P227219501e_name > list_Late_freeRes > list_Late_freeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__List__Olist_It__Late____Semantics__Osubject_J,type,
perm_n1812647369ubject: list_P227219501e_name > list_Late_subject > list_Late_subject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__List__Olist_It__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J_J,type,
perm_n1160739829e_name: list_P227219501e_name > list_P227219501e_name > list_P227219501e_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
perm_n1255502110_pi_pi: list_P227219501e_name > produc1141751126_pi_pi > produc1141751126_pi_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
perm_n1415585007_pi_pi: list_P227219501e_name > product_prod_pi_pi > product_prod_pi_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Oname_J,type,
perm_n258463228s_name: list_P227219501e_name > produc2052722628s_name > produc2052722628s_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi_J,type,
perm_n1211707594Res_pi: list_P227219501e_name > produc992857746Res_pi > produc992857746Res_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Agent__Opi____Rep_J,type,
perm_n840427369pi_Rep: list_P227219501e_name > produc1777919905pi_Rep > produc1777919905pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
perm_n169932155reeRes: list_P227219501e_name > produc1357834675reeRes > produc1357834675reeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__Osubject_J,type,
perm_n1174226579ubject: list_P227219501e_name > produc214645451ubject > produc214645451ubject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Oname_J,type,
perm_n204483300t_name: list_P227219501e_name > produc1998742700t_name > produc1998742700t_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi_J,type,
perm_n359102898ect_pi: list_P227219501e_name > produc140253050ect_pi > produc140253050ect_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Agent__Opi____Rep_J,type,
perm_n1467004033pi_Rep: list_P227219501e_name > produc257012921pi_Rep > produc257012921pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__OfreeRes_J,type,
perm_n1314686611reeRes: list_P227219501e_name > produc355105483reeRes > produc355105483reeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
perm_n171497387ubject: list_P227219501e_name > produc1359399907ubject > produc1359399907ubject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Product____Type__Ounit,type,
perm_n1960409557t_unit: list_P227219501e_name > product_unit > product_unit ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Oname_J,type,
perm_name_set_name: list_P227219501e_name > set_name > set_name ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi_J,type,
perm_name_set_pi: list_P227219501e_name > set_pi > set_pi ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Agent__Opi____Rep_J,type,
perm_name_set_pi_Rep: list_P227219501e_name > set_pi_Rep > set_pi_Rep ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__OfreeRes_J,type,
perm_n1555914327reeRes: list_P227219501e_name > set_Late_freeRes > set_Late_freeRes ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Late____Semantics__Osubject_J,type,
perm_n412725103ubject: list_P227219501e_name > set_Late_subject > set_Late_subject ).
thf(sy_c_Nominal_Operm_001t__Agent__Oname_001t__Set__Oset_It__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J_J,type,
perm_n675238095_pi_pi: list_P227219501e_name > set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi ).
thf(sy_c_Nominal_Oswap_001t__Agent__Oname,type,
swap_name2: produc367475239e_name > name > name ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Oname,type,
produc1570949143e_name: name > name > produc367475239e_name ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Agent__Opi,type,
product_Pair_name_pi: name > pi > product_prod_name_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Oprod_It__Agent__Opi_Mt__Agent__Opi_J,type,
produc235456326_pi_pi: name > product_prod_pi_pi > produc1141751126_pi_pi ).
thf(sy_c_Product__Type_OPair_001t__Agent__Oname_001t__Product____Type__Ounit,type,
produc1785453612t_unit: name > product_unit > produc546891580t_unit ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi_001t__Agent__Oname,type,
product_Pair_pi_name: pi > name > product_prod_pi_name ).
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__Agent__Opi_001t__Product____Type__Ounit,type,
produc1831798878t_unit: pi > product_unit > produc1028309998t_unit ).
thf(sy_c_Product__Type_OPair_001t__Agent__Opi____Rep_001t__Agent__Opi____Rep,type,
produc784048711pi_Rep: pi_Rep > pi_Rep > produc1212344719pi_Rep ).
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__Agent__Opi____Rep,type,
produc216486617pi_Rep: late_freeRes > pi_Rep > produc1777919905pi_Rep ).
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__Agent__Opi____Rep,type,
produc843063281pi_Rep: late_subject > pi_Rep > produc257012921pi_Rep ).
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_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Oname,type,
produc421428802t_name: product_unit > name > produc135724498t_name ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Agent__Opi,type,
produc1806354576nit_pi: product_unit > pi > produc738223008nit_pi ).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
produc1076565719t_unit: product_unit > product_unit > produc971140967t_unit ).
thf(sy_c_Product__Type_OUnity,type,
product_Unity: product_unit ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Oname,type,
eqvt_name: set_Pr443758855e_name > $o ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi,type,
eqvt_pi: set_Pr1834926343_pi_pi > $o ).
thf(sy_c_Rel_Oeqvt_001t__Agent__Opi____Rep,type,
eqvt_pi_Rep: set_Pr1131282415pi_Rep > $o ).
thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__OfreeRes,type,
eqvt_Late_freeRes: set_Pr1780909331reeRes > $o ).
thf(sy_c_Rel_Oeqvt_001t__Late____Semantics__Osubject,type,
eqvt_Late_subject: set_Pr806375235ubject > $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__Agent__Oname,type,
member_name: name > set_name > $o ).
thf(sy_c_member_001t__Agent__Opi,type,
member_pi: pi > set_pi > $o ).
thf(sy_c_member_001t__Agent__Opi____Rep,type,
member_pi_Rep: pi_Rep > set_pi_Rep > $o ).
thf(sy_c_member_001t__Late____Semantics__OfreeRes,type,
member_Late_freeRes: late_freeRes > set_Late_freeRes > $o ).
thf(sy_c_member_001t__Late____Semantics__Osubject,type,
member_Late_subject: late_subject > set_Late_subject > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Agent__Oname_Mt__Agent__Oname_J,type,
member695284560e_name: produc367475239e_name > set_Pr443758855e_name > $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_c_member_001t__Product____Type__Oprod_It__Agent__Opi____Rep_Mt__Agent__Opi____Rep_J,type,
member1671908408pi_Rep: produc1212344719pi_Rep > set_Pr1131282415pi_Rep > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__OfreeRes_Mt__Late____Semantics__OfreeRes_J,type,
member1584979804reeRes: produc1357834675reeRes > set_Pr1780909331reeRes > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Late____Semantics__Osubject_Mt__Late____Semantics__Osubject_J,type,
member1586545036ubject: produc1359399907ubject > set_Pr806375235ubject > $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_aa____,type,
aa: late_subject ).
thf(sy_v_ab____,type,
ab: name ).
thf(sy_v_b____,type,
b: name ).
thf(sy_v_c____,type,
c: 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_ya____,type,
ya: name ).
% Relevant facts (350)
thf(fact_0_cComm1_Ohyps_I5_J,axiom,
ya != b ).
% cComm1.hyps(5)
thf(fact_1_cComm1_Ohyps_I9_J,axiom,
( ( late_OutputR @ ab @ x )
= late_TauR ) ).
% cComm1.hyps(9)
thf(fact_2_cOpen_Ohyps_I2_J,axiom,
ab != x ).
% cOpen.hyps(2)
thf(fact_3_cComm1_Ohyps_I6_J,axiom,
ya != c ).
% cComm1.hyps(6)
thf(fact_4_cOpen_Ohyps_I3_J,axiom,
( aa
= ( late_BoundOutputS @ ab ) ) ).
% cOpen.hyps(3)
thf(fact_5_assms_I3_J,axiom,
eqvt_pi @ rel ).
% assms(3)
thf(fact_6__092_060open_062y_____A_092_060noteq_062_Ax_092_060close_062,axiom,
y != x ).
% \<open>y__ \<noteq> x\<close>
thf(fact_7_Bound_Ohyps_I1_J,axiom,
late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_BoundR @ aa @ y @ xPQ ) ).
% Bound.hyps(1)
thf(fact_8_assms_I1_J,axiom,
fresh_name_pi @ x @ p ).
% assms(1)
thf(fact_9_cComm1_Ohyps_I3_J,axiom,
fresh_name_pi @ ya @ p ).
% cComm1.hyps(3)
thf(fact_10_cComm1_Ohyps_I4_J,axiom,
fresh_name_pi @ ya @ q ).
% cComm1.hyps(4)
thf(fact_11_cComm1_Ohyps_I7_J,axiom,
fresh_name_pi @ ya @ q2 ).
% cComm1.hyps(7)
thf(fact_12_Bound_Ohyps_I3_J,axiom,
fresh_name_pi @ y @ ( res @ x @ ( par @ p @ q ) ) ).
% Bound.hyps(3)
thf(fact_13_Bound_Ohyps_I2_J,axiom,
fresh_name_pi @ y @ ( par @ p @ ( res @ x @ q ) ) ).
% Bound.hyps(2)
thf(fact_14_Strong__Late__Sim__SC__Mirabelle__ygjvazaixl_OsubstRes3,axiom,
! [A: name,P: pi,X: name] :
( ( subs @ ( res @ A @ P ) @ X @ A )
= ( res @ X @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ A ) @ nil_Pr743626285e_name ) @ P ) ) ) ).
% Strong_Late_Sim_SC_Mirabelle_ygjvazaixl.substRes3
thf(fact_15_cComm1_Ohyps_I1_J,axiom,
late_transitions @ p @ ( late_BoundR @ ( late_InputS @ b ) @ ya @ p2 ) ).
% cComm1.hyps(1)
thf(fact_16_perm__swap_I1_J,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_17_perm__swap_I1_J,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_18_perm__swap_I1_J,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_19_perm__swap_I1_J,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_20_perm__swap_I1_J,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(1)
thf(fact_21_name__id,axiom,
! [A: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_22_name__id,axiom,
! [A: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_23_name__id,axiom,
! [A: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_24_name__id,axiom,
! [A: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_25_name__id,axiom,
! [A: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ A ) @ nil_Pr743626285e_name ) @ X )
= X ) ).
% name_id
thf(fact_26_name__swap,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_27_name__swap,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_28_name__swap,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_29_name__swap,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_30_name__swap,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) ) ).
% name_swap
thf(fact_31_name__swap__bij,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_32_name__swap__bij,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_33_name__swap__bij,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_34_name__swap__bij,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_35_name__swap__bij,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% name_swap_bij
thf(fact_36_cOpen_Ohyps_I1_J,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ ( late_OutputR @ ab @ x ) @ pq ) ).
% cOpen.hyps(1)
thf(fact_37_pi_Operm_I8_J,axiom,
! [Pi: list_P227219501e_name,X2: pi,X1: pi] :
( ( perm_name_pi @ Pi @ ( par @ X2 @ X1 ) )
= ( par @ ( perm_name_pi @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% pi.perm(8)
thf(fact_38_simps_I8_J,axiom,
! [P: pi,Q: pi,C: name,D: name] :
( ( subs @ ( par @ P @ Q ) @ C @ D )
= ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% simps(8)
thf(fact_39_simps_I9_J,axiom,
! [X: name,C: name,D: name,P: pi] :
( ( X != C )
=> ( ( X != D )
=> ( ( subs @ ( res @ X @ P ) @ C @ D )
= ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% simps(9)
thf(fact_40_pt__name1,axiom,
! [X: late_subject] :
( ( perm_n1559866809ubject @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_41_pt__name1,axiom,
! [X: late_freeRes] :
( ( perm_n336613537reeRes @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_42_pt__name1,axiom,
! [X: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_43_pt__name1,axiom,
! [X: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_44_pt__name1,axiom,
! [X: pi] :
( ( perm_name_pi @ nil_Pr743626285e_name @ X )
= X ) ).
% pt_name1
thf(fact_45_cComm1_Ohyps_I2_J,axiom,
late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ c ) @ q2 ) ).
% cComm1.hyps(2)
thf(fact_46__092_060open_062y_____A_092_060sharp_062_AP_A_092_060parallel_062_AQ_092_060close_062,axiom,
fresh_name_pi @ y @ ( par @ p @ q ) ).
% \<open>y__ \<sharp> P \<parallel> Q\<close>
thf(fact_47_subst__identity,axiom,
! [P: pi,A: name] :
( ( subs @ P @ A @ A )
= P ) ).
% subst_identity
thf(fact_48_pi__perm__empty,axiom,
! [Pi_Rep: pi_Rep] :
( ( perm_name_pi_Rep @ nil_Pr743626285e_name @ Pi_Rep )
= Pi_Rep ) ).
% pi_perm_empty
thf(fact_49__092_060open_062y_____A_092_060sharp_062_AP_092_060close_062,axiom,
fresh_name_pi @ y @ p ).
% \<open>y__ \<sharp> P\<close>
thf(fact_50__092_060open_062y_____A_092_060sharp_062_AQ_092_060close_062,axiom,
fresh_name_pi @ y @ q ).
% \<open>y__ \<sharp> Q\<close>
thf(fact_51_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_52_pi_Operm_I9_J,axiom,
! [Pi: list_P227219501e_name,X1: name,X2: pi] :
( ( perm_name_pi @ Pi @ ( res @ X1 @ X2 ) )
= ( res @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% pi.perm(9)
thf(fact_53_perm__fresh__fresh,axiom,
! [A: name,X: late_subject,B: name] :
( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ B @ X )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_54_perm__fresh__fresh,axiom,
! [A: name,X: late_freeRes,B: name] :
( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ B @ X )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_55_perm__fresh__fresh,axiom,
! [A: name,X: pi_Rep,B: name] :
( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ B @ X )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_56_perm__fresh__fresh,axiom,
! [A: name,X: product_unit,B: name] :
( ( fresh_1143631827t_unit @ A @ X )
=> ( ( fresh_1143631827t_unit @ B @ X )
=> ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_57_perm__fresh__fresh,axiom,
! [A: name,X: produc1141751126_pi_pi,B: name] :
( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ B @ X )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_58_perm__fresh__fresh,axiom,
! [A: name,X: name,B: name] :
( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ B @ X )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_59_perm__fresh__fresh,axiom,
! [A: name,X: pi,B: name] :
( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ B @ X )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_60_perm__fresh__fresh,axiom,
! [A: name,X: name > noption_pi,B: name] :
( ( fresh_543891186ion_pi @ A @ X )
=> ( ( fresh_543891186ion_pi @ B @ X )
=> ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% perm_fresh_fresh
thf(fact_61_name__fresh__fresh,axiom,
! [A: name,X: late_subject,B: name] :
( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ B @ X )
=> ( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_62_name__fresh__fresh,axiom,
! [A: name,X: late_freeRes,B: name] :
( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ B @ X )
=> ( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_63_name__fresh__fresh,axiom,
! [A: name,X: pi_Rep,B: name] :
( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ B @ X )
=> ( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_64_name__fresh__fresh,axiom,
! [A: name,X: product_unit,B: name] :
( ( fresh_1143631827t_unit @ A @ X )
=> ( ( fresh_1143631827t_unit @ B @ X )
=> ( ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_65_name__fresh__fresh,axiom,
! [A: name,X: produc1141751126_pi_pi,B: name] :
( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ B @ X )
=> ( ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_66_name__fresh__fresh,axiom,
! [A: name,X: name,B: name] :
( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ B @ X )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_67_name__fresh__fresh,axiom,
! [A: name,X: pi,B: name] :
( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ B @ X )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_68_name__fresh__fresh,axiom,
! [A: name,X: name > noption_pi,B: name] :
( ( fresh_543891186ion_pi @ A @ X )
=> ( ( fresh_543891186ion_pi @ B @ X )
=> ( ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X )
= X ) ) ) ).
% name_fresh_fresh
thf(fact_69_Bound_Ohyps_I4_J,axiom,
fresh_717452603ubject @ y @ aa ).
% Bound.hyps(4)
thf(fact_70_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: late_subject] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_717452603ubject @ A @ X )
=> ( fresh_717452603ubject @ A @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_71_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: late_freeRes] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_1641682979reeRes @ A @ X )
=> ( fresh_1641682979reeRes @ A @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_72_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: pi_Rep] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_pi_Rep @ A @ X )
=> ( fresh_name_pi_Rep @ A @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_73_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: product_unit] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_1143631827t_unit @ A @ X )
=> ( fresh_1143631827t_unit @ A @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_74_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: produc1141751126_pi_pi] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_1376661020_pi_pi @ A @ X )
=> ( fresh_1376661020_pi_pi @ A @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_75_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: name] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_name @ A @ X )
=> ( fresh_name_name @ A @ ( perm_name_name @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_76_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: pi] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_name_pi @ A @ X )
=> ( fresh_name_pi @ A @ ( perm_name_pi @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_77_fresh__perm__app,axiom,
! [A: name,Pi: list_P227219501e_name,X: name > noption_pi] :
( ( fresh_922791155e_name @ A @ Pi )
=> ( ( fresh_543891186ion_pi @ A @ X )
=> ( fresh_543891186ion_pi @ A @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ) ).
% fresh_perm_app
thf(fact_78_name__exists__fresh,axiom,
! [X: product_unit] :
~ ! [C2: name] :
~ ( fresh_1143631827t_unit @ C2 @ X ) ).
% name_exists_fresh
thf(fact_79_name__exists__fresh,axiom,
! [X: produc1141751126_pi_pi] :
~ ! [C2: name] :
~ ( fresh_1376661020_pi_pi @ C2 @ X ) ).
% name_exists_fresh
thf(fact_80_name__exists__fresh,axiom,
! [X: name] :
~ ! [C2: name] :
~ ( fresh_name_name @ C2 @ X ) ).
% name_exists_fresh
thf(fact_81_name__exists__fresh,axiom,
! [X: pi] :
~ ! [C2: name] :
~ ( fresh_name_pi @ C2 @ X ) ).
% name_exists_fresh
thf(fact_82_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_subject] :
( ( perm_name_o @ Pi @ ( fresh_717452603ubject @ A @ X ) )
= ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_83_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
( ( perm_name_o @ Pi @ ( fresh_1641682979reeRes @ A @ X ) )
= ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_84_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
( ( perm_name_o @ Pi @ ( fresh_name_pi_Rep @ A @ X ) )
= ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_85_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: product_unit] :
( ( perm_name_o @ Pi @ ( fresh_1143631827t_unit @ A @ X ) )
= ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_86_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
( ( perm_name_o @ Pi @ ( fresh_1376661020_pi_pi @ A @ X ) )
= ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_87_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: name] :
( ( perm_name_o @ Pi @ ( fresh_name_name @ A @ X ) )
= ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_88_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi] :
( ( perm_name_o @ Pi @ ( fresh_name_pi @ A @ X ) )
= ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_89_fresh__eqvt,axiom,
! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
( ( perm_name_o @ Pi @ ( fresh_543891186ion_pi @ A @ X ) )
= ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) ) ) ).
% fresh_eqvt
thf(fact_90_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_subject] :
( ( fresh_717452603ubject @ ( perm_name_name @ Pi @ A ) @ ( perm_n1559866809ubject @ Pi @ X ) )
= ( fresh_717452603ubject @ A @ X ) ) ).
% fresh_bij
thf(fact_91_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: late_freeRes] :
( ( fresh_1641682979reeRes @ ( perm_name_name @ Pi @ A ) @ ( perm_n336613537reeRes @ Pi @ X ) )
= ( fresh_1641682979reeRes @ A @ X ) ) ).
% fresh_bij
thf(fact_92_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi_Rep] :
( ( fresh_name_pi_Rep @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi_Rep @ Pi @ X ) )
= ( fresh_name_pi_Rep @ A @ X ) ) ).
% fresh_bij
thf(fact_93_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: product_unit] :
( ( fresh_1143631827t_unit @ ( perm_name_name @ Pi @ A ) @ ( perm_n1960409557t_unit @ Pi @ X ) )
= ( fresh_1143631827t_unit @ A @ X ) ) ).
% fresh_bij
thf(fact_94_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1255502110_pi_pi @ Pi @ X ) )
= ( fresh_1376661020_pi_pi @ A @ X ) ) ).
% fresh_bij
thf(fact_95_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: name] :
( ( fresh_name_name @ ( perm_name_name @ Pi @ A ) @ ( perm_name_name @ Pi @ X ) )
= ( fresh_name_name @ A @ X ) ) ).
% fresh_bij
thf(fact_96_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: pi] :
( ( fresh_name_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_name_pi @ Pi @ X ) )
= ( fresh_name_pi @ A @ X ) ) ).
% fresh_bij
thf(fact_97_fresh__bij,axiom,
! [Pi: list_P227219501e_name,A: name,X: name > noption_pi] :
( ( fresh_543891186ion_pi @ ( perm_name_name @ Pi @ A ) @ ( perm_n1667196784ion_pi @ Pi @ X ) )
= ( fresh_543891186ion_pi @ A @ X ) ) ).
% fresh_bij
thf(fact_98_freshRes,axiom,
! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% freshRes
thf(fact_99_fresh__fact2,axiom,
! [A: name,B: name,P: pi] :
( ( A != B )
=> ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% fresh_fact2
thf(fact_100_fresh__fact1,axiom,
! [A: name,P: pi,C: name,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( A != C )
=> ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% fresh_fact1
thf(fact_101_forget,axiom,
! [A: name,P: pi,B: name] :
( ( fresh_name_pi @ A @ P )
=> ( ( subs @ P @ A @ B )
= P ) ) ).
% forget
thf(fact_102_name__calc_I2_J,axiom,
! [X: name] :
( ( perm_name_name @ nil_Pr743626285e_name @ X )
= X ) ).
% name_calc(2)
thf(fact_103_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_104_Collect__mem__eq,axiom,
! [A2: set_Pr1834926343_pi_pi] :
( ( collec1051790738_pi_pi
@ ^ [X3: product_prod_pi_pi] : ( member558706512_pi_pi @ X3 @ A2 ) )
= A2 ) ).
% Collect_mem_eq
thf(fact_105_Agent_OsubstRes3,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( res @ A @ P ) @ A @ B )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% Agent.substRes3
thf(fact_106_substRes2,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( res @ A @ P )
= ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% substRes2
thf(fact_107_eqvt__subs,axiom,
! [P2: list_P227219501e_name,P: pi,A: name,B: name] :
( ( perm_name_pi @ P2 @ ( subs @ P @ A @ B ) )
= ( subs @ ( perm_name_pi @ P2 @ P ) @ ( perm_name_name @ P2 @ A ) @ ( perm_name_name @ P2 @ B ) ) ) ).
% eqvt_subs
thf(fact_108_swap__simps_I1_J,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ A )
= B ) ).
% swap_simps(1)
thf(fact_109_swap__simps_I2_J,axiom,
! [A: name,B: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ B )
= A ) ).
% swap_simps(2)
thf(fact_110_swap__simps_I3_J,axiom,
! [A: name,C: name,B: name] :
( ( A != C )
=> ( ( B != C )
=> ( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ C )
= C ) ) ) ).
% swap_simps(3)
thf(fact_111_fresh__aux,axiom,
! [C: name,A: name,X: late_subject,B: name] :
( ( C != A )
=> ( ( fresh_717452603ubject @ A @ X )
=> ( ( fresh_717452603ubject @ C @ X )
=> ( fresh_717452603ubject @ C @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_112_fresh__aux,axiom,
! [C: name,A: name,X: late_freeRes,B: name] :
( ( C != A )
=> ( ( fresh_1641682979reeRes @ A @ X )
=> ( ( fresh_1641682979reeRes @ C @ X )
=> ( fresh_1641682979reeRes @ C @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_113_fresh__aux,axiom,
! [C: name,A: name,X: pi_Rep,B: name] :
( ( C != A )
=> ( ( fresh_name_pi_Rep @ A @ X )
=> ( ( fresh_name_pi_Rep @ C @ X )
=> ( fresh_name_pi_Rep @ C @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_114_fresh__aux,axiom,
! [C: name,A: name,X: product_unit,B: name] :
( ( C != A )
=> ( ( fresh_1143631827t_unit @ A @ X )
=> ( ( fresh_1143631827t_unit @ C @ X )
=> ( fresh_1143631827t_unit @ C @ ( perm_n1960409557t_unit @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_115_fresh__aux,axiom,
! [C: name,A: name,X: produc1141751126_pi_pi,B: name] :
( ( C != A )
=> ( ( fresh_1376661020_pi_pi @ A @ X )
=> ( ( fresh_1376661020_pi_pi @ C @ X )
=> ( fresh_1376661020_pi_pi @ C @ ( perm_n1255502110_pi_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_116_fresh__aux,axiom,
! [C: name,A: name,X: name,B: name] :
( ( C != A )
=> ( ( fresh_name_name @ A @ X )
=> ( ( fresh_name_name @ C @ X )
=> ( fresh_name_name @ C @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_117_fresh__aux,axiom,
! [C: name,A: name,X: pi,B: name] :
( ( C != A )
=> ( ( fresh_name_pi @ A @ X )
=> ( ( fresh_name_pi @ C @ X )
=> ( fresh_name_pi @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_118_fresh__aux,axiom,
! [C: name,A: name,X: name > noption_pi,B: name] :
( ( C != A )
=> ( ( fresh_543891186ion_pi @ A @ X )
=> ( ( fresh_543891186ion_pi @ C @ X )
=> ( fresh_543891186ion_pi @ C @ ( perm_n1667196784ion_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ X ) ) ) ) ) ).
% fresh_aux
thf(fact_119_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi1 @ ( perm_n1559866809ubject @ Pi2 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n1559866809ubject @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_120_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi1 @ ( perm_n336613537reeRes @ Pi2 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_n336613537reeRes @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_121_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi1 @ ( perm_name_pi_Rep @ Pi2 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi_Rep @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_122_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi1 @ ( perm_name_name @ Pi2 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_name @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_123_cp__name__name1,axiom,
! [Pi1: list_P227219501e_name,Pi2: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi1 @ ( perm_name_pi @ Pi2 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi1 @ Pi2 ) @ ( perm_name_pi @ Pi1 @ X ) ) ) ).
% cp_name_name1
thf(fact_124_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_125_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_126_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_127_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_128_name__perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% name_perm_compose
thf(fact_129_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_subject] :
( ( perm_n1559866809ubject @ Pi2 @ ( perm_n1559866809ubject @ Pi1 @ X ) )
= ( perm_n1559866809ubject @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n1559866809ubject @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_130_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi2 @ ( perm_n336613537reeRes @ Pi1 @ X ) )
= ( perm_n336613537reeRes @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_n336613537reeRes @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_131_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi_Rep] :
( ( perm_name_pi_Rep @ Pi2 @ ( perm_name_pi_Rep @ Pi1 @ X ) )
= ( perm_name_pi_Rep @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi_Rep @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_132_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: name] :
( ( perm_name_name @ Pi2 @ ( perm_name_name @ Pi1 @ X ) )
= ( perm_name_name @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_name @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_133_perm__compose,axiom,
! [Pi2: list_P227219501e_name,Pi1: list_P227219501e_name,X: pi] :
( ( perm_name_pi @ Pi2 @ ( perm_name_pi @ Pi1 @ X ) )
= ( perm_name_pi @ ( perm_n1160739829e_name @ Pi2 @ Pi1 ) @ ( perm_name_pi @ Pi2 @ X ) ) ) ).
% perm_compose
thf(fact_134_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
( ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y ) )
= ( X = Y ) ) ).
% perm_bij
thf(fact_135_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
( ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y ) )
= ( X = Y ) ) ).
% perm_bij
thf(fact_136_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
( ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y ) )
= ( X = Y ) ) ).
% perm_bij
thf(fact_137_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: name,Y: name] :
( ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y ) )
= ( X = Y ) ) ).
% perm_bij
thf(fact_138_perm__bij,axiom,
! [Pi: list_P227219501e_name,X: pi,Y: pi] :
( ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y ) )
= ( X = Y ) ) ).
% perm_bij
thf(fact_139_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_subject > late_subject,X: late_subject] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n1447856217ubject @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% perm_app
thf(fact_140_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_freeRes > late_subject,X: late_freeRes] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n303101761ubject @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% perm_app
thf(fact_141_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi_Rep > late_subject,X: pi_Rep] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n698371375ubject @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% perm_app
thf(fact_142_perm__app,axiom,
! [Pi: list_P227219501e_name,F: name > late_subject,X: name] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n1387060402ubject @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% perm_app
thf(fact_143_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi > late_subject,X: pi] :
( ( perm_n1559866809ubject @ Pi @ ( F @ X ) )
= ( perm_n190055296ubject @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% perm_app
thf(fact_144_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_subject > late_freeRes,X: late_subject] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n443561793reeRes @ Pi @ F @ ( perm_n1559866809ubject @ Pi @ X ) ) ) ).
% perm_app
thf(fact_145_perm__app,axiom,
! [Pi: list_P227219501e_name,F: late_freeRes > late_freeRes,X: late_freeRes] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1446290985reeRes @ Pi @ F @ ( perm_n336613537reeRes @ Pi @ X ) ) ) ).
% perm_app
thf(fact_146_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi_Rep > late_freeRes,X: pi_Rep] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1841560599reeRes @ Pi @ F @ ( perm_name_pi_Rep @ Pi @ X ) ) ) ).
% perm_app
thf(fact_147_perm__app,axiom,
! [Pi: list_P227219501e_name,F: name > late_freeRes,X: name] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n382765978reeRes @ Pi @ F @ ( perm_name_name @ Pi @ X ) ) ) ).
% perm_app
thf(fact_148_perm__app,axiom,
! [Pi: list_P227219501e_name,F: pi > late_freeRes,X: pi] :
( ( perm_n336613537reeRes @ Pi @ ( F @ X ) )
= ( perm_n1333244520reeRes @ Pi @ F @ ( perm_name_pi @ Pi @ X ) ) ) ).
% perm_app
thf(fact_149_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: product_prod_pi_pi,X4: set_Pr1834926343_pi_pi] :
( ( perm_name_o @ Pi @ ( member558706512_pi_pi @ X @ X4 ) )
= ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Pi @ X ) @ ( perm_n675238095_pi_pi @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_150_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,X4: set_Late_subject] :
( ( perm_name_o @ Pi @ ( member_Late_subject @ X @ X4 ) )
= ( member_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n412725103ubject @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_151_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,X4: set_Late_freeRes] :
( ( perm_name_o @ Pi @ ( member_Late_freeRes @ X @ X4 ) )
= ( member_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1555914327reeRes @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_152_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,X4: set_pi_Rep] :
( ( perm_name_o @ Pi @ ( member_pi_Rep @ X @ X4 ) )
= ( member_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_name_set_pi_Rep @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_153_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,X4: set_name] :
( ( perm_name_o @ Pi @ ( member_name @ X @ X4 ) )
= ( member_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_set_name @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_154_in__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,X4: set_pi] :
( ( perm_name_o @ Pi @ ( member_pi @ X @ X4 ) )
= ( member_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_set_pi @ Pi @ X4 ) ) ) ).
% in_eqvt
thf(fact_155_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
( ( perm_name_o @ Pi @ ( X = Y ) )
= ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% eq_eqvt
thf(fact_156_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
( ( perm_name_o @ Pi @ ( X = Y ) )
= ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% eq_eqvt
thf(fact_157_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
( ( perm_name_o @ Pi @ ( X = Y ) )
= ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% eq_eqvt
thf(fact_158_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,Y: name] :
( ( perm_name_o @ Pi @ ( X = Y ) )
= ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y ) ) ) ).
% eq_eqvt
thf(fact_159_eq__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,Y: pi] :
( ( perm_name_o @ Pi @ ( X = Y ) )
= ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y ) ) ) ).
% eq_eqvt
thf(fact_160_pi_Oinject_I7_J,axiom,
! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
( ( ( par @ X2 @ X1 )
= ( par @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% pi.inject(7)
thf(fact_161_alphaRes,axiom,
! [C: name,P: pi,A: name] :
( ( fresh_name_pi @ C @ P )
=> ( ( res @ A @ P )
= ( res @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% alphaRes
thf(fact_162_injPermSubst,axiom,
! [B: name,P: pi,A: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ P )
= ( subs @ P @ A @ B ) ) ) ).
% injPermSubst
thf(fact_163_renaming,axiom,
! [C: name,P: pi,A: name,B: name] :
( ( fresh_name_pi @ C @ P )
=> ( ( subs @ P @ A @ B )
= ( subs @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ C @ A ) @ nil_Pr743626285e_name ) @ P ) @ C @ B ) ) ) ).
% renaming
thf(fact_164_pi_Odistinct_I85_J,axiom,
! [Pi1: pi,Pi2: pi,Name: name,Pi3: pi] :
( ( par @ Pi1 @ Pi2 )
!= ( res @ Name @ Pi3 ) ) ).
% pi.distinct(85)
thf(fact_165_perm__swap_I2_J,axiom,
! [A: name,B: name,X: late_subject] :
( ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n1559866809ubject @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_166_perm__swap_I2_J,axiom,
! [A: name,B: name,X: late_freeRes] :
( ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_n336613537reeRes @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_167_perm__swap_I2_J,axiom,
! [A: name,B: name,X: pi_Rep] :
( ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi_Rep @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_168_perm__swap_I2_J,axiom,
! [A: name,B: name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_169_perm__swap_I2_J,axiom,
! [A: name,B: name,X: pi] :
( ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ nil_Pr743626285e_name ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ B @ A ) @ nil_Pr743626285e_name ) @ X ) )
= X ) ).
% perm_swap(2)
thf(fact_170_transitions_OClose2,axiom,
! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
=> ( ( 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 @ P3 )
=> ( ( Y != A )
=> ( ( fresh_name_pi @ Y @ Q2 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close2
thf(fact_171_transitions_OClose1,axiom,
! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
=> ( ( 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 @ P3 )
=> ( ( X != Y )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Close1
thf(fact_172_Late__Semantics_OClose2,axiom,
! [P: pi,A: name,Y: name,P3: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P3 ) )
=> ( ( 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 @ P3 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% Late_Semantics.Close2
thf(fact_173_Late__Semantics_OClose1,axiom,
! [P: pi,A: name,X: name,P3: pi,Q: pi,Y: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
=> ( ( 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 @ P3 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% Late_Semantics.Close1
thf(fact_174_transitions_OComm2,axiom,
! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B )
=> ( ( fresh_name_pi @ X @ P3 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm2
thf(fact_175_transitions_OComm1,axiom,
! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( X != A )
=> ( ( X != B )
=> ( ( fresh_name_pi @ X @ Q2 )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% transitions.Comm1
thf(fact_176_Late__Semantics_OComm2,axiom,
! [P: pi,A: name,B: name,P3: pi,Q: pi,X: name,Q2: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
=> ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P3 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% Late_Semantics.Comm2
thf(fact_177_Late__Semantics_OComm1,axiom,
! [P: pi,A: name,X: name,P3: pi,Q: pi,B: name,Q2: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P3 ) )
=> ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P3 @ X @ B ) @ Q2 ) ) ) ) ) ).
% Late_Semantics.Comm1
thf(fact_178_alphaBoundResidual,axiom,
! [X5: name,P: pi,A: late_subject,X: name] :
( ( fresh_name_pi @ X5 @ P )
=> ( ( late_BoundR @ A @ X @ P )
= ( late_BoundR @ A @ X5 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ X5 ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% alphaBoundResidual
thf(fact_179_freeRes__perm__empty,axiom,
! [FreeRes_Rep: late_freeRes_Rep] :
( ( perm_n1938283068es_Rep @ nil_Pr743626285e_name @ FreeRes_Rep )
= FreeRes_Rep ) ).
% freeRes_perm_empty
thf(fact_180_subject__perm__empty,axiom,
! [Subject_Rep: late_subject_Rep] :
( ( perm_n697952036ct_Rep @ nil_Pr743626285e_name @ Subject_Rep )
= Subject_Rep ) ).
% subject_perm_empty
thf(fact_181_residual__perm__empty,axiom,
! [Residual_Rep: late_residual_Rep] :
( ( perm_n890803237al_Rep @ nil_Pr743626285e_name @ Residual_Rep )
= Residual_Rep ) ).
% residual_perm_empty
thf(fact_182_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_183_Late__Semantics_OfreeRes_Oinject,axiom,
! [X2: name,X1: name,Y2: name,Y1: name] :
( ( ( late_OutputR @ X2 @ X1 )
= ( late_OutputR @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% Late_Semantics.freeRes.inject
thf(fact_184_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_185_freeRes_Ofresh_I2_J,axiom,
! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% freeRes.fresh(2)
thf(fact_186_freeRes_Operm_I2_J,axiom,
! [Pi: list_P227219501e_name] :
( ( perm_n336613537reeRes @ Pi @ late_TauR )
= late_TauR ) ).
% freeRes.perm(2)
thf(fact_187_cComm1_Ohyps_I8_J,axiom,
fresh_1143631827t_unit @ ya @ product_Unity ).
% cComm1.hyps(8)
thf(fact_188_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_189_substTrans,axiom,
! [B: name,P: pi,A: name,C: name] :
( ( fresh_name_pi @ B @ P )
=> ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
= ( subs @ P @ A @ C ) ) ) ).
% substTrans
thf(fact_190_residual_Operm_I2_J,axiom,
! [Pi: list_P227219501e_name,X2: late_freeRes,X1: pi] :
( ( perm_n414416632sidual @ Pi @ ( late_FreeR @ X2 @ X1 ) )
= ( late_FreeR @ ( perm_n336613537reeRes @ Pi @ X2 ) @ ( perm_name_pi @ Pi @ X1 ) ) ) ).
% residual.perm(2)
thf(fact_191_freeRes_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X2: name,X1: name] :
( ( perm_n336613537reeRes @ Pi @ ( late_OutputR @ X2 @ X1 ) )
= ( late_OutputR @ ( perm_name_name @ Pi @ X2 ) @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% freeRes.perm(1)
thf(fact_192_subject_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X1: name] :
( ( perm_n1559866809ubject @ Pi @ ( late_InputS @ X1 ) )
= ( late_InputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% subject.perm(1)
thf(fact_193_subject_Operm_I2_J,axiom,
! [Pi: list_P227219501e_name,X1: name] :
( ( perm_n1559866809ubject @ Pi @ ( late_BoundOutputS @ X1 ) )
= ( late_BoundOutputS @ ( perm_name_name @ Pi @ X1 ) ) ) ).
% subject.perm(2)
thf(fact_194_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_195_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_196_residual_Operm_I1_J,axiom,
! [Pi: list_P227219501e_name,X32: late_subject,X1: name,X2: pi] :
( ( perm_n414416632sidual @ Pi @ ( late_BoundR @ X32 @ X1 @ X2 ) )
= ( late_BoundR @ ( perm_n1559866809ubject @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% residual.perm(1)
thf(fact_197_name__bij,axiom,
! [Pi: list_P227219501e_name,X: name,Y: name] :
( ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y ) )
= ( X = Y ) ) ).
% name_bij
thf(fact_198_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_199_resCasesF,axiom,
! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F2: pi > $o] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
=> ( ! [P4: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha )
=> ( F2 @ ( res @ X @ P4 ) ) ) )
=> ( F2 @ XP ) ) ) ).
% resCasesF
thf(fact_200_resCasesF_H,axiom,
! [X: name,P: pi,Alpha: late_freeRes,P3: pi] :
( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) )
=> ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P5 ) )
=> ( ( ( late_FreeR @ Alpha @ P3 )
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
=> ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% resCasesF'
thf(fact_201_ResF,axiom,
! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
=> ( ( fresh_1641682979reeRes @ Y @ Alpha )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P3 ) ) ) ) ) ).
% ResF
thf(fact_202_Late__Semantics_OResB,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( ( Y != X )
=> ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P3 ) ) ) ) ) ) ).
% Late_Semantics.ResB
thf(fact_203_freshFreeDerivative_I1_J,axiom,
! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% freshFreeDerivative(1)
thf(fact_204_freshBoundDerivative_I1_J,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_717452603ubject @ Y @ A ) ) ) ).
% freshBoundDerivative(1)
thf(fact_205_transitions_OResB,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( 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 @ P3 ) ) ) ) ) ) ) ) ).
% transitions.ResB
thf(fact_206_parCasesB_H,axiom,
! [P: pi,Q: pi,B: late_subject,Y: name,P3: pi] :
( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P3 ) )
=> ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Q3: pi] :
( ( ( par @ P @ Q )
= ( par @ P5 @ Q3 ) )
=> ( ( ( late_BoundR @ B @ Y @ P3 )
= ( late_BoundR @ A3 @ X6 @ ( par @ P4 @ Q3 ) ) )
=> ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
=> ( ( fresh_name_pi @ X6 @ P5 )
=> ( ( fresh_name_pi @ X6 @ Q3 )
=> ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) )
=> ~ ! [Q3: pi,A3: late_subject,X6: name,Q4: pi,P5: pi] :
( ( ( par @ P @ Q )
= ( par @ P5 @ Q3 ) )
=> ( ( ( late_BoundR @ B @ Y @ P3 )
= ( late_BoundR @ A3 @ X6 @ ( par @ P5 @ Q4 ) ) )
=> ( ( late_transitions @ Q3 @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
=> ( ( fresh_name_pi @ X6 @ P5 )
=> ( ( fresh_name_pi @ X6 @ Q3 )
=> ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ).
% parCasesB'
thf(fact_207_transitions_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( fresh_name_pi @ X @ P )
=> ( ( fresh_name_pi @ X @ Q )
=> ( ( fresh_717452603ubject @ X @ A )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ) ) ).
% transitions.Par1B
thf(fact_208_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_209_resCases_H,axiom,
! [X: name,P: pi,Rs: late_residual] :
( ( late_transitions @ ( res @ X @ P ) @ Rs )
=> ( ! [P5: pi,A3: name,B2: name] :
( ( ( res @ X @ P )
= ( res @ B2 @ P5 ) )
=> ! [P4: pi] :
( ( Rs
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
=> ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
=> ( A3 = B2 ) ) ) )
=> ( ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P5 ) )
=> ( ( Rs
= ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
=> ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X6 )
=> ( ( fresh_name_pi @ X6 @ P5 )
=> ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) )
=> ~ ! [P5: pi,Alpha2: late_freeRes,P4: pi,Y3: name] :
( ( ( res @ X @ P )
= ( res @ Y3 @ P5 ) )
=> ( ( Rs
= ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P4 ) ) )
=> ( ( late_transitions @ P5 @ ( late_FreeR @ Alpha2 @ P4 ) )
=> ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% resCases'
thf(fact_210_residual_Oinject_I2_J,axiom,
! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
( ( ( late_FreeR @ X2 @ X1 )
= ( late_FreeR @ Y2 @ Y1 ) )
= ( ( X2 = Y2 )
& ( X1 = Y1 ) ) ) ).
% residual.inject(2)
thf(fact_211_resCasesB_H,axiom,
! [X5: name,P: pi,A: late_subject,Y4: name,P3: pi] :
( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P3 ) )
=> ( ! [P5: pi,A3: name,B2: name] :
( ( ( res @ X5 @ P )
= ( res @ B2 @ P5 ) )
=> ! [P4: pi] :
( ( ( late_BoundR @ A @ Y4 @ P3 )
= ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P4 ) )
=> ( ( late_transitions @ P5 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) )
=> ( A3 = B2 ) ) ) )
=> ~ ! [P5: pi,A3: late_subject,X6: name,P4: pi,Y3: name] :
( ( ( res @ X5 @ P )
= ( res @ Y3 @ P5 ) )
=> ( ( ( late_BoundR @ A @ Y4 @ P3 )
= ( late_BoundR @ A3 @ X6 @ ( res @ Y3 @ P4 ) ) )
=> ( ( late_transitions @ P5 @ ( late_BoundR @ A3 @ X6 @ P4 ) )
=> ( ( fresh_717452603ubject @ Y3 @ A3 )
=> ( ( Y3 != X6 )
=> ( ( fresh_name_pi @ X6 @ P5 )
=> ~ ( fresh_717452603ubject @ X6 @ A3 ) ) ) ) ) ) ) ) ) ).
% resCasesB'
thf(fact_212_residual_Odistinct_I1_J,axiom,
! [Subject: late_subject,Name2: name,Pi: pi,FreeRes: late_freeRes,Pi3: pi] :
( ( late_BoundR @ Subject @ Name2 @ Pi )
!= ( late_FreeR @ FreeRes @ Pi3 ) ) ).
% residual.distinct(1)
thf(fact_213_residual_Oinducts,axiom,
! [P: late_residual > $o,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi] : ( P @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Residual ) ) ) ).
% residual.inducts
thf(fact_214_eqvt,axiom,
! [X1: pi,X2: late_residual,Pi: list_P227219501e_name] :
( ( late_transitions @ X1 @ X2 )
=> ( late_transitions @ ( perm_name_pi @ Pi @ X1 ) @ ( perm_n414416632sidual @ Pi @ X2 ) ) ) ).
% eqvt
thf(fact_215_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_216_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
! [Name12: name,Name23: name] :
( ( late_OutputR @ Name12 @ Name23 )
!= late_TauR ) ).
% Late_Semantics.freeRes.distinct(1)
thf(fact_217_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
! [Name2: name,Name: name] :
( ( late_InputS @ Name2 )
!= ( late_BoundOutputS @ Name ) ) ).
% Late_Semantics.subject.distinct(1)
thf(fact_218_subject_Oinducts,axiom,
! [P: late_subject > $o,Subject: late_subject] :
( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
=> ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
=> ( P @ Subject ) ) ) ).
% subject.inducts
thf(fact_219_resCasesB,axiom,
! [Y: name,P: pi,A: late_subject,X: name,YP: pi,F2: late_subject > pi > $o] :
( ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ YP ) )
=> ( ( X != Y )
=> ( ( fresh_name_pi @ X @ P )
=> ( ! [B2: name,P4: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ B2 @ Y ) @ P4 ) )
=> ( ( B2 != Y )
=> ( ( A
= ( late_BoundOutputS @ B2 ) )
=> ( F2 @ ( late_BoundOutputS @ B2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P4 ) ) ) ) )
=> ( ! [P4: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
=> ( ( fresh_717452603ubject @ Y @ A )
=> ( F2 @ A @ ( res @ Y @ P4 ) ) ) )
=> ( F2 @ A @ YP ) ) ) ) ) ) ).
% resCasesB
thf(fact_220_Par1F,axiom,
! [P: pi,Alpha: late_freeRes,P3: pi,Q: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P3 @ Q ) ) ) ) ).
% Par1F
thf(fact_221_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_222_freshBoundDerivative_I2_J,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( Y != X )
=> ( fresh_name_pi @ Y @ P3 ) ) ) ) ).
% freshBoundDerivative(2)
thf(fact_223_residual_Ostrong__inducts,axiom,
! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
( ( fresh_1143631827t_unit @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_224_residual_Ostrong__inducts,axiom,
! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_225_residual_Ostrong__inducts,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
( ( fresh_name_name @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_226_residual_Ostrong__inducts,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
( ( fresh_name_pi @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_inducts
thf(fact_227_residual_Ostrong__induct,axiom,
! [P: product_unit > late_residual > $o,Z: product_unit,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: product_unit] :
( ( fresh_1143631827t_unit @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: product_unit] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_228_residual_Ostrong__induct,axiom,
! [P: produc1141751126_pi_pi > late_residual > $o,Z: produc1141751126_pi_pi,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: produc1141751126_pi_pi] :
( ( fresh_1376661020_pi_pi @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: produc1141751126_pi_pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_229_residual_Ostrong__induct,axiom,
! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: name] :
( ( fresh_name_name @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_230_residual_Ostrong__induct,axiom,
! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
( ! [Subject2: late_subject,Name3: name,Pi4: pi,Z2: pi] :
( ( fresh_name_pi @ Name3 @ Z2 )
=> ( ( fresh_717452603ubject @ Name3 @ Subject2 )
=> ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi4 ) ) ) )
=> ( ! [FreeRes2: late_freeRes,Pi4: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes2 @ Pi4 ) )
=> ( P @ Z @ Residual ) ) ) ).
% residual.strong_induct
thf(fact_231_freshFreeDerivative_I2_J,axiom,
! [P: pi,Alpha: late_freeRes,P3: pi,Y: name] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
=> ( ( fresh_name_pi @ Y @ P )
=> ( fresh_name_pi @ Y @ P3 ) ) ) ).
% freshFreeDerivative(2)
thf(fact_232_Late__Semantics_OPar1B,axiom,
! [P: pi,A: late_subject,X: name,P3: pi,Q: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
=> ( ( fresh_name_pi @ X @ Q )
=> ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P3 @ Q ) ) ) ) ) ).
% Late_Semantics.Par1B
thf(fact_233_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_234_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 )
=> ( ! [P4: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
=> ( Prop @ ( par @ P4 @ Q ) ) )
=> ( ! [Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q4 ) )
=> ( Prop @ ( par @ P @ Q4 ) ) )
=> ( Prop @ PQ ) ) ) ) ) ) ).
% parCasesB
thf(fact_235_Open,axiom,
! [P: pi,A: name,B: name,P3: pi] :
( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P3 ) )
=> ( ( A != B )
=> ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P3 ) ) ) ) ).
% Open
thf(fact_236_derivativeEqvtI2,axiom,
! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
=> ( ( eqvt_pi @ Rel )
=> ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ A @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% derivativeEqvtI2
thf(fact_237_derivativeEqvtI,axiom,
! [P: pi,Q: pi,A: late_subject,X: name,Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name] :
( ( strong2129052853vative @ P @ Q @ A @ X @ Rel )
=> ( ( eqvt_pi @ Rel )
=> ( strong2129052853vative @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) @ ( perm_n1559866809ubject @ Perm @ A ) @ ( perm_name_name @ Perm @ X ) @ Rel ) ) ) ).
% derivativeEqvtI
thf(fact_238_fresh__prod,axiom,
! [A: name,X: product_unit,Y: product_unit] :
( ( fresh_994967853t_unit @ A @ ( produc1076565719t_unit @ X @ Y ) )
= ( ( fresh_1143631827t_unit @ A @ X )
& ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_239_fresh__prod,axiom,
! [A: name,X: product_unit,Y: name] :
( ( fresh_1826856600t_name @ A @ ( produc421428802t_name @ X @ Y ) )
= ( ( fresh_1143631827t_unit @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_240_fresh__prod,axiom,
! [A: name,X: product_unit,Y: pi] :
( ( fresh_707692390nit_pi @ A @ ( produc1806354576nit_pi @ X @ Y ) )
= ( ( fresh_1143631827t_unit @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_241_fresh__prod,axiom,
! [A: name,X: name,Y: product_unit] :
( ( fresh_90540034t_unit @ A @ ( produc1785453612t_unit @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_242_fresh__prod,axiom,
! [A: name,X: name,Y: pi] :
( ( fresh_93646139ame_pi @ A @ ( product_Pair_name_pi @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_243_fresh__prod,axiom,
! [A: name,X: pi,Y: product_unit] :
( ( fresh_997779380t_unit @ A @ ( produc1831798878t_unit @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_1143631827t_unit @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_244_fresh__prod,axiom,
! [A: name,X: pi,Y: name] :
( ( fresh_261416607i_name @ A @ ( product_Pair_pi_name @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_245_fresh__prod,axiom,
! [A: name,X: name,Y: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_name @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_246_fresh__prod,axiom,
! [A: name,X: pi,Y: pi] :
( ( fresh_1627595501_pi_pi @ A @ ( product_Pair_pi_pi @ X @ Y ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_247_fresh__prod,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_1627595501_pi_pi @ A @ Y ) ) ) ).
% fresh_prod
thf(fact_248_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_249_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_250_fresh__list__cons,axiom,
! [A: name,X: product_unit,Xs: list_Product_unit] :
( ( fresh_1732817625t_unit @ A @ ( cons_Product_unit @ X @ Xs ) )
= ( ( fresh_1143631827t_unit @ A @ X )
& ( fresh_1732817625t_unit @ A @ Xs ) ) ) ).
% fresh_list_cons
thf(fact_251_fresh__list__cons,axiom,
! [A: name,X: produc1141751126_pi_pi,Xs: list_P431515740_pi_pi] :
( ( fresh_1958133282_pi_pi @ A @ ( cons_P749510156_pi_pi @ X @ Xs ) )
= ( ( fresh_1376661020_pi_pi @ A @ X )
& ( fresh_1958133282_pi_pi @ A @ Xs ) ) ) ).
% fresh_list_cons
thf(fact_252_fresh__list__cons,axiom,
! [A: name,X: name,Xs: list_name] :
( ( fresh_name_list_name @ A @ ( cons_name @ X @ Xs ) )
= ( ( fresh_name_name @ A @ X )
& ( fresh_name_list_name @ A @ Xs ) ) ) ).
% fresh_list_cons
thf(fact_253_fresh__list__cons,axiom,
! [A: name,X: pi,Xs: list_pi] :
( ( fresh_name_list_pi @ A @ ( cons_pi @ X @ Xs ) )
= ( ( fresh_name_pi @ A @ X )
& ( fresh_name_list_pi @ A @ Xs ) ) ) ).
% fresh_list_cons
thf(fact_254_fresh__list__cons,axiom,
! [A: name,X: name > noption_pi,Xs: list_name_noption_pi] :
( ( fresh_1135477378ion_pi @ A @ ( cons_name_noption_pi @ X @ Xs ) )
= ( ( fresh_543891186ion_pi @ A @ X )
& ( fresh_1135477378ion_pi @ A @ Xs ) ) ) ).
% fresh_list_cons
thf(fact_255_Bound_Ohyps_I5_J,axiom,
fresh_1376661020_pi_pi @ y @ ( produc235456326_pi_pi @ x @ ( product_Pair_pi_pi @ p @ q ) ) ).
% Bound.hyps(5)
thf(fact_256_name__fresh,axiom,
( fresh_name_name
= ( ^ [A4: name,B3: name] : A4 != B3 ) ) ).
% name_fresh
thf(fact_257_fresh__unit,axiom,
! [A: name] : ( fresh_1143631827t_unit @ A @ product_Unity ) ).
% fresh_unit
thf(fact_258_freshUnit,axiom,
! [Y: name] : ( fresh_1143631827t_unit @ Y @ product_Unity ) ).
% freshUnit
thf(fact_259_allE__Nil,axiom,
! [P: list_P227219501e_name > $o] :
( ! [X_1: list_P227219501e_name] : ( P @ X_1 )
=> ( P @ nil_Pr743626285e_name ) ) ).
% allE_Nil
thf(fact_260_abs__fun__if,axiom,
! [C: $o,Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
( ( C
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
= ( perm_n1559866809ubject @ Pi @ X ) ) )
& ( ~ C
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ C @ X @ Y ) )
= ( perm_n1559866809ubject @ Pi @ Y ) ) ) ) ).
% abs_fun_if
thf(fact_261_abs__fun__if,axiom,
! [C: $o,Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
( ( C
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
= ( perm_n336613537reeRes @ Pi @ X ) ) )
& ( ~ C
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ C @ X @ Y ) )
= ( perm_n336613537reeRes @ Pi @ Y ) ) ) ) ).
% abs_fun_if
thf(fact_262_abs__fun__if,axiom,
! [C: $o,Pi: list_P227219501e_name,X: pi_Rep,Y: pi_Rep] :
( ( C
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
= ( perm_name_pi_Rep @ Pi @ X ) ) )
& ( ~ C
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ C @ X @ Y ) )
= ( perm_name_pi_Rep @ Pi @ Y ) ) ) ) ).
% abs_fun_if
thf(fact_263_abs__fun__if,axiom,
! [C: $o,Pi: list_P227219501e_name,X: name,Y: name] :
( ( C
=> ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
= ( perm_name_name @ Pi @ X ) ) )
& ( ~ C
=> ( ( perm_name_name @ Pi @ ( if_name @ C @ X @ Y ) )
= ( perm_name_name @ Pi @ Y ) ) ) ) ).
% abs_fun_if
thf(fact_264_abs__fun__if,axiom,
! [C: $o,Pi: list_P227219501e_name,X: pi,Y: pi] :
( ( C
=> ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
= ( perm_name_pi @ Pi @ X ) ) )
& ( ~ C
=> ( ( perm_name_pi @ Pi @ ( if_pi @ C @ X @ Y ) )
= ( perm_name_pi @ Pi @ Y ) ) ) ) ).
% abs_fun_if
thf(fact_265_pt__bij3,axiom,
! [X: late_subject,Y: late_subject,Pi: list_P227219501e_name] :
( ( X = Y )
=> ( ( perm_n1559866809ubject @ Pi @ X )
= ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% pt_bij3
thf(fact_266_pt__bij3,axiom,
! [X: late_freeRes,Y: late_freeRes,Pi: list_P227219501e_name] :
( ( X = Y )
=> ( ( perm_n336613537reeRes @ Pi @ X )
= ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% pt_bij3
thf(fact_267_pt__bij3,axiom,
! [X: pi_Rep,Y: pi_Rep,Pi: list_P227219501e_name] :
( ( X = Y )
=> ( ( perm_name_pi_Rep @ Pi @ X )
= ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% pt_bij3
thf(fact_268_pt__bij3,axiom,
! [X: name,Y: name,Pi: list_P227219501e_name] :
( ( X = Y )
=> ( ( perm_name_name @ Pi @ X )
= ( perm_name_name @ Pi @ Y ) ) ) ).
% pt_bij3
thf(fact_269_pt__bij3,axiom,
! [X: pi,Y: pi,Pi: list_P227219501e_name] :
( ( X = Y )
=> ( ( perm_name_pi @ Pi @ X )
= ( perm_name_pi @ Pi @ Y ) ) ) ).
% pt_bij3
thf(fact_270_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: late_subject] :
( ( perm_n171497387ubject @ Pi @ ( produc1465345179ubject @ X @ Y ) )
= ( produc1465345179ubject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_271_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: late_freeRes] :
( ( perm_n1314686611reeRes @ Pi @ ( produc242091907reeRes @ X @ Y ) )
= ( produc242091907reeRes @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_272_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: pi_Rep] :
( ( perm_n1467004033pi_Rep @ Pi @ ( produc843063281pi_Rep @ X @ Y ) )
= ( produc843063281pi_Rep @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_273_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: name] :
( ( perm_n204483300t_name @ Pi @ ( produc1647375838t_name @ X @ Y ) )
= ( produc1647375838t_name @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_274_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Y: pi] :
( ( perm_n359102898ect_pi @ Pi @ ( produc324947500ect_pi @ X @ Y ) )
= ( produc324947500ect_pi @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_275_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_subject] :
( ( perm_n1174226579ubject @ Pi @ ( produc320590723ubject @ X @ Y ) )
= ( produc320590723ubject @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n1559866809ubject @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_276_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: late_freeRes] :
( ( perm_n169932155reeRes @ Pi @ ( produc1244821099reeRes @ X @ Y ) )
= ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n336613537reeRes @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_277_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi_Rep] :
( ( perm_n840427369pi_Rep @ Pi @ ( produc216486617pi_Rep @ X @ Y ) )
= ( produc216486617pi_Rep @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi_Rep @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_278_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: name] :
( ( perm_n258463228s_name @ Pi @ ( produc1701355766s_name @ X @ Y ) )
= ( produc1701355766s_name @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_name @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_279_perm__prod_Osimps,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Y: pi] :
( ( perm_n1211707594Res_pi @ Pi @ ( produc1177552196Res_pi @ X @ Y ) )
= ( produc1177552196Res_pi @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_name_pi @ Pi @ Y ) ) ) ).
% perm_prod.simps
thf(fact_280_fresh__prodD_I2_J,axiom,
! [A: name,X: name,Y: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
=> ( fresh_name_name @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_281_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_282_fresh__prodD_I2_J,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
=> ( fresh_1627595501_pi_pi @ A @ Y ) ) ).
% fresh_prodD(2)
thf(fact_283_fresh__prodD_I1_J,axiom,
! [A: name,X: name,Y: name] :
( ( fresh_441084397e_name @ A @ ( produc1570949143e_name @ X @ Y ) )
=> ( fresh_name_name @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_284_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_285_fresh__prodD_I1_J,axiom,
! [A: name,X: name,Y: product_prod_pi_pi] :
( ( fresh_1376661020_pi_pi @ A @ ( produc235456326_pi_pi @ X @ Y ) )
=> ( fresh_name_name @ A @ X ) ) ).
% fresh_prodD(1)
thf(fact_286_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: late_subject,C22: late_subject] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
= ( perm_n1559866809ubject @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_n1559866809ubject @ Pi @ ( if_Late_subject @ B @ C1 @ C22 ) )
= ( perm_n1559866809ubject @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_287_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: late_freeRes,C22: late_freeRes] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
= ( perm_n336613537reeRes @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_n336613537reeRes @ Pi @ ( if_Late_freeRes @ B @ C1 @ C22 ) )
= ( perm_n336613537reeRes @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_288_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: pi_Rep,C22: pi_Rep] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
= ( perm_name_pi_Rep @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi_Rep @ Pi @ ( if_pi_Rep @ B @ C1 @ C22 ) )
= ( perm_name_pi_Rep @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_289_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: name,C22: name] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
= ( perm_name_name @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_name @ Pi @ ( if_name @ B @ C1 @ C22 ) )
= ( perm_name_name @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_290_if__eqvt,axiom,
! [Pi: list_P227219501e_name,B: $o,C1: pi,C22: pi] :
( ( ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
= ( perm_name_pi @ Pi @ C1 ) ) )
& ( ~ ( perm_name_o @ Pi @ B )
=> ( ( perm_name_pi @ Pi @ ( if_pi @ B @ C1 @ C22 ) )
= ( perm_name_pi @ Pi @ C22 ) ) ) ) ).
% if_eqvt
thf(fact_291_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_subject,Xs: list_Late_subject] :
( ( perm_n1812647369ubject @ Pi @ ( cons_Late_subject @ X @ Xs ) )
= ( cons_Late_subject @ ( perm_n1559866809ubject @ Pi @ X ) @ ( perm_n1812647369ubject @ Pi @ Xs ) ) ) ).
% cons_eqvt
thf(fact_292_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: late_freeRes,Xs: list_Late_freeRes] :
( ( perm_n808352945reeRes @ Pi @ ( cons_Late_freeRes @ X @ Xs ) )
= ( cons_Late_freeRes @ ( perm_n336613537reeRes @ Pi @ X ) @ ( perm_n808352945reeRes @ Pi @ Xs ) ) ) ).
% cons_eqvt
thf(fact_293_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi_Rep,Xs: list_pi_Rep] :
( ( perm_n729617823pi_Rep @ Pi @ ( cons_pi_Rep @ X @ Xs ) )
= ( cons_pi_Rep @ ( perm_name_pi_Rep @ Pi @ X ) @ ( perm_n729617823pi_Rep @ Pi @ Xs ) ) ) ).
% cons_eqvt
thf(fact_294_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: name,Xs: list_name] :
( ( perm_name_list_name @ Pi @ ( cons_name @ X @ Xs ) )
= ( cons_name @ ( perm_name_name @ Pi @ X ) @ ( perm_name_list_name @ Pi @ Xs ) ) ) ).
% cons_eqvt
thf(fact_295_cons__eqvt,axiom,
! [Pi: list_P227219501e_name,X: pi,Xs: list_pi] :
( ( perm_name_list_pi @ Pi @ ( cons_pi @ X @ Xs ) )
= ( cons_pi @ ( perm_name_pi @ Pi @ X ) @ ( perm_name_list_pi @ Pi @ Xs ) ) ) ).
% cons_eqvt
thf(fact_296_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: product_unit] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_1143631827t_unit @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_297_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: produc1141751126_pi_pi] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_1376661020_pi_pi @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_298_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_name_name @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_299_resSimCases,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,X: name,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [Q4: pi,A3: name] :
( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A3 @ X ) @ Q4 ) )
=> ( ( A3 != X )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ X @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) ) )
=> ( ! [Q4: pi,A3: late_subject,Y3: name] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_717452603ubject @ X @ A3 )
=> ( ( X != Y3 )
=> ( ( fresh_name_pi @ Y3 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ ( res @ X @ Q4 ) @ A3 @ Y3 @ Rel ) ) ) ) ) )
=> ( ! [Q4: pi,Alpha2: late_freeRes] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ( ( fresh_1641682979reeRes @ X @ Alpha2 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ ( res @ X @ Q4 ) ) @ Rel ) ) ) )
=> ( strong743114133lation @ P @ Rel @ ( res @ X @ Q ) ) ) ) ) ) ).
% resSimCases
thf(fact_300_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: product_unit] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X6: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
=> ( ( fresh_name_pi @ X6 @ P )
=> ( ( fresh_name_pi @ X6 @ Q )
=> ( ( fresh_717452603ubject @ X6 @ A3 )
=> ( ( fresh_1143631827t_unit @ X6 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_301_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: produc1141751126_pi_pi] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X6: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
=> ( ( fresh_name_pi @ X6 @ P )
=> ( ( fresh_name_pi @ X6 @ Q )
=> ( ( fresh_717452603ubject @ X6 @ A3 )
=> ( ( fresh_1376661020_pi_pi @ X6 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_302_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: name] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X6: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
=> ( ( fresh_name_pi @ X6 @ P )
=> ( ( fresh_name_pi @ X6 @ Q )
=> ( ( fresh_717452603ubject @ X6 @ A3 )
=> ( ( fresh_name_name @ X6 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_303_simCasesCont,axiom,
! [Rel: set_Pr1834926343_pi_pi,Q: pi,P: pi,C3: pi] :
( ( eqvt_pi @ Rel )
=> ( ! [A3: late_subject,X6: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ X6 @ Q4 ) )
=> ( ( fresh_name_pi @ X6 @ P )
=> ( ( fresh_name_pi @ X6 @ Q )
=> ( ( fresh_717452603ubject @ X6 @ A3 )
=> ( ( fresh_name_pi @ X6 @ C3 )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ X6 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ X6 @ Rel ) ) ) ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ) ).
% simCasesCont
thf(fact_304_eqvtRelI,axiom,
! [Rel: set_Pr806375235ubject,P: late_subject,Q: late_subject,Perm: list_P227219501e_name] :
( ( eqvt_Late_subject @ Rel )
=> ( ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel )
=> ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_305_eqvtRelI,axiom,
! [Rel: set_Pr1780909331reeRes,P: late_freeRes,Q: late_freeRes,Perm: list_P227219501e_name] :
( ( eqvt_Late_freeRes @ Rel )
=> ( ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel )
=> ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_306_eqvtRelI,axiom,
! [Rel: set_Pr1131282415pi_Rep,P: pi_Rep,Q: pi_Rep,Perm: list_P227219501e_name] :
( ( eqvt_pi_Rep @ Rel )
=> ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel )
=> ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_307_eqvtRelI,axiom,
! [Rel: set_Pr443758855e_name,P: name,Q: name,Perm: list_P227219501e_name] :
( ( eqvt_name @ Rel )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel )
=> ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_308_eqvtRelI,axiom,
! [Rel: set_Pr1834926343_pi_pi,P: pi,Q: pi,Perm: list_P227219501e_name] :
( ( eqvt_pi @ Rel )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel ) ) ) ).
% eqvtRelI
thf(fact_309_eqvtRelE,axiom,
! [Rel: set_Pr806375235ubject,Perm: list_P227219501e_name,P: late_subject,Q: late_subject] :
( ( eqvt_Late_subject @ Rel )
=> ( ( member1586545036ubject @ ( produc1465345179ubject @ ( perm_n1559866809ubject @ Perm @ P ) @ ( perm_n1559866809ubject @ Perm @ Q ) ) @ Rel )
=> ( member1586545036ubject @ ( produc1465345179ubject @ P @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_310_eqvtRelE,axiom,
! [Rel: set_Pr1780909331reeRes,Perm: list_P227219501e_name,P: late_freeRes,Q: late_freeRes] :
( ( eqvt_Late_freeRes @ Rel )
=> ( ( member1584979804reeRes @ ( produc1244821099reeRes @ ( perm_n336613537reeRes @ Perm @ P ) @ ( perm_n336613537reeRes @ Perm @ Q ) ) @ Rel )
=> ( member1584979804reeRes @ ( produc1244821099reeRes @ P @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_311_eqvtRelE,axiom,
! [Rel: set_Pr1131282415pi_Rep,Perm: list_P227219501e_name,P: pi_Rep,Q: pi_Rep] :
( ( eqvt_pi_Rep @ Rel )
=> ( ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ ( perm_name_pi_Rep @ Perm @ P ) @ ( perm_name_pi_Rep @ Perm @ Q ) ) @ Rel )
=> ( member1671908408pi_Rep @ ( produc784048711pi_Rep @ P @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_312_eqvtRelE,axiom,
! [Rel: set_Pr443758855e_name,Perm: list_P227219501e_name,P: name,Q: name] :
( ( eqvt_name @ Rel )
=> ( ( member695284560e_name @ ( produc1570949143e_name @ ( perm_name_name @ Perm @ P ) @ ( perm_name_name @ Perm @ Q ) ) @ Rel )
=> ( member695284560e_name @ ( produc1570949143e_name @ P @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_313_eqvtRelE,axiom,
! [Rel: set_Pr1834926343_pi_pi,Perm: list_P227219501e_name,P: pi,Q: pi] :
( ( eqvt_pi @ Rel )
=> ( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( perm_name_pi @ Perm @ P ) @ ( perm_name_pi @ Perm @ Q ) ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P @ Q ) @ Rel ) ) ) ).
% eqvtRelE
thf(fact_314_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,X6: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ R2 @ S2 ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ R2 ) @ ( res @ X6 @ S2 ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ P @ Q ) @ Rel @ ( par @ Q @ P ) ) ) ) ).
% parSym
thf(fact_315_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 ) )
=> ? [P4: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P4 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P4 @ Q2 ) @ Rel ) ) ) ) ).
% simE(2)
thf(fact_316_eqvt__def,axiom,
( eqvt_pi
= ( ^ [Rel2: set_Pr1834926343_pi_pi] :
! [X3: product_prod_pi_pi,Perm2: list_P227219501e_name] :
( ( member558706512_pi_pi @ X3 @ Rel2 )
=> ( member558706512_pi_pi @ ( perm_n1415585007_pi_pi @ Perm2 @ X3 ) @ Rel2 ) ) ) ) ).
% eqvt_def
thf(fact_317_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,X6: name] :
( ( member558706512_pi_pi @ ( product_Pair_pi_pi @ S2 @ T ) @ Rel )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ S2 ) @ ( res @ X6 @ T ) ) @ Rel ) )
=> ( ! [S2: pi,T: pi,U: pi,X6: name] :
( ( fresh_name_pi @ X6 @ S2 )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( res @ X6 @ ( par @ ( par @ S2 @ T ) @ U ) ) @ ( par @ S2 @ ( res @ X6 @ ( par @ T @ U ) ) ) ) @ Rel ) )
=> ( ! [S2: pi,T: pi,U: pi,X6: name] :
( ( fresh_name_pi @ X6 @ U )
=> ( member558706512_pi_pi @ ( product_Pair_pi_pi @ ( par @ ( res @ X6 @ ( par @ S2 @ T ) ) @ U ) @ ( res @ X6 @ ( par @ S2 @ ( par @ T @ U ) ) ) ) @ Rel ) )
=> ( strong743114133lation @ ( par @ ( par @ P @ Q ) @ R ) @ Rel @ ( par @ P @ ( par @ Q @ R ) ) ) ) ) ) ) ).
% parAssocLeft
thf(fact_318_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 )
=> ? [P4: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P4 ) )
& ( strong2129052853vative @ P4 @ Q2 @ A @ X @ Rel ) ) ) ) ) ).
% simE(1)
thf(fact_319_simCases,axiom,
! [Q: pi,P: pi,Rel: set_Pr1834926343_pi_pi] :
( ! [A3: late_subject,Y3: name,Q4: pi] :
( ( late_transitions @ Q @ ( late_BoundR @ A3 @ Y3 @ Q4 ) )
=> ( ( fresh_name_pi @ Y3 @ P )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_BoundR @ A3 @ Y3 @ P6 ) )
& ( strong2129052853vative @ P6 @ Q4 @ A3 @ Y3 @ Rel ) ) ) )
=> ( ! [Alpha2: late_freeRes,Q4: pi] :
( ( late_transitions @ Q @ ( late_FreeR @ Alpha2 @ Q4 ) )
=> ? [P6: pi] :
( ( late_transitions @ P @ ( late_FreeR @ Alpha2 @ P6 ) )
& ( member558706512_pi_pi @ ( product_Pair_pi_pi @ P6 @ Q4 ) @ Rel ) ) )
=> ( strong743114133lation @ P @ Rel @ Q ) ) ) ).
% simCases
thf(fact_320_simulation__def,axiom,
( strong743114133lation
= ( ^ [P7: pi,Rel2: set_Pr1834926343_pi_pi,Q5: pi] :
( ! [A4: late_subject,X3: name,Q6: pi] :
( ( ( late_transitions @ Q5 @ ( late_BoundR @ A4 @ X3 @ Q6 ) )
& ( fresh_name_pi @ X3 @ P7 ) )
=> ? [P8: pi] :
( ( late_transitions @ P7 @ ( late_BoundR @ A4 @ X3 @ P8 ) )
& ( strong2129052853vative @ P8 @ Q6 @ A4 @ 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_321_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
! [X2: name,Y2: name] :
( ( ( late_BoundOutputS @ X2 )
= ( late_BoundOutputS @ Y2 ) )
= ( X2 = Y2 ) ) ).
% Late_Semantics1.subject.inject(2)
thf(fact_322_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_323_Late__Semantics1_OfreeRes_Oinject,axiom,
! [X11: name,X12: name,Y11: name,Y12: name] :
( ( ( late_OutputR @ X11 @ X12 )
= ( late_OutputR @ Y11 @ Y12 ) )
= ( ( X11 = Y11 )
& ( X12 = Y12 ) ) ) ).
% Late_Semantics1.freeRes.inject
thf(fact_324_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
! [X11: name,X12: name] :
( ( late_OutputR @ X11 @ X12 )
!= late_TauR ) ).
% Late_Semantics1.freeRes.distinct(1)
thf(fact_325_freeRes_Oexhaust,axiom,
! [Y: late_freeRes] :
( ! [X112: name,X122: name] :
( Y
!= ( late_OutputR @ X112 @ X122 ) )
=> ( Y = late_TauR ) ) ).
% freeRes.exhaust
thf(fact_326_subject_Oexhaust,axiom,
! [Y: late_subject] :
( ! [X13: name] :
( Y
!= ( late_InputS @ X13 ) )
=> ~ ! [X22: name] :
( Y
!= ( late_BoundOutputS @ X22 ) ) ) ).
% subject.exhaust
thf(fact_327_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
! [X1: name,X2: name] :
( ( late_InputS @ X1 )
!= ( late_BoundOutputS @ X2 ) ) ).
% Late_Semantics1.subject.distinct(1)
thf(fact_328_inputCases,axiom,
! [A: name,X: name,P: pi,B: late_subject,Y: name,YP: pi,Prop: late_subject > name > pi > $o] :
( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ YP ) )
=> ( ( Y != A )
=> ( ( Y != X )
=> ( ( fresh_name_pi @ Y @ P )
=> ( ( ( B
= ( late_InputS @ A ) )
=> ( ( YP
= ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) )
=> ( Prop @ ( late_InputS @ A ) @ Y @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ Y ) @ nil_Pr743626285e_name ) @ P ) ) ) )
=> ( Prop @ B @ Y @ YP ) ) ) ) ) ) ).
% inputCases
thf(fact_329_list_Oinject,axiom,
! [X21: produc367475239e_name,X222: list_P227219501e_name,Y21: produc367475239e_name,Y22: list_P227219501e_name] :
( ( ( cons_P1213805021e_name @ X21 @ X222 )
= ( cons_P1213805021e_name @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% list.inject
thf(fact_330_pi_Operm_I4_J,axiom,
! [Pi: list_P227219501e_name,X32: name,X1: name,X2: pi] :
( ( perm_name_pi @ Pi @ ( input @ X32 @ X1 @ X2 ) )
= ( input @ ( perm_name_name @ Pi @ X32 ) @ ( perm_name_name @ Pi @ X1 ) @ ( perm_name_pi @ Pi @ X2 ) ) ) ).
% pi.perm(4)
thf(fact_331_pi_Odistinct_I57_J,axiom,
! [Name12: name,Name23: name,Pi: pi,Name: name,Pi3: pi] :
( ( input @ Name12 @ Name23 @ Pi )
!= ( res @ Name @ Pi3 ) ) ).
% pi.distinct(57)
thf(fact_332_pi_Odistinct_I55_J,axiom,
! [Name12: name,Name23: name,Pi: pi,Pi12: pi,Pi22: pi] :
( ( input @ Name12 @ Name23 @ Pi )
!= ( par @ Pi12 @ Pi22 ) ) ).
% pi.distinct(55)
thf(fact_333_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_334_inputFreeTrans,axiom,
! [A: name,X: name,P: pi,Alpha: late_freeRes,P3: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% inputFreeTrans
thf(fact_335_resInputFreeTrans,axiom,
! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P3: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P3 ) ) ).
% resInputFreeTrans
thf(fact_336_old_Ounit_Oinducts,axiom,
! [P: product_unit > $o,Unit: product_unit] :
( ( P @ product_Unity )
=> ( P @ Unit ) ) ).
% old.unit.inducts
thf(fact_337_old_Ounit_Oexhaust,axiom,
! [Y: product_unit] : Y = product_Unity ).
% old.unit.exhaust
thf(fact_338_inputBoundOutputTrans,axiom,
! [A: name,X: name,P: pi,B: name,Y: name,P3: pi] :
~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P3 ) ) ).
% inputBoundOutputTrans
thf(fact_339_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_340_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_341_inputIneqTrans,axiom,
! [A: name,X: name,P: pi,B: late_subject,Y: name,P3: pi] :
( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P3 ) )
=> ~ ( fresh_717452603ubject @ A @ B ) ) ).
% inputIneqTrans
thf(fact_342_resInputBoundOutputTrans,axiom,
! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P3: pi] :
~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P3 ) ) ).
% resInputBoundOutputTrans
thf(fact_343_alphaInput,axiom,
! [C: name,P: pi,A: name,X: name] :
( ( fresh_name_pi @ C @ P )
=> ( ( input @ A @ X @ P )
= ( input @ A @ C @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ X @ C ) @ nil_Pr743626285e_name ) @ P ) ) ) ) ).
% alphaInput
thf(fact_344_default__unit__def,axiom,
defaul1399868459t_unit = product_Unity ).
% default_unit_def
thf(fact_345_residual__Rep_Oinject_I2_J,axiom,
! [X21: late_freeRes,X222: pi,Y21: late_freeRes,Y22: pi] :
( ( ( late_r347633188eR_Rep @ X21 @ X222 )
= ( late_r347633188eR_Rep @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X222 = Y22 ) ) ) ).
% residual_Rep.inject(2)
thf(fact_346_name__calc_I1_J,axiom,
! [A: name,B: name,Pi: list_P227219501e_name,X: name] :
( ( perm_name_name @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ A @ B ) @ Pi ) @ X )
= ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ ( perm_name_name @ Pi @ X ) ) ) ).
% name_calc(1)
thf(fact_347_name__calc_I3_J,axiom,
! [A: name,C: name,B: name] :
( ( ( A = C )
=> ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
= B ) )
& ( ( A != C )
=> ( ( ( B = C )
=> ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
= A ) )
& ( ( B != C )
=> ( ( swap_name2 @ ( produc1570949143e_name @ A @ B ) @ C )
= C ) ) ) ) ) ).
% name_calc(3)
thf(fact_348_Agent_Oswap__name__def,axiom,
swap_name2 = swap_name ).
% Agent.swap_name_def
thf(fact_349_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)
% Helper facts (11)
thf(help_If_2_1_If_001t__Agent__Opi_T,axiom,
! [X: pi,Y: pi] :
( ( if_pi @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Agent__Opi_T,axiom,
! [X: pi,Y: pi] :
( ( if_pi @ $true @ X @ Y )
= X ) ).
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 ) ).
thf(help_If_2_1_If_001t__Agent__Opi____Rep_T,axiom,
! [X: pi_Rep,Y: pi_Rep] :
( ( if_pi_Rep @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Agent__Opi____Rep_T,axiom,
! [X: pi_Rep,Y: pi_Rep] :
( ( if_pi_Rep @ $true @ X @ Y )
= X ) ).
thf(help_If_2_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
! [X: late_freeRes,Y: late_freeRes] :
( ( if_Late_freeRes @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Late____Semantics__OfreeRes_T,axiom,
! [X: late_freeRes,Y: late_freeRes] :
( ( if_Late_freeRes @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [X: late_subject,Y: late_subject] :
( ( if_Late_subject @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Late____Semantics__Osubject_T,axiom,
! [X: late_subject,Y: late_subject] :
( ( if_Late_subject @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
? [P6: pi] :
( ( late_transitions @ ( par @ p @ ( res @ x @ q ) ) @ ( late_BoundR @ ( late_BoundOutputS @ ab ) @ y @ P6 ) )
& ( strong2129052853vative @ P6 @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ ( par @ ( subs @ p2 @ ya @ c ) @ q2 ) ) @ ( late_BoundOutputS @ ab ) @ y @ rel ) ) ).
%------------------------------------------------------------------------------